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Surface Measurement of a Large Inflatable Reflector in Cryogenic Vacuum

Surface Measurement of a Large Inflatable Reflector in Cryogenic Vacuum hv photonics Article Surface Measurement of a Large Inflatable Reflector in Cryogenic Vacuum 1 1 1 , 2 2 1 , 3 1 Henry Quach , Hyukmo Kang , Siddhartha Sirsi , Aman Chandra , Heejoo Choi , Marcos Esparza , 1 1 1 4 5 Karlene Karrfalt , Joel Berkson , Yuzuru Takashima , Art Palisoc , Jonathan W. Arenberg , 1 , 2 6 1 , 2 , 3 , Christopher Walker , Christian Drouet d’Aubigny and Daewook Kim * Wyant College of Optical Sciences, University of Arizona, 1630 East University Blvd., Tucson, AZ 85721, USA; henryquach@optics.arizona.edu (H.Q.); hkang@optics.arizona.edu (H.K.); ssirsi@email.arizona.edu (S.S.); hchoi@optics.arizona.edu (H.C.); maesparza@email.arizona.edu (M.E.); kkarrfalt@email.arizona.edu (K.K.); joelsteraz@email.arizona.edu (J.B.); ytakashima@optics.arizona.edu (Y.T.); cwalker@arizona.edu (C.W.) Department of Astronomy and Steward Observatory, University of Arizona, 933 North Cherry Avenue, Tucson, AZ 85721, USA; achandra@email.arizona.edu Large Binocular Telescope Observatory, University of Arizona, 933 North Cherry Avenue, Tucson, AZ 85721, USA L’Garde, Inc., 15181 Woodlawn Avenue, Tustin, CA 92780, USA; Art_Palisoc@lgarde.com Northrop Grumman Systems Corporation—Space Sector, 1 Space Park Drive, Redondo Beach, CA 90278, USA; jon.arenberg@ngc.com Lunar and Planetary Laboratory, University of Arizona, 1629 East University Blvd., Tucson, AZ 85721, USA; cdaubign@orex.lpl.arizona.edu * Correspondence: dkim@optics.arizona.edu Abstract: The metrology of membrane structures, especially inflatable, curved, optical surfaces, remains challenging. Internal pressure, mechanical membrane properties, and circumferential bound- ary conditions imbue highly dynamic slopes to the final optic surface. Here, we present our method and experimental results for measuring a 1 m inflatable reflector ’s shape response to dynamic pertur- bations in a thermal vacuum chamber. Our method uses phase-measuring deflectometry to track Citation: Quach, H.; Kang, H.; Sirsi, shape change in response to pressure change, thermal gradient, and controlled puncture. We use S.; Chandra, A.; Choi, H.; Esparza, an initial measurement as a virtual null reference, allowing us to compare 500 mm of measurable M.; Karrfalt, K.; Berkson, J.; aperture of the concave f/2, 1-meter diameter inflatable optic. We built a custom deflectometer that Takashima, Y.; Palisoc, A.; et al. attaches to the TVAC window to make full use of its clear aperture, with kinematic references behind Surface Measurement of a Large the test article for calibration. Our method produces 500  500 pixel resolution 3D surface maps with Inflatable Reflector in Cryogenic a repeatability of 150 nm RMS within a cryogenic vacuum environment (T = 140 K, P = 0.11 Pa). Vacuum. Photonics 2022, 9, 1. https://doi.org/10.3390/ photonics9010001 Keywords: deflectometry; inflatable optics; thermal vacuum testing; terahertz astronomy Received: 16 November 2021 Accepted: 16 December 2021 Published: 21 December 2021 1. Introduction Publisher’s Note: MDPI stays neutral Gossamer space structures are not a recent invention. From the Inflatable Aperture with regard to jurisdictional claims in Experiment in 1996 to the sunshield assembly of the James Webb Space Telescope, mem- published maps and institutional affil- brane spacecraft assemblies continue to be actively deployed [1]. Up to tens of microns iations. thick, environmentally resistant films such as Mylar and Kapton form large monolithic surface areas. A promising example of future gossamer structures is OASIS, or the Orbit- ing Astronomical Satellite for Investigating Stellar Systems. OASIS is a proposed ~14 to 20-meter class space observatory that will perform high spectral resolution observations at Copyright: © 2021 by the authors. terahertz frequencies [2]. The advantage for such structures is that they can achieve 7X the Licensee MDPI, Basel, Switzerland. This article is an open access article collecting area as space observatories with traditionally polished apertures for less than distributed under the terms and one third of the mass [3]. A spaceborne observatory with a 14 meter diameter size produces conditions of the Creative Commons a signal-to-noise ratio unobtainable at ground level for far-infrared spectra, enabling the Attribution (CC BY) license (https:// quantitative science of detecting water in distant protoplanetary disks and solar system creativecommons.org/licenses/by/ objects. 4.0/). Photonics 2022, 9, 1. https://doi.org/10.3390/photonics9010001 https://www.mdpi.com/journal/photonics Photonics 2021, 8, x FOR PEER REVIEW 2 of 15 Photonics 2022, 9, 1 2 of 15 enabling the quantitative science of detecting water in distant protoplanetary disks and solar system objects. For inflatable apertures, technical characteristics of interest include shape response For inflatable apertures, technical characteristics of interest include shape response to to environmental temperature and pressure, thermal gradients, and puncture by micro- environmental temperature and pressure, thermal gradients, and puncture by micromete- meteoroid. Unfortunately, full-field, temporal behavior of inflatable highly aspheric mem- oroid. Unfortunately, full-field, temporal behavior of inflatable highly aspheric membrane brane optical surfaces has not been extensively studied in high resolution, no less in a optical surfaces has not been extensively studied in high resolution, no less in a cryogenic cryogenic vacuum or in puncture. vacuum or in puncture. 1.1. Geometrical Shape of Pneumatic Membranes 1.1. Geometrical Shape of Pneumatic Membranes Two varieties of pneumatic reflectors exist: monolithic membranes and composite Two varieties of pneumatic reflectors exist: monolithic membranes and composite gored membranes. This paper concerns the measurement of monolithic membranes, gored membranes. This paper concerns the measurement of monolithic membranes, which which have higher dynamic slopes than their counterparts stitched from triangular pieces have higher dynamic slopes than their counterparts stitched from triangular pieces [4]. [4]. Monolithic membranes, if composed of ideal mechanically isotropic films, produce a Monolithic membranes, if composed of ideal mechanically isotropic films, produce a ra- radially symmetric, spherically aberrated shape known as a Hencky Curve Surface [5,6]. dially symmetric, spherically aberrated shape known as a Hencky Curve Surface [5,6]. In In the Zernike description, the Hencky Curve Surface is the sum of defocus and spherical the Zernike description, the Hencky Curve Surface is the sum of defocus and spherical terms. When constructed of real films such as Mylar, pressurization generates astigma- terms. When constructed of real films such as Mylar, pressurization generates astigmatism tism because manufacturing polymer films imbues different Young’s Moduli across or- because manufacturing polymer films imbues different Young’s Moduli across orthogonal thogonal axes. At lower pressures, wrinkles sprout from the perimeter of the reflector, axes. At lower pressures, wrinkles sprout from the perimeter of the reflector, introducing introducing higher order spatial frequency errors [7]. These artifacts rapidly diminish at higher order spatial frequency errors [7]. These artifacts rapidly diminish at higher pres- higher pressure because the stress experienced across the entire aperture grows more uni- sure because the stress experienced across the entire aperture grows more uniform in all form in all directions under pneumatic loading [8]. directions under pneumatic loading [8]. In In 2019, 2019, the the University University of of Arizona Arizona constr construct ucted ed a a 1 1 meter meter surr surro ogate gate r ref eflector lector to to test test optical optical metr metro ology logy techniques, techniques, shown shown in in Figur Figure e 1 1 [ [9 9] ].. A A monolithic, monolithic, Hencky-forming Hencky-forming con con- - struction was chosen because of its simplicity and requisite lead time of a gored parabolic struction was chosen because of its simplicity and requisite lead time of a gored parabolic assembly assembly.. Our Our r requirement equirement for for a a general general metr metrology ology technique technique r re equir quired ed capturing capturing surface surface shapes that are relatively unknown due to latent wrinkles and possible thermoforming shapes that are relatively unknown due to latent wrinkles and possible thermoforming variation. We considered tactile solutions such as low-force contact profilometers and variation. We considered tactile solutions such as low-force contact profilometers and con- confocal probes. However, both systems require a motion travel range at least as large as focal probes. However, both systems require a motion travel range at least as large as the the unit under test (UUT), and their pointwise, mechanically driven acquisitions would unit under test (UUT), and their pointwise, mechanically driven acquisitions would se- severely limit sampling speed. verely limit sampling speed. Figure 1. An inflatable membrane mirror is constructed by clamping two Mylar sheets between Figure 1. An inflatable membrane mirror is constructed by clamping two Mylar sheets between three three machined aluminum rings. During inflation, the rear aluminized Mylar becomes the concave machined aluminum rings (a). During inflation, the rear aluminized Mylar becomes the concave reflecting surface of interest, while the clear convex Mylar front surface helps hold pressure. The reflecting surface of interest, while the clear convex Mylar front surface helps hold pres-sure (b). The convex Mylar surface is known as the canopy. In the final full-sized assembly, the canopy will be convex Mylar surface is known as the canopy. In the final full-sized assembly, the canopy will be black polyimide, which is opaque in the visible but transparent with some loss in the target opera- black polyimide, which is opaque in the visible but transparent with some loss in the target operation tion wavelengths (~80–660 µ m). wavelengths (~80–660 m). 1.2. Thermal Vacuum Chamber Testing and Surface Testing Thermal Vacuum Chamber (TVAC) testing is a regular milestone in space hardware verification; emulating the conditions of device operation in space is important to predict the behavior of hardware already tested on land. Small optical surfaces have been measured through TVAC with careful optomechanical compensation of optical path length [10]. Photonics 2021, 8, x FOR PEER REVIEW 3 of 15 1.2. Thermal Vacuum Chamber Testing and Surface Testing Thermal Vacuum Chamber (TVAC) testing is a regular milestone in space hardware verification; emulating the conditions of device operation in space is important to predict the behavior of hardware already tested on land. Small optical surfaces have been meas- Photonics 2022, 9, 1 3 of 15 ured through TVAC with careful optomechanical compensation of optical path length [10]. Photogrammetry has also been adopted but is difficult to configure outside-of-cham- Photogrammetry has also been adopted but is difficult to configure outside-of-chamber ber because its resolution increases with the distance from cameras to the unit under test because its resolution increases with the distance from cameras to the unit under test and and also with the angular subtense between the two cameras and the UUT [11,12]. Finally, also with the angular subtense between the two cameras and the UUT [11,12]. Finally, specular surface measurement with photogrammetry requires the placement of hundreds specular surface measurement with photogrammetry requires the placement of hundreds of well-placed diffuse fiducials so that higher spatial frequencies are detectable. of well-placed diffuse fiducials so that higher spatial frequencies are detectable. Laser radar is a frequency chirped LiDAR technology that has been used in TVAC to Laser radar is a frequency chirped LiDAR technology that has been used in TVAC to measure positions through a TVAC chamber window. However, path lengths must also measure positions through a TVAC chamber window. However, path lengths must also be carefully compensated, else millimeter-scale errors at multiples of the window length be carefully compensated, else millimeter-scale errors at multiples of the window length appear [13]. It is our own experience with a Nikon APDIS laser radar metrology system appear [13]. It is our own experience with a Nikon APDIS laser radar metrology system that 800-point sampling across one diameter of the 1 meter prototype takes on the order that 800-point sampling across one diameter of the 1 meter prototype takes on the order of of 5 min. The duration of point scanning scales linearly with the number of samples, so 5 min. The duration of point scanning scales linearly with the number of samples, so larger larger apertures require far more scanning time for equivalent areal sampling density. apertures require far more scanning time for equivalent areal sampling density. 1.3. Regular Deflectometry Measurement 1.3. Regular Deflectometry Measurement The large range of possible inflatable surface shapes, whether gored parabola or mon- The large range of possible inflatable surface shapes, whether gored parabola or olithic Hencky Curve Surface, compels the use of phase-measuring deflectometry (PMD). monolithic Hencky Curve Surface, compels the use of phase-measuring deflectometry The speed at which full-field measurements must be made of a dynamic inflatable surface (PMD). The speed at which full-field measurements must be made of a dynamic inflatable is not accessible by contact-based methods or interferometry. surface is not accessible by contact-based methods or interferometry. Illustrated in Figure 2, PMD is an incoherent measurement technique that has a vast Illustrated in Figure 2, PMD is an incoherent measurement technique that has a slope measurement range and does not require a physical null. The only hardware re- vast slope measurement range and does not require a physical null. The only hardware quired is a spatially modulated light source such as a liquid crystal display (LCD) screen required is a spatially modulated light source such as a liquid crystal display (LCD) screen and a camera to observe the reflection of the display at the UUT. Briefly, an imaging cam- and a camera to observe the reflection of the display at the UUT. Briefly, an imaging era establishes conjugate imaging with the UUT surface, while the LCD illuminates the camera establishes conjugate imaging with the UUT surface, while the LCD illuminates UUT aperture with black and white sinusoidal fringes. Advancing the screen pattern by the UUT aperture with black and white sinusoidal fringes. Advancing the screen pattern a sequence of fixed phase steps and capturing an image of the UUT at each step, we de- by a sequence of fixed phase steps and capturing an image of the UUT at each step, we termine corresponding points between the screen, UUT, and camera as related by the law determine corresponding points between the screen, UUT, and camera as related by the of specular reflection via a phase-shifting algorithm. Knowledge of these associations al- law of specular reflection via a phase-shifting algorithm. Knowledge of these associations lows us to calculate surface slopes. If regions of the UUT are both seen by the camera and allows us to calculate surface slopes. If regions of the UUT are both seen by the camera and il illuminated luminated b by y the so the sour urce ce, , t then hen t those hose re regions gions a ar re e w within ithin the r the range ange of of PMD PMD me measur asuremen ement. t. Figure 2. Between an illumination source, a camera, and a UUT, the law of specular reflection is Figure 2. Between an illumination source, a camera, and a UUT, the law of specular reflection is sat satisfied. isfied. H Her ere, e, the the dir direc ection tion z ˆ𝑧 is ̂ is parallel paralleto l to the the optical optical ax axi is of s oa f spherical a spherical optic, optic the , the dirdi ection rection y ˆ in 𝑦 ̂ the in the tangential meridional plane, and the direction 𝑥 ̂ in the sagittal plane. The coordinates 𝑦 , 𝑦 , tangential meridional plane, and the direction x ˆ in the sagittal plane. The coordinates y , y , and m 𝑚s 𝑠 and 𝑦 represent the y-coordinates of the mirror, source, and a pinhole camera as related by the law y represent the y-coordinates of the mirror, source, and a pinhole camera as related by the law of specular reflection. d and d represent the absolute distances between the mirror and screen m2s m2c and mirror and camera, and z and z represent the distances of these physical locations along m2s m2c the direction z ˆ. W x , y is the sag of the optic. ( ) m m Recently, diverse advances in PMD have enabled the measurement of extremely chal- lenging surfaces. Xu et al. introduced a segmentation-based, data-fusion PMD approach to reconstruct the absolute surface of a monolithic, stepped multi-mirror array [14]. Taking Photonics 2022, 9, 1 4 of 15 advantage of total internal reflection at a water-air interface, PMD has also been used to measure disturbances of a fluid surface [15]. Willomitzer et al. introduced stitched panoramic measurements of stained-glass windows with a mobile device [16]. PMD for more traditional technical surfaces is well-described in recent literature reviews [17,18]. One instructive representation of deflectometry slope calculation is derived from Ritter ’s expression for surface slopes, S , in the single directional case in y (a similar calculation follows in the x-slopes, S , shown in Figure 2) [19,20]. The assumptions in the approximation are that the configuration is highly on axis, or z  d and m2s m2s z  d , and that the testing distance is very large relative to the sag of the optic, m2c m2c z , z  W x , y . ( ) m2s m2c m m y y y y m s m c 1 y y y y d d m s m c m2s m2c S x , y =  + (1) ( ) y m m z W(x ,y ) z W(x ,y ) m m m m m2s m2c 2 z z m2s m2c d d m2s m2c The assumption of low-order UUT coordinates for surface calculation is not redundant with the result of a physical deflectometry test. This is because the overall sag of the optic plays a tiny role in the slope calculation when z z  W(x , y ). When accurate m2s, m2c m m calibration parameters are fed into the slope calculation, accurate slopes across the UUT aperture are sampled. The mid-high spatial frequencies of the UUT’s true shape are revealed in the final surface height maps, which were not modeled in the virtual null [21]. For absolute surface reconstruction accuracy, calibration is critical and requires measur- ing the spatial positions of the camera pinhole, screen, and UUT. To illustrate the influence of measurement errors during calibration, we can modify expression (1) for calculating S (x , y ) with the calibration errors terms # , # , # , # , and # . y m m y,m y,s y,c z, m2s z,m2c y + # y + # y + # y + # m y,m s y,s m y,m c y,c S (x , y )  + (2) y m m 2 z + # z + # m2s z,m2s m2c z,m2c Non-zero values of # , # , # produce erroneous slope deviation from the true y,m y,s y,c slopes. Surface reconstruction with these lateral calibration errors is akin to miscalculating power in the tangential meridional plane, but not additional power in the sagittal plane (i.e., the x-slopes, S ); hence, excess astigmatism is embedded into the measurement. Similarly, a miscalibration in longitudinal coordinates # and # produces equal slope deviation z,m2s z,m2c across both planes, so power error is imbedded into the surface reconstruction. 2. Theory and Simulation for Deflectometry Measurement 2.1. Differential Deflectometry Measurement While calibration errors produce low-frequency figure errors in absolute measure- ments, the subtraction of two deflectometry measurements that use identical calibration parameters produces a high-fidelity shape difference [22]. In Figure 3, a small internal pressure adjustment causes the surface shape change to from W(x, y) to W (x, y), surface 0 0 0 normals from n ˆ to n ˆ , and difference in surface slopes DS = S S and DS = S S . y y y y y x x x Photonics 2021, 8, x FOR PEER REVIEW 5 of 15 2. Theory and Simulation for Deflectometry Measurement 2.1. Differential Deflectometry Measurement While calibration errors produce low-frequency figure errors in absolute measure- ments, the subtraction of two deflectometry measurements that use identical calibration parameters produces a high-fidelity shape difference [22]. In Figure 3, a small internal pressure adjustment causes the surface shape change to from 𝑊 (𝑥 , 𝑦 ) to 𝑊 ′(𝑥 , 𝑦 ), surface Photonics 2022, 9, 1 5 of 15 normals from 𝑛 ̂ to 𝑛 ̂ ′ , and difference in surface slopes 𝛥 𝑆 = 𝑆 − 𝑆 ′ and 𝛥 𝑆 = 𝑦 𝑦 𝑦 𝑦 𝑦 𝑥 𝑆 − 𝑆 ′ . 𝑥 𝑥 Figure 3. A unique aspect of inflatable optics is that the tensioning ring is a static datum between all Figure 3. A unique aspect of inflatable optics is that the tensioning ring is a static datum between all varifocal states of the optic. The location of the aperture edge is stationary; only the surface slopes varifocal states of the optic. The location of the aperture edge is stationary; only the surface slopes and height change within this circular area. Since the position of the UUT within the field of view and height change within this circular area. Since the position of the UUT within the field of view of of th the e camer camera a does does not not change, change, v 𝑣̂ ˆ = ≅ v 𝑣̂ ˆ ’. . In In th the e diagram diagram,, rays rays are are r revers everse e tr traced aced fr from om the the camera camera to to 11 1 1 UUT for a more intuitive visualization of ray slope deflection. UUT for a more intuitive visualization of ray slope deflection. If we take the difference of two deflectometry measurements from the same hardware If we take the difference of two deflectometry measurements from the same hard- configuration and calculated with the same calibration parameters, we will find that the ware configuration and calculated with the same calibration parameters, we will find that influence of the calibration measurement error is largely removed. The next expression (3) the influence of the calibration measurement error is largely removed. The next expression illustrates this error removal. (3) illustrates this error removal. ( ) ( ) ( ) Δ𝑆 𝑥 ,D 𝑦 S (= x 𝑆 , y 𝑥 ) ,= 𝑦 S−(𝑆 x′ , 𝑥y ) , 𝑦 S (x , y ) 𝑦 𝑚 𝑚 y m 𝑦 m 𝑚 𝑚 y m 𝑦 𝑚m 𝑚 y m m y +# y +# y +# y +# ( m y,m) ( s y,s) ( m y,m) ( c y,c) (𝑦 + 𝜀 ) − (𝑦 + 𝜀 ) (𝑦 + 𝜀 ) − (𝑦 + 𝜀 ) = + 𝑚 𝑦 ,𝑚 𝑠 𝑦 ,𝑠 𝑚 𝑦 ,𝑚 𝑐 𝑦 ,𝑐 2 z +# z +# m2s z,m2s m2c z,m2c = [ + ] 2 𝑧 + 𝜀 𝑧 + 𝜀 𝑚 2𝑠 𝑧 ,𝑚 2𝑠 𝑚 2𝑐 𝑧 ,𝑚 2𝑐 (3) 0 0 0 0 (y +# )(y +# ) (y +# )(y +# ) y,m y,s y,m y,c 1 m s m c ′ ′0 ′ 0 ′ 2 z +# z +# (𝑦 + 𝜀 ) − (𝑦 m2+ s 𝜀 m2s) (𝑦 + 𝜀 m )2− c ( m 𝑦 2c + 𝜀 ) 𝑦 ,𝑚 𝑦 ,𝑠 𝑦 ,𝑚 𝑦 ,𝑐 𝑚 𝑠 𝑚 𝑐 − [ + ] ′ ′ y y 2 𝑧 + 𝜀s 𝑧 + 𝜀 𝑚 2𝑠 𝑚 2𝑠 𝑚 2𝑐 𝑚 2𝑐 2(z +# ) m2s z,m2s 𝑦 − 𝑦 𝑠 𝑠 = 0 0 0 In successive measurements of an inflated optic, y = y , y = y , and z = z m m c c (3) 2(𝑧 + 𝜀 ) m2c m2c 𝑚 2𝑠 𝑧 ,𝑚 2𝑠 because the positions of the camera pinhole and UUT aperture do not change between In successive measurements of an inflated optic, 𝑦 ′ = 𝑦 , 𝑦 ′ = 𝑦 , and 𝑧 ′ = 𝑚 𝑚 𝑐 𝑐 𝑚 2𝑐 acquisitions. Similarly, all calibration measurement errors # , # , # , # , and # y,m y,s y,c z, m2s z,m2c 𝑧 because the positions of the came0 ra pinhole and UUT aperture do not change be- 𝑚 2𝑐 are identical between S (x , y ) and S (x , y ) because they share the same hardware y m m y m m tween acquisitions. Similarly, all calibration measurement errors 𝜀 , 𝜀 , 𝜀 , 𝜀 , 𝑦 ,𝑚 𝑦 ,𝑠 𝑦 ,𝑐 𝑧 ,𝑚 2𝑠 configuration and use the same calibration parameters during calculation. Simplifying the and 𝜀 are identical between 𝑆 (𝑥 , 𝑦 ) and 𝑆 ′ (𝑥 , 𝑦 ) because they share the 𝑧 ,𝑚 2𝑐 𝑦 𝑚 𝑚 𝑦 𝑚 𝑚 expression by cancelling identical variable pairs, the slope change DS is dominated by the same hardware configuration and use the same calibration parameters during calculation. difference of the deflected ray intercepts, Dy = y y , and the distance from the UUT to s s Simplifying the expression by cancelling identical variable pairs, the slope change 𝛥 𝑆 is the screen, z . 𝑦 m2s dominated by the difference of the deflected ray intercepts, 𝛥 𝑦 = 𝑦 − 𝑦 , and the dis- Longitudinal calibration measurement uncertainty # directly influences the slope dif- 𝑠 𝑠 𝑠 z,m2s tance from the UUT to the screen, 𝑧 . ference calculation. However, the uncertainty is conservatively constrained to # = 10 m 𝑚 2𝑠 z,m2s whenLongitud using aincommon al calibration lasermeas tracker urement . We uncerta calculate inty the 𝜀 induced directdefocus ly influences error th as e 𝑧 ,𝑚 2𝑠 D slW ope d= iffere 1/8 nce f ca# lculatio = n. 312.5 Howev nm,er or , th equivalently e uncertain ,ty Z is= con 1.08 serv atively m PV for conthe strai f/2 ned op- to 020 z,m2s 4 tic [23]. If one’s objective is to calculate the shape change of an inflatable UUT surface when 𝜀 = 10 𝜇𝑚 when using a common laser tracker. We calculate the induced defocus 𝑧 ,𝑚 2𝑠 internal pressure, external environment, or even internal gas composition are altered, then error as ∆𝑊 = 1/8(𝑓 )𝜀 = 312.5 nm, or equivalently, 𝑍 = 1.08 𝜇 m PV for the f/2 020 # 𝑧 ,𝑚 2𝑠 4 the optic dif [23] ferential . If one’ deflectometry s objective ismethod to calcula is well-poised te the shape for change the task. of an inflatable UUT surface 2.2. Unique Geometry of Thermal Vacuum Chamber An ordinary deflectometry configuration has no intermediate surface interactions between the light source and the UUT and from that UUT to the camera entrance pupil. In a modified configuration through a TVAC window for an inflatable reflector, we have additional refractive surface interactions to consider: those at a plane window, a thin trans- parent convex canopy, and then backwards through these components. These interactions introduce geometric ray deviations whose influence must be considered in the context of shape reconstruction and are shown exaggerated in Figure 4. Photonics 2021, 8, x FOR PEER REVIEW 6 of 15 when internal pressure, external environment, or even internal gas composition are al- tered, then the differential deflectometry method is well-poised for the task. 2.2. Unique Geometry of Thermal Vacuum Chamber An ordinary deflectometry configuration has no intermediate surface interactions be- tween the light source and the UUT and from that UUT to the camera entrance pupil. In a modified configuration through a TVAC window for an inflatable reflector, we have additional refractive surface interactions to consider: those at a plane window, a thin transparent convex canopy, and then backwards through these components. These inter- Photonics 2022, 9, 1 6 of 15 actions introduce geometric ray deviations whose influence must be considered in the context of shape reconstruction and are shown exaggerated in Figure 4. Figure 4. We examine the effects of a plane window between a room temperature and pressure Figure 4. We examine the effects of a plane window between a room temperature and pressure environment (RTP) and a cryogenic vacuum (a). A camera focuses through the plate and transpar- environment (RTP) and a cryogenic vacuum (a). A camera focuses through the plate and transparent ent Mylar canopy to the reflective Mylar surface. The circular meniscus window is 254 mm in di- Mylar canopy to the reflective Mylar surface. The circular meniscus window is 254 mm in diameter, ameter, while the full UUT aperture is 1 m. Rays from the UUT generally intercept the plate at non- while the full UUT aperture is 1 m. Rays from the UUT generally intercept the plate at non-normal normal incidence and introduce transverse displacement deviation 𝜀 as a function of ray slope incidence and introduce transverse displacement deviation # as a function of ray slope vˆ . The ray y 2 𝑣̂. The ray slope 𝑣̂′ ≠ 𝑣̂ for any PPP tilt, 𝜃 , and wedge, 𝛼 , as seen in (b). In absence of the plate, 2 2 2 slope vˆ 6= vˆ for any PPP tilt, q, and wedge, a, as seen in (b). In absence of the plate, the screen 2 2 the screen y-intercept position would be 𝑦 , rather than the plate-displaced 𝑦 ′ . The ray path from 𝑠 𝑠 y-intercept position would be y , rather than the plate-displaced y . The ray path from the camera to the camera to the UUT is also de s viated by the plate, but its detail is s not highlighted in this schematic. the UUT is also deviated by the plate, but its detail is not highlighted in this schematic. The existing viewport into Northrop Grumman’s TVAC, a plane window, is used to The existing viewport into Northrop Grumman’s TVAC, a plane window, is used to peer into the interior of the chamber volume. The 11.8” (300 mm) diameter plate is 9.14 peer into the interior of the chamber volume. The 11.8” (300 mm) diameter plate is 9.14 mm mm thick and modeled with the properties of fused silica. The glass plate is bolted thick and modeled with the properties of fused silica. The glass plate is bolted through through thru-holes onto the chamber, atop a 10” (254 mm) steel circular aperture, essen- thru-holes onto the chamber, atop a 10” (254 mm) steel circular aperture, essentially loading tially loading the glass like a simply supported circular plate. the glass like a simply supported circular plate. First, we consider the 2 mil (50.8 µ m) clear canopy in front of the optic being tested. First, we consider the 2 mil (50.8 m) clear canopy in front of the optic being tested. The canopy is thin, assumed to have uniform thickness, and not considered, given the 4 The canopy is thin, assumed to have uniform thickness, and not considered, given the meter scale of the test configuration. We consider the influence of the plate far larger. An 4 meter scale of the test configuration. We consider the influence of the plate far larger. An ideal, unloaded plane parallel plate (PPP) introduces defocus to an imaging configuration. ideal, unloaded plane parallel plate (PPP) introduces defocus to an imaging configuration. Refocusing the camera re-establishes conjugate imaging between the detector and the Refocusing the camera re-establishes conjugate imaging between the detector and the UUT UUT surface, but the deviation from an interrupted ray path between the camera and the surface, but the deviation from an interrupted ray path between the camera and the UUT UUT still exists. First, the longitudinal displacement of a PPP with thickness t and refrac- still exists. First, the longitudinal displacement of a PPP with thickness t and refractive tive index n = 1.46 that affects the deflectometry calculation is given by Smith [24]. index n = 1.46 that affects the deflectometry calculation is given by Smith [24]. 𝑡 (𝑛 − 1) 𝜀 = (4) 𝑃𝑃𝑃 ,𝑡 ℎ𝑠𝑖𝑐𝑘𝑛𝑒𝑠 t(n 1) # = (4) PPP,thickness Calculating the deflectometry measurement with an uncompensated ε 𝑃𝑃𝑃 ,𝑡 ℎ𝑛𝑒𝑠𝑠𝑖𝑐𝑘 reduce Calculating s the power the ofdeflectometry the reconstruct measur ed surface ement beca with use an the uncompensated image points are # physically PPP,thickness dis reduces placed the in power the long of itudi then ral econstr direction ucted from surface the val because ue (mea the sur image ed during points calibrati are physically on) of the displaced in the longitudinal direction from the value (measured during calibration) of the camera stop position. Next, if the ideal plate is tilted relative to the incident ray at angle 𝜃 camera stop position. Next, if the ideal plate is tilted relative to the incident ray at angle q from the PPP normal, the transverse ray displacement is 𝜀 [24]. 𝑃𝑃𝑃 ,𝑡 𝑖 from the PPP normal, the transverse ray displacement is # [24]. PPP,tilt 2 3 1 sin q tq(n 1) 4 5 # = tsin(q) 1  (5) PPP,tilt 2 2 n sin q n If two rays of different incidence angles, q and q , intercept the refractive plane plate at the same position, they will emerge separated by # . Inherent parallelism error, or PPP,tilt wedge, also induces angle-dependent errors. If we have wedge in the plate, we take the formalism of prism deviation and multiply by d = 100 mm, the distance from the plane 𝑙𝑡 Photonics 2022, 9, 1 7 of 15 window to the screen, to find the transverse error contribution towards the deflected ray intercept y at the screen [24]. q (n + 1) #  ad(n 1) 1 + (6) PPP,wedge (2n) Now because of the difference between external room temperature and pressure (RTP) and internal TVAC environmental conditions, the pressure gradient deforms the shape of the window rear into a meniscus with weak curvature [13]. 4Et R(D p) = (7) 3(1 n)(3 + n)a D p With the vacuum pressure differential, a meniscus is formed. Using plate thickness t = 9.14 mm, Poisson’s ratio  = 0.15, plate radius a = 127 mm, Young’s Modulus E = 72 GPa, and pressure differential D p  100, 000 Pa, this results in the radius of curvature RoC = 16.7 m. Compared to a ray refracting through two parallel flat interfaces, a ray refracting through two curved interfaces will generally possess a different ray slope than when it had entered. For example, an extreme ray from the edge of the 1 m UUT intercepts the center of the first window surface at a 10.5 angle of incidence (AOI) relative to the optical axis of the UUT. Refracting and propagating through 9 mm of glass, it exits the second surface into air at 10.4983 , a 6 arcsecond difference from the initial AOI. In absolute deflectometry measurements, the holistic effect is that the meniscus window will induce spatially varying error in slope, manifesting as excess defocus and spherical aberration in the integrated height. Trigonometric raytracing is required to discover and compensate for these absolute errors. For differential deflectometry measurements, the influence of the meniscus is min- imized by the subtraction of two measurements. Incrementally inflated or perturbed surfaces still deflect rays through similar angles and surface interception AOIs, especially for the two slow RoC = 16,700 mm surfaces, so we do not consider them in this analysis of differential shape change. 2.3. Plane Parallel Plate Geometry with Differential Deflectometry For an absolute deflectometry surface measurement, we observe that a measurement of the deflected ray intercept at the screen and plate thickness must compensate for the transverse error quantities # , # , and # . We can rewrite the expres- PPP,tilt PPP,wedge PPP,thickness sion for the true slope S in terms of the measured screen deflection intercept y y, true s, meas and the error terms, which can be dependent on the angle between the deflected ray v from the UUT relative to the plate normal. y # (v ) # (v ) s,meas PPP,wedge 2 PPP,tilt 2 S = (8) y,true 2(z # ) m2s PPP,thickness Subtracting slope two measurement calculations, afforded by the knowledge that there was no change in system configuration or calibration, we obtain a new expression, 0 0 (y y ) D# (v , v ) D# (v , v ) s,meas,2 s,meas,1 2 2 2 2 PPP,wedge PPP,tilt DS = (9) y,true 2 z # ( ) m2s PPP,thickness Photonics 2022, 9, 1 8 of 15 The vector v denotes the new vector from a second measurement. The induced errors in wedge and tilt are functions of both v and v . We next express the angles between the 2 2 0 0 plane window and v and v as q and q . 2 2 v2 v2 ad n 1 ( ) t(n1) 2 2 0 0 (y y ) q q (q q ) s,meas,2 s,meas,1 v2 v2 v2 v2 2n n DS = (10) y,true t(n1) 2 z m2s In this expression, the wedge term is insignificant and can be ignored because plane 2 2 0 glass plates can routinely achieve < 5 arcmin, and the difference of q and q ; will v2 v2 also be insignificant. As for the tilt term, the difference quantity q q is approximately v2 v2 twice that of our measurand of interest, DS . To show this, we begin with the observation 0 0 that for small angles q  v , so q q  v v = Dv . For example, the slope v2 2 v2 v2 2 2 2 difference at the aperture edge of a f/3 optic (? = 1000 mm) inflated to a steep f/1 mirror is 175 mrad yet produces only 1.8 mrad of error with this approximation. Next, we observe that S ?n ˆ , so DS = Dn ˆ because the surface normal is always perpendicular to the y y y y surface tangent. Since an angle change q in surface normal n produces twice the deviation in the deflected ray slope, Dv = 2Dn ˆ = 2DS . Thus, q q  Dv = 2DS . Now 2 y y v2 v2 2 y substituting, y y s,meas,2 s,meas,1 DS =   (11) y,true 2t(n1) 2 z m2s Taking two measurements of a common aperture with equivalent static calibration, we calculate differential measurement results even with the introduction of a plane parallel plate. We see that the overall influence of a window, modeled as a plane parallel plate, is to reduce the magnitude of the ray deflection and is compensated in the denominator of the differential slope calculation DS , and similarly so for DS . With both surface y,true x,true slopes obtained, surface integration obtains the induced sag difference between the two measurements of the inflated optic. 3. Experimental Setups For TVAC testing, the Mylar sheets of the 1 m UUT were replaced with new 2 mil thick material, seen in Figure 5. Team members iteratively pulled the circumference of the membrane taut to achieve subjectively uniform edge loading. In our experience, non- uniform tensioning forms visible wrinkles. Uniformity can be quantified by sampling the boundary with sensitive force gages for iterative adjustment, but that procedure was not performed for this experiment. After clamping, the UUT was mounted in a custom optomechanical mounting fixture with 3 degrees of freedom [25]. A fixed mechanical Photonics 2021, 8, x FOR PEER REVIEW 9 of 15 datum consisting of three spherical steel tooling balls was placed behind the reflective surface. Figure 5. Four team members pull the reflective surface taut before clamping it the frame (a). One Figure 5. Four team members pull the reflective surface taut before clamping it the frame (a). One tooling ball just barely touches the rear side of the reflective mylar UUT (b). The full optomechanical tooling ball just barely touches the rear side of the reflective mylar UUT (b). The full optomechanical mounting scheme for the 1 m mirror is described in detail [18]. mounting scheme for the 1 m mirror is described in detail [18]. A deflectometer, shown in Figure 6, was specially designed to mount to the TVAC window at eight flange bolts. The system consisted of a 12.9” (328 mm) iPad Pro (#A2378) illumination source, a Point Grey monochrome camera (FL3-U3-13Y3M-C) with a f = 12 mm lens, and machined aluminum baseplate frame. Several degrees of tilt and decenter adjustment permitted alignment to the TVAC window for maximum reconstruction sig- nal capture. Figure 6. The mechanical deflectometer frame consists of two 356 mm × 356 mm aluminum plates with mounting holes to allow flexible mounting for a camera and illumination screen (a). Standoffs fastened through aluminum slots allow for longitudinal adjustment. The plates were fastened to existing 3/8” bolts. The deflectometer assembly was rotated 22 degrees about the window normal in order to match the orientation of the in-situ bolt hole pattern (b). A design choice of 100 pixels per black/white fringe, 7-step phase shifts, and 3 averages per shot was optimized on-site. Outside the chamber volume, a vacuum inflation control unit provided by FreeFall Aerospace set the internal UUT pressure to a resolution of 10 Pa. The internal pressure was nominally set to 520 Pa relative to the chamber-controlled environmental pressure, which ranged from atmospheric (~100,000 Pa) to near-vacuum (0.11 Pa). In Figure 7, the view of the UUT in its mounting fixture as well as the deflectometer mounting are appar- ent. Calibration was performed with a Leica laser tracker and spherically mounted retroreflectors (SMRs). The calibration procedure obtained the distances between SMR references at the “X”-like tabs of the UUT tensioning ring, the aluminum tensioning frame plane, the plane of the window, the camera, and the iPad illumination screen plane. Photonics 2021, 8, x FOR PEER REVIEW 9 of 15 Figure 5. Four team members pull the reflective surface taut before clamping it the frame (a). One Photonics 2022, 9, 1 9 of 15 tooling ball just barely touches the rear side of the reflective mylar UUT (b). The full optomechanical mounting scheme for the 1 m mirror is described in detail [18]. A deflectometer, shown in Figure 6, was specially designed to mount to the TVAC A deflectometer, shown in Figure 6, was specially designed to mount to the TVAC window at eight flange bolts. The system consisted of a 12.9” (328 mm) iPad Pro (#A2378) il- window at eight flange bolts. The system consisted of a 12.9” (328 mm) iPad Pro (#A2378) lumination source, a Point Grey monochrome camera (FL3-U3-13Y3M-C) with a f = 12 mm illumination source, a Point Grey monochrome camera (FL3-U3-13Y3M-C) with a f = 12 lens, and machined aluminum baseplate frame. Several degrees of tilt and decenter ad- mm lens, and machined aluminum baseplate frame. Several degrees of tilt and decenter justment permitted alignment to the TVAC window for maximum reconstruction signal adjustment permitted alignment to the TVAC window for maximum reconstruction sig- capture. nal capture. Figure 6. The mechanical deflectometer frame consists of two 356 mm × 356 mm aluminum plates Figure 6. The mechanical deflectometer frame consists of two 356 mm  356 mm aluminum plates with mounting holes to allow flexible mounting for a camera and illumination screen (a). Standoffs with mounting holes to allow flexible mounting for a camera and illumination screen (a). Standoffs fastened through aluminum slots allow for longitudinal adjustment. The plates were fastened to fastened through aluminum slots allow for longitudinal adjustment. The plates were fastened to existing 3/8” bolts. The deflectometer assembly was rotated 22 degrees about the window normal existing 3/8” bolts. The deflectometer assembly was rotated 22 degrees about the window normal in in order to match the orientation of the in-situ bolt hole pattern (b). A design choice of 100 pixels order to match the orientation of the in-situ bolt hole pattern (b). A design choice of 100 pixels per per black/white fringe, 7-step phase shifts, and 3 averages per shot was optimized on-site. black/white fringe, 7-step phase shifts, and 3 averages per shot was optimized on-site. Outside the chamber volume, a vacuum inflation control unit provided by FreeFall Outside the chamber volume, a vacuum inflation control unit provided by FreeFall Aerospace set the internal UUT pressure to a resolution of 10 Pa. The internal pressure Aerospace set the internal UUT pressure to a resolution of 10 Pa. The internal pressure was nominally set to 520 Pa relative to the chamber-controlled environmental pressure, was nominally set to 520 Pa relative to the chamber-controlled environmental pressure, which ranged from atmospheric (~100,000 Pa) to near-vacuum (0.11 Pa). In Figure 7, the which ranged from atmospheric (~100,000 Pa) to near-vacuum (0.11 Pa). In Figure 7, view of the UUT in its mounting fixture as well as the deflectometer mounting are appar- the view of the UUT in its mounting fixture as well as the deflectometer mounting are ent. Calibration was performed with a Leica laser tracker and spherically mounted apparent. Calibration was performed with a Leica laser tracker and spherically mounted retroreflectors (SMRs). The calibration procedure obtained the distances between SMR retroreflectors (SMRs). The calibration procedure obtained the distances between SMR references at the “X”-like tabs of the UUT tensioning ring, the aluminum tensioning frame references at the “X”-like tabs of the UUT tensioning ring, the aluminum tensioning frame plane, the plane of the window, the camera, and the iPad illumination screen plane. plane, the plane of the window, the camera, and the iPad illumination screen plane. Photonics 2022, 9, 1 10 of 15 Photonics Photonics 2021 2021, , 8 8, , x FO x FOR P R PEE EER R RE REVIEW VIEW 10 10 of of 15 15 Figure Figure 7. 7. The The iinflated nflated te test st art artic icle le is is m moun ounte ted d at at bac back k of of the the chamber chamber cylin cylinde der r ((a a). ). The The s scal cale e of of the the Figure 7. The inflated test article is mounted at back of the chamber cylinder (a). The scale of the entire entire te test st co confi nfigu guration ration was was n nearly early 4 4 m m,, whi whic ch h plac place es s the the d def efle lect ctometer ometer appr approximately oximately at at tthe he radius radius entire test configuration was nearly 4 m, which places the deflectometer approximately at the radius of curvature of the inflated optic at its inflation pressure range of 500–700 Pa (b). During testing, the of curvature of the inflated optic at its inflation pressure range of 500–700 Pa (b). During testing, the of curvature of the inflated optic at its inflation pressure range of 500–700 Pa (b). During testing, the firs firstt Fr Fres esnel nel ref refle lect ctio ion n at at the the a acryli crylic c window window interfac interface e was was ffaint aint enou enough gh to to not not s signific ignificantl antly y reduce reduce first Fresnel reflection at the acrylic window interface was faint enough to not significantly reduce si sign gnal al c contrast ontrast at at the the camera camera de detec tector tor.. Di Diffuse ffuse m machined achined in internal ternal surfaces surfaces sc scatter atter the the iill llu um minati ination on signal contrast at the camera detector. Diffuse machined internal surfaces scatter the illumination from from outsi outside de tthe c he cham hamber, ber, al also so s sli ligh ghtl tly red y reducing reco ucing reconstr nstructio uction s n signal ignal c contrast. ontrast. from outside the chamber, also slightly reducing reconstruction signal contrast. 4. 4. E Exp xperim erimen ental tal R Results esults 4. Experimental Results 4.1. Deflectometer Repeatability Measurements 4.1. Deflectometer Repeatability Measurements 4.1. Deflectometer Repeatability Measurements Test Testing ing to took ok pla place ce ov over er on one e week week at at th the e North Northrop rop Gr Grumm umman an Spac Space e Sy System stems s ffac acil ility ity Testing took place over one week at the Northrop Grumman Space Systems facility in in in Redon Redondo do B Bea each. ch. Ov Over er 80 80 sur surfface ace me measuremen asurements ts wer were e taken taken of of th the e sa same me s surface urface,, subject subject Redondo Beach. Over 80 surface measurements were taken of the same surface, subject to to to a a vari variety o ety off environm environment ental al s setp etpoints within TVAC oints within TVAC. . At each f At each fre resh sh inf infllation o ation of f th the mem e mem-- a variety of environmental setpoints within TVAC. At each fresh inflation of the membrane, the brane, brane, membrane th the e me memb mb vertex ra rane ne ve was vertex rtex br wa ought was s bro bro into ugh ugh contact t t into into con con with ttact act the with with rear th the e mechanical rear rear mec mechani hani datum c cal al d datum atum and then and and the th then en external th the e ext exter pr ernal essur nal pres pres e contr sur sure e ol con con unit tro tro stepped l l un unit it s step tep back ped ped inflation back back iinflation nflation pressurpre pre e by ss ss 10 ure ure Pa by by until 10 10 P P the a a until until surface th the e no surface surface longer no no contacted lo longer nger con con the tact tact mechanical e ed d th the e mec mechan han datum. ical ical d d For atum. atum. an F Ar For or gon an an Ar gas Argon gon fill,g gan as as fill internal fill, , an an internal internal pressur pr pr ees- es- of 700 sur sure e Pa, o of f 700 chamber 700 P Pa, a, ch ch pr amber amber essurpr e prof essure essure 0.11 of Pa, of 0.1 0.1 and 1 1 Pa Pa chamber ,, and and cha cha temperatur mb mber er tem temperature perature e of 137 o o K, f f 13 13 the 7 7 K K total , , th the e RMS to total tal difference across the surface was about 100–250 nanometers, shown in Figure 8. This RM RMS S di diff ffe eren rence ce acros across s th the e s surface urface w was as about about 10 100 0– –250 250 n nanomet anometers, ers, sh shown own in in Fi Fig gur ure e 8. 8. Th This is repeatability is a fraction of the wavelength for the smallest band of interest for OASIS’s repeatab repeatability ility is is a a ffra ract ction ion o of f th the e wave wavelen length gth for for th the e s smal malles lest t b band and of of interest interest for for OA OASIS’s SIS’s terahertz optics, ~80 m [3]. terahertz terahertz opt optiics, ~80 cs, ~80 µ µm [ m [3]. 3]. Figure 8. Three differential deflectometry measurements show the repeatability of the central 525 mm Figure 8. Three differential deflectometry measurements show the repeatability of the central 525 Figure 8. Three differential deflectometry measurements show the repeatability of the central 525 apertur m mm m aperture. aperture. e. Changes Ch Chang ang within es es within within the first the the two firs first t minute-separated two two m minute inute--se separated parated acquisitions acquisiti acquisiti resemble ons ons rese resem m coma ble ble co co but m ma a flip but but in fli fli sign. p p in in sign. At the end of the third minute acquisition, fluctuations damped significantly. Experience with sign. At the end of the third minute acquisition, fluctuations damped significantly. Experience with At the end of the third minute acquisition, fluctuations damped significantly. Experience with the the inflat inflatio ion n un unit it hints hints that that tthe he press pressur ure e co contr ntrol ol un unit it st stron rongly gly co converg nverges es towards towards the the se settpoint, point, but but the inflation unit hints that the pressure control unit strongly converges towards the setpoint, but suffic sufficie ient nt it iterat erativ ive e co con nvergenc vergence oc e occurs on curs on llong onger er ti tim mes escal cale es. s. Here, Here, the the 700 700 P Pa a press pressur ure s e setp etpoi oint nt was was sufficient iterative convergence occurs on longer timescales. Here, the 700 Pa pressure setpoint was m met et and and held held tto o the 10 the 10 Pa Pa re res sol olution i ution ind ndic icat ated ed by the by the un unit it.. met and held to the 10 Pa resolution indicated by the unit. Amo Among ng all all p perturbed erturbed mea measur suremen ements ts o off th the e f/2 f/2 op optic, tic, no no mo more re th than an 600 600 mm mm of of th the e Among all perturbed measurements of the f/2 optic, no more than 600 mm of the dia diamet meter er w was as bo both th il illlumin uminated ated by by th the e s scre creen en and and ca capt ptured ured by by th the e camer camera. a. Th The e steep steep in- in- diameter was both illuminated by the screen and captured by the camera. The steep inflated flated flated state state w was as dem demanded anded by by th the e f/# f/# desi design gn re regi gime me r releva elevant nt to to th the e OASIS OASIS ffull ull--sized sized pri pri-- state was demanded by the f/# design regime relevant to the OASIS full-sized primary mary mary r ref eflector. lector. Th The e com comm mon on ar are ea a w was as crop cropped ped to to ab about out 525 525 mm mm in in th these ese mea measur suremen ementt reflector. The common area was cropped to about 525 mm in these measurement maps and maps maps and and all all subse subsequent quent maps maps fo for r di dire rect ct com compa paris riso on n of of sh shape ape ch change. ange. A A la lar rge ger r meas measure ure-- all subsequent maps for direct comparison of shape change. A larger measurement area men ment t ar area ea r ran ange ge is is li lim mited ited by by th the e si size ze o of f th the e TVAC TVAC window window, , wh whiich ch con constrai strain ns s th the e sl slop ope es s range is limited by the size of the TVAC window, which constrains the slopes measurable Photonics 2021, 8, x FOR PEER REVIEW 11 of 15 Photonics 2022, 9, 1 11 of 15 measurable by the deflectometry system. A larger window can extend the dynamic meas- by the deflectometry system. A larger window can extend the dynamic measuring slope uring slope range at the cost of additional window thickness to maintain structural re- range at the cost of additional window thickness to maintain structural requirements for a quirements for a large vacuum chamber. large vacuum chamber. 4.2. Induced Thermal Gradient by Artifical Sun 4.2. Induced Thermal Gradient by Artifical Sun A small overhead heat source (or ‘Artificial Sun’) illuminated the membrane assem- A small overhead heat source (or ‘Artificial Sun’) illuminated the membrane assembly bly half a meter away. The source was positioned closest to the aperture’s 12 o’clock posi- half a meter away. The source was positioned closest to the aperture’s 12 o’clock position tion (north). Chamber temperature was set to T = 142 K and pressure P = 0.11 Pa was en- (north). Chamber temperature was set to T = 142 K and pressure P = 0.11 Pa was enforced. forced. Once the radiation source was turned on, the reflective Mylar surface began warm- Once the radiation source was turned on, the reflective Mylar surface began warming. Four ing. Four T-type thermocouples were attached at the four cardinal points near the tension- T-type thermocouples were attached at the four cardinal points near the tensioning ring ing ring periphery of the back membranes. For the next half hour, the temperature detected periphery of the back membranes. For the next half hour, the temperature detected at each at each sensor rose by 1 K for the east, west, and south thermocouples, but rose by 5 K for sensor rose by 1 K for the east, west, and south thermocouples, but rose by 5 K for the north the north sensor, which was closest to the UUT. sensor, which was closest to the UUT. Cumulative thermal change resulted in a predominantly surface change in power, as Cumulative thermal change resulted in a predominantly surface change in power, as shown in Figure 9. This is the surface response to transient conduction across the large, shown in Figure 9. This is the surface response to transient conduction across the large, thin metallized surface and dimensional lengthening of the material with heat. Spatial thin metallized surface and dimensional lengthening of the material with heat. Spatial asymmetry, seen at surface change map at ∆𝑡 = 120 s, damped out towards ∆𝑡 = 600𝑠 , asymmetry, seen at surface change map at Dt = 120 s, damped out towards Dt = 600 s, where the vertex of the concave surface began contacting one of the spherical datums be- where the vertex of the concave surface began contacting one of the spherical datums hind the UUT. The protruding surface point in front of the leftmost ball is the most visually behind the UUT. The protruding surface point in front of the leftmost ball is the most apparent feature as a consequence of the thermally induced material expansion. visually apparent feature as a consequence of the thermally induced material expansion. Figure 9. Shape differences were observed successively on the timescale of hundreds of seconds. It is Figure 9. Shape differences were observed successively on the timescale of hundreds of seconds. It interesting that the proximity of the heat source to the northern region of the UUT did not produce is interesting that the proximity of the heat source to the northern region of the UUT did not produce lo local cal non non-uniformity -uniformity at atthe the ce center nter apertu apertur re e region region dedespite spite loc local al temper temperatur ature de iff dif erences. ferences. In thi Ins this ex- periment, the inflatant gas was Argon, which most recently expelled a mix of Helium, Argon, and experiment, the inflatant gas was Argon, which most recently expelled a mix of Helium, Argon, and Xenon from the lenticular UUT volume. Xenon from the lenticular UUT volume. Eventually Eventually , , the the two two outermost outermost balls balls of of the the physical physical r refer eference ence fiducial fiducial are are vis visible ible by by ∆D𝑡 t = = 132 1320 0 s s. . F Finite inite fri friction ction on onth the e ref reflective lective mem membrane brane ba back ck su surface rface pre prevents vents th the e outer outer tw two o balls from slipping and obscures the influence of the central ball. The high sensitivity and Photonics 2021, 8, x FOR PEER REVIEW 12 of 15 Photonics 2021, 8, x FOR PEER REVIEW 12 of 15 Photonics 2022, 9, 1 12 of 15 balls from slipping and obscures the influence of the central ball. The high sensitivity and balls from slipping and obscures the influence of the central ball. The high sensitivity and precision of differential deflectometry towards radiation-induced effects suggest that it precision of differential deflectometry towards radiation-induced effects suggest that it will precision of differential deflectometry towards radiation-induced effects suggest that it will be an asset to space system surface metrology and calibration. be an asset to space system surface metrology and calibration. will be an asset to space system surface metrology and calibration. 4.3. Induced Puncture Response 4.3. Induced Puncture Response 4.3. Induced Puncture Response The final segment of our protocol was a simulated micrometeoroid puncture test The final segment of our protocol was a simulated micrometeoroid puncture test shown in Figures 10 and 11. A feature of Northrop Grumman’s TVAC chamber added The final segment of our protocol was a simulated micrometeoroid puncture test shown in Figures 10 and 11. A feature of Northrop Grumman’s TVAC chamber added for for this test is an externally controllable mechanical actuator. Wielding a thin needle in shown in Figures 10 and 11. A feature of Northrop Grumman’s TVAC chamber added for this test is an externally controllable mechanical actuator. Wielding a thin needle in an arc- an arc-like motion, the actuator pierced a hole into the back reflective membrane. The this test is an externally controllable mechanical actuator. Wielding a thin needle in an arc- like motion, the actuator pierced a hole into the back reflective membrane. The cylindrical cylindrical body of the needle had a diameter of 0.6 mm. The spatial puncture location was like motion, the actuator pierced a hole into the back reflective membrane. The cylindrical body of the needle had a diameter of 0.6 mm. The spatial puncture location was chosen at chosen at the north cardinal position near the aperture edge of the membrane assembly. bo th dy e nort of th h e cardi needle nal hpo ad sa itio din ameter near th of e 0.6 aperture mm. Th edg e spat e of ial thpunct e mem ur bra e lne ocation assem w bly as . chosen Figure at 10 Figure 10 reveals the reflected signal before puncture and three snapshots after puncture. the north cardinal position near the aperture edge of the membrane assembly. Figure 10 reveals the reflected signal before puncture and three snapshots after puncture. Videos Videos were taken using the same camera in the deflectometry setup while a single static reveals the reflected signal before puncture and three snapshots after puncture. Videos were taken using the same camera in the deflectometry setup while a single static fringe fringe was displayed. In this experiment, the chamber temperature was kept to T = 293 K were taken using the same camera in the deflectometry setup while a single static fringe was displayed. In this experiment, the chamber temperature was kept to T = 293 K and and the inflatant had been solely Argon for four consecutive days. was displayed. In this experiment, the chamber temperature was kept to T = 293 K and the inflatant had been solely Argon for four consecutive days. the inflatant had been solely Argon for four consecutive days. Figure 10. After the unpunctured reflector (first subplot) is pierced, the number of fringes increases Figure 10. After the unpunctured reflector (first subplot) is pierced, the number of fringes increases (second subplot). With knowledge of the testing distance (𝑧 ≈ 3800 mm) and fringe width at the Figure 10. After the unpunctured reflector (first subplot) is pierced, the number of fringes increases (second subplot). With knowledge of the testing distance (z  3800 mm) and fringe width at the (ssc ecreen ond (subplo 𝜉 ≈ 9.62 t). mm Wit), h one knowl can ed co ge unof t the the number testing of distance fringes (pass 𝑧 ≈ ing 3800 thr mm oug ) h and a given fringpixe e wil dth to co at ars the el y screen (x  9.62 mm ), one can count the number of fringes passing through a given pixel to sc es reen timate (𝜉 ≈ the 9.62 slope mmchang ), one e can in y co -di un recti t the on. number In the of third fring subfi es pass gure, ing a shado throug w h precl a given udes pixe slop l to e co mars easel ur ye- coarsely estimate the slope change in y-direction. In the third subfigure, a shadow precludes slope es m tient mate at the this slope local chang surface e in reg y-io di n, recti indicati on. In ng the that third the subfi slope gu ch re, ang a shado e exceed w precl s the udes meas sl ur op able e m dynam easure-ic measurement at this local surface region, indicating that the slope change exceeds the measurable m ran ent ge at of th this e lo de cal fle surface ctometer reg in ioi n, ts indicati current ng posi that tion. Th the sle ope shado chang w shrink e exceed s and s the grm ows at easura able low dynam tempor ica l dynamic range of the deflectometer in its current position. The shadow shrinks and grows at a low ran frequ ge of th ency eun deti fle l it ct fully ometer reco in ver its s curr and ent is m posi eas tu io rable n. Thagain e shado wit w hou shrink t the s and subapertu grows at re dat a lo a w votempor id. Cham al - frequ temporal ber press ency fr ur un equency e tiin l it creas fully until ed reco from it ver fully 0. s 84 and recovers Pa is to m7 eas .and 07 u P rable is a after measurable again punctur witagain hou e. t the without subapertu the subapertur re data vo eid. data Chvoid. am- ber Chamber pressur pr e essur increas e incr ed from eased 0. fr 84 om Pa 0.84 to 7Pa .07 to Pa 7.07 after Papu after nctur punctur e. e. Figure 11. The second puncture showed recovery without substantial dynamic change over tens of Figure minutes. 11. The Cha m seber cond press punctur ure increas e showed ed from recovery 7.07 without Pa to 10. s6 ubstantial 6 Pa after dynam the secic ond chang punctur e over e. tens A third of Figure 11. The second puncture showed recovery without substantial dynamic change over tens of m pu inutes. nctur e Ch brou amber ght press the cham ure increas ber press edur from e to 13 7.07 .33 Pa Pa to . 10.66 Pa after the second puncture. A third minutes. Chamber pressure increased from 7.07 Pa to 10.66 Pa after the second puncture. A third puncture brought the chamber pressure to 13.33 Pa. puncture brought the chamber pressure to 13.33 Pa. In Figure 11, we show differential measurements of the puncture after a second punc- In Figure 11, we show differential measurements of the puncture after a second punc- ture in the back concave membrane. The apparent difference in surface flips sign on the In Figure 11, we show differential measurements of the puncture after a second punc- ture in the back concave membrane. The apparent difference in surface flips sign on the scale of every few minutes, now with error 8 µ m peak-to-valley and 5.08 µ m rms by ∆t = ture in the back concave membrane. The apparent difference in surface flips sign on the scale of every few minutes, now with error 8 µ m peak-to-valley and 5.08 µ m rms by ∆t = 800 s. Again, these fluctuations resemble low-order power, which is consistent with power scale of every few minutes, now with error 8 m peak-to-valley and 5.08 m rms by 800 s. Again, these fluctuations resemble low-order power, which is consistent with power being the dominant shape response to internal pressure setpoint [5]. The undulation is not Dt = 800 s. Again, these fluctuations resemble low-order power, which is consistent with being the dominant shape response to internal pressure setpoint [5]. The undulation is not the transient response of the rear membrane surface alone, but a dynamic response of the power being the dominant shape response to internal pressure setpoint [5]. The undulation the transient response of the rear membrane surface alone, but a dynamic response of the inflation unit regulation algorithm. That is, the 0.6 mm diameter puncture immediately is not the transient response of the rear membrane surface alone, but a dynamic response of inflation unit regulation algorithm. That is, the 0.6 mm diameter puncture immediately decreased the UUT internal pressure, triggering a cyclic overshoot and undershoot to- the inflation unit regulation algorithm. That is, the 0.6 mm diameter puncture immediately decreased the UUT internal pressure, triggering a cyclic overshoot and undershoot to- wards the setpoint pressure. The second puncture did not decrease the internal pressure decreased the UUT internal pressure, triggering a cyclic overshoot and undershoot towards wards the setpoint pressure. The second puncture did not decrease the internal pressure the setpoint pressure. The second puncture did not decrease the internal pressure of the Photonics 2022, 9, 1 13 of 15 UUT beyond the minimum incremental resolution (10 Pa), but did immediately increase chamber pressure by 3 Pa. During punctured shape measurement, a single fringe’s undulation was noticeable at the timescale of 20 s up to one minute. Given the similarity to the overall length of deflectometry acquisition (~25 s), dynamic drift will alter the surface measurement to an effect similar to that of vibration during phase-shifting interferometry. This temporal effect does not exist for the thermal gradient study, whose reflected fringes at the camera did not undulate and gradually moved over the course of surface temperatures changing by 5 K over 20 min. Single-shot display and PMD processing techniques exist which could reduce the effects of the dynamic surface drift [26,27]. A final comment is that the micrometeoroid puncture test performed is actually an accelerated simulation of the puncture of a large spaceborne membrane reflector. A surface shape change fluctuation of 5.08 m RMS due to puncture is conservative because the 1 m monolithic surface UUT was constructed of two flat membranes, which requires higher internal inflation pressure to achieve the same f/# as an identically sized, preformed gored construction. The high time resolution of this full-field metrology solution allows temporal characterization of inflatable primary reflectors—a next step towards realizing the next generation of large-aperture space observatories. 5. Conclusions TVAC testing results are reported for a 1 m inflatable membrane reflector in response to perturbations in low-temperature, near-vacuum conditions. Surface change was observed with phase-measuring deflectometry, particularly a differential deflectometry method that compensates for the influence of a plane window environmentally separating the test hardware from the UUT. To perform measurements, a custom deflectometer was constructed and mounted to the window plate of a large TVAC chamber, and a laser tracker provided geometric calibration references. A week-long campaign allowed the chamber to reach environmental setpoints dictated by the experimental protocol, and the static deflectometer measured surface shape responses at high spatial resolution. While desirable, using phase-measuring deflectometry to obtain absolute surface maps is not implemented, because an accurate virtual null is not assumed. Only in the differential variant are the errors induced by a virtual null negated. Errors in calibration can be mitigated by extra calibration devices, which leave the possibility of absolute deflectometry once an approximate virtual null with low-order figure has been established. For absolute shape measurement, studies with a laser radar system have measured the shape down to 50 m repeatability, but with sparser spatial sampling [28]. At the present, measuring a 14 m, f/1.5 reflector is also desirable. To monitor shape change, a differential deflectometry configuration would set its hardware at the radius of curvature of the optic, or 21 m away. The scale of measurement would be challenging as finite radiance of the illumination screen at each pixel must be considered for sufficient surface reconstruction signal to arrive at the camera detector. Additionally, transverse aberrations of the manufactured mirror scale directly with mirror size and may demand a much larger screen to fully illuminate the aperture. However, if sufficient radiance and size of a screen can be achieved for this long- distance testing configuration, differential deflectometry will be an invaluable asset to final shape monitoring and mirror characterization. This is because large membrane reflectors achieve identical f/#’s to smaller ones (such as our 1 m surrogate) at a much lower internal pressure (<10 Pa), and will therefore be more sensitive to a finite pressure control resolution. In the limit of finite incremental pressure control, differential deflectometry can keep the influence of systematic pressure drifts at bay, while other non-contact metrology techniques obtain the absolute low-order shape of the large reflector. Author Contributions: H.Q. provided the design, test, and assembly of the deflectometer and its prototypes, and its processing. H.K., H.C. and D.K. primarily ran the deflectometry experiments over 1 week of TVAC testing. M.E., K.K. and H.K. provided testing development support in atmospheric Photonics 2022, 9, 1 14 of 15 test runs. C.D.d. managed shipping the larger membrane assembly and project management guidance. All other coauthors (S.S., A.C., J.B., Y.T., A.P., J.W.A. and C.W.) provided similar levels of support in testing, ideation, validation, and supervision. All authors have read and agreed to the published version of the manuscript. Funding: The authors would like to acknowledge the II-VI Foundation Block-Gift, Technology Re- search Initiative Fund Optics/Imaging Program, and Friends of Tucson Optics Endowed Scholarships in Optical Sciences for helping support the metrology research conducted in the LOFT group. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Data available upon request. Acknowledgments: We would like to acknowledge FreeFall Aerospace in Tucson, Arizona for supplying the vacuum pressure modular pumps to maintain internal gas pressure during testing. Finally, we would like to thank the Northrop Grumman Aerospace Systems team for their incredible help during a full week of testing. Conflicts of Interest: The authors declare no conflict of interest. References 1. Freeland, R.E.; Bilyeu, G. In-Step Inflatable Antenna Experiment. Acta Astronaut. 1993, 30, 29–40. [CrossRef] 2. Walker, C.K.; Chin, G.; Aalto, S.; Anderson, C.M.; Arenberg, J.W.; Battersby, C.; Bergin, E.; Bergner, J.; Biver, N.; Bjorakerb, G.L.; et al. Orbiting Astronomical Satellite for Investigating Stellar Systems (OASIS): Following the water trail from the interstellar medium to oceans. In Proceedings of the Astronomical Optics: Design, Manufacture, and Test of Space and Ground Systems III., San Diego, CA, USA, 1–5 August 2021; p. 26. [CrossRef] 3. Arenberg, J.W.; Villareal, M.N.; Yamane, J.; Yu, T.; Lazear, J.; Pohner, J.; Sangalis, M.; Jackson, S.L.; Morse, E.; Tyler, R.; et al. OASIS architecture: Key features. In Proceedings of the Astronomical Optics: Design, Manufacture, and Test of Space and Ground Systems III., San Diego, CA, USA, 1–5 August 2021; p. 30. [CrossRef] 4. Palisoc, A.; Pardoen, G.; Takashima, Y.; Chandra, A.; Sirsi, S.; Choi, H.; Kim, D.W.; Quach, H.; Arenberg, J.; Walker, C.K. Analytical and finite element analysis tool for nonlinear membrane antenna modeling for astronomical applications. In Proceedings of the Astronomical Optics: Design, Manufacture, and Test of Space and Ground Systems III., San Diego, CA, USA, 1–5 August 2021; p. 32. [CrossRef] 5. Hencky, H. Über den Spannungszustand in kreisrunden Platten. Z. Angew. Math. Mech. 1915, 63, 311–317. 6. Quach, H.; Esparza, M.A.; Kang, H.; Chandra, A.; Choi, H.; Berkson, J.; Karrfalt, K.; Sirsi, S.; Takashima, Y.; Palisoc, A.; et al. Deflectometry-based thermal vacuum testing for a pneumatic terahertz antenna. In Proceedings of the Astronomical Optics: Design, Manufacture, and Test of Space and Ground Systems III., San Diego, CA, USA, 1–5 August 2021; p. 34. [CrossRef] 7. Chandra, A.; Walker, C.K. Thermally formed inflatable reflectors for space telescopes. 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Jain, U.; Gauthier, A.; van der Meer, D. Total-internal-reflection deflectometry for measuring small deflections of a fluid surface. Exp. Fluids 2021, 62, 1–14. [CrossRef] Photonics 2022, 9, 1 15 of 15 16. Willomitzer, F.; Yeh, C.-K.; Gupta, V.; Spies, W.; Schiffers, F.; Katsaggelos, A.; Walton, M.; Cossairt, O. Hand-guided qualitative deflectometry with a mobile device. Opt. Express 2020, 28, 9027. [CrossRef] [PubMed] 17. Huang, L.; Idir, M.; Zuo, C.; Asundi, A. Review of phase measuring deflectometry. Opt. Lasers Eng. 2018, 107, 247–257. [CrossRef] 18. Xu, Y.; Gao, F.; Jiang, X. A brief review of the technological advancements of phase measuring deflectometry. PhotoniX 2020, 1, 1–10. [CrossRef] 19. Ritter, R.; Hahn, R. Contribution to analysis of the reflection grating method. Opt. Lasers Eng. 1983, 4, 13–24. [CrossRef] 20. Su, P.; Parks, R.E.; Wang, L.; Angel, R.P.; Burge, J.H. Software configurable optical test system: A computerized reverse Hartmann test. Appl. 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[CrossRef] [PubMed] 27. Nguyen, M.T.; Ghim, Y.S.; Rhee, H.G. Single-shot deflectometry for dynamic 3D surface profile measurement by modified spatial-carrier frequency phase-shifting method. Sci. Rep. 2019, 9, 1–15. [CrossRef] [PubMed] 28. Sirsi, S. Orbiting Astronomical Satellite for Investigating Stellar Systems (OASIS) Space Telescope; The University of Arizona: Tucson, AZ, USA, 2021. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Photonics Multidisciplinary Digital Publishing Institute

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hv photonics Article Surface Measurement of a Large Inflatable Reflector in Cryogenic Vacuum 1 1 1 , 2 2 1 , 3 1 Henry Quach , Hyukmo Kang , Siddhartha Sirsi , Aman Chandra , Heejoo Choi , Marcos Esparza , 1 1 1 4 5 Karlene Karrfalt , Joel Berkson , Yuzuru Takashima , Art Palisoc , Jonathan W. Arenberg , 1 , 2 6 1 , 2 , 3 , Christopher Walker , Christian Drouet d’Aubigny and Daewook Kim * Wyant College of Optical Sciences, University of Arizona, 1630 East University Blvd., Tucson, AZ 85721, USA; henryquach@optics.arizona.edu (H.Q.); hkang@optics.arizona.edu (H.K.); ssirsi@email.arizona.edu (S.S.); hchoi@optics.arizona.edu (H.C.); maesparza@email.arizona.edu (M.E.); kkarrfalt@email.arizona.edu (K.K.); joelsteraz@email.arizona.edu (J.B.); ytakashima@optics.arizona.edu (Y.T.); cwalker@arizona.edu (C.W.) Department of Astronomy and Steward Observatory, University of Arizona, 933 North Cherry Avenue, Tucson, AZ 85721, USA; achandra@email.arizona.edu Large Binocular Telescope Observatory, University of Arizona, 933 North Cherry Avenue, Tucson, AZ 85721, USA L’Garde, Inc., 15181 Woodlawn Avenue, Tustin, CA 92780, USA; Art_Palisoc@lgarde.com Northrop Grumman Systems Corporation—Space Sector, 1 Space Park Drive, Redondo Beach, CA 90278, USA; jon.arenberg@ngc.com Lunar and Planetary Laboratory, University of Arizona, 1629 East University Blvd., Tucson, AZ 85721, USA; cdaubign@orex.lpl.arizona.edu * Correspondence: dkim@optics.arizona.edu Abstract: The metrology of membrane structures, especially inflatable, curved, optical surfaces, remains challenging. Internal pressure, mechanical membrane properties, and circumferential bound- ary conditions imbue highly dynamic slopes to the final optic surface. Here, we present our method and experimental results for measuring a 1 m inflatable reflector ’s shape response to dynamic pertur- bations in a thermal vacuum chamber. Our method uses phase-measuring deflectometry to track Citation: Quach, H.; Kang, H.; Sirsi, shape change in response to pressure change, thermal gradient, and controlled puncture. We use S.; Chandra, A.; Choi, H.; Esparza, an initial measurement as a virtual null reference, allowing us to compare 500 mm of measurable M.; Karrfalt, K.; Berkson, J.; aperture of the concave f/2, 1-meter diameter inflatable optic. We built a custom deflectometer that Takashima, Y.; Palisoc, A.; et al. attaches to the TVAC window to make full use of its clear aperture, with kinematic references behind Surface Measurement of a Large the test article for calibration. Our method produces 500  500 pixel resolution 3D surface maps with Inflatable Reflector in Cryogenic a repeatability of 150 nm RMS within a cryogenic vacuum environment (T = 140 K, P = 0.11 Pa). Vacuum. Photonics 2022, 9, 1. https://doi.org/10.3390/ photonics9010001 Keywords: deflectometry; inflatable optics; thermal vacuum testing; terahertz astronomy Received: 16 November 2021 Accepted: 16 December 2021 Published: 21 December 2021 1. Introduction Publisher’s Note: MDPI stays neutral Gossamer space structures are not a recent invention. From the Inflatable Aperture with regard to jurisdictional claims in Experiment in 1996 to the sunshield assembly of the James Webb Space Telescope, mem- published maps and institutional affil- brane spacecraft assemblies continue to be actively deployed [1]. Up to tens of microns iations. thick, environmentally resistant films such as Mylar and Kapton form large monolithic surface areas. A promising example of future gossamer structures is OASIS, or the Orbit- ing Astronomical Satellite for Investigating Stellar Systems. OASIS is a proposed ~14 to 20-meter class space observatory that will perform high spectral resolution observations at Copyright: © 2021 by the authors. terahertz frequencies [2]. The advantage for such structures is that they can achieve 7X the Licensee MDPI, Basel, Switzerland. This article is an open access article collecting area as space observatories with traditionally polished apertures for less than distributed under the terms and one third of the mass [3]. A spaceborne observatory with a 14 meter diameter size produces conditions of the Creative Commons a signal-to-noise ratio unobtainable at ground level for far-infrared spectra, enabling the Attribution (CC BY) license (https:// quantitative science of detecting water in distant protoplanetary disks and solar system creativecommons.org/licenses/by/ objects. 4.0/). Photonics 2022, 9, 1. https://doi.org/10.3390/photonics9010001 https://www.mdpi.com/journal/photonics Photonics 2021, 8, x FOR PEER REVIEW 2 of 15 Photonics 2022, 9, 1 2 of 15 enabling the quantitative science of detecting water in distant protoplanetary disks and solar system objects. For inflatable apertures, technical characteristics of interest include shape response For inflatable apertures, technical characteristics of interest include shape response to to environmental temperature and pressure, thermal gradients, and puncture by micro- environmental temperature and pressure, thermal gradients, and puncture by micromete- meteoroid. Unfortunately, full-field, temporal behavior of inflatable highly aspheric mem- oroid. Unfortunately, full-field, temporal behavior of inflatable highly aspheric membrane brane optical surfaces has not been extensively studied in high resolution, no less in a optical surfaces has not been extensively studied in high resolution, no less in a cryogenic cryogenic vacuum or in puncture. vacuum or in puncture. 1.1. Geometrical Shape of Pneumatic Membranes 1.1. Geometrical Shape of Pneumatic Membranes Two varieties of pneumatic reflectors exist: monolithic membranes and composite Two varieties of pneumatic reflectors exist: monolithic membranes and composite gored membranes. This paper concerns the measurement of monolithic membranes, gored membranes. This paper concerns the measurement of monolithic membranes, which which have higher dynamic slopes than their counterparts stitched from triangular pieces have higher dynamic slopes than their counterparts stitched from triangular pieces [4]. [4]. Monolithic membranes, if composed of ideal mechanically isotropic films, produce a Monolithic membranes, if composed of ideal mechanically isotropic films, produce a ra- radially symmetric, spherically aberrated shape known as a Hencky Curve Surface [5,6]. dially symmetric, spherically aberrated shape known as a Hencky Curve Surface [5,6]. In In the Zernike description, the Hencky Curve Surface is the sum of defocus and spherical the Zernike description, the Hencky Curve Surface is the sum of defocus and spherical terms. When constructed of real films such as Mylar, pressurization generates astigma- terms. When constructed of real films such as Mylar, pressurization generates astigmatism tism because manufacturing polymer films imbues different Young’s Moduli across or- because manufacturing polymer films imbues different Young’s Moduli across orthogonal thogonal axes. At lower pressures, wrinkles sprout from the perimeter of the reflector, axes. At lower pressures, wrinkles sprout from the perimeter of the reflector, introducing introducing higher order spatial frequency errors [7]. These artifacts rapidly diminish at higher order spatial frequency errors [7]. These artifacts rapidly diminish at higher pres- higher pressure because the stress experienced across the entire aperture grows more uni- sure because the stress experienced across the entire aperture grows more uniform in all form in all directions under pneumatic loading [8]. directions under pneumatic loading [8]. In In 2019, 2019, the the University University of of Arizona Arizona constr construct ucted ed a a 1 1 meter meter surr surro ogate gate r ref eflector lector to to test test optical optical metr metro ology logy techniques, techniques, shown shown in in Figur Figure e 1 1 [ [9 9] ].. A A monolithic, monolithic, Hencky-forming Hencky-forming con con- - struction was chosen because of its simplicity and requisite lead time of a gored parabolic struction was chosen because of its simplicity and requisite lead time of a gored parabolic assembly assembly.. Our Our r requirement equirement for for a a general general metr metrology ology technique technique r re equir quired ed capturing capturing surface surface shapes that are relatively unknown due to latent wrinkles and possible thermoforming shapes that are relatively unknown due to latent wrinkles and possible thermoforming variation. We considered tactile solutions such as low-force contact profilometers and variation. We considered tactile solutions such as low-force contact profilometers and con- confocal probes. However, both systems require a motion travel range at least as large as focal probes. However, both systems require a motion travel range at least as large as the the unit under test (UUT), and their pointwise, mechanically driven acquisitions would unit under test (UUT), and their pointwise, mechanically driven acquisitions would se- severely limit sampling speed. verely limit sampling speed. Figure 1. An inflatable membrane mirror is constructed by clamping two Mylar sheets between Figure 1. An inflatable membrane mirror is constructed by clamping two Mylar sheets between three three machined aluminum rings. During inflation, the rear aluminized Mylar becomes the concave machined aluminum rings (a). During inflation, the rear aluminized Mylar becomes the concave reflecting surface of interest, while the clear convex Mylar front surface helps hold pressure. The reflecting surface of interest, while the clear convex Mylar front surface helps hold pres-sure (b). The convex Mylar surface is known as the canopy. In the final full-sized assembly, the canopy will be convex Mylar surface is known as the canopy. In the final full-sized assembly, the canopy will be black polyimide, which is opaque in the visible but transparent with some loss in the target opera- black polyimide, which is opaque in the visible but transparent with some loss in the target operation tion wavelengths (~80–660 µ m). wavelengths (~80–660 m). 1.2. Thermal Vacuum Chamber Testing and Surface Testing Thermal Vacuum Chamber (TVAC) testing is a regular milestone in space hardware verification; emulating the conditions of device operation in space is important to predict the behavior of hardware already tested on land. Small optical surfaces have been measured through TVAC with careful optomechanical compensation of optical path length [10]. Photonics 2021, 8, x FOR PEER REVIEW 3 of 15 1.2. Thermal Vacuum Chamber Testing and Surface Testing Thermal Vacuum Chamber (TVAC) testing is a regular milestone in space hardware verification; emulating the conditions of device operation in space is important to predict the behavior of hardware already tested on land. Small optical surfaces have been meas- Photonics 2022, 9, 1 3 of 15 ured through TVAC with careful optomechanical compensation of optical path length [10]. Photogrammetry has also been adopted but is difficult to configure outside-of-cham- Photogrammetry has also been adopted but is difficult to configure outside-of-chamber ber because its resolution increases with the distance from cameras to the unit under test because its resolution increases with the distance from cameras to the unit under test and and also with the angular subtense between the two cameras and the UUT [11,12]. Finally, also with the angular subtense between the two cameras and the UUT [11,12]. Finally, specular surface measurement with photogrammetry requires the placement of hundreds specular surface measurement with photogrammetry requires the placement of hundreds of well-placed diffuse fiducials so that higher spatial frequencies are detectable. of well-placed diffuse fiducials so that higher spatial frequencies are detectable. Laser radar is a frequency chirped LiDAR technology that has been used in TVAC to Laser radar is a frequency chirped LiDAR technology that has been used in TVAC to measure positions through a TVAC chamber window. However, path lengths must also measure positions through a TVAC chamber window. However, path lengths must also be carefully compensated, else millimeter-scale errors at multiples of the window length be carefully compensated, else millimeter-scale errors at multiples of the window length appear [13]. It is our own experience with a Nikon APDIS laser radar metrology system appear [13]. It is our own experience with a Nikon APDIS laser radar metrology system that 800-point sampling across one diameter of the 1 meter prototype takes on the order that 800-point sampling across one diameter of the 1 meter prototype takes on the order of of 5 min. The duration of point scanning scales linearly with the number of samples, so 5 min. The duration of point scanning scales linearly with the number of samples, so larger larger apertures require far more scanning time for equivalent areal sampling density. apertures require far more scanning time for equivalent areal sampling density. 1.3. Regular Deflectometry Measurement 1.3. Regular Deflectometry Measurement The large range of possible inflatable surface shapes, whether gored parabola or mon- The large range of possible inflatable surface shapes, whether gored parabola or olithic Hencky Curve Surface, compels the use of phase-measuring deflectometry (PMD). monolithic Hencky Curve Surface, compels the use of phase-measuring deflectometry The speed at which full-field measurements must be made of a dynamic inflatable surface (PMD). The speed at which full-field measurements must be made of a dynamic inflatable is not accessible by contact-based methods or interferometry. surface is not accessible by contact-based methods or interferometry. Illustrated in Figure 2, PMD is an incoherent measurement technique that has a vast Illustrated in Figure 2, PMD is an incoherent measurement technique that has a slope measurement range and does not require a physical null. The only hardware re- vast slope measurement range and does not require a physical null. The only hardware quired is a spatially modulated light source such as a liquid crystal display (LCD) screen required is a spatially modulated light source such as a liquid crystal display (LCD) screen and a camera to observe the reflection of the display at the UUT. Briefly, an imaging cam- and a camera to observe the reflection of the display at the UUT. Briefly, an imaging era establishes conjugate imaging with the UUT surface, while the LCD illuminates the camera establishes conjugate imaging with the UUT surface, while the LCD illuminates UUT aperture with black and white sinusoidal fringes. Advancing the screen pattern by the UUT aperture with black and white sinusoidal fringes. Advancing the screen pattern a sequence of fixed phase steps and capturing an image of the UUT at each step, we de- by a sequence of fixed phase steps and capturing an image of the UUT at each step, we termine corresponding points between the screen, UUT, and camera as related by the law determine corresponding points between the screen, UUT, and camera as related by the of specular reflection via a phase-shifting algorithm. Knowledge of these associations al- law of specular reflection via a phase-shifting algorithm. Knowledge of these associations lows us to calculate surface slopes. If regions of the UUT are both seen by the camera and allows us to calculate surface slopes. If regions of the UUT are both seen by the camera and il illuminated luminated b by y the so the sour urce ce, , t then hen t those hose re regions gions a ar re e w within ithin the r the range ange of of PMD PMD me measur asuremen ement. t. Figure 2. Between an illumination source, a camera, and a UUT, the law of specular reflection is Figure 2. Between an illumination source, a camera, and a UUT, the law of specular reflection is sat satisfied. isfied. H Her ere, e, the the dir direc ection tion z ˆ𝑧 is ̂ is parallel paralleto l to the the optical optical ax axi is of s oa f spherical a spherical optic, optic the , the dirdi ection rection y ˆ in 𝑦 ̂ the in the tangential meridional plane, and the direction 𝑥 ̂ in the sagittal plane. The coordinates 𝑦 , 𝑦 , tangential meridional plane, and the direction x ˆ in the sagittal plane. The coordinates y , y , and m 𝑚s 𝑠 and 𝑦 represent the y-coordinates of the mirror, source, and a pinhole camera as related by the law y represent the y-coordinates of the mirror, source, and a pinhole camera as related by the law of specular reflection. d and d represent the absolute distances between the mirror and screen m2s m2c and mirror and camera, and z and z represent the distances of these physical locations along m2s m2c the direction z ˆ. W x , y is the sag of the optic. ( ) m m Recently, diverse advances in PMD have enabled the measurement of extremely chal- lenging surfaces. Xu et al. introduced a segmentation-based, data-fusion PMD approach to reconstruct the absolute surface of a monolithic, stepped multi-mirror array [14]. Taking Photonics 2022, 9, 1 4 of 15 advantage of total internal reflection at a water-air interface, PMD has also been used to measure disturbances of a fluid surface [15]. Willomitzer et al. introduced stitched panoramic measurements of stained-glass windows with a mobile device [16]. PMD for more traditional technical surfaces is well-described in recent literature reviews [17,18]. One instructive representation of deflectometry slope calculation is derived from Ritter ’s expression for surface slopes, S , in the single directional case in y (a similar calculation follows in the x-slopes, S , shown in Figure 2) [19,20]. The assumptions in the approximation are that the configuration is highly on axis, or z  d and m2s m2s z  d , and that the testing distance is very large relative to the sag of the optic, m2c m2c z , z  W x , y . ( ) m2s m2c m m y y y y m s m c 1 y y y y d d m s m c m2s m2c S x , y =  + (1) ( ) y m m z W(x ,y ) z W(x ,y ) m m m m m2s m2c 2 z z m2s m2c d d m2s m2c The assumption of low-order UUT coordinates for surface calculation is not redundant with the result of a physical deflectometry test. This is because the overall sag of the optic plays a tiny role in the slope calculation when z z  W(x , y ). When accurate m2s, m2c m m calibration parameters are fed into the slope calculation, accurate slopes across the UUT aperture are sampled. The mid-high spatial frequencies of the UUT’s true shape are revealed in the final surface height maps, which were not modeled in the virtual null [21]. For absolute surface reconstruction accuracy, calibration is critical and requires measur- ing the spatial positions of the camera pinhole, screen, and UUT. To illustrate the influence of measurement errors during calibration, we can modify expression (1) for calculating S (x , y ) with the calibration errors terms # , # , # , # , and # . y m m y,m y,s y,c z, m2s z,m2c y + # y + # y + # y + # m y,m s y,s m y,m c y,c S (x , y )  + (2) y m m 2 z + # z + # m2s z,m2s m2c z,m2c Non-zero values of # , # , # produce erroneous slope deviation from the true y,m y,s y,c slopes. Surface reconstruction with these lateral calibration errors is akin to miscalculating power in the tangential meridional plane, but not additional power in the sagittal plane (i.e., the x-slopes, S ); hence, excess astigmatism is embedded into the measurement. Similarly, a miscalibration in longitudinal coordinates # and # produces equal slope deviation z,m2s z,m2c across both planes, so power error is imbedded into the surface reconstruction. 2. Theory and Simulation for Deflectometry Measurement 2.1. Differential Deflectometry Measurement While calibration errors produce low-frequency figure errors in absolute measure- ments, the subtraction of two deflectometry measurements that use identical calibration parameters produces a high-fidelity shape difference [22]. In Figure 3, a small internal pressure adjustment causes the surface shape change to from W(x, y) to W (x, y), surface 0 0 0 normals from n ˆ to n ˆ , and difference in surface slopes DS = S S and DS = S S . y y y y y x x x Photonics 2021, 8, x FOR PEER REVIEW 5 of 15 2. Theory and Simulation for Deflectometry Measurement 2.1. Differential Deflectometry Measurement While calibration errors produce low-frequency figure errors in absolute measure- ments, the subtraction of two deflectometry measurements that use identical calibration parameters produces a high-fidelity shape difference [22]. In Figure 3, a small internal pressure adjustment causes the surface shape change to from 𝑊 (𝑥 , 𝑦 ) to 𝑊 ′(𝑥 , 𝑦 ), surface Photonics 2022, 9, 1 5 of 15 normals from 𝑛 ̂ to 𝑛 ̂ ′ , and difference in surface slopes 𝛥 𝑆 = 𝑆 − 𝑆 ′ and 𝛥 𝑆 = 𝑦 𝑦 𝑦 𝑦 𝑦 𝑥 𝑆 − 𝑆 ′ . 𝑥 𝑥 Figure 3. A unique aspect of inflatable optics is that the tensioning ring is a static datum between all Figure 3. A unique aspect of inflatable optics is that the tensioning ring is a static datum between all varifocal states of the optic. The location of the aperture edge is stationary; only the surface slopes varifocal states of the optic. The location of the aperture edge is stationary; only the surface slopes and height change within this circular area. Since the position of the UUT within the field of view and height change within this circular area. Since the position of the UUT within the field of view of of th the e camer camera a does does not not change, change, v 𝑣̂ ˆ = ≅ v 𝑣̂ ˆ ’. . In In th the e diagram diagram,, rays rays are are r revers everse e tr traced aced fr from om the the camera camera to to 11 1 1 UUT for a more intuitive visualization of ray slope deflection. UUT for a more intuitive visualization of ray slope deflection. If we take the difference of two deflectometry measurements from the same hardware If we take the difference of two deflectometry measurements from the same hard- configuration and calculated with the same calibration parameters, we will find that the ware configuration and calculated with the same calibration parameters, we will find that influence of the calibration measurement error is largely removed. The next expression (3) the influence of the calibration measurement error is largely removed. The next expression illustrates this error removal. (3) illustrates this error removal. ( ) ( ) ( ) Δ𝑆 𝑥 ,D 𝑦 S (= x 𝑆 , y 𝑥 ) ,= 𝑦 S−(𝑆 x′ , 𝑥y ) , 𝑦 S (x , y ) 𝑦 𝑚 𝑚 y m 𝑦 m 𝑚 𝑚 y m 𝑦 𝑚m 𝑚 y m m y +# y +# y +# y +# ( m y,m) ( s y,s) ( m y,m) ( c y,c) (𝑦 + 𝜀 ) − (𝑦 + 𝜀 ) (𝑦 + 𝜀 ) − (𝑦 + 𝜀 ) = + 𝑚 𝑦 ,𝑚 𝑠 𝑦 ,𝑠 𝑚 𝑦 ,𝑚 𝑐 𝑦 ,𝑐 2 z +# z +# m2s z,m2s m2c z,m2c = [ + ] 2 𝑧 + 𝜀 𝑧 + 𝜀 𝑚 2𝑠 𝑧 ,𝑚 2𝑠 𝑚 2𝑐 𝑧 ,𝑚 2𝑐 (3) 0 0 0 0 (y +# )(y +# ) (y +# )(y +# ) y,m y,s y,m y,c 1 m s m c ′ ′0 ′ 0 ′ 2 z +# z +# (𝑦 + 𝜀 ) − (𝑦 m2+ s 𝜀 m2s) (𝑦 + 𝜀 m )2− c ( m 𝑦 2c + 𝜀 ) 𝑦 ,𝑚 𝑦 ,𝑠 𝑦 ,𝑚 𝑦 ,𝑐 𝑚 𝑠 𝑚 𝑐 − [ + ] ′ ′ y y 2 𝑧 + 𝜀s 𝑧 + 𝜀 𝑚 2𝑠 𝑚 2𝑠 𝑚 2𝑐 𝑚 2𝑐 2(z +# ) m2s z,m2s 𝑦 − 𝑦 𝑠 𝑠 = 0 0 0 In successive measurements of an inflated optic, y = y , y = y , and z = z m m c c (3) 2(𝑧 + 𝜀 ) m2c m2c 𝑚 2𝑠 𝑧 ,𝑚 2𝑠 because the positions of the camera pinhole and UUT aperture do not change between In successive measurements of an inflated optic, 𝑦 ′ = 𝑦 , 𝑦 ′ = 𝑦 , and 𝑧 ′ = 𝑚 𝑚 𝑐 𝑐 𝑚 2𝑐 acquisitions. Similarly, all calibration measurement errors # , # , # , # , and # y,m y,s y,c z, m2s z,m2c 𝑧 because the positions of the came0 ra pinhole and UUT aperture do not change be- 𝑚 2𝑐 are identical between S (x , y ) and S (x , y ) because they share the same hardware y m m y m m tween acquisitions. Similarly, all calibration measurement errors 𝜀 , 𝜀 , 𝜀 , 𝜀 , 𝑦 ,𝑚 𝑦 ,𝑠 𝑦 ,𝑐 𝑧 ,𝑚 2𝑠 configuration and use the same calibration parameters during calculation. Simplifying the and 𝜀 are identical between 𝑆 (𝑥 , 𝑦 ) and 𝑆 ′ (𝑥 , 𝑦 ) because they share the 𝑧 ,𝑚 2𝑐 𝑦 𝑚 𝑚 𝑦 𝑚 𝑚 expression by cancelling identical variable pairs, the slope change DS is dominated by the same hardware configuration and use the same calibration parameters during calculation. difference of the deflected ray intercepts, Dy = y y , and the distance from the UUT to s s Simplifying the expression by cancelling identical variable pairs, the slope change 𝛥 𝑆 is the screen, z . 𝑦 m2s dominated by the difference of the deflected ray intercepts, 𝛥 𝑦 = 𝑦 − 𝑦 , and the dis- Longitudinal calibration measurement uncertainty # directly influences the slope dif- 𝑠 𝑠 𝑠 z,m2s tance from the UUT to the screen, 𝑧 . ference calculation. However, the uncertainty is conservatively constrained to # = 10 m 𝑚 2𝑠 z,m2s whenLongitud using aincommon al calibration lasermeas tracker urement . We uncerta calculate inty the 𝜀 induced directdefocus ly influences error th as e 𝑧 ,𝑚 2𝑠 D slW ope d= iffere 1/8 nce f ca# lculatio = n. 312.5 Howev nm,er or , th equivalently e uncertain ,ty Z is= con 1.08 serv atively m PV for conthe strai f/2 ned op- to 020 z,m2s 4 tic [23]. If one’s objective is to calculate the shape change of an inflatable UUT surface when 𝜀 = 10 𝜇𝑚 when using a common laser tracker. We calculate the induced defocus 𝑧 ,𝑚 2𝑠 internal pressure, external environment, or even internal gas composition are altered, then error as ∆𝑊 = 1/8(𝑓 )𝜀 = 312.5 nm, or equivalently, 𝑍 = 1.08 𝜇 m PV for the f/2 020 # 𝑧 ,𝑚 2𝑠 4 the optic dif [23] ferential . If one’ deflectometry s objective ismethod to calcula is well-poised te the shape for change the task. of an inflatable UUT surface 2.2. Unique Geometry of Thermal Vacuum Chamber An ordinary deflectometry configuration has no intermediate surface interactions between the light source and the UUT and from that UUT to the camera entrance pupil. In a modified configuration through a TVAC window for an inflatable reflector, we have additional refractive surface interactions to consider: those at a plane window, a thin trans- parent convex canopy, and then backwards through these components. These interactions introduce geometric ray deviations whose influence must be considered in the context of shape reconstruction and are shown exaggerated in Figure 4. Photonics 2021, 8, x FOR PEER REVIEW 6 of 15 when internal pressure, external environment, or even internal gas composition are al- tered, then the differential deflectometry method is well-poised for the task. 2.2. Unique Geometry of Thermal Vacuum Chamber An ordinary deflectometry configuration has no intermediate surface interactions be- tween the light source and the UUT and from that UUT to the camera entrance pupil. In a modified configuration through a TVAC window for an inflatable reflector, we have additional refractive surface interactions to consider: those at a plane window, a thin transparent convex canopy, and then backwards through these components. These inter- Photonics 2022, 9, 1 6 of 15 actions introduce geometric ray deviations whose influence must be considered in the context of shape reconstruction and are shown exaggerated in Figure 4. Figure 4. We examine the effects of a plane window between a room temperature and pressure Figure 4. We examine the effects of a plane window between a room temperature and pressure environment (RTP) and a cryogenic vacuum (a). A camera focuses through the plate and transpar- environment (RTP) and a cryogenic vacuum (a). A camera focuses through the plate and transparent ent Mylar canopy to the reflective Mylar surface. The circular meniscus window is 254 mm in di- Mylar canopy to the reflective Mylar surface. The circular meniscus window is 254 mm in diameter, ameter, while the full UUT aperture is 1 m. Rays from the UUT generally intercept the plate at non- while the full UUT aperture is 1 m. Rays from the UUT generally intercept the plate at non-normal normal incidence and introduce transverse displacement deviation 𝜀 as a function of ray slope incidence and introduce transverse displacement deviation # as a function of ray slope vˆ . The ray y 2 𝑣̂. The ray slope 𝑣̂′ ≠ 𝑣̂ for any PPP tilt, 𝜃 , and wedge, 𝛼 , as seen in (b). In absence of the plate, 2 2 2 slope vˆ 6= vˆ for any PPP tilt, q, and wedge, a, as seen in (b). In absence of the plate, the screen 2 2 the screen y-intercept position would be 𝑦 , rather than the plate-displaced 𝑦 ′ . The ray path from 𝑠 𝑠 y-intercept position would be y , rather than the plate-displaced y . The ray path from the camera to the camera to the UUT is also de s viated by the plate, but its detail is s not highlighted in this schematic. the UUT is also deviated by the plate, but its detail is not highlighted in this schematic. The existing viewport into Northrop Grumman’s TVAC, a plane window, is used to The existing viewport into Northrop Grumman’s TVAC, a plane window, is used to peer into the interior of the chamber volume. The 11.8” (300 mm) diameter plate is 9.14 peer into the interior of the chamber volume. The 11.8” (300 mm) diameter plate is 9.14 mm mm thick and modeled with the properties of fused silica. The glass plate is bolted thick and modeled with the properties of fused silica. The glass plate is bolted through through thru-holes onto the chamber, atop a 10” (254 mm) steel circular aperture, essen- thru-holes onto the chamber, atop a 10” (254 mm) steel circular aperture, essentially loading tially loading the glass like a simply supported circular plate. the glass like a simply supported circular plate. First, we consider the 2 mil (50.8 µ m) clear canopy in front of the optic being tested. First, we consider the 2 mil (50.8 m) clear canopy in front of the optic being tested. The canopy is thin, assumed to have uniform thickness, and not considered, given the 4 The canopy is thin, assumed to have uniform thickness, and not considered, given the meter scale of the test configuration. We consider the influence of the plate far larger. An 4 meter scale of the test configuration. We consider the influence of the plate far larger. An ideal, unloaded plane parallel plate (PPP) introduces defocus to an imaging configuration. ideal, unloaded plane parallel plate (PPP) introduces defocus to an imaging configuration. Refocusing the camera re-establishes conjugate imaging between the detector and the Refocusing the camera re-establishes conjugate imaging between the detector and the UUT UUT surface, but the deviation from an interrupted ray path between the camera and the surface, but the deviation from an interrupted ray path between the camera and the UUT UUT still exists. First, the longitudinal displacement of a PPP with thickness t and refrac- still exists. First, the longitudinal displacement of a PPP with thickness t and refractive tive index n = 1.46 that affects the deflectometry calculation is given by Smith [24]. index n = 1.46 that affects the deflectometry calculation is given by Smith [24]. 𝑡 (𝑛 − 1) 𝜀 = (4) 𝑃𝑃𝑃 ,𝑡 ℎ𝑠𝑖𝑐𝑘𝑛𝑒𝑠 t(n 1) # = (4) PPP,thickness Calculating the deflectometry measurement with an uncompensated ε 𝑃𝑃𝑃 ,𝑡 ℎ𝑛𝑒𝑠𝑠𝑖𝑐𝑘 reduce Calculating s the power the ofdeflectometry the reconstruct measur ed surface ement beca with use an the uncompensated image points are # physically PPP,thickness dis reduces placed the in power the long of itudi then ral econstr direction ucted from surface the val because ue (mea the sur image ed during points calibrati are physically on) of the displaced in the longitudinal direction from the value (measured during calibration) of the camera stop position. Next, if the ideal plate is tilted relative to the incident ray at angle 𝜃 camera stop position. Next, if the ideal plate is tilted relative to the incident ray at angle q from the PPP normal, the transverse ray displacement is 𝜀 [24]. 𝑃𝑃𝑃 ,𝑡 𝑖 from the PPP normal, the transverse ray displacement is # [24]. PPP,tilt 2 3 1 sin q tq(n 1) 4 5 # = tsin(q) 1  (5) PPP,tilt 2 2 n sin q n If two rays of different incidence angles, q and q , intercept the refractive plane plate at the same position, they will emerge separated by # . Inherent parallelism error, or PPP,tilt wedge, also induces angle-dependent errors. If we have wedge in the plate, we take the formalism of prism deviation and multiply by d = 100 mm, the distance from the plane 𝑙𝑡 Photonics 2022, 9, 1 7 of 15 window to the screen, to find the transverse error contribution towards the deflected ray intercept y at the screen [24]. q (n + 1) #  ad(n 1) 1 + (6) PPP,wedge (2n) Now because of the difference between external room temperature and pressure (RTP) and internal TVAC environmental conditions, the pressure gradient deforms the shape of the window rear into a meniscus with weak curvature [13]. 4Et R(D p) = (7) 3(1 n)(3 + n)a D p With the vacuum pressure differential, a meniscus is formed. Using plate thickness t = 9.14 mm, Poisson’s ratio  = 0.15, plate radius a = 127 mm, Young’s Modulus E = 72 GPa, and pressure differential D p  100, 000 Pa, this results in the radius of curvature RoC = 16.7 m. Compared to a ray refracting through two parallel flat interfaces, a ray refracting through two curved interfaces will generally possess a different ray slope than when it had entered. For example, an extreme ray from the edge of the 1 m UUT intercepts the center of the first window surface at a 10.5 angle of incidence (AOI) relative to the optical axis of the UUT. Refracting and propagating through 9 mm of glass, it exits the second surface into air at 10.4983 , a 6 arcsecond difference from the initial AOI. In absolute deflectometry measurements, the holistic effect is that the meniscus window will induce spatially varying error in slope, manifesting as excess defocus and spherical aberration in the integrated height. Trigonometric raytracing is required to discover and compensate for these absolute errors. For differential deflectometry measurements, the influence of the meniscus is min- imized by the subtraction of two measurements. Incrementally inflated or perturbed surfaces still deflect rays through similar angles and surface interception AOIs, especially for the two slow RoC = 16,700 mm surfaces, so we do not consider them in this analysis of differential shape change. 2.3. Plane Parallel Plate Geometry with Differential Deflectometry For an absolute deflectometry surface measurement, we observe that a measurement of the deflected ray intercept at the screen and plate thickness must compensate for the transverse error quantities # , # , and # . We can rewrite the expres- PPP,tilt PPP,wedge PPP,thickness sion for the true slope S in terms of the measured screen deflection intercept y y, true s, meas and the error terms, which can be dependent on the angle between the deflected ray v from the UUT relative to the plate normal. y # (v ) # (v ) s,meas PPP,wedge 2 PPP,tilt 2 S = (8) y,true 2(z # ) m2s PPP,thickness Subtracting slope two measurement calculations, afforded by the knowledge that there was no change in system configuration or calibration, we obtain a new expression, 0 0 (y y ) D# (v , v ) D# (v , v ) s,meas,2 s,meas,1 2 2 2 2 PPP,wedge PPP,tilt DS = (9) y,true 2 z # ( ) m2s PPP,thickness Photonics 2022, 9, 1 8 of 15 The vector v denotes the new vector from a second measurement. The induced errors in wedge and tilt are functions of both v and v . We next express the angles between the 2 2 0 0 plane window and v and v as q and q . 2 2 v2 v2 ad n 1 ( ) t(n1) 2 2 0 0 (y y ) q q (q q ) s,meas,2 s,meas,1 v2 v2 v2 v2 2n n DS = (10) y,true t(n1) 2 z m2s In this expression, the wedge term is insignificant and can be ignored because plane 2 2 0 glass plates can routinely achieve < 5 arcmin, and the difference of q and q ; will v2 v2 also be insignificant. As for the tilt term, the difference quantity q q is approximately v2 v2 twice that of our measurand of interest, DS . To show this, we begin with the observation 0 0 that for small angles q  v , so q q  v v = Dv . For example, the slope v2 2 v2 v2 2 2 2 difference at the aperture edge of a f/3 optic (? = 1000 mm) inflated to a steep f/1 mirror is 175 mrad yet produces only 1.8 mrad of error with this approximation. Next, we observe that S ?n ˆ , so DS = Dn ˆ because the surface normal is always perpendicular to the y y y y surface tangent. Since an angle change q in surface normal n produces twice the deviation in the deflected ray slope, Dv = 2Dn ˆ = 2DS . Thus, q q  Dv = 2DS . Now 2 y y v2 v2 2 y substituting, y y s,meas,2 s,meas,1 DS =   (11) y,true 2t(n1) 2 z m2s Taking two measurements of a common aperture with equivalent static calibration, we calculate differential measurement results even with the introduction of a plane parallel plate. We see that the overall influence of a window, modeled as a plane parallel plate, is to reduce the magnitude of the ray deflection and is compensated in the denominator of the differential slope calculation DS , and similarly so for DS . With both surface y,true x,true slopes obtained, surface integration obtains the induced sag difference between the two measurements of the inflated optic. 3. Experimental Setups For TVAC testing, the Mylar sheets of the 1 m UUT were replaced with new 2 mil thick material, seen in Figure 5. Team members iteratively pulled the circumference of the membrane taut to achieve subjectively uniform edge loading. In our experience, non- uniform tensioning forms visible wrinkles. Uniformity can be quantified by sampling the boundary with sensitive force gages for iterative adjustment, but that procedure was not performed for this experiment. After clamping, the UUT was mounted in a custom optomechanical mounting fixture with 3 degrees of freedom [25]. A fixed mechanical Photonics 2021, 8, x FOR PEER REVIEW 9 of 15 datum consisting of three spherical steel tooling balls was placed behind the reflective surface. Figure 5. Four team members pull the reflective surface taut before clamping it the frame (a). One Figure 5. Four team members pull the reflective surface taut before clamping it the frame (a). One tooling ball just barely touches the rear side of the reflective mylar UUT (b). The full optomechanical tooling ball just barely touches the rear side of the reflective mylar UUT (b). The full optomechanical mounting scheme for the 1 m mirror is described in detail [18]. mounting scheme for the 1 m mirror is described in detail [18]. A deflectometer, shown in Figure 6, was specially designed to mount to the TVAC window at eight flange bolts. The system consisted of a 12.9” (328 mm) iPad Pro (#A2378) illumination source, a Point Grey monochrome camera (FL3-U3-13Y3M-C) with a f = 12 mm lens, and machined aluminum baseplate frame. Several degrees of tilt and decenter adjustment permitted alignment to the TVAC window for maximum reconstruction sig- nal capture. Figure 6. The mechanical deflectometer frame consists of two 356 mm × 356 mm aluminum plates with mounting holes to allow flexible mounting for a camera and illumination screen (a). Standoffs fastened through aluminum slots allow for longitudinal adjustment. The plates were fastened to existing 3/8” bolts. The deflectometer assembly was rotated 22 degrees about the window normal in order to match the orientation of the in-situ bolt hole pattern (b). A design choice of 100 pixels per black/white fringe, 7-step phase shifts, and 3 averages per shot was optimized on-site. Outside the chamber volume, a vacuum inflation control unit provided by FreeFall Aerospace set the internal UUT pressure to a resolution of 10 Pa. The internal pressure was nominally set to 520 Pa relative to the chamber-controlled environmental pressure, which ranged from atmospheric (~100,000 Pa) to near-vacuum (0.11 Pa). In Figure 7, the view of the UUT in its mounting fixture as well as the deflectometer mounting are appar- ent. Calibration was performed with a Leica laser tracker and spherically mounted retroreflectors (SMRs). The calibration procedure obtained the distances between SMR references at the “X”-like tabs of the UUT tensioning ring, the aluminum tensioning frame plane, the plane of the window, the camera, and the iPad illumination screen plane. Photonics 2021, 8, x FOR PEER REVIEW 9 of 15 Figure 5. Four team members pull the reflective surface taut before clamping it the frame (a). One Photonics 2022, 9, 1 9 of 15 tooling ball just barely touches the rear side of the reflective mylar UUT (b). The full optomechanical mounting scheme for the 1 m mirror is described in detail [18]. A deflectometer, shown in Figure 6, was specially designed to mount to the TVAC A deflectometer, shown in Figure 6, was specially designed to mount to the TVAC window at eight flange bolts. The system consisted of a 12.9” (328 mm) iPad Pro (#A2378) il- window at eight flange bolts. The system consisted of a 12.9” (328 mm) iPad Pro (#A2378) lumination source, a Point Grey monochrome camera (FL3-U3-13Y3M-C) with a f = 12 mm illumination source, a Point Grey monochrome camera (FL3-U3-13Y3M-C) with a f = 12 lens, and machined aluminum baseplate frame. Several degrees of tilt and decenter ad- mm lens, and machined aluminum baseplate frame. Several degrees of tilt and decenter justment permitted alignment to the TVAC window for maximum reconstruction signal adjustment permitted alignment to the TVAC window for maximum reconstruction sig- capture. nal capture. Figure 6. The mechanical deflectometer frame consists of two 356 mm × 356 mm aluminum plates Figure 6. The mechanical deflectometer frame consists of two 356 mm  356 mm aluminum plates with mounting holes to allow flexible mounting for a camera and illumination screen (a). Standoffs with mounting holes to allow flexible mounting for a camera and illumination screen (a). Standoffs fastened through aluminum slots allow for longitudinal adjustment. The plates were fastened to fastened through aluminum slots allow for longitudinal adjustment. The plates were fastened to existing 3/8” bolts. The deflectometer assembly was rotated 22 degrees about the window normal existing 3/8” bolts. The deflectometer assembly was rotated 22 degrees about the window normal in in order to match the orientation of the in-situ bolt hole pattern (b). A design choice of 100 pixels order to match the orientation of the in-situ bolt hole pattern (b). A design choice of 100 pixels per per black/white fringe, 7-step phase shifts, and 3 averages per shot was optimized on-site. black/white fringe, 7-step phase shifts, and 3 averages per shot was optimized on-site. Outside the chamber volume, a vacuum inflation control unit provided by FreeFall Outside the chamber volume, a vacuum inflation control unit provided by FreeFall Aerospace set the internal UUT pressure to a resolution of 10 Pa. The internal pressure Aerospace set the internal UUT pressure to a resolution of 10 Pa. The internal pressure was nominally set to 520 Pa relative to the chamber-controlled environmental pressure, was nominally set to 520 Pa relative to the chamber-controlled environmental pressure, which ranged from atmospheric (~100,000 Pa) to near-vacuum (0.11 Pa). In Figure 7, the which ranged from atmospheric (~100,000 Pa) to near-vacuum (0.11 Pa). In Figure 7, view of the UUT in its mounting fixture as well as the deflectometer mounting are appar- the view of the UUT in its mounting fixture as well as the deflectometer mounting are ent. Calibration was performed with a Leica laser tracker and spherically mounted apparent. Calibration was performed with a Leica laser tracker and spherically mounted retroreflectors (SMRs). The calibration procedure obtained the distances between SMR retroreflectors (SMRs). The calibration procedure obtained the distances between SMR references at the “X”-like tabs of the UUT tensioning ring, the aluminum tensioning frame references at the “X”-like tabs of the UUT tensioning ring, the aluminum tensioning frame plane, the plane of the window, the camera, and the iPad illumination screen plane. plane, the plane of the window, the camera, and the iPad illumination screen plane. Photonics 2022, 9, 1 10 of 15 Photonics Photonics 2021 2021, , 8 8, , x FO x FOR P R PEE EER R RE REVIEW VIEW 10 10 of of 15 15 Figure Figure 7. 7. The The iinflated nflated te test st art artic icle le is is m moun ounte ted d at at bac back k of of the the chamber chamber cylin cylinde der r ((a a). ). The The s scal cale e of of the the Figure 7. The inflated test article is mounted at back of the chamber cylinder (a). The scale of the entire entire te test st co confi nfigu guration ration was was n nearly early 4 4 m m,, whi whic ch h plac place es s the the d def efle lect ctometer ometer appr approximately oximately at at tthe he radius radius entire test configuration was nearly 4 m, which places the deflectometer approximately at the radius of curvature of the inflated optic at its inflation pressure range of 500–700 Pa (b). During testing, the of curvature of the inflated optic at its inflation pressure range of 500–700 Pa (b). During testing, the of curvature of the inflated optic at its inflation pressure range of 500–700 Pa (b). During testing, the firs firstt Fr Fres esnel nel ref refle lect ctio ion n at at the the a acryli crylic c window window interfac interface e was was ffaint aint enou enough gh to to not not s signific ignificantl antly y reduce reduce first Fresnel reflection at the acrylic window interface was faint enough to not significantly reduce si sign gnal al c contrast ontrast at at the the camera camera de detec tector tor.. Di Diffuse ffuse m machined achined in internal ternal surfaces surfaces sc scatter atter the the iill llu um minati ination on signal contrast at the camera detector. Diffuse machined internal surfaces scatter the illumination from from outsi outside de tthe c he cham hamber, ber, al also so s sli ligh ghtl tly red y reducing reco ucing reconstr nstructio uction s n signal ignal c contrast. ontrast. from outside the chamber, also slightly reducing reconstruction signal contrast. 4. 4. E Exp xperim erimen ental tal R Results esults 4. Experimental Results 4.1. Deflectometer Repeatability Measurements 4.1. Deflectometer Repeatability Measurements 4.1. Deflectometer Repeatability Measurements Test Testing ing to took ok pla place ce ov over er on one e week week at at th the e North Northrop rop Gr Grumm umman an Spac Space e Sy System stems s ffac acil ility ity Testing took place over one week at the Northrop Grumman Space Systems facility in in in Redon Redondo do B Bea each. ch. Ov Over er 80 80 sur surfface ace me measuremen asurements ts wer were e taken taken of of th the e sa same me s surface urface,, subject subject Redondo Beach. Over 80 surface measurements were taken of the same surface, subject to to to a a vari variety o ety off environm environment ental al s setp etpoints within TVAC oints within TVAC. . At each f At each fre resh sh inf infllation o ation of f th the mem e mem-- a variety of environmental setpoints within TVAC. At each fresh inflation of the membrane, the brane, brane, membrane th the e me memb mb vertex ra rane ne ve was vertex rtex br wa ought was s bro bro into ugh ugh contact t t into into con con with ttact act the with with rear th the e mechanical rear rear mec mechani hani datum c cal al d datum atum and then and and the th then en external th the e ext exter pr ernal essur nal pres pres e contr sur sure e ol con con unit tro tro stepped l l un unit it s step tep back ped ped inflation back back iinflation nflation pressurpre pre e by ss ss 10 ure ure Pa by by until 10 10 P P the a a until until surface th the e no surface surface longer no no contacted lo longer nger con con the tact tact mechanical e ed d th the e mec mechan han datum. ical ical d d For atum. atum. an F Ar For or gon an an Ar gas Argon gon fill,g gan as as fill internal fill, , an an internal internal pressur pr pr ees- es- of 700 sur sure e Pa, o of f 700 chamber 700 P Pa, a, ch ch pr amber amber essurpr e prof essure essure 0.11 of Pa, of 0.1 0.1 and 1 1 Pa Pa chamber ,, and and cha cha temperatur mb mber er tem temperature perature e of 137 o o K, f f 13 13 the 7 7 K K total , , th the e RMS to total tal difference across the surface was about 100–250 nanometers, shown in Figure 8. This RM RMS S di diff ffe eren rence ce acros across s th the e s surface urface w was as about about 10 100 0– –250 250 n nanomet anometers, ers, sh shown own in in Fi Fig gur ure e 8. 8. Th This is repeatability is a fraction of the wavelength for the smallest band of interest for OASIS’s repeatab repeatability ility is is a a ffra ract ction ion o of f th the e wave wavelen length gth for for th the e s smal malles lest t b band and of of interest interest for for OA OASIS’s SIS’s terahertz optics, ~80 m [3]. terahertz terahertz opt optiics, ~80 cs, ~80 µ µm [ m [3]. 3]. Figure 8. Three differential deflectometry measurements show the repeatability of the central 525 mm Figure 8. Three differential deflectometry measurements show the repeatability of the central 525 Figure 8. Three differential deflectometry measurements show the repeatability of the central 525 apertur m mm m aperture. aperture. e. Changes Ch Chang ang within es es within within the first the the two firs first t minute-separated two two m minute inute--se separated parated acquisitions acquisiti acquisiti resemble ons ons rese resem m coma ble ble co co but m ma a flip but but in fli fli sign. p p in in sign. At the end of the third minute acquisition, fluctuations damped significantly. Experience with sign. At the end of the third minute acquisition, fluctuations damped significantly. Experience with At the end of the third minute acquisition, fluctuations damped significantly. Experience with the the inflat inflatio ion n un unit it hints hints that that tthe he press pressur ure e co contr ntrol ol un unit it st stron rongly gly co converg nverges es towards towards the the se settpoint, point, but but the inflation unit hints that the pressure control unit strongly converges towards the setpoint, but suffic sufficie ient nt it iterat erativ ive e co con nvergenc vergence oc e occurs on curs on llong onger er ti tim mes escal cale es. s. Here, Here, the the 700 700 P Pa a press pressur ure s e setp etpoi oint nt was was sufficient iterative convergence occurs on longer timescales. Here, the 700 Pa pressure setpoint was m met et and and held held tto o the 10 the 10 Pa Pa re res sol olution i ution ind ndic icat ated ed by the by the un unit it.. met and held to the 10 Pa resolution indicated by the unit. Amo Among ng all all p perturbed erturbed mea measur suremen ements ts o off th the e f/2 f/2 op optic, tic, no no mo more re th than an 600 600 mm mm of of th the e Among all perturbed measurements of the f/2 optic, no more than 600 mm of the dia diamet meter er w was as bo both th il illlumin uminated ated by by th the e s scre creen en and and ca capt ptured ured by by th the e camer camera. a. Th The e steep steep in- in- diameter was both illuminated by the screen and captured by the camera. The steep inflated flated flated state state w was as dem demanded anded by by th the e f/# f/# desi design gn re regi gime me r releva elevant nt to to th the e OASIS OASIS ffull ull--sized sized pri pri-- state was demanded by the f/# design regime relevant to the OASIS full-sized primary mary mary r ref eflector. lector. Th The e com comm mon on ar are ea a w was as crop cropped ped to to ab about out 525 525 mm mm in in th these ese mea measur suremen ementt reflector. The common area was cropped to about 525 mm in these measurement maps and maps maps and and all all subse subsequent quent maps maps fo for r di dire rect ct com compa paris riso on n of of sh shape ape ch change. ange. A A la lar rge ger r meas measure ure-- all subsequent maps for direct comparison of shape change. A larger measurement area men ment t ar area ea r ran ange ge is is li lim mited ited by by th the e si size ze o of f th the e TVAC TVAC window window, , wh whiich ch con constrai strain ns s th the e sl slop ope es s range is limited by the size of the TVAC window, which constrains the slopes measurable Photonics 2021, 8, x FOR PEER REVIEW 11 of 15 Photonics 2022, 9, 1 11 of 15 measurable by the deflectometry system. A larger window can extend the dynamic meas- by the deflectometry system. A larger window can extend the dynamic measuring slope uring slope range at the cost of additional window thickness to maintain structural re- range at the cost of additional window thickness to maintain structural requirements for a quirements for a large vacuum chamber. large vacuum chamber. 4.2. Induced Thermal Gradient by Artifical Sun 4.2. Induced Thermal Gradient by Artifical Sun A small overhead heat source (or ‘Artificial Sun’) illuminated the membrane assem- A small overhead heat source (or ‘Artificial Sun’) illuminated the membrane assembly bly half a meter away. The source was positioned closest to the aperture’s 12 o’clock posi- half a meter away. The source was positioned closest to the aperture’s 12 o’clock position tion (north). Chamber temperature was set to T = 142 K and pressure P = 0.11 Pa was en- (north). Chamber temperature was set to T = 142 K and pressure P = 0.11 Pa was enforced. forced. Once the radiation source was turned on, the reflective Mylar surface began warm- Once the radiation source was turned on, the reflective Mylar surface began warming. Four ing. Four T-type thermocouples were attached at the four cardinal points near the tension- T-type thermocouples were attached at the four cardinal points near the tensioning ring ing ring periphery of the back membranes. For the next half hour, the temperature detected periphery of the back membranes. For the next half hour, the temperature detected at each at each sensor rose by 1 K for the east, west, and south thermocouples, but rose by 5 K for sensor rose by 1 K for the east, west, and south thermocouples, but rose by 5 K for the north the north sensor, which was closest to the UUT. sensor, which was closest to the UUT. Cumulative thermal change resulted in a predominantly surface change in power, as Cumulative thermal change resulted in a predominantly surface change in power, as shown in Figure 9. This is the surface response to transient conduction across the large, shown in Figure 9. This is the surface response to transient conduction across the large, thin metallized surface and dimensional lengthening of the material with heat. Spatial thin metallized surface and dimensional lengthening of the material with heat. Spatial asymmetry, seen at surface change map at ∆𝑡 = 120 s, damped out towards ∆𝑡 = 600𝑠 , asymmetry, seen at surface change map at Dt = 120 s, damped out towards Dt = 600 s, where the vertex of the concave surface began contacting one of the spherical datums be- where the vertex of the concave surface began contacting one of the spherical datums hind the UUT. The protruding surface point in front of the leftmost ball is the most visually behind the UUT. The protruding surface point in front of the leftmost ball is the most apparent feature as a consequence of the thermally induced material expansion. visually apparent feature as a consequence of the thermally induced material expansion. Figure 9. Shape differences were observed successively on the timescale of hundreds of seconds. It is Figure 9. Shape differences were observed successively on the timescale of hundreds of seconds. It interesting that the proximity of the heat source to the northern region of the UUT did not produce is interesting that the proximity of the heat source to the northern region of the UUT did not produce lo local cal non non-uniformity -uniformity at atthe the ce center nter apertu apertur re e region region dedespite spite loc local al temper temperatur ature de iff dif erences. ferences. In thi Ins this ex- periment, the inflatant gas was Argon, which most recently expelled a mix of Helium, Argon, and experiment, the inflatant gas was Argon, which most recently expelled a mix of Helium, Argon, and Xenon from the lenticular UUT volume. Xenon from the lenticular UUT volume. Eventually Eventually , , the the two two outermost outermost balls balls of of the the physical physical r refer eference ence fiducial fiducial are are vis visible ible by by ∆D𝑡 t = = 132 1320 0 s s. . F Finite inite fri friction ction on onth the e ref reflective lective mem membrane brane ba back ck su surface rface pre prevents vents th the e outer outer tw two o balls from slipping and obscures the influence of the central ball. The high sensitivity and Photonics 2021, 8, x FOR PEER REVIEW 12 of 15 Photonics 2021, 8, x FOR PEER REVIEW 12 of 15 Photonics 2022, 9, 1 12 of 15 balls from slipping and obscures the influence of the central ball. The high sensitivity and balls from slipping and obscures the influence of the central ball. The high sensitivity and precision of differential deflectometry towards radiation-induced effects suggest that it precision of differential deflectometry towards radiation-induced effects suggest that it will precision of differential deflectometry towards radiation-induced effects suggest that it will be an asset to space system surface metrology and calibration. be an asset to space system surface metrology and calibration. will be an asset to space system surface metrology and calibration. 4.3. Induced Puncture Response 4.3. Induced Puncture Response 4.3. Induced Puncture Response The final segment of our protocol was a simulated micrometeoroid puncture test The final segment of our protocol was a simulated micrometeoroid puncture test shown in Figures 10 and 11. A feature of Northrop Grumman’s TVAC chamber added The final segment of our protocol was a simulated micrometeoroid puncture test shown in Figures 10 and 11. A feature of Northrop Grumman’s TVAC chamber added for for this test is an externally controllable mechanical actuator. Wielding a thin needle in shown in Figures 10 and 11. A feature of Northrop Grumman’s TVAC chamber added for this test is an externally controllable mechanical actuator. Wielding a thin needle in an arc- an arc-like motion, the actuator pierced a hole into the back reflective membrane. The this test is an externally controllable mechanical actuator. Wielding a thin needle in an arc- like motion, the actuator pierced a hole into the back reflective membrane. The cylindrical cylindrical body of the needle had a diameter of 0.6 mm. The spatial puncture location was like motion, the actuator pierced a hole into the back reflective membrane. The cylindrical body of the needle had a diameter of 0.6 mm. The spatial puncture location was chosen at chosen at the north cardinal position near the aperture edge of the membrane assembly. bo th dy e nort of th h e cardi needle nal hpo ad sa itio din ameter near th of e 0.6 aperture mm. Th edg e spat e of ial thpunct e mem ur bra e lne ocation assem w bly as . chosen Figure at 10 Figure 10 reveals the reflected signal before puncture and three snapshots after puncture. the north cardinal position near the aperture edge of the membrane assembly. Figure 10 reveals the reflected signal before puncture and three snapshots after puncture. Videos Videos were taken using the same camera in the deflectometry setup while a single static reveals the reflected signal before puncture and three snapshots after puncture. Videos were taken using the same camera in the deflectometry setup while a single static fringe fringe was displayed. In this experiment, the chamber temperature was kept to T = 293 K were taken using the same camera in the deflectometry setup while a single static fringe was displayed. In this experiment, the chamber temperature was kept to T = 293 K and and the inflatant had been solely Argon for four consecutive days. was displayed. In this experiment, the chamber temperature was kept to T = 293 K and the inflatant had been solely Argon for four consecutive days. the inflatant had been solely Argon for four consecutive days. Figure 10. After the unpunctured reflector (first subplot) is pierced, the number of fringes increases Figure 10. After the unpunctured reflector (first subplot) is pierced, the number of fringes increases (second subplot). With knowledge of the testing distance (𝑧 ≈ 3800 mm) and fringe width at the Figure 10. After the unpunctured reflector (first subplot) is pierced, the number of fringes increases (second subplot). With knowledge of the testing distance (z  3800 mm) and fringe width at the (ssc ecreen ond (subplo 𝜉 ≈ 9.62 t). mm Wit), h one knowl can ed co ge unof t the the number testing of distance fringes (pass 𝑧 ≈ ing 3800 thr mm oug ) h and a given fringpixe e wil dth to co at ars the el y screen (x  9.62 mm ), one can count the number of fringes passing through a given pixel to sc es reen timate (𝜉 ≈ the 9.62 slope mmchang ), one e can in y co -di un recti t the on. number In the of third fring subfi es pass gure, ing a shado throug w h precl a given udes pixe slop l to e co mars easel ur ye- coarsely estimate the slope change in y-direction. In the third subfigure, a shadow precludes slope es m tient mate at the this slope local chang surface e in reg y-io di n, recti indicati on. In ng the that third the subfi slope gu ch re, ang a shado e exceed w precl s the udes meas sl ur op able e m dynam easure-ic measurement at this local surface region, indicating that the slope change exceeds the measurable m ran ent ge at of th this e lo de cal fle surface ctometer reg in ioi n, ts indicati current ng posi that tion. Th the sle ope shado chang w shrink e exceed s and s the grm ows at easura able low dynam tempor ica l dynamic range of the deflectometer in its current position. The shadow shrinks and grows at a low ran frequ ge of th ency eun deti fle l it ct fully ometer reco in ver its s curr and ent is m posi eas tu io rable n. Thagain e shado wit w hou shrink t the s and subapertu grows at re dat a lo a w votempor id. Cham al - frequ temporal ber press ency fr ur un equency e tiin l it creas fully until ed reco from it ver fully 0. s 84 and recovers Pa is to m7 eas .and 07 u P rable is a after measurable again punctur witagain hou e. t the without subapertu the subapertur re data vo eid. data Chvoid. am- ber Chamber pressur pr e essur increas e incr ed from eased 0. fr 84 om Pa 0.84 to 7Pa .07 to Pa 7.07 after Papu after nctur punctur e. e. Figure 11. The second puncture showed recovery without substantial dynamic change over tens of Figure minutes. 11. The Cha m seber cond press punctur ure increas e showed ed from recovery 7.07 without Pa to 10. s6 ubstantial 6 Pa after dynam the secic ond chang punctur e over e. tens A third of Figure 11. The second puncture showed recovery without substantial dynamic change over tens of m pu inutes. nctur e Ch brou amber ght press the cham ure increas ber press edur from e to 13 7.07 .33 Pa Pa to . 10.66 Pa after the second puncture. A third minutes. Chamber pressure increased from 7.07 Pa to 10.66 Pa after the second puncture. A third puncture brought the chamber pressure to 13.33 Pa. puncture brought the chamber pressure to 13.33 Pa. In Figure 11, we show differential measurements of the puncture after a second punc- In Figure 11, we show differential measurements of the puncture after a second punc- ture in the back concave membrane. The apparent difference in surface flips sign on the In Figure 11, we show differential measurements of the puncture after a second punc- ture in the back concave membrane. The apparent difference in surface flips sign on the scale of every few minutes, now with error 8 µ m peak-to-valley and 5.08 µ m rms by ∆t = ture in the back concave membrane. The apparent difference in surface flips sign on the scale of every few minutes, now with error 8 µ m peak-to-valley and 5.08 µ m rms by ∆t = 800 s. Again, these fluctuations resemble low-order power, which is consistent with power scale of every few minutes, now with error 8 m peak-to-valley and 5.08 m rms by 800 s. Again, these fluctuations resemble low-order power, which is consistent with power being the dominant shape response to internal pressure setpoint [5]. The undulation is not Dt = 800 s. Again, these fluctuations resemble low-order power, which is consistent with being the dominant shape response to internal pressure setpoint [5]. The undulation is not the transient response of the rear membrane surface alone, but a dynamic response of the power being the dominant shape response to internal pressure setpoint [5]. The undulation the transient response of the rear membrane surface alone, but a dynamic response of the inflation unit regulation algorithm. That is, the 0.6 mm diameter puncture immediately is not the transient response of the rear membrane surface alone, but a dynamic response of inflation unit regulation algorithm. That is, the 0.6 mm diameter puncture immediately decreased the UUT internal pressure, triggering a cyclic overshoot and undershoot to- the inflation unit regulation algorithm. That is, the 0.6 mm diameter puncture immediately decreased the UUT internal pressure, triggering a cyclic overshoot and undershoot to- wards the setpoint pressure. The second puncture did not decrease the internal pressure decreased the UUT internal pressure, triggering a cyclic overshoot and undershoot towards wards the setpoint pressure. The second puncture did not decrease the internal pressure the setpoint pressure. The second puncture did not decrease the internal pressure of the Photonics 2022, 9, 1 13 of 15 UUT beyond the minimum incremental resolution (10 Pa), but did immediately increase chamber pressure by 3 Pa. During punctured shape measurement, a single fringe’s undulation was noticeable at the timescale of 20 s up to one minute. Given the similarity to the overall length of deflectometry acquisition (~25 s), dynamic drift will alter the surface measurement to an effect similar to that of vibration during phase-shifting interferometry. This temporal effect does not exist for the thermal gradient study, whose reflected fringes at the camera did not undulate and gradually moved over the course of surface temperatures changing by 5 K over 20 min. Single-shot display and PMD processing techniques exist which could reduce the effects of the dynamic surface drift [26,27]. A final comment is that the micrometeoroid puncture test performed is actually an accelerated simulation of the puncture of a large spaceborne membrane reflector. A surface shape change fluctuation of 5.08 m RMS due to puncture is conservative because the 1 m monolithic surface UUT was constructed of two flat membranes, which requires higher internal inflation pressure to achieve the same f/# as an identically sized, preformed gored construction. The high time resolution of this full-field metrology solution allows temporal characterization of inflatable primary reflectors—a next step towards realizing the next generation of large-aperture space observatories. 5. Conclusions TVAC testing results are reported for a 1 m inflatable membrane reflector in response to perturbations in low-temperature, near-vacuum conditions. Surface change was observed with phase-measuring deflectometry, particularly a differential deflectometry method that compensates for the influence of a plane window environmentally separating the test hardware from the UUT. To perform measurements, a custom deflectometer was constructed and mounted to the window plate of a large TVAC chamber, and a laser tracker provided geometric calibration references. A week-long campaign allowed the chamber to reach environmental setpoints dictated by the experimental protocol, and the static deflectometer measured surface shape responses at high spatial resolution. While desirable, using phase-measuring deflectometry to obtain absolute surface maps is not implemented, because an accurate virtual null is not assumed. Only in the differential variant are the errors induced by a virtual null negated. Errors in calibration can be mitigated by extra calibration devices, which leave the possibility of absolute deflectometry once an approximate virtual null with low-order figure has been established. For absolute shape measurement, studies with a laser radar system have measured the shape down to 50 m repeatability, but with sparser spatial sampling [28]. At the present, measuring a 14 m, f/1.5 reflector is also desirable. To monitor shape change, a differential deflectometry configuration would set its hardware at the radius of curvature of the optic, or 21 m away. The scale of measurement would be challenging as finite radiance of the illumination screen at each pixel must be considered for sufficient surface reconstruction signal to arrive at the camera detector. Additionally, transverse aberrations of the manufactured mirror scale directly with mirror size and may demand a much larger screen to fully illuminate the aperture. However, if sufficient radiance and size of a screen can be achieved for this long- distance testing configuration, differential deflectometry will be an invaluable asset to final shape monitoring and mirror characterization. This is because large membrane reflectors achieve identical f/#’s to smaller ones (such as our 1 m surrogate) at a much lower internal pressure (<10 Pa), and will therefore be more sensitive to a finite pressure control resolution. In the limit of finite incremental pressure control, differential deflectometry can keep the influence of systematic pressure drifts at bay, while other non-contact metrology techniques obtain the absolute low-order shape of the large reflector. Author Contributions: H.Q. provided the design, test, and assembly of the deflectometer and its prototypes, and its processing. H.K., H.C. and D.K. primarily ran the deflectometry experiments over 1 week of TVAC testing. M.E., K.K. and H.K. provided testing development support in atmospheric Photonics 2022, 9, 1 14 of 15 test runs. C.D.d. managed shipping the larger membrane assembly and project management guidance. All other coauthors (S.S., A.C., J.B., Y.T., A.P., J.W.A. and C.W.) provided similar levels of support in testing, ideation, validation, and supervision. All authors have read and agreed to the published version of the manuscript. Funding: The authors would like to acknowledge the II-VI Foundation Block-Gift, Technology Re- search Initiative Fund Optics/Imaging Program, and Friends of Tucson Optics Endowed Scholarships in Optical Sciences for helping support the metrology research conducted in the LOFT group. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Data available upon request. Acknowledgments: We would like to acknowledge FreeFall Aerospace in Tucson, Arizona for supplying the vacuum pressure modular pumps to maintain internal gas pressure during testing. Finally, we would like to thank the Northrop Grumman Aerospace Systems team for their incredible help during a full week of testing. 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Journal

PhotonicsMultidisciplinary Digital Publishing Institute

Published: Dec 21, 2021

Keywords: deflectometry; inflatable optics; thermal vacuum testing; terahertz astronomy

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