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Single-Shot On-Axis Fizeau Polarization Phase-Shifting Digital Holography for Complex-Valued Dynamic Object Imaging

Single-Shot On-Axis Fizeau Polarization Phase-Shifting Digital Holography for Complex-Valued... hv photonics Article Single-Shot On-Axis Fizeau Polarization Phase-Shifting Digital Holography for Complex-Valued Dynamic Object Imaging Hanzi Liu, Vinu R. V. , Hongliang Ren, Xingpeng Du, Ziyang Chen * and Jixiong Pu Fujian Key Laboratory of Light Propagation and Transformation, College of Information Science and Engineering, Huaqiao University, Xiamen 361021, China; 20013082008@stu.hqu.edu.cn (H.L.); vinurv@hqu.edu.cn (V.R.V.); renhongliang@ustc.edu (H.R.); 1915111006@stu.hqu.edu.cn (X.D.); jixiong@hqu.edu.cn (J.P.) * Correspondence: ziyang@hqu.edu.cn Abstract: Digital holography assisted with inline phase-shifting methods has the benefit of a large field of view and a high resolution, but it is limited in dynamic imaging due to sequential detection of multiple holograms. Here we propose and experimentally demonstrate a single-shot phase-shifting digital holography system based on a highly stable on-axis Fizeau-type polarization interferometry. The compact on-axis design of the system with the capability of instantaneous recording of multiple phase-shifted holograms and with robust stability features makes the technique a novel tool for the imaging of complex-valued dynamic objects. The efficacy of the approach is demonstrated experimentally by complex field imaging of various kinds of reflecting-type static and dynamic objects. Moreover, a quantitative analysis on the robust phase stability and sensitivity of the technique is evaluated by comparing the approach with conventional phase-shifting methods. The high phase stability and dynamic imaging potential of the technique are expected to make the system an ideal tool for quantitative phase imaging and real-time imaging of dynamic samples. Keywords: digital holography; interferometry; phase-shifting; polarization; complex field imaging; quantitative phase imaging Citation: Liu, H.; R. V., V.; Ren, H.; Du, X.; Chen, Z.; Pu, J. Single-Shot On-Axis Fizeau Polarization Phase-Shifting Digital Holography 1. Introduction for Complex-Valued Dynamic Object The applied domains of digital holography (DH) have an urge of interest in recent Imaging. Photonics 2022, 9, 126. times with advancements in high resolution image sensors and modulators with poten- https://doi.org/10.3390/ tial applications in the areas of interferometry, microscopy, quantitative phase imaging photonics9030126 (QPI), three-dimensional (3D) imaging, ultra-fast imaging, imaging through scattering Received: 17 January 2022 medium, ghost imaging, etc. [1–8]. DH can achieve the demand of simultaneous imaging Accepted: 14 February 2022 or of the characterization of multidimensional information, such as 3D structure, am- Published: 23 February 2022 plitude, phase, polarization, etc., by making use of either inline or off-axis DH based approaches [9–13]. However, the quality of image restoration in holographic techniques Publisher’s Note: MDPI stays neutral suffers from undesirable zero order and twin image occupancy in the hologram. The with regard to jurisdictional claims in evolution of computational techniques in the last two decades, with the introduction of published maps and institutional affil- phase retrieval algorithms [14–16] and machine learning [17,18] approaches, brings forth iations. the high-quality imaging in DH, but it may be limited in some imaging scenarios due to the phase convergence issue, computational time, learning mechanisms, etc. Alternatively, the integration of phase-shifting in DH has prominent advantages, as the reconstructed image Copyright: © 2022 by the authors. is free from the undesired terms of zero order and from conjugate terms with the cost of a Licensee MDPI, Basel, Switzerland. sequential multiple recording of the phase-shifted holograms for the reliable reconstruction This article is an open access article of the image [19,20]. Thus, the phase-shifting approaches permit the implementation of an distributed under the terms and inline geometry with full space-bandwidth utilization of the camera, and thereby provide a conditions of the Creative Commons large field of view and a high spatial resolution to the imaging system. Usually, the sequen- Attribution (CC BY) license (https:// tial phase modulation is achieved by the utilization of piezoelectric mirrors, spatial light creativecommons.org/licenses/by/ modulators, rotating retarders, acousto-optic or electro-optic modulators, etc. Although 4.0/). Photonics 2022, 9, 126. https://doi.org/10.3390/photonics9030126 https://www.mdpi.com/journal/photonics Photonics 2022, 9, 126 2 of 10 phase-shifting digital holography (PSDH) has its full potential in 3D complex field image reconstruction, the sequential multiple recording of the holograms limits the execution of the system in dynamic object imaging. Owing to the dynamic imaging challenge in PSDH techniques, a parallel-PSDH tech- nique, with the potential feature of instantaneous recording of the multiple phase-shifted holograms, is demonstrated by using the phase-shifting array device in the reference arm of the holography system [21,22]. Later, the parallel phase-shifting approaches were extended to high-speed imaging with the utilization of sophisticated spatial light modula- tors [23,24] and a polarized camera [24]. Subsequently, the effectiveness of the polarized camera in combination with phase-shifting approaches was demonstrated by develop- ing a simultaneous polarization Mirau interferometer [25], by the imaging of flow and sound [26,27], by a snapshot diffraction microscope [28], etc. In addition, the potential of parallel phase-shifting techniques with polarized image sensors is exploited to develop a single-shot incoherent digital holography system and to develop a further extension to microscopy [29–31]. Later, the imaging of dynamic objects with parallel phase-shifting approaches was demonstrated with the help of two-channel holography schemes [32,33], dual polarization imaging cameras [34], etc. However, the two-channel configurations may suffer from spatial and temporal phase stability issues due to external vibrations in the medium and due to the aberrations in the optical components as the beam propagation occurs through a different optical path. In the present work, we propose and experimentally demonstrate a single-shot on-axis phase-shifting digital holography system that utilizes a Fizeau-type polarization interfer- ometry technique for complex-valued dynamic object imaging. The developed system relies on the Fizeau-type interferometry scheme, in which the orthogonal polarization com- ponents for the object and reference beams were facilitated by using a wire grid polarizer (WGP). The technique makes use of the parallel phase-shifting approach with space divi- sion multiplexing for the development of high-speed instantaneous recording of multiple phase-shifted holograms. This is realized by using the combination of a quarter wave plate (QWP) and a micro polarizer array with different orientations encoded in the polarized camera to detect polarized light fields from the Fizeau polarization system. The compact on-axis design makes the system robust to external vibrations and provides high spatial and temporal stability to the holography scheme. Furthermore, the applicability of the pro- posed technique is experimentally demonstrated for simultaneous complex field imaging of various static and dynamic complex-valued objects. Additionally, a quantitative analysis is performed to evaluate the phase stability and sensitivity of the system in comparison with conventional phase-shifting methods. 2. Principles and Methods 2.1. Fizeau Polarization Phase-Shifting Digital Holography (FP-PSDH) The FP-PSDH system makes use of a highly stable Fizeau-polarization interferometry scheme for the generation of on-axis near common-path propagating orthogonal reference and object beams. The compact on-axis design of the polarization interferometry technique is facilitated by employing a wire grid polarizer (WGP) consisting of an array of metallic wires. A conceptual schematic of the orthogonal polarized beam generation with a WGP is represented in Figure 1a. The illumination of a linearly 45 polarized beam relative to the wire grid on the WGP results in a reflected beam with the polarization component parallel to the direction of the wire grid (s-polarized) and in a transmitted beam with the polarization component perpendicular to the wire grid (p-polarized). In our proposed scheme, the s-polarized component serves as the reference beam, and the p-polarized component serves as the object beam for polarization phase-shifting. The back-scattered p-polarized object beam propagates along with the reference beam in a common path Photonics 2022, 9, 126 3 of 10 Photonics 2022, 9, x FOR PEER REVIEW 3 of 10 after interacting with the object. The resulting common-path propagating light fields are given by, E (rˆ)= A (rˆ) exp(i (rˆ)) p p p (1) E (r ˆ) = A (r ˆ) exp(if (r ˆ)) p p p E (rˆ)= A (rˆ) exp(i (rˆ)) (1) s s s E (r ˆ) = A (r ˆ) exp(if (r ˆ)) s s s ˆ ˆ ˆ ˆ where A () r and A () r are the amplitude information, and where  () r and  () r are p s p s where A (r ˆ) and A (r ˆ) are the amplitude information, and where f (r ˆ) and f (r ˆ) are p s p s the phase information of the object modulated p-polarized and reference s-polarized the phase information of the object modulated p-polarized and reference s-polarized beams, respectively. beams, respectively. Figure 1. (a) Conceptual schematic of orthogonal polarized beam generation with the wire grid polar- Figure 1. (a) Conceptual schematic of orthogonal polarized beam generation with the wire grid polarizer izer (WGP); (b) Schematic of the space division multiplexing mechanism with QWP and polarization (WGP); (b) Schematic of the space division multiplexing mechanism with QWP and polarization filters in the polarized camera for single-shot detection of multiple phase-shifted holograms. filters in the polarized camera for single-shot detection of multiple phase-shifted holograms. To implement a single-shot recording of the multiple phase-shifting holograms, we To implement a single-shot recording of the multiple phase-shifting holograms, we utilized the space division multiplexing technique with the combination of a QWP and a utilized the space division multiplexing technique with the combination of a QWP and polarized camera [29]. A conceptual schematic of the multiplexing implementation in the a polarized camera [29]. A conceptual schematic of the multiplexing implementation in proposed approach is demonstrated in Figure 1b. The on-axis propagating reference and the proposed approach is demonstrated in Figure 1b. The on-axis propagating reference object beams passed through the QWP with its fast axis at 45° with respect to the common- and object beams passed through the QWP with its fast axis at 45 with respect to the path propagating polarized beams, thereby changing the polarization state to the respec- common-path propagating polarized beams, thereby changing the polarization state to tive circularly polarized beams and reaching the polarized camera sensor plane. The cam- the respective circularly polarized beams and reaching the polarized camera sensor plane. era sensor comprises unique nano-wire grid arrays with four separate polarizing filters The camera sensor comprises unique nano-wire grid arrays with four separate polarizing angled at 0°, 45°, 90°, and 135° positioned in a systematic pattern across the sensor. The filters angled at 0 , 45 , 90 , and 135 positioned in a systematic pattern across the sensor. electric field components of the circularly polarized beams at the exit plane of the polar- iz The ing felectric ilters of th field e sen components sor plane are gi of ve the n by, cir cularly polarized beams at the exit plane of the polarizing filters of the sensor plane are given by,  1 i 1 cos  cos sin EE (rr )=   ( )  (2) kk  2 2 1 coscos sinq scos in q sin qi 1 1 i   E (r) = p E (r ˆ) (2) k k cos q sin q sin q i 1 where k = p or s , the matrices represent the Jones matrices corresponding to the polarizer filters at  orientations and the QWP with its fast axis at 45°, respectively, and ˆ where k = p or s, the matrices represent the Jones matrices corresponding to E the () r polarizer ps or re filters presenat ts th q eorientations polariz and ed bthe eams QWP with with the respec its fast tive axis Jones at repr 45ese , n respectively tation. There , -and E (r ˆ) represents the p or s polarized beams with the respective Jones representation. Therefore, fore, the intensity distribution I (r)= E (r)E (r) at the sensor plane is expressed by, kk the intensity distribution I(r) = E (r)E (r) at the sensor plane is expressed by,  I (r )= A (r )+ A (r )+ 2A (r )A (r ) cos( 2 − (r )) (3) h i p s p s  2 2 I(r) = A (r) + A (r) + 2 A (r) A (r) cos(2q Df(r)) (3) p s p s where Df(r) = f (r) f (r) is the phase difference between the object and the reference p s field at the sensor plane. The space-division multiplexing, resulting from the interaction of circularly polarized object and reference beams with the polarization filters at specific Photonics 2022, 9, 126 4 of 10 angles, produces four phase-shifting holograms: I(r; 0), I(r; p/2), I(r; p) & I(r; 3p/2) with p/2 phase-shift represented in the conceptual schematic of Figure 1b. The single-shot detection of the multiple phase-shifted holograms at the sensor plane provides the flexible advantage of extraction of the complex field distribution of the object modulated informa- tion using the conventional phase-shifting interferometry relation, which is expressed as, E(r) = ( I(r; 0) I(r; p)) + i( I(r; 3p/2) I(r; p/2)) (4) The retrieval of the complex field distribution at the sensor plane gives the provision for the recovery of the amplitude and phase distribution of the complex-valued object at any arbitrary plane by using the digital backpropagation approaches [35]. 2.2. Experimental Design A schematic sketch of the experimental design of FP-PSDH is shown in Figure 2. A vertically polarized He-Ne laser source (CVI Melles Griot-25-LHP-928-230) of wavelength 632.8 nm, which is converted in to a linearly 45 polarized by a half wave plate (HWP), acts as the source beam for the proposed Fizeau polarization system. The beam is spatially filtered and collimated to generate a uniform beam with a plane wavefront. The transmitted beam from a non-polarizing beam splitter (BS) illuminates the WGP (ThorLab-WP50L-VIS) and produces two orthogonal polarization components from the input polarized beam, where the reflected beam (s-polarized) acts as the reference beam and where the transmitted beam (p-polarized) acts as the object beam for the Fizeau polarization interferometry. The p-polarized beam interacts with the desired object, and the backscattered object beam transmits again through the WGP and propagates in an on-axis common-path with the s-polarized beam. The object and the reference beam from the WGP propagate in an on-axis geometry and are reflected from the BS. These on-axis propagated polarized light fields transmit through the QWP with their fast axis oriented at 45 before reaching the monochrome polarization camera. The camera is 5.1 megapixels with a Sony IMX250MZR CMOS polarized sensor (active pixels 2464  2056 with pixel size 3.45 m and having 74 frames per second). The systematic arrangement of polarization filters with orientations of 0 , 45 , 90 , and 135 in the polarized camera is represented in the inset of Figure 2. The polarized camera records the raw intensity distribution of the hologram, and then Photonics 2022, 9, x FOR PEER REVIEW 5 of 10 simultaneously extracts the four multiple phase-shifted holograms without any spectral trade-offs. Figure 2. Experimental geometry of FP-PSDH: He-Ne laser: Helium-Neon laser source; HWP: Half Figure 2. Experimental geometry of FP-PSDH: He-Ne laser: Helium-Neon laser source; HWP: Half Wave Plate; M: Mirror; SF: Spatial Filter assembly; L: Lens; BS: Nonpolarizing Beam Splitter; WGP: Wave Plate; M: Mirror; SF: Spatial Filter assembly; L: Lens; BS: Nonpolarizing Beam Splitter; WGP: Wire Grid Polarizer; QWP: Quarter Wave Plate. In inset, the polarization filter arrangements in the Wire Grid Polarizer; QWP: Quarter Wave Plate. In inset, the polarization filter arrangements in the polarized camera and respective orientation angles are represented. polarized camera and respective orientation angles are represented. 3. Results and Discussion 3.1. Complex-Valued and Dynamic Object Imaging The performance and applicability of the FP-PSDH technique was experimentally tested for various objects and imaging conditions. To demonstrate the complex-valued imaging potential of the technique, we utilized the spatial light modulator (SLM) to intro- duce various complex-valued and pure phase objects. The complex-valued objects uti- lized for validating the technique were introduced using the phase-only SLM (PLUTO- VIS, Holoeye with total pixels 1920 × 1080, pixel pitch of 8µ m, and an image frame rate of 60 Hz). A complex-valued object was designed to encode the SLM using the checkerboard method [36,37], in which the alternate pixels were assigned with a uniform binary phase value of 0 and π (see Supplementary S1). We designed a complex object of Chinese char- acters ‘Hua (华)’ with an amplitude distribution and ‘Da (大)’ with a phase distribution, each consisting of size 3.9 mm × 3.9 mm as shown in Figure 3a. The polarization camera recorded a single-shot hologram of the object, and the recorded intensity of the hologram is shown in Figure 3b. Consequently, the four phase-shifted holograms were extracted from the single-shot hologram, and the complex amplitude distribution of the object at the sensor plane was successfully retrieved from these phase-shifted holograms by utiliz- ing Equation (4). The retrieved amplitude and phase distribution at the sensor plane are shown in Figure 3c and Figure 3d, respectively. The recovery of the complex field distri- bution at the sensor plane using the phase-shifting technique provided the flexibility to reconstruct the object information at the desired plane using digital propagation based on the angular spectrum method [35]. The focused object information retrieved from the pro- posed technique is shown in Figure 3e and Figure 3f. The amplitude distribution in Figure 3e shows a focused reconstruction of the amplitude ‘华’ at the object plane and a blurred ‘大’, as it is a pure phase distribution. In a similar way, Figure 3f represents the focused phase distribution of the object, in which the phase part is reconstructed with good qual- ity. Ph Pho ot to on niic cs s 2 20 02 22 2,, 9 9,, x x F FO OR R P PEE EER R R RE EV VI IEW EW 5 5 o of f 10 10 Photonics 2Ph 022 ot , o9 n , ix cs F2 O 0R 22 P , 9 EE , x R F R O E R V P IEW EER REVIEW 5 of 10 5 of 10 Fig Figure ure 2 2.. Ex Expe per rimen iment ta all g geo eom met etr ry y o of f F FP P- -P PS SDH DH:: H He e- -N Ne e la lase ser r:: H Hel elium ium- -N Ne eo on n la lase ser r so source urce;; H HWP WP:: H Ha alf lf Wa Wav ve e P Pla lat te e;; M: M: M Mir irr ro or r;; S SF F:: S Spa pat tia ial l F Fil ilt ter er a ass ssemb embly ly;; L: L: L Len ens s;; B BS S:: N No on np po ola lar riz izin ing g Be Bea am m S Spli plit tt ter er;; WG WGP P:: Wir Wire e G Gr rid id P Po ola lar riz izer er;; QWP QWP:: Qu Qua ar rt ter er Wa Wav ve e P Pla lat te. e. I In n iin nse set t,, t th he e po pola lar riz iza at tio ion n fil filt ter er a ar rr ra an ng gemen ement ts s in in t th he e Photonics 2022, 9, 126 5 of 10 po pola lar riz ized ed c ca am me er ra a a an nd d r res espec pect tiiv ve e o or rie ien nt ta at tio ion n a an ng gle les s a ar re e r repr epre ese sen nt ted ed.. 3 3.. R Re esu sul lt ts s a an nd d Di Disc scu uss ssi ion on 3. Results and Discussion 3 3..1 1.. C Com omp ple lex x- -V Value alued d and and D Dy ynam namic ic O Ob bje ject ct I Im mag aging ing 3.1. Complex-Valued and Dynamic Object Imaging The The pe perf rfo orma rman nce ce a an nd d a appl ppliica cab biilliity ty o of f th the e FP FP- -PS PSDH DH t tec ech hn niiq que ue wa was s e ex xpe peri rim ment enta allly ly The performance and applicability of the FP-PSDH technique was experimentally tested tested f fo or r v va ari rio ous us o ob bjjec ects ts a an nd d iim ma agi gin ng g co con nd diiti tio on ns. s. To To d demo emon nst stra rate te t th he e co com mpl plex ex- -va vallued ued tested for various objects and imaging conditions. To demonstrate the complex-valued iim ma agi gin ng g po potenti tentia all o of f th the e tec tech hn niiq que, ue, we we uti utilliiz ze ed d th the e spa spat tiia all lliigh ght t m mo od dul ula ato tor r ( (S SL LM M) ) to to iin ntro tro- - imaging potential of the technique, we utilized the spatial light modulator (SLM) to intro- d duc uce e va vari rio ous us co com mpl plex ex- -va vallued ued a an nd d pur pure e ph pha ase se o ob bjjec ect ts s.. The The co com mpl plex ex- -va vallued ued o ob bjjec ects ts uti uti- - duce various complex-valued and pure phase objects. The complex-valued objects utilized lliiz zed ed f fo or r v va alliid da ati tin ng g th the e tec tech hn niiq que ue were were iin ntro trod duce uced d usi usin ng g th the e pha phase se- -o on nlly y S SL LM M ( (PLU PLUTO TO- - for validating the technique were introduced using the phase-only SLM (PLUTO-VIS, Figure 2. Fig Expe ure rimen 2. Ex ta pe l g rimen eomet ta rly g o eo f F m Pet -P rS yDH of F : P H -e P-S N DH e la : se Hr e:- N He ella ium ser-:N H eel on ium lase -N r e so on urce lase ; H r so WP urce : H;a H lf WP: Half VIS VIS,, Ho Hollo oeye eye wi with th to tota tall pi pix xel els s 1 19 92 20 0 × × 1 10 08 80 0,, p piix xel el pi pitch tch o of f 8 8µ µm m,, a an nd d a an n iim ma age ge f fr ra am me e ra rate te o of f Holoeye with total pixels 1920  1080, pixel pitch of 8m, and an image frame rate of Wave PlaWa te; M: ve P M la ir tr eo ; r M: ; S F M : ir Spa rot ria ; S l F F:il Stpa er ta ia ss l emb Filter ly a ; ss L:emb Lenly s; ;B L: S: L N en on sp ; B oS la : rN izo in ng p o Be laa rm izin Spli g Be tter am ; WG Spli P t:t er; WGP: 6 60 0 H Hz z) ).. A A co com mplex plex- -va vallued ued o ob bjjec ect t w wa as s d desi esign gned ed to to enco encod de e th the e S SL LM M usi usin ng g th the e checke checker rb bo oa ard rd 60 Hz). A complex-valued object was designed to encode the SLM using the checkerboard Wire Grid Wir Poe laG riz rid er ;P QWP olariz : er Qu ; QWP arter :Wa Qu v ae rtP er la Wa te. Iv n e iP nla sette. , t h In e ipo nse la tr , iz tha e tio po nla fil riz ter at a io rn ra fil ng temen er arrt as nin gemen the ts in the m metho ethod d [ [3 36 6,,3 37 7] ], , iin n wh whiich ch th the e a allter tern na ate te pi pix xel els s were were a ass ssiign gned ed wi with th a a u un niif fo orm rm b biin na ar ry y pha phase se method [36,37], in which the alternate pixels were assigned with a uniform binary phase polarizedpo cala m re iz ra ed a n cd am res erpec a an tid v e res orpec ienttia v te ioo nr ie an ng ta le ts ioa nr e an repr gles ese arn e tr ed epr . esented. va vallue ue o of f 0 0 a an nd d π π ( (see see S Supple upplem ment enta ary ry S S1 1) ).. We We d desi esign gned ed a a co com mpl plex ex o ob bjjec ect t o of f Chi Chin nese ese cha char- r- value of 0 and  (see Supplementary S1). We designed a complex object of Chinese char- a acte cters rs ‘Hu ‘Hua a ( (华华) )’ ’ wi with th a an n a am mpl pliitude tude d diist stri rib buti utio on n a an nd d ‘D ‘Da a ( (大大) )’ ’ wi with th a a ph pha ase se d diist strib ribu uti tio on n,, acters ‘Hua ( )’ with an amplitude distribution and ‘Da ( )’ with a phase distribution, 3. Result3s. a R n ed su Di lts sc au nss d iDi onsc ussion ea each ch co con nsi sist stiin ng g o of f si siz ze e 3 3..9 9 m mm m × × 3. 3.9 9 m mm m a as s sh sho ow wn n iin n Fi Figure gure 3 3a a.. The The po polla ari riz za ati tio on n ca cam mer era a each consisting of size 3.9 mm  3.9 mm as shown in Figure 3a. The polarization camera 3.1. Comp 3le .1x . -C Vom alue ple d x and -Value Dyd nam and ic D O yb nam ject ic Im O ag bje ing ct Imaging re reco cord rded ed a a si sin ngl gle e- -sh sho ot t h ho ollo ogra gram m o of f th the e o ob bjjec ect, t, a an nd d t th he e re reco cord rded ed iin ntens tensiity ty o of f th the e h ho ollo ogra gram m recorded a single-shot hologram of the object, and the recorded intensity of the hologram The performance and applicability of the FP-PSDH technique was experimentally The performance and applicability of the FP-PSDH technique was experimentally i is is s shown sh sho own wn in iin n Figur Fi Figure gure e 3 3 3b. b b.. Co Consequently Con nseq sequentl uently, y, , the th the e four f fo our ur phase-shifted ph pha ase se- -sh shiif fted ted holograms h ho olo logra gram ms s wer were were e extracted ex extr tra acte cted d tested fotested r vari ofus or o vb ari jec ots us ao nb d jec im tsa a gi nn dg im coa ngi di n ti g on co s. nd To itid on emo s. To nstd ra emo te tn hst e ra cote mpl thex e co -va m lued plex -valued from the single-shot hologram, and the complex amplitude distribution of the object at f fr ro om m the the single-shot single-shot hologram, hologram,and and the the complex complex amplitude amplitude distribution distributio of n to he f th object e objec at t the at imaging ipo ma tenti ging alpo oftenti the a tec l o h fn th iq e ue, tec we hniuti que, liz we ed th uti e lispa zed ti th al e lispa ght tm iao l l d igh ula t to m r o(d Sul LM ato ) to r ( S in Ltro M)- to intro- th sensor the e sen senso plane sor r pl pla a was n ne e wa wa successfully s s succe succes ssful sful rletrieved ly y re retr triiev evfr ed ed o m f fro ro the m m th se these ese phase-shifted pha phase se- -sh shiif fted ted holograms h ho ollo ogra gram m by s b s b utilizing y y uti utili liz z- - duce vari do uc us e va com rio pl us exco -va m lued plex - ava nd lued pur e an ph d a pur se e ob ph jec atse s. The objec co tsm . The plexco -va m lued plex - o va bjl ec ued ts uti ob-jects uti- i Equation in ng g E Eq qu ua at t(4). iion on The ( (4 4) ).. r The The etrieved re retri trie e amplitude v ved ed a am mpl pliitude and tudephase a an nd d p p distribution h ha ase se d diist stri rib bat uti uti the o on n sensor a at t th the e se se plane n nso sor r ar pl pl ea ashown n ne e a are re lized forl iv za ed lid fa oti r n v g alth ide ati tec ng hn th iq e ue tecwere hniq ue intro were duce in d tro usi duce ng d th e usi pha ng se th -e on pha ly S se L-M on (lPLU y SLTO M ( -PLUTO- in Figures 3c,d, respectively. The recovery of the complex field distribution at the sensor sh sho own wn iin n Fi Figure gure 3c 3c,,d d,, re respec specti tiv vel ely. y. The The re reco cov ver ery y o of f th the e co com mpl plex ex f fiiel eld d d diist stri rib buti utio on n a at t th the e VIS, HolVIS oeye , Ho wil th oeye tota wi l pi th x el tos ta 1l9 pi 20 x el × 1 s 0 18 90 2,0 p × ix1 el 0 8 pi 0,tch pixo el f 8 pi µtch m, a on f d 8µ am n ,i m an ad ge an fr i am ma e ge raf te rao m f e rate of plane using the phase-shifting technique provided the flexibility to reconstruct the object sen senso sor r pl pla an ne e usi usin ng g th the e pha phas se e- -sh shiif fti tin ng g tec tech hn niiq que ue pr pro ov viid de ed d th the e f fllex exiib biili lity ty to to re reco con nst struc ruct t th the e 60 Hz). A complex-valued object was designed to encode the SLM using the checkerboard 60 Hz). A complex-valued object was designed to encode the SLM using the checkerboard information at the desired plane using digital propagation based on the angular spectrum o ob bjjec ect t iin nf fo orma rmati tio on n a at t t th he e d desi esire red d pl pla an ne e usi usin ng g d diigi gita tall pr pro opa paga gati tio on n ba based sed o on n t th he e a an ngul gula ar r method m [36 etho ,37]d , i[ n 3 6 wh ,37 i] ch , in th wh e ailch tern th ae te api lter xel na s te were pix el ass s were igned a wi ssith gn a ed u n wi ifth orm a u bn in ifa orrm y pha bin se ary phase method [35]. The focused object information retrieved from the proposed technique is spec spectrum trum m metho ethod d [ [35] 35].. The The f fo ocused cused o ob bjjec ect t iin nf fo orma rmati tio on n re retri triev eved ed f fro rom m th the e pr pro opo pose sed d tec tech h- - value of va 0 a lue nd o π f ( 0see an d S upple π (see m Sent upple arym S1 ent ). We ary d S1 esi ). gn We ed d a esi co gn m ed pl ex a co ob m jec plt ex of o Chi bjec nt ese of Chi chan r-ese char- shown in Figure 3e,f. The amplitude distribution in Figure 3e shows a focused recon- n niiq que ue iis s sh sho ow wn n iin n Fi Figure gure 3e 3e,f ,f.. The The a am mpl pliitude tude d diist stri rib buti utio on n iin n Fi Figure gure 3e 3e sh sho ows ws a a f fo ocused cused acters ‘Hu acte a ( rs 华‘Hu )’ wi ath (华 a) n ’ wi am th pl iatude n am d pl ist itude ributi do ist n ri an buti d ‘D on a a (大 nd) ’ ‘D wi a th (大 a) ’ ph wi ase th d a iph strib ase uti do ist n,rib ution, struction of the amplitude ‘ ’ at the object plane and a blurred ‘ ’, as it is a pure phase re reco con nst struc ructi tio on n o of f th the e a am mpl pliit tude ude ‘‘华华’’ a at t th the e o ob bjjec ect t pl pla an ne e a an nd d a a b bllurr urred ed ‘‘大大’’,, a as s iit t iis s a a pur pure e Photonics 2022, 9, x FOR PEER REVIEW 6 of 10 each conea sist ch inco g n osi f si stz in e g 3.o 9f m sim ze × 3.3. 9 9 m m mm × a 3. s 9sh m om w n a s in sh Fi ow gure n in 3 a Fi . gure The po 3al. aThe rizati po on la ri ca zm ati er oa n camera distribution. In a similar way, Figure 3f represents the focused phase distribution of the pha phase se d diist stri rib buti utio on n.. In In a a si sim miilla ar r wa way y,, Fi Figure gure 3 3f f re repr prese esen nts ts t th he e f fo ocused cused ph pha ase se d diist stri rib buti utio on n object,re inco which rded re a the co sird n phase gl ed e- a sh si part on t gl ho e is l-o sh rgra econstr ot m ho o lf o ucted gra the m ob with o jec f th t, e good an od b jt ec h quality e t, re an co d rd .thed e re in co tens rded ity in otens f the ity hoo lo f gra the m ho logram o of f th the e o ob bjjec ect, t, iin n wh whiich th ch the e pha phase se p pa art rt iis r s rec eco on nst struc ructed ted wi with th go goo od d q qua ualliity. ty. is shown is in sh Fi own gure in 3 Fi b. gure Con seq 3b.uentl Conseq y, th uentl e foy, ur th ph e afse our -sh ph ifted ase - h sh olo ifted gra m ho s lo were gram ex s tr were acte d ex tracted from the fro sin m gl th e-e sh si on t gl ho el -o sh go ra t m ho , la o n g d ra tm he , a co nm d pl thex e co am mp pl liex tude am d pilst itude ributi do ist n ri ob f uti the on o b ojf ec th t e ato bject at the senso th r e pl sen ane so wa r pl s a succe ne wa ssful s succe ly re str sful iev ly ed re ftr roim ev ed these fro pha m th se ese -sh pha ifted se h -sh oli o fgra tedm ho s b loy gra uti m lis b z- y utiliz- ing Equa it n ig on E q (4 u )a . t The ion re (4) tri . The eved re atri me pl vi ed tude am a pl nd itude pha se and d ip sth ri ab se uti do ist n ri at buti the ose n n at so th r e pl se an ne so ar re pl ane are shown in sh Fi own gure in 3c Fi ,d gure , respec 3c,d ti , v re elspec y. The tivel re y. coThe very re oco f th ver e y coo m f pl thex e co fim eld pl d ex ist fri iel bd uti do ist n ri ab t uti the o n at the sensor plane using the phase-shifting technique provided the flexibility to reconstruct the sensor plane using the phase-shifting technique provided the flexibility to reconstruct the object ino fo brma ject ti in ofn o rma at th tie on d esi at re thd e pl desi anre e d usi pl na g nd e iusi gita nlg pr do igi pa ta ga l ti pr oo npa ba ga sed tio n o n ba th sed e a o nn gul th ae r angular spectrum spec metho trum d [ m 35] etho . The d [35] focused . The f oo bcused ject in o fo brma ject ti in ofn o rma retriti ev on ed re ftri rom ev ed the fro prm opo th se e d pr tec opo h-sed tech- nique is n sh iq o ue wn is in sh Fi ow gure n in 3e Fi ,fgure . The 3e am ,f.pl The itude am d pl ist itude ributi do ist n ri in b uti Figure on in 3e Fi sh gure ows 3e a sh foo cused ws a focused reconstruc reco tion nst o ruc f th tie on am opl f th itude e am ‘pl华i’t ude at th ‘e 华 o’b a jec t th t pl e o ab nje ec at npl d a an b e lurr and ed a ‘b大 lurr ’, a ed s i t ‘大 is ’,a apur s it e is a pure phase dipha strib se uti do ist n.ri In buti a o sin m . iIn la r a wa sim y,i lFi ar gure way ,3 f Fi re gure prese 3fn re tspr these e fo ncused ts the f ph ocused ase d iph stri ab se uti do ist n ribution of the obo jec f th t, e in o wh bjec ich th t, in wh e pha ich th se p e apha rt is r se ec pa ort nst is r ruc ec ted on st wi ruc thted goo wi d q th ua go lity. od quality. Figure 3. Complex field reconstruction results: (a) complex-valued object encoded in the SLM; (b) Figure 3. Complex field reconstruction results: (a) complex-valued object encoded in the SLM; single-shot intensity of hologram recorded; (c) retrieved amplitude distribution at the sensor plane; (b) single-shot intensity of hologram recorded; (c) retrieved amplitude distribution at the sensor (d) retrieved phase distribution at the sensor plane; (e) reconstructed amplitude distribution at the plane; (d) retrieved phase distribution at the sensor plane; (e) reconstructed amplitude distribution at object plane; (f) reconstructed phase distribution at the object plane. Scale bar is 1.0 mm. the object plane; (f) reconstructed phase distribution at the object plane. Scale bar is 1.0 mm. Additionally Additionally , the , the potential potentia of l of the th technique e technique is demonstrated is demonstrated for r feal-time or real-tim imaging e imagi ofng of dynamic sample by utilizing the single-shot imaging capability of the FP-PSDH. A dynamic dynamic sample by utilizing the single-shot imaging capability of the FP-PSDH. A dy- phase object (running fox of size 7.2 mm  3.6 mm) is designed and projected into the namic phase object (running fox of size 7.2 mm × 3.6 mm) is designed and projected into system using the SLM. A single-shot recording captures the hologram of the object in an the system using the SLM. A single-shot recording captures the hologram of the object in instant, and further digital processing retrieves the four phase-shifted holograms. The an instant, and further digital processing retrieves the four phase-shifted holograms. The phase object at the desired plane is reconstructed using the phase-shifting interferometry phase object at the desired plane is reconstructed using the phase-shifting interferometry technique. To demonstrate the real time imaging of the moving target, we have recorded technique. To demonstrate the real time imaging of the moving target, we have recorded several intensity images in the sensor plane with a time interval of 0.1 s. The reconstructed several intensity images in the sensor plane with a time interval of 0.1 s. The reconstructed motion pictures at different instants of time of the moving phase object are shown in motion pictures at different instants of time of the moving phase object are shown in Fig- ure 4. The reconstructed dynamic phase distribution of the object is presented in Visuali- zation S1. Figure 4. Experimental results for dynamic pure phase objects: (a–f) reconstructed motion picture phase distribution at the sensor plane for various instants of time. Scale bar is 0.86 mm. 3.2. Weakly Reflective Object Imaging Furthermore, we have investigated the image reconstruction quality of the FP-PSDH system for the case of real-world weakly reflective type objects. As the light reflection from these objects are comparatively weak, we integrated a 4f-imaging geometry along with the system to grab the light from the object surface to the sensor plane. Experiments were carried out for butterfly wings and a standard USAF negative (reflective) target, and the respective experimental results are shown in Figure 5. Figure 5a and Figure 5d represent the single-shot raw intensity distribution of the recorded hologram corresponding to the butterfly wing and resolution test target, respectively. Subsequently, the multiple phase- shifted holograms were extracted from the single-shot recorded hologram, and the respec- tive complex amplitude distribution of the object at the sensor plane was successfully Photonics 2022, 9, x FOR PEER REVIEW 6 of 10 Figure 3. Complex field reconstruction results: (a) complex-valued object encoded in the SLM; (b) single-shot intensity of hologram recorded; (c) retrieved amplitude distribution at the sensor plane; (d) retrieved phase distribution at the sensor plane; (e) reconstructed amplitude distribution at the object plane; (f) reconstructed phase distribution at the object plane. Scale bar is 1.0 mm. Additionally, the potential of the technique is demonstrated for real-time imaging of dynamic sample by utilizing the single-shot imaging capability of the FP-PSDH. A dy- namic phase object (running fox of size 7.2 mm × 3.6 mm) is designed and projected into the system using the SLM. A single-shot recording captures the hologram of the object in an instant, and further digital processing retrieves the four phase-shifted holograms. The phase object at the desired plane is reconstructed using the phase-shifting interferometry Photonics 2022, 9, 126 6 of 10 technique. To demonstrate the real time imaging of the moving target, we have recorded several intensity images in the sensor plane with a time interval of 0.1 s. The reconstructed motion pictures at different instants of time of the moving phase object are shown in Fig- Figure 4. The reconstructed dynamic phase distribution of the object is presented in ure 4. The reconstructed dynamic phase distribution of the object is presented in Visuali- Visualization S1. zation S1. Figure 4. Experimental results for dynamic pure phase objects: (a–f) reconstructed motion picture Figure 4. Experimental results for dynamic pure phase objects: (a–f) reconstructed motion picture phase distribution at the sensor plane for various instants of time. Scale bar is 0.86 mm. phase distribution at the sensor plane for various instants of time. Scale bar is 0.86 mm. 3.2. Weakly Reflective Object Imaging 3.2. Weakly Reflective Object Imaging Furthermore, we have investigated the image reconstruction quality of the FP-PSDH Furthermore, we have investigated the image reconstruction quality of the FP-PSDH system for the case of real-world weakly reflective type objects. As the light reflection from system for the case of real-world weakly reflective type objects. As the light reflection from these objects are comparatively weak, we integrated a 4f-imaging geometry along with these objects are comparatively weak, we integrated a 4f-imaging geometry along with the system to grab the light from the object surface to the sensor plane. Experiments were the system to grab the light from the object surface to the sensor plane. Experiments were carried out for butterfly wings and a standard USAF negative (reflective) target, and the carried out for butterfly wings and a standard USAF negative (reflective) target, and the respective experimental results are shown in Figure 5. Figure 5a,d represent the single-shot respective experimental results are shown in Figure 5. Figure 5a and Figure 5d represent raw intensity distribution of the recorded hologram corresponding to the butterfly wing the single-shot raw intensity distribution of the recorded hologram corresponding to the and resolution test target, respectively. Subsequently, the multiple phase-shifted holograms butterfly wing and resolution test target, respectively. Subsequently, the multiple phase- were extracted from the single-shot recorded hologram, and the respective complex am- shifted holograms were extracted from the single-shot recorded hologram, and the respec- plitude distribution of the object at the sensor plane was successfully retrieved from these tive complex amplitude distribution of the object at the sensor plane was successfully multiple phase-shifted holograms using Equation (4). The reconstructed amplitude and phase distributions of butterfly wings is shown in Figures 5b,c, respectively. The phase distribution of butterfly wings shows a clear distinction between the discal cell and inner margin. In a similar way, the amplitude and phase distribution of the USAF resolution test target were reconstructed from digitally extracted multiple phase-shifted holograms, and the corresponding results are shown in Figures 5e,f, respectively. The system had a good resolving ability up to group 5 element 6 of the USAF resolution test target, which corresponds to 57.0-line pairs/mm. 3.3. Quantitative Analysis of System Stability and Sensitivity To evaluate the robustness of the system in environmental fluctuations and other noise mechanisms, we estimated the phase stability and sensitivity of the FP-PSDH system and compared it with other phase-shifting based methods. The performance was evaluated using time sequential detection of single-shot holograms in FP-PSDH, and it was compared with the two configurations of the Mach Zehnder interferometry (MZI) based phase-shifting scheme, namely multiple-shot phase-shifting MZI (MP-MZI) and single-shot polarization phase-shifting MZI (PP-MZI) (see Supplementary S1). In the case of FP-PSDH and PP- MZI, the sequential detections of 50 single-shot holograms with a polarized camera in sample-free configuration were carried out with a time interval of 0.1 s, and the phase map was recovered from respective digitally processed multiple phase shifted holograms. On the other hand, in the case of MP-MZI, the sequential detections of 50 holograms for each of the four phase-shifted holograms were recorded manually using a monochrome camera, and the respective phase was recovered. To evaluate the temporal stability, we estimated the phase fluctuation of a specific point in the recovered phase map with respect to the same point in the entire 50 recovered phase maps. The corresponding plot of the phase fluctuations with respect to the time sequential measurements is shown in Figure 6a. Photonics 2022, 9, 126 7 of 10 The estimation of standard deviation (STD) from the phase fluctuations shows that the proposed FP-PSDH technique has a lower STD (4.02 mRad) in comparison to MP-MZI Photonics 2022, 9, x FOR PEER REVIEW 7 of 10 (STD of 18.95 mRad) and PP-MZI (STD of 12.20 mRad). Furthermore, we also estimated the spatial sensitivity, which is the minimum detectable phase change in a recovered phase map for a particular measurement [38]. We evaluated the STD corresponding to total pixels retrieved from these multiple phase-shifted holograms using Equation (4). The recon- in each of the 50 recovered phase maps for the respective phase-shifting based approaches. structed amplitude and phase distributions of butterfly wings is shown in Figure 5b and The box plot corresponding to all three configurations are shown in Figure 6b. The estimated Figure 5c, respectively. The phase distribution of butterfly wings shows a clear distinction STD for FP-PSDH is low in comparison to other techniques, which can be attributed to between the discal cell and inner margin. In a similar way, the amplitude and phase dis- the high spatial sensitivity of the proposed technique. A quantitative comparison of the tribution of the USAF resolution test target were reconstructed from digitally extracted FP-PSDH system performance to MZI-based on-axis techniques is summarized in Table 1. multiple phase-shifted holograms, and the corresponding results are shown in Figure 5e The plots in Figure 6a,b and the quantitative evaluation in Table 1 manifest the dominance and Figure 5f, respectively. The system had a good resolving ability up to group 5 element of on-axis single-shot FP-PSDH in complex-valued dynamic object imaging over other 6 techniques of the USA in F r the eso noise-assisted lution test targe envir t, wh onments. ich corresponds to 57.0-line pairs/mm. Fig Figure ure 5 5. . Ex Experimental perimental rres esults: ults: But Butterfly terfly w wing; ing; ((a a) )rraw aw in intensity tensity di distribution stribution of ofsi single-shot ngle-shot rre ecor corde ded d hologram; (b) reconstructed amplitude distribution; (c) reconstructed phase distribution. USAF neg- hologram; (b) reconstructed amplitude distribution; (c) reconstructed phase distribution. USAF ative (reflective) target; (d) raw intensity distribution of single-shot recorded hologram; (e) recon- negative (reflective) target; (d) raw intensity distribution of single-shot recorded hologram; (e) re- structed amplitude distribution; (f) reconstructed phase distribution. A 4f-imaging system with constructed amplitude distribution; (f) reconstructed phase distribution. A 4f-imaging system with lenses of focal length 100 mm and 200 mm is utilized to image the object plane to the sensor plane. lenses of focal length 100 mm and 200 mm is utilized to image the object plane to the sensor plane. Scale bar: (a–c) 300 μm, (d–f) 100 μm. Scale bar: (a–c) 300 m, (d–f) 100 m. 3.3. Quantitative Analysis of System Stability and Sensitivity Table 1. Quantitative comparison of FP-PSDH system performance with MP-MZI and PP- To evaluate the robustness of the system in environmental fluctuations and other MZI techniques. noise mechanisms, we estimated the phase stability and sensitivity of the FP-PSDH sys- tem and compared it with other phase-shifting based metho T d emporal s. The performance Spatial was eval- Interferometry Type of Detection Stability Sensitivity uated using time sequential detection of single-shot holograms in FP-PSDH, and it was Scheme Geometry Scheme (mRad) (mRad) compared with the two configurations of the Mach Zehnder interferometry (MZI) based MP-MZI double path four-shot 18.95 27.76 phase-shifting scheme, namely multiple-shot phase-shifting MZI (MP-MZI) and single- PP-MZI double path single-shot 12.20 24.86 shot polarization phase-shifting MZI (PP-MZI) (see Supplementary S1). In the case of FP- FP-PSDH single path single-shot 4.02 17.47 PSDH and PP-MZI, the sequential detections of 50 single-shot holograms with a polarized camera in sample-free configuration were carried out with a time interval of 0.1 s, and the phase map was recovered from respective digitally processed multiple phase shifted hol- ograms. On the other hand, in the case of MP-MZI, the sequential detections of 50 holo- grams for each of the four phase-shifted holograms were recorded manually using a mon- ochrome camera, and the respective phase was recovered. To evaluate the temporal sta- bility, we estimated the phase fluctuation of a specific point in the recovered phase map with respect to the same point in the entire 50 recovered phase maps. The corresponding plot of the phase fluctuations with respect to the time sequential measurements is shown in Figure 6a. The estimation of standard deviation (STD) from the phase fluctuations shows that the proposed FP-PSDH technique has a lower STD (4.02 mRad) in comparison Photonics 2022, 9, x FOR PEER REVIEW 8 of 10 to MP-MZI (STD of 18.95 mRad) and PP-MZI (STD of 12.20 mRad). Furthermore, we also estimated the spatial sensitivity, which is the minimum detectable phase change in a re- covered phase map for a particular measurement [38]. We evaluated the STD correspond- ing to total pixels in each of the 50 recovered phase maps for the respective phase-shifting based approaches. The box plot corresponding to all three configurations are shown in Figure 6b. The estimated STD for FP-PSDH is low in comparison to other techniques, which can be attributed to the high spatial sensitivity of the proposed technique. A quan- titative comparison of the FP-PSDH system performance to MZI-based on-axis techniques is summarized in Table 1. The plots in Figure 6a and Figure 6b and the quantitative eval- uation in Table 1 manifest the dominance of on-axis single-shot FP-PSDH in complex- Photonics 2022, 9, 126 8 of 10 valued dynamic object imaging over other techniques in the noise-assisted environments. Figure 6. Quantitative evaluation of system stability and sensitivity: (a) Temporal stability evaluation Figure 6. Quantitative evaluation of system stability and sensitivity: (a) Temporal stability evalua- of MP-MZI, PP-MZI, and FP-PSDH. The X-axis represents the time sequential measurements, and the tion of MP-MZI, PP-MZI, and FP-PSDH. The X-axis represents the time sequential measurements, Y-axis represents the respective phase fluctuations for a specific point in the recovered phase map; and the Y-axis represents the respective phase fluctuations for a specific point in the recovered phase (b) Spatial sensitivity evaluation of MP-MZI, PP-MZI, and FP-PSDH with the respective box plots. In map; (b) Spatial sensitivity evaluation of MP-MZI, PP-MZI, and FP-PSDH with the respective box each box plot, the lower and upper boundaries represent the first and third quartiles, respectively, plots. In each box plot, the lower and upper boundaries represent the first and third quartiles, re- and the line in each box represents the median value. spectively, and the line in each box represents the median value. 4. Conclusions Table 1. Quantitative comparison of FP-PSDH system performance with MP-MZI and PP-MZI tech- In conclusion, we have developed a single-shot on-axis PSDH technique based on a niques. Fizeau polarization interferometry approach for complex-valued static and dynamic object Interferometry Detection Temporal Spatial Sensitivity imaging. The adoption of the space division multiplexing along with the utilization of a Type of Geometry Scheme Scheme Stability (mRad) (mRad) polarized camera provides the potential realization in the development of a highly stable MP-MZI double path four-shot 18.95 27.76 real-time complex field imaging system. The effectiveness of the technique is experimentally PP-MZI double path single-shot 12.20 24.86 demonstrated by imaging different kinds of reflecting-type complex-valued samples. The compact FP-PSdesign DH of FP-PSDH single pa with th on-axis singeometry gle-shot exhibits 4.0 the 2 dominance of1the 7.47 pr oposed technique over conventional phase-shifting techniques for the imaging of dynamic events. 4Mor . Conc eover lusi ,ons the near common-path single-shot phase-shifting technique utilized in the FP-PSDH system enhances the space-bandwidth in comparison to the existing off-axis In conclusion, we have developed a single-shot on-axis PSDH technique based on a digital holography systems with its unique compact on-axis design. In addition, the high- Fizeau polarization interferometry approach for complex-valued static and dynamic ob- stability feature resulting from on-axis interferometry geometry provides the possible ject imaging. The adoption of the space division multiplexing along with the utilization of integration of an optical microscopy system for the development of a robust quantitative a polarized camera provides the potential realization in the development of a highly stable phase microscopy system for dynamic phase measurements. real-time complex field imaging system. The effectiveness of the technique is experimen- tally demonstrated by imaging different kinds of reflecting-type complex-valued samples. Supplementary Materials: The following are available online at https://www.mdpi.com/article/10 The compact design of FP-PSDH with on-axis geometry exhibits the dominance of the .3390/photonics9030126/s1, The digital reconstruction scheme (Figure S1), complex-valued object proposed technique over conventional phase-shifting techniques for the imaging of dy- details (Figure S2), experimental design of MZI scheme (Figure S3), and the dynamic phase object namic events. Moreover, the near common-path single-shot phase-shifting technique uti- visualization S1. lized in the FP-PSDH system enhances the space-bandwidth in comparison to the existing Author Contributions: Conceptualization, V.R.V.; methodology, H.L. and V.R.V.; formal analysis, off-axis digital holography systems with its unique compact on-axis design. In addition, H.R. and V.R.V.; investigation, H.L., X.D., and V.R.V.; data curation, H.L. and V.R.V.; writing—original the high-stability feature resulting from on-axis interferometry geometry provides the draft preparation, H.L. and V.R.V.; writing—review and editing, V.R.V., Z.C., and J.P.; supervision, J.P.; funding acquisition, Z.C. and V.R.V. All authors have read and agreed to the published version of the manuscript. Funding: This work was supported by the Natural Science Foundation of China (NSFC) under Grants No. 11674111, No. 62005086, and No. 12150410318. Institutional Review Board Statement: Not applicable. 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Single-Shot On-Axis Fizeau Polarization Phase-Shifting Digital Holography for Complex-Valued Dynamic Object Imaging

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hv photonics Article Single-Shot On-Axis Fizeau Polarization Phase-Shifting Digital Holography for Complex-Valued Dynamic Object Imaging Hanzi Liu, Vinu R. V. , Hongliang Ren, Xingpeng Du, Ziyang Chen * and Jixiong Pu Fujian Key Laboratory of Light Propagation and Transformation, College of Information Science and Engineering, Huaqiao University, Xiamen 361021, China; 20013082008@stu.hqu.edu.cn (H.L.); vinurv@hqu.edu.cn (V.R.V.); renhongliang@ustc.edu (H.R.); 1915111006@stu.hqu.edu.cn (X.D.); jixiong@hqu.edu.cn (J.P.) * Correspondence: ziyang@hqu.edu.cn Abstract: Digital holography assisted with inline phase-shifting methods has the benefit of a large field of view and a high resolution, but it is limited in dynamic imaging due to sequential detection of multiple holograms. Here we propose and experimentally demonstrate a single-shot phase-shifting digital holography system based on a highly stable on-axis Fizeau-type polarization interferometry. The compact on-axis design of the system with the capability of instantaneous recording of multiple phase-shifted holograms and with robust stability features makes the technique a novel tool for the imaging of complex-valued dynamic objects. The efficacy of the approach is demonstrated experimentally by complex field imaging of various kinds of reflecting-type static and dynamic objects. Moreover, a quantitative analysis on the robust phase stability and sensitivity of the technique is evaluated by comparing the approach with conventional phase-shifting methods. The high phase stability and dynamic imaging potential of the technique are expected to make the system an ideal tool for quantitative phase imaging and real-time imaging of dynamic samples. Keywords: digital holography; interferometry; phase-shifting; polarization; complex field imaging; quantitative phase imaging Citation: Liu, H.; R. V., V.; Ren, H.; Du, X.; Chen, Z.; Pu, J. Single-Shot On-Axis Fizeau Polarization Phase-Shifting Digital Holography 1. Introduction for Complex-Valued Dynamic Object The applied domains of digital holography (DH) have an urge of interest in recent Imaging. Photonics 2022, 9, 126. times with advancements in high resolution image sensors and modulators with poten- https://doi.org/10.3390/ tial applications in the areas of interferometry, microscopy, quantitative phase imaging photonics9030126 (QPI), three-dimensional (3D) imaging, ultra-fast imaging, imaging through scattering Received: 17 January 2022 medium, ghost imaging, etc. [1–8]. DH can achieve the demand of simultaneous imaging Accepted: 14 February 2022 or of the characterization of multidimensional information, such as 3D structure, am- Published: 23 February 2022 plitude, phase, polarization, etc., by making use of either inline or off-axis DH based approaches [9–13]. However, the quality of image restoration in holographic techniques Publisher’s Note: MDPI stays neutral suffers from undesirable zero order and twin image occupancy in the hologram. The with regard to jurisdictional claims in evolution of computational techniques in the last two decades, with the introduction of published maps and institutional affil- phase retrieval algorithms [14–16] and machine learning [17,18] approaches, brings forth iations. the high-quality imaging in DH, but it may be limited in some imaging scenarios due to the phase convergence issue, computational time, learning mechanisms, etc. Alternatively, the integration of phase-shifting in DH has prominent advantages, as the reconstructed image Copyright: © 2022 by the authors. is free from the undesired terms of zero order and from conjugate terms with the cost of a Licensee MDPI, Basel, Switzerland. sequential multiple recording of the phase-shifted holograms for the reliable reconstruction This article is an open access article of the image [19,20]. Thus, the phase-shifting approaches permit the implementation of an distributed under the terms and inline geometry with full space-bandwidth utilization of the camera, and thereby provide a conditions of the Creative Commons large field of view and a high spatial resolution to the imaging system. Usually, the sequen- Attribution (CC BY) license (https:// tial phase modulation is achieved by the utilization of piezoelectric mirrors, spatial light creativecommons.org/licenses/by/ modulators, rotating retarders, acousto-optic or electro-optic modulators, etc. Although 4.0/). Photonics 2022, 9, 126. https://doi.org/10.3390/photonics9030126 https://www.mdpi.com/journal/photonics Photonics 2022, 9, 126 2 of 10 phase-shifting digital holography (PSDH) has its full potential in 3D complex field image reconstruction, the sequential multiple recording of the holograms limits the execution of the system in dynamic object imaging. Owing to the dynamic imaging challenge in PSDH techniques, a parallel-PSDH tech- nique, with the potential feature of instantaneous recording of the multiple phase-shifted holograms, is demonstrated by using the phase-shifting array device in the reference arm of the holography system [21,22]. Later, the parallel phase-shifting approaches were extended to high-speed imaging with the utilization of sophisticated spatial light modula- tors [23,24] and a polarized camera [24]. Subsequently, the effectiveness of the polarized camera in combination with phase-shifting approaches was demonstrated by develop- ing a simultaneous polarization Mirau interferometer [25], by the imaging of flow and sound [26,27], by a snapshot diffraction microscope [28], etc. In addition, the potential of parallel phase-shifting techniques with polarized image sensors is exploited to develop a single-shot incoherent digital holography system and to develop a further extension to microscopy [29–31]. Later, the imaging of dynamic objects with parallel phase-shifting approaches was demonstrated with the help of two-channel holography schemes [32,33], dual polarization imaging cameras [34], etc. However, the two-channel configurations may suffer from spatial and temporal phase stability issues due to external vibrations in the medium and due to the aberrations in the optical components as the beam propagation occurs through a different optical path. In the present work, we propose and experimentally demonstrate a single-shot on-axis phase-shifting digital holography system that utilizes a Fizeau-type polarization interfer- ometry technique for complex-valued dynamic object imaging. The developed system relies on the Fizeau-type interferometry scheme, in which the orthogonal polarization com- ponents for the object and reference beams were facilitated by using a wire grid polarizer (WGP). The technique makes use of the parallel phase-shifting approach with space divi- sion multiplexing for the development of high-speed instantaneous recording of multiple phase-shifted holograms. This is realized by using the combination of a quarter wave plate (QWP) and a micro polarizer array with different orientations encoded in the polarized camera to detect polarized light fields from the Fizeau polarization system. The compact on-axis design makes the system robust to external vibrations and provides high spatial and temporal stability to the holography scheme. Furthermore, the applicability of the pro- posed technique is experimentally demonstrated for simultaneous complex field imaging of various static and dynamic complex-valued objects. Additionally, a quantitative analysis is performed to evaluate the phase stability and sensitivity of the system in comparison with conventional phase-shifting methods. 2. Principles and Methods 2.1. Fizeau Polarization Phase-Shifting Digital Holography (FP-PSDH) The FP-PSDH system makes use of a highly stable Fizeau-polarization interferometry scheme for the generation of on-axis near common-path propagating orthogonal reference and object beams. The compact on-axis design of the polarization interferometry technique is facilitated by employing a wire grid polarizer (WGP) consisting of an array of metallic wires. A conceptual schematic of the orthogonal polarized beam generation with a WGP is represented in Figure 1a. The illumination of a linearly 45 polarized beam relative to the wire grid on the WGP results in a reflected beam with the polarization component parallel to the direction of the wire grid (s-polarized) and in a transmitted beam with the polarization component perpendicular to the wire grid (p-polarized). In our proposed scheme, the s-polarized component serves as the reference beam, and the p-polarized component serves as the object beam for polarization phase-shifting. The back-scattered p-polarized object beam propagates along with the reference beam in a common path Photonics 2022, 9, 126 3 of 10 Photonics 2022, 9, x FOR PEER REVIEW 3 of 10 after interacting with the object. The resulting common-path propagating light fields are given by, E (rˆ)= A (rˆ) exp(i (rˆ)) p p p (1) E (r ˆ) = A (r ˆ) exp(if (r ˆ)) p p p E (rˆ)= A (rˆ) exp(i (rˆ)) (1) s s s E (r ˆ) = A (r ˆ) exp(if (r ˆ)) s s s ˆ ˆ ˆ ˆ where A () r and A () r are the amplitude information, and where  () r and  () r are p s p s where A (r ˆ) and A (r ˆ) are the amplitude information, and where f (r ˆ) and f (r ˆ) are p s p s the phase information of the object modulated p-polarized and reference s-polarized the phase information of the object modulated p-polarized and reference s-polarized beams, respectively. beams, respectively. Figure 1. (a) Conceptual schematic of orthogonal polarized beam generation with the wire grid polar- Figure 1. (a) Conceptual schematic of orthogonal polarized beam generation with the wire grid polarizer izer (WGP); (b) Schematic of the space division multiplexing mechanism with QWP and polarization (WGP); (b) Schematic of the space division multiplexing mechanism with QWP and polarization filters in the polarized camera for single-shot detection of multiple phase-shifted holograms. filters in the polarized camera for single-shot detection of multiple phase-shifted holograms. To implement a single-shot recording of the multiple phase-shifting holograms, we To implement a single-shot recording of the multiple phase-shifting holograms, we utilized the space division multiplexing technique with the combination of a QWP and a utilized the space division multiplexing technique with the combination of a QWP and polarized camera [29]. A conceptual schematic of the multiplexing implementation in the a polarized camera [29]. A conceptual schematic of the multiplexing implementation in proposed approach is demonstrated in Figure 1b. The on-axis propagating reference and the proposed approach is demonstrated in Figure 1b. The on-axis propagating reference object beams passed through the QWP with its fast axis at 45° with respect to the common- and object beams passed through the QWP with its fast axis at 45 with respect to the path propagating polarized beams, thereby changing the polarization state to the respec- common-path propagating polarized beams, thereby changing the polarization state to tive circularly polarized beams and reaching the polarized camera sensor plane. The cam- the respective circularly polarized beams and reaching the polarized camera sensor plane. era sensor comprises unique nano-wire grid arrays with four separate polarizing filters The camera sensor comprises unique nano-wire grid arrays with four separate polarizing angled at 0°, 45°, 90°, and 135° positioned in a systematic pattern across the sensor. The filters angled at 0 , 45 , 90 , and 135 positioned in a systematic pattern across the sensor. electric field components of the circularly polarized beams at the exit plane of the polar- iz The ing felectric ilters of th field e sen components sor plane are gi of ve the n by, cir cularly polarized beams at the exit plane of the polarizing filters of the sensor plane are given by,  1 i 1 cos  cos sin EE (rr )=   ( )  (2) kk  2 2 1 coscos sinq scos in q sin qi 1 1 i   E (r) = p E (r ˆ) (2) k k cos q sin q sin q i 1 where k = p or s , the matrices represent the Jones matrices corresponding to the polarizer filters at  orientations and the QWP with its fast axis at 45°, respectively, and ˆ where k = p or s, the matrices represent the Jones matrices corresponding to E the () r polarizer ps or re filters presenat ts th q eorientations polariz and ed bthe eams QWP with with the respec its fast tive axis Jones at repr 45ese , n respectively tation. There , -and E (r ˆ) represents the p or s polarized beams with the respective Jones representation. Therefore, fore, the intensity distribution I (r)= E (r)E (r) at the sensor plane is expressed by, kk the intensity distribution I(r) = E (r)E (r) at the sensor plane is expressed by,  I (r )= A (r )+ A (r )+ 2A (r )A (r ) cos( 2 − (r )) (3) h i p s p s  2 2 I(r) = A (r) + A (r) + 2 A (r) A (r) cos(2q Df(r)) (3) p s p s where Df(r) = f (r) f (r) is the phase difference between the object and the reference p s field at the sensor plane. The space-division multiplexing, resulting from the interaction of circularly polarized object and reference beams with the polarization filters at specific Photonics 2022, 9, 126 4 of 10 angles, produces four phase-shifting holograms: I(r; 0), I(r; p/2), I(r; p) & I(r; 3p/2) with p/2 phase-shift represented in the conceptual schematic of Figure 1b. The single-shot detection of the multiple phase-shifted holograms at the sensor plane provides the flexible advantage of extraction of the complex field distribution of the object modulated informa- tion using the conventional phase-shifting interferometry relation, which is expressed as, E(r) = ( I(r; 0) I(r; p)) + i( I(r; 3p/2) I(r; p/2)) (4) The retrieval of the complex field distribution at the sensor plane gives the provision for the recovery of the amplitude and phase distribution of the complex-valued object at any arbitrary plane by using the digital backpropagation approaches [35]. 2.2. Experimental Design A schematic sketch of the experimental design of FP-PSDH is shown in Figure 2. A vertically polarized He-Ne laser source (CVI Melles Griot-25-LHP-928-230) of wavelength 632.8 nm, which is converted in to a linearly 45 polarized by a half wave plate (HWP), acts as the source beam for the proposed Fizeau polarization system. The beam is spatially filtered and collimated to generate a uniform beam with a plane wavefront. The transmitted beam from a non-polarizing beam splitter (BS) illuminates the WGP (ThorLab-WP50L-VIS) and produces two orthogonal polarization components from the input polarized beam, where the reflected beam (s-polarized) acts as the reference beam and where the transmitted beam (p-polarized) acts as the object beam for the Fizeau polarization interferometry. The p-polarized beam interacts with the desired object, and the backscattered object beam transmits again through the WGP and propagates in an on-axis common-path with the s-polarized beam. The object and the reference beam from the WGP propagate in an on-axis geometry and are reflected from the BS. These on-axis propagated polarized light fields transmit through the QWP with their fast axis oriented at 45 before reaching the monochrome polarization camera. The camera is 5.1 megapixels with a Sony IMX250MZR CMOS polarized sensor (active pixels 2464  2056 with pixel size 3.45 m and having 74 frames per second). The systematic arrangement of polarization filters with orientations of 0 , 45 , 90 , and 135 in the polarized camera is represented in the inset of Figure 2. The polarized camera records the raw intensity distribution of the hologram, and then Photonics 2022, 9, x FOR PEER REVIEW 5 of 10 simultaneously extracts the four multiple phase-shifted holograms without any spectral trade-offs. Figure 2. Experimental geometry of FP-PSDH: He-Ne laser: Helium-Neon laser source; HWP: Half Figure 2. Experimental geometry of FP-PSDH: He-Ne laser: Helium-Neon laser source; HWP: Half Wave Plate; M: Mirror; SF: Spatial Filter assembly; L: Lens; BS: Nonpolarizing Beam Splitter; WGP: Wave Plate; M: Mirror; SF: Spatial Filter assembly; L: Lens; BS: Nonpolarizing Beam Splitter; WGP: Wire Grid Polarizer; QWP: Quarter Wave Plate. In inset, the polarization filter arrangements in the Wire Grid Polarizer; QWP: Quarter Wave Plate. In inset, the polarization filter arrangements in the polarized camera and respective orientation angles are represented. polarized camera and respective orientation angles are represented. 3. Results and Discussion 3.1. Complex-Valued and Dynamic Object Imaging The performance and applicability of the FP-PSDH technique was experimentally tested for various objects and imaging conditions. To demonstrate the complex-valued imaging potential of the technique, we utilized the spatial light modulator (SLM) to intro- duce various complex-valued and pure phase objects. The complex-valued objects uti- lized for validating the technique were introduced using the phase-only SLM (PLUTO- VIS, Holoeye with total pixels 1920 × 1080, pixel pitch of 8µ m, and an image frame rate of 60 Hz). A complex-valued object was designed to encode the SLM using the checkerboard method [36,37], in which the alternate pixels were assigned with a uniform binary phase value of 0 and π (see Supplementary S1). We designed a complex object of Chinese char- acters ‘Hua (华)’ with an amplitude distribution and ‘Da (大)’ with a phase distribution, each consisting of size 3.9 mm × 3.9 mm as shown in Figure 3a. The polarization camera recorded a single-shot hologram of the object, and the recorded intensity of the hologram is shown in Figure 3b. Consequently, the four phase-shifted holograms were extracted from the single-shot hologram, and the complex amplitude distribution of the object at the sensor plane was successfully retrieved from these phase-shifted holograms by utiliz- ing Equation (4). The retrieved amplitude and phase distribution at the sensor plane are shown in Figure 3c and Figure 3d, respectively. The recovery of the complex field distri- bution at the sensor plane using the phase-shifting technique provided the flexibility to reconstruct the object information at the desired plane using digital propagation based on the angular spectrum method [35]. The focused object information retrieved from the pro- posed technique is shown in Figure 3e and Figure 3f. The amplitude distribution in Figure 3e shows a focused reconstruction of the amplitude ‘华’ at the object plane and a blurred ‘大’, as it is a pure phase distribution. In a similar way, Figure 3f represents the focused phase distribution of the object, in which the phase part is reconstructed with good qual- ity. Ph Pho ot to on niic cs s 2 20 02 22 2,, 9 9,, x x F FO OR R P PEE EER R R RE EV VI IEW EW 5 5 o of f 10 10 Photonics 2Ph 022 ot , o9 n , ix cs F2 O 0R 22 P , 9 EE , x R F R O E R V P IEW EER REVIEW 5 of 10 5 of 10 Fig Figure ure 2 2.. Ex Expe per rimen iment ta all g geo eom met etr ry y o of f F FP P- -P PS SDH DH:: H He e- -N Ne e la lase ser r:: H Hel elium ium- -N Ne eo on n la lase ser r so source urce;; H HWP WP:: H Ha alf lf Wa Wav ve e P Pla lat te e;; M: M: M Mir irr ro or r;; S SF F:: S Spa pat tia ial l F Fil ilt ter er a ass ssemb embly ly;; L: L: L Len ens s;; B BS S:: N No on np po ola lar riz izin ing g Be Bea am m S Spli plit tt ter er;; WG WGP P:: Wir Wire e G Gr rid id P Po ola lar riz izer er;; QWP QWP:: Qu Qua ar rt ter er Wa Wav ve e P Pla lat te. e. I In n iin nse set t,, t th he e po pola lar riz iza at tio ion n fil filt ter er a ar rr ra an ng gemen ement ts s in in t th he e Photonics 2022, 9, 126 5 of 10 po pola lar riz ized ed c ca am me er ra a a an nd d r res espec pect tiiv ve e o or rie ien nt ta at tio ion n a an ng gle les s a ar re e r repr epre ese sen nt ted ed.. 3 3.. R Re esu sul lt ts s a an nd d Di Disc scu uss ssi ion on 3. Results and Discussion 3 3..1 1.. C Com omp ple lex x- -V Value alued d and and D Dy ynam namic ic O Ob bje ject ct I Im mag aging ing 3.1. Complex-Valued and Dynamic Object Imaging The The pe perf rfo orma rman nce ce a an nd d a appl ppliica cab biilliity ty o of f th the e FP FP- -PS PSDH DH t tec ech hn niiq que ue wa was s e ex xpe peri rim ment enta allly ly The performance and applicability of the FP-PSDH technique was experimentally tested tested f fo or r v va ari rio ous us o ob bjjec ects ts a an nd d iim ma agi gin ng g co con nd diiti tio on ns. s. To To d demo emon nst stra rate te t th he e co com mpl plex ex- -va vallued ued tested for various objects and imaging conditions. To demonstrate the complex-valued iim ma agi gin ng g po potenti tentia all o of f th the e tec tech hn niiq que, ue, we we uti utilliiz ze ed d th the e spa spat tiia all lliigh ght t m mo od dul ula ato tor r ( (S SL LM M) ) to to iin ntro tro- - imaging potential of the technique, we utilized the spatial light modulator (SLM) to intro- d duc uce e va vari rio ous us co com mpl plex ex- -va vallued ued a an nd d pur pure e ph pha ase se o ob bjjec ect ts s.. The The co com mpl plex ex- -va vallued ued o ob bjjec ects ts uti uti- - duce various complex-valued and pure phase objects. The complex-valued objects utilized lliiz zed ed f fo or r v va alliid da ati tin ng g th the e tec tech hn niiq que ue were were iin ntro trod duce uced d usi usin ng g th the e pha phase se- -o on nlly y S SL LM M ( (PLU PLUTO TO- - for validating the technique were introduced using the phase-only SLM (PLUTO-VIS, Figure 2. Fig Expe ure rimen 2. Ex ta pe l g rimen eomet ta rly g o eo f F m Pet -P rS yDH of F : P H -e P-S N DH e la : se Hr e:- N He ella ium ser-:N H eel on ium lase -N r e so on urce lase ; H r so WP urce : H;a H lf WP: Half VIS VIS,, Ho Hollo oeye eye wi with th to tota tall pi pix xel els s 1 19 92 20 0 × × 1 10 08 80 0,, p piix xel el pi pitch tch o of f 8 8µ µm m,, a an nd d a an n iim ma age ge f fr ra am me e ra rate te o of f Holoeye with total pixels 1920  1080, pixel pitch of 8m, and an image frame rate of Wave PlaWa te; M: ve P M la ir tr eo ; r M: ; S F M : ir Spa rot ria ; S l F F:il Stpa er ta ia ss l emb Filter ly a ; ss L:emb Lenly s; ;B L: S: L N en on sp ; B oS la : rN izo in ng p o Be laa rm izin Spli g Be tter am ; WG Spli P t:t er; WGP: 6 60 0 H Hz z) ).. A A co com mplex plex- -va vallued ued o ob bjjec ect t w wa as s d desi esign gned ed to to enco encod de e th the e S SL LM M usi usin ng g th the e checke checker rb bo oa ard rd 60 Hz). A complex-valued object was designed to encode the SLM using the checkerboard Wire Grid Wir Poe laG riz rid er ;P QWP olariz : er Qu ; QWP arter :Wa Qu v ae rtP er la Wa te. Iv n e iP nla sette. , t h In e ipo nse la tr , iz tha e tio po nla fil riz ter at a io rn ra fil ng temen er arrt as nin gemen the ts in the m metho ethod d [ [3 36 6,,3 37 7] ], , iin n wh whiich ch th the e a allter tern na ate te pi pix xel els s were were a ass ssiign gned ed wi with th a a u un niif fo orm rm b biin na ar ry y pha phase se method [36,37], in which the alternate pixels were assigned with a uniform binary phase polarizedpo cala m re iz ra ed a n cd am res erpec a an tid v e res orpec ienttia v te ioo nr ie an ng ta le ts ioa nr e an repr gles ese arn e tr ed epr . esented. va vallue ue o of f 0 0 a an nd d π π ( (see see S Supple upplem ment enta ary ry S S1 1) ).. We We d desi esign gned ed a a co com mpl plex ex o ob bjjec ect t o of f Chi Chin nese ese cha char- r- value of 0 and  (see Supplementary S1). We designed a complex object of Chinese char- a acte cters rs ‘Hu ‘Hua a ( (华华) )’ ’ wi with th a an n a am mpl pliitude tude d diist stri rib buti utio on n a an nd d ‘D ‘Da a ( (大大) )’ ’ wi with th a a ph pha ase se d diist strib ribu uti tio on n,, acters ‘Hua ( )’ with an amplitude distribution and ‘Da ( )’ with a phase distribution, 3. Result3s. a R n ed su Di lts sc au nss d iDi onsc ussion ea each ch co con nsi sist stiin ng g o of f si siz ze e 3 3..9 9 m mm m × × 3. 3.9 9 m mm m a as s sh sho ow wn n iin n Fi Figure gure 3 3a a.. The The po polla ari riz za ati tio on n ca cam mer era a each consisting of size 3.9 mm  3.9 mm as shown in Figure 3a. The polarization camera 3.1. Comp 3le .1x . -C Vom alue ple d x and -Value Dyd nam and ic D O yb nam ject ic Im O ag bje ing ct Imaging re reco cord rded ed a a si sin ngl gle e- -sh sho ot t h ho ollo ogra gram m o of f th the e o ob bjjec ect, t, a an nd d t th he e re reco cord rded ed iin ntens tensiity ty o of f th the e h ho ollo ogra gram m recorded a single-shot hologram of the object, and the recorded intensity of the hologram The performance and applicability of the FP-PSDH technique was experimentally The performance and applicability of the FP-PSDH technique was experimentally i is is s shown sh sho own wn in iin n Figur Fi Figure gure e 3 3 3b. b b.. Co Consequently Con nseq sequentl uently, y, , the th the e four f fo our ur phase-shifted ph pha ase se- -sh shiif fted ted holograms h ho olo logra gram ms s wer were were e extracted ex extr tra acte cted d tested fotested r vari ofus or o vb ari jec ots us ao nb d jec im tsa a gi nn dg im coa ngi di n ti g on co s. nd To itid on emo s. To nstd ra emo te tn hst e ra cote mpl thex e co -va m lued plex -valued from the single-shot hologram, and the complex amplitude distribution of the object at f fr ro om m the the single-shot single-shot hologram, hologram,and and the the complex complex amplitude amplitude distribution distributio of n to he f th object e objec at t the at imaging ipo ma tenti ging alpo oftenti the a tec l o h fn th iq e ue, tec we hniuti que, liz we ed th uti e lispa zed ti th al e lispa ght tm iao l l d igh ula t to m r o(d Sul LM ato ) to r ( S in Ltro M)- to intro- th sensor the e sen senso plane sor r pl pla a was n ne e wa wa successfully s s succe succes ssful sful rletrieved ly y re retr triiev evfr ed ed o m f fro ro the m m th se these ese phase-shifted pha phase se- -sh shiif fted ted holograms h ho ollo ogra gram m by s b s b utilizing y y uti utili liz z- - duce vari do uc us e va com rio pl us exco -va m lued plex - ava nd lued pur e an ph d a pur se e ob ph jec atse s. The objec co tsm . The plexco -va m lued plex - o va bjl ec ued ts uti ob-jects uti- i Equation in ng g E Eq qu ua at t(4). iion on The ( (4 4) ).. r The The etrieved re retri trie e amplitude v ved ed a am mpl pliitude and tudephase a an nd d p p distribution h ha ase se d diist stri rib bat uti uti the o on n sensor a at t th the e se se plane n nso sor r ar pl pl ea ashown n ne e a are re lized forl iv za ed lid fa oti r n v g alth ide ati tec ng hn th iq e ue tecwere hniq ue intro were duce in d tro usi duce ng d th e usi pha ng se th -e on pha ly S se L-M on (lPLU y SLTO M ( -PLUTO- in Figures 3c,d, respectively. The recovery of the complex field distribution at the sensor sh sho own wn iin n Fi Figure gure 3c 3c,,d d,, re respec specti tiv vel ely. y. The The re reco cov ver ery y o of f th the e co com mpl plex ex f fiiel eld d d diist stri rib buti utio on n a at t th the e VIS, HolVIS oeye , Ho wil th oeye tota wi l pi th x el tos ta 1l9 pi 20 x el × 1 s 0 18 90 2,0 p × ix1 el 0 8 pi 0,tch pixo el f 8 pi µtch m, a on f d 8µ am n ,i m an ad ge an fr i am ma e ge raf te rao m f e rate of plane using the phase-shifting technique provided the flexibility to reconstruct the object sen senso sor r pl pla an ne e usi usin ng g th the e pha phas se e- -sh shiif fti tin ng g tec tech hn niiq que ue pr pro ov viid de ed d th the e f fllex exiib biili lity ty to to re reco con nst struc ruct t th the e 60 Hz). A complex-valued object was designed to encode the SLM using the checkerboard 60 Hz). A complex-valued object was designed to encode the SLM using the checkerboard information at the desired plane using digital propagation based on the angular spectrum o ob bjjec ect t iin nf fo orma rmati tio on n a at t t th he e d desi esire red d pl pla an ne e usi usin ng g d diigi gita tall pr pro opa paga gati tio on n ba based sed o on n t th he e a an ngul gula ar r method m [36 etho ,37]d , i[ n 3 6 wh ,37 i] ch , in th wh e ailch tern th ae te api lter xel na s te were pix el ass s were igned a wi ssith gn a ed u n wi ifth orm a u bn in ifa orrm y pha bin se ary phase method [35]. The focused object information retrieved from the proposed technique is spec spectrum trum m metho ethod d [ [35] 35].. The The f fo ocused cused o ob bjjec ect t iin nf fo orma rmati tio on n re retri triev eved ed f fro rom m th the e pr pro opo pose sed d tec tech h- - value of va 0 a lue nd o π f ( 0see an d S upple π (see m Sent upple arym S1 ent ). We ary d S1 esi ). gn We ed d a esi co gn m ed pl ex a co ob m jec plt ex of o Chi bjec nt ese of Chi chan r-ese char- shown in Figure 3e,f. The amplitude distribution in Figure 3e shows a focused recon- n niiq que ue iis s sh sho ow wn n iin n Fi Figure gure 3e 3e,f ,f.. The The a am mpl pliitude tude d diist stri rib buti utio on n iin n Fi Figure gure 3e 3e sh sho ows ws a a f fo ocused cused acters ‘Hu acte a ( rs 华‘Hu )’ wi ath (华 a) n ’ wi am th pl iatude n am d pl ist itude ributi do ist n ri an buti d ‘D on a a (大 nd) ’ ‘D wi a th (大 a) ’ ph wi ase th d a iph strib ase uti do ist n,rib ution, struction of the amplitude ‘ ’ at the object plane and a blurred ‘ ’, as it is a pure phase re reco con nst struc ructi tio on n o of f th the e a am mpl pliit tude ude ‘‘华华’’ a at t th the e o ob bjjec ect t pl pla an ne e a an nd d a a b bllurr urred ed ‘‘大大’’,, a as s iit t iis s a a pur pure e Photonics 2022, 9, x FOR PEER REVIEW 6 of 10 each conea sist ch inco g n osi f si stz in e g 3.o 9f m sim ze × 3.3. 9 9 m m mm × a 3. s 9sh m om w n a s in sh Fi ow gure n in 3 a Fi . gure The po 3al. aThe rizati po on la ri ca zm ati er oa n camera distribution. In a similar way, Figure 3f represents the focused phase distribution of the pha phase se d diist stri rib buti utio on n.. In In a a si sim miilla ar r wa way y,, Fi Figure gure 3 3f f re repr prese esen nts ts t th he e f fo ocused cused ph pha ase se d diist stri rib buti utio on n object,re inco which rded re a the co sird n phase gl ed e- a sh si part on t gl ho e is l-o sh rgra econstr ot m ho o lf o ucted gra the m ob with o jec f th t, e good an od b jt ec h quality e t, re an co d rd .thed e re in co tens rded ity in otens f the ity hoo lo f gra the m ho logram o of f th the e o ob bjjec ect, t, iin n wh whiich th ch the e pha phase se p pa art rt iis r s rec eco on nst struc ructed ted wi with th go goo od d q qua ualliity. ty. is shown is in sh Fi own gure in 3 Fi b. gure Con seq 3b.uentl Conseq y, th uentl e foy, ur th ph e afse our -sh ph ifted ase - h sh olo ifted gra m ho s lo were gram ex s tr were acte d ex tracted from the fro sin m gl th e-e sh si on t gl ho el -o sh go ra t m ho , la o n g d ra tm he , a co nm d pl thex e co am mp pl liex tude am d pilst itude ributi do ist n ri ob f uti the on o b ojf ec th t e ato bject at the senso th r e pl sen ane so wa r pl s a succe ne wa ssful s succe ly re str sful iev ly ed re ftr roim ev ed these fro pha m th se ese -sh pha ifted se h -sh oli o fgra tedm ho s b loy gra uti m lis b z- y utiliz- ing Equa it n ig on E q (4 u )a . t The ion re (4) tri . The eved re atri me pl vi ed tude am a pl nd itude pha se and d ip sth ri ab se uti do ist n ri at buti the ose n n at so th r e pl se an ne so ar re pl ane are shown in sh Fi own gure in 3c Fi ,d gure , respec 3c,d ti , v re elspec y. The tivel re y. coThe very re oco f th ver e y coo m f pl thex e co fim eld pl d ex ist fri iel bd uti do ist n ri ab t uti the o n at the sensor plane using the phase-shifting technique provided the flexibility to reconstruct the sensor plane using the phase-shifting technique provided the flexibility to reconstruct the object ino fo brma ject ti in ofn o rma at th tie on d esi at re thd e pl desi anre e d usi pl na g nd e iusi gita nlg pr do igi pa ta ga l ti pr oo npa ba ga sed tio n o n ba th sed e a o nn gul th ae r angular spectrum spec metho trum d [ m 35] etho . The d [35] focused . The f oo bcused ject in o fo brma ject ti in ofn o rma retriti ev on ed re ftri rom ev ed the fro prm opo th se e d pr tec opo h-sed tech- nique is n sh iq o ue wn is in sh Fi ow gure n in 3e Fi ,fgure . The 3e am ,f.pl The itude am d pl ist itude ributi do ist n ri in b uti Figure on in 3e Fi sh gure ows 3e a sh foo cused ws a focused reconstruc reco tion nst o ruc f th tie on am opl f th itude e am ‘pl华i’t ude at th ‘e 华 o’b a jec t th t pl e o ab nje ec at npl d a an b e lurr and ed a ‘b大 lurr ’, a ed s i t ‘大 is ’,a apur s it e is a pure phase dipha strib se uti do ist n.ri In buti a o sin m . iIn la r a wa sim y,i lFi ar gure way ,3 f Fi re gure prese 3fn re tspr these e fo ncused ts the f ph ocused ase d iph stri ab se uti do ist n ribution of the obo jec f th t, e in o wh bjec ich th t, in wh e pha ich th se p e apha rt is r se ec pa ort nst is r ruc ec ted on st wi ruc thted goo wi d q th ua go lity. od quality. Figure 3. Complex field reconstruction results: (a) complex-valued object encoded in the SLM; (b) Figure 3. Complex field reconstruction results: (a) complex-valued object encoded in the SLM; single-shot intensity of hologram recorded; (c) retrieved amplitude distribution at the sensor plane; (b) single-shot intensity of hologram recorded; (c) retrieved amplitude distribution at the sensor (d) retrieved phase distribution at the sensor plane; (e) reconstructed amplitude distribution at the plane; (d) retrieved phase distribution at the sensor plane; (e) reconstructed amplitude distribution at object plane; (f) reconstructed phase distribution at the object plane. Scale bar is 1.0 mm. the object plane; (f) reconstructed phase distribution at the object plane. Scale bar is 1.0 mm. Additionally Additionally , the , the potential potentia of l of the th technique e technique is demonstrated is demonstrated for r feal-time or real-tim imaging e imagi ofng of dynamic sample by utilizing the single-shot imaging capability of the FP-PSDH. A dynamic dynamic sample by utilizing the single-shot imaging capability of the FP-PSDH. A dy- phase object (running fox of size 7.2 mm  3.6 mm) is designed and projected into the namic phase object (running fox of size 7.2 mm × 3.6 mm) is designed and projected into system using the SLM. A single-shot recording captures the hologram of the object in an the system using the SLM. A single-shot recording captures the hologram of the object in instant, and further digital processing retrieves the four phase-shifted holograms. The an instant, and further digital processing retrieves the four phase-shifted holograms. The phase object at the desired plane is reconstructed using the phase-shifting interferometry phase object at the desired plane is reconstructed using the phase-shifting interferometry technique. To demonstrate the real time imaging of the moving target, we have recorded technique. To demonstrate the real time imaging of the moving target, we have recorded several intensity images in the sensor plane with a time interval of 0.1 s. The reconstructed several intensity images in the sensor plane with a time interval of 0.1 s. The reconstructed motion pictures at different instants of time of the moving phase object are shown in motion pictures at different instants of time of the moving phase object are shown in Fig- ure 4. The reconstructed dynamic phase distribution of the object is presented in Visuali- zation S1. Figure 4. Experimental results for dynamic pure phase objects: (a–f) reconstructed motion picture phase distribution at the sensor plane for various instants of time. Scale bar is 0.86 mm. 3.2. Weakly Reflective Object Imaging Furthermore, we have investigated the image reconstruction quality of the FP-PSDH system for the case of real-world weakly reflective type objects. As the light reflection from these objects are comparatively weak, we integrated a 4f-imaging geometry along with the system to grab the light from the object surface to the sensor plane. Experiments were carried out for butterfly wings and a standard USAF negative (reflective) target, and the respective experimental results are shown in Figure 5. Figure 5a and Figure 5d represent the single-shot raw intensity distribution of the recorded hologram corresponding to the butterfly wing and resolution test target, respectively. Subsequently, the multiple phase- shifted holograms were extracted from the single-shot recorded hologram, and the respec- tive complex amplitude distribution of the object at the sensor plane was successfully Photonics 2022, 9, x FOR PEER REVIEW 6 of 10 Figure 3. Complex field reconstruction results: (a) complex-valued object encoded in the SLM; (b) single-shot intensity of hologram recorded; (c) retrieved amplitude distribution at the sensor plane; (d) retrieved phase distribution at the sensor plane; (e) reconstructed amplitude distribution at the object plane; (f) reconstructed phase distribution at the object plane. Scale bar is 1.0 mm. Additionally, the potential of the technique is demonstrated for real-time imaging of dynamic sample by utilizing the single-shot imaging capability of the FP-PSDH. A dy- namic phase object (running fox of size 7.2 mm × 3.6 mm) is designed and projected into the system using the SLM. A single-shot recording captures the hologram of the object in an instant, and further digital processing retrieves the four phase-shifted holograms. The phase object at the desired plane is reconstructed using the phase-shifting interferometry Photonics 2022, 9, 126 6 of 10 technique. To demonstrate the real time imaging of the moving target, we have recorded several intensity images in the sensor plane with a time interval of 0.1 s. The reconstructed motion pictures at different instants of time of the moving phase object are shown in Fig- Figure 4. The reconstructed dynamic phase distribution of the object is presented in ure 4. The reconstructed dynamic phase distribution of the object is presented in Visuali- Visualization S1. zation S1. Figure 4. Experimental results for dynamic pure phase objects: (a–f) reconstructed motion picture Figure 4. Experimental results for dynamic pure phase objects: (a–f) reconstructed motion picture phase distribution at the sensor plane for various instants of time. Scale bar is 0.86 mm. phase distribution at the sensor plane for various instants of time. Scale bar is 0.86 mm. 3.2. Weakly Reflective Object Imaging 3.2. Weakly Reflective Object Imaging Furthermore, we have investigated the image reconstruction quality of the FP-PSDH Furthermore, we have investigated the image reconstruction quality of the FP-PSDH system for the case of real-world weakly reflective type objects. As the light reflection from system for the case of real-world weakly reflective type objects. As the light reflection from these objects are comparatively weak, we integrated a 4f-imaging geometry along with these objects are comparatively weak, we integrated a 4f-imaging geometry along with the system to grab the light from the object surface to the sensor plane. Experiments were the system to grab the light from the object surface to the sensor plane. Experiments were carried out for butterfly wings and a standard USAF negative (reflective) target, and the carried out for butterfly wings and a standard USAF negative (reflective) target, and the respective experimental results are shown in Figure 5. Figure 5a,d represent the single-shot respective experimental results are shown in Figure 5. Figure 5a and Figure 5d represent raw intensity distribution of the recorded hologram corresponding to the butterfly wing the single-shot raw intensity distribution of the recorded hologram corresponding to the and resolution test target, respectively. Subsequently, the multiple phase-shifted holograms butterfly wing and resolution test target, respectively. Subsequently, the multiple phase- were extracted from the single-shot recorded hologram, and the respective complex am- shifted holograms were extracted from the single-shot recorded hologram, and the respec- plitude distribution of the object at the sensor plane was successfully retrieved from these tive complex amplitude distribution of the object at the sensor plane was successfully multiple phase-shifted holograms using Equation (4). The reconstructed amplitude and phase distributions of butterfly wings is shown in Figures 5b,c, respectively. The phase distribution of butterfly wings shows a clear distinction between the discal cell and inner margin. In a similar way, the amplitude and phase distribution of the USAF resolution test target were reconstructed from digitally extracted multiple phase-shifted holograms, and the corresponding results are shown in Figures 5e,f, respectively. The system had a good resolving ability up to group 5 element 6 of the USAF resolution test target, which corresponds to 57.0-line pairs/mm. 3.3. Quantitative Analysis of System Stability and Sensitivity To evaluate the robustness of the system in environmental fluctuations and other noise mechanisms, we estimated the phase stability and sensitivity of the FP-PSDH system and compared it with other phase-shifting based methods. The performance was evaluated using time sequential detection of single-shot holograms in FP-PSDH, and it was compared with the two configurations of the Mach Zehnder interferometry (MZI) based phase-shifting scheme, namely multiple-shot phase-shifting MZI (MP-MZI) and single-shot polarization phase-shifting MZI (PP-MZI) (see Supplementary S1). In the case of FP-PSDH and PP- MZI, the sequential detections of 50 single-shot holograms with a polarized camera in sample-free configuration were carried out with a time interval of 0.1 s, and the phase map was recovered from respective digitally processed multiple phase shifted holograms. On the other hand, in the case of MP-MZI, the sequential detections of 50 holograms for each of the four phase-shifted holograms were recorded manually using a monochrome camera, and the respective phase was recovered. To evaluate the temporal stability, we estimated the phase fluctuation of a specific point in the recovered phase map with respect to the same point in the entire 50 recovered phase maps. The corresponding plot of the phase fluctuations with respect to the time sequential measurements is shown in Figure 6a. Photonics 2022, 9, 126 7 of 10 The estimation of standard deviation (STD) from the phase fluctuations shows that the proposed FP-PSDH technique has a lower STD (4.02 mRad) in comparison to MP-MZI Photonics 2022, 9, x FOR PEER REVIEW 7 of 10 (STD of 18.95 mRad) and PP-MZI (STD of 12.20 mRad). Furthermore, we also estimated the spatial sensitivity, which is the minimum detectable phase change in a recovered phase map for a particular measurement [38]. We evaluated the STD corresponding to total pixels retrieved from these multiple phase-shifted holograms using Equation (4). The recon- in each of the 50 recovered phase maps for the respective phase-shifting based approaches. structed amplitude and phase distributions of butterfly wings is shown in Figure 5b and The box plot corresponding to all three configurations are shown in Figure 6b. The estimated Figure 5c, respectively. The phase distribution of butterfly wings shows a clear distinction STD for FP-PSDH is low in comparison to other techniques, which can be attributed to between the discal cell and inner margin. In a similar way, the amplitude and phase dis- the high spatial sensitivity of the proposed technique. A quantitative comparison of the tribution of the USAF resolution test target were reconstructed from digitally extracted FP-PSDH system performance to MZI-based on-axis techniques is summarized in Table 1. multiple phase-shifted holograms, and the corresponding results are shown in Figure 5e The plots in Figure 6a,b and the quantitative evaluation in Table 1 manifest the dominance and Figure 5f, respectively. The system had a good resolving ability up to group 5 element of on-axis single-shot FP-PSDH in complex-valued dynamic object imaging over other 6 techniques of the USA in F r the eso noise-assisted lution test targe envir t, wh onments. ich corresponds to 57.0-line pairs/mm. Fig Figure ure 5 5. . Ex Experimental perimental rres esults: ults: But Butterfly terfly w wing; ing; ((a a) )rraw aw in intensity tensity di distribution stribution of ofsi single-shot ngle-shot rre ecor corde ded d hologram; (b) reconstructed amplitude distribution; (c) reconstructed phase distribution. USAF neg- hologram; (b) reconstructed amplitude distribution; (c) reconstructed phase distribution. USAF ative (reflective) target; (d) raw intensity distribution of single-shot recorded hologram; (e) recon- negative (reflective) target; (d) raw intensity distribution of single-shot recorded hologram; (e) re- structed amplitude distribution; (f) reconstructed phase distribution. A 4f-imaging system with constructed amplitude distribution; (f) reconstructed phase distribution. A 4f-imaging system with lenses of focal length 100 mm and 200 mm is utilized to image the object plane to the sensor plane. lenses of focal length 100 mm and 200 mm is utilized to image the object plane to the sensor plane. Scale bar: (a–c) 300 μm, (d–f) 100 μm. Scale bar: (a–c) 300 m, (d–f) 100 m. 3.3. Quantitative Analysis of System Stability and Sensitivity Table 1. Quantitative comparison of FP-PSDH system performance with MP-MZI and PP- To evaluate the robustness of the system in environmental fluctuations and other MZI techniques. noise mechanisms, we estimated the phase stability and sensitivity of the FP-PSDH sys- tem and compared it with other phase-shifting based metho T d emporal s. The performance Spatial was eval- Interferometry Type of Detection Stability Sensitivity uated using time sequential detection of single-shot holograms in FP-PSDH, and it was Scheme Geometry Scheme (mRad) (mRad) compared with the two configurations of the Mach Zehnder interferometry (MZI) based MP-MZI double path four-shot 18.95 27.76 phase-shifting scheme, namely multiple-shot phase-shifting MZI (MP-MZI) and single- PP-MZI double path single-shot 12.20 24.86 shot polarization phase-shifting MZI (PP-MZI) (see Supplementary S1). In the case of FP- FP-PSDH single path single-shot 4.02 17.47 PSDH and PP-MZI, the sequential detections of 50 single-shot holograms with a polarized camera in sample-free configuration were carried out with a time interval of 0.1 s, and the phase map was recovered from respective digitally processed multiple phase shifted hol- ograms. On the other hand, in the case of MP-MZI, the sequential detections of 50 holo- grams for each of the four phase-shifted holograms were recorded manually using a mon- ochrome camera, and the respective phase was recovered. To evaluate the temporal sta- bility, we estimated the phase fluctuation of a specific point in the recovered phase map with respect to the same point in the entire 50 recovered phase maps. The corresponding plot of the phase fluctuations with respect to the time sequential measurements is shown in Figure 6a. The estimation of standard deviation (STD) from the phase fluctuations shows that the proposed FP-PSDH technique has a lower STD (4.02 mRad) in comparison Photonics 2022, 9, x FOR PEER REVIEW 8 of 10 to MP-MZI (STD of 18.95 mRad) and PP-MZI (STD of 12.20 mRad). Furthermore, we also estimated the spatial sensitivity, which is the minimum detectable phase change in a re- covered phase map for a particular measurement [38]. We evaluated the STD correspond- ing to total pixels in each of the 50 recovered phase maps for the respective phase-shifting based approaches. The box plot corresponding to all three configurations are shown in Figure 6b. The estimated STD for FP-PSDH is low in comparison to other techniques, which can be attributed to the high spatial sensitivity of the proposed technique. A quan- titative comparison of the FP-PSDH system performance to MZI-based on-axis techniques is summarized in Table 1. The plots in Figure 6a and Figure 6b and the quantitative eval- uation in Table 1 manifest the dominance of on-axis single-shot FP-PSDH in complex- Photonics 2022, 9, 126 8 of 10 valued dynamic object imaging over other techniques in the noise-assisted environments. Figure 6. Quantitative evaluation of system stability and sensitivity: (a) Temporal stability evaluation Figure 6. Quantitative evaluation of system stability and sensitivity: (a) Temporal stability evalua- of MP-MZI, PP-MZI, and FP-PSDH. The X-axis represents the time sequential measurements, and the tion of MP-MZI, PP-MZI, and FP-PSDH. The X-axis represents the time sequential measurements, Y-axis represents the respective phase fluctuations for a specific point in the recovered phase map; and the Y-axis represents the respective phase fluctuations for a specific point in the recovered phase (b) Spatial sensitivity evaluation of MP-MZI, PP-MZI, and FP-PSDH with the respective box plots. In map; (b) Spatial sensitivity evaluation of MP-MZI, PP-MZI, and FP-PSDH with the respective box each box plot, the lower and upper boundaries represent the first and third quartiles, respectively, plots. In each box plot, the lower and upper boundaries represent the first and third quartiles, re- and the line in each box represents the median value. spectively, and the line in each box represents the median value. 4. Conclusions Table 1. Quantitative comparison of FP-PSDH system performance with MP-MZI and PP-MZI tech- In conclusion, we have developed a single-shot on-axis PSDH technique based on a niques. Fizeau polarization interferometry approach for complex-valued static and dynamic object Interferometry Detection Temporal Spatial Sensitivity imaging. The adoption of the space division multiplexing along with the utilization of a Type of Geometry Scheme Scheme Stability (mRad) (mRad) polarized camera provides the potential realization in the development of a highly stable MP-MZI double path four-shot 18.95 27.76 real-time complex field imaging system. The effectiveness of the technique is experimentally PP-MZI double path single-shot 12.20 24.86 demonstrated by imaging different kinds of reflecting-type complex-valued samples. The compact FP-PSdesign DH of FP-PSDH single pa with th on-axis singeometry gle-shot exhibits 4.0 the 2 dominance of1the 7.47 pr oposed technique over conventional phase-shifting techniques for the imaging of dynamic events. 4Mor . Conc eover lusi ,ons the near common-path single-shot phase-shifting technique utilized in the FP-PSDH system enhances the space-bandwidth in comparison to the existing off-axis In conclusion, we have developed a single-shot on-axis PSDH technique based on a digital holography systems with its unique compact on-axis design. In addition, the high- Fizeau polarization interferometry approach for complex-valued static and dynamic ob- stability feature resulting from on-axis interferometry geometry provides the possible ject imaging. The adoption of the space division multiplexing along with the utilization of integration of an optical microscopy system for the development of a robust quantitative a polarized camera provides the potential realization in the development of a highly stable phase microscopy system for dynamic phase measurements. real-time complex field imaging system. The effectiveness of the technique is experimen- tally demonstrated by imaging different kinds of reflecting-type complex-valued samples. Supplementary Materials: The following are available online at https://www.mdpi.com/article/10 The compact design of FP-PSDH with on-axis geometry exhibits the dominance of the .3390/photonics9030126/s1, The digital reconstruction scheme (Figure S1), complex-valued object proposed technique over conventional phase-shifting techniques for the imaging of dy- details (Figure S2), experimental design of MZI scheme (Figure S3), and the dynamic phase object namic events. Moreover, the near common-path single-shot phase-shifting technique uti- visualization S1. lized in the FP-PSDH system enhances the space-bandwidth in comparison to the existing Author Contributions: Conceptualization, V.R.V.; methodology, H.L. and V.R.V.; formal analysis, off-axis digital holography systems with its unique compact on-axis design. In addition, H.R. and V.R.V.; investigation, H.L., X.D., and V.R.V.; data curation, H.L. and V.R.V.; writing—original the high-stability feature resulting from on-axis interferometry geometry provides the draft preparation, H.L. and V.R.V.; writing—review and editing, V.R.V., Z.C., and J.P.; supervision, J.P.; funding acquisition, Z.C. and V.R.V. All authors have read and agreed to the published version of the manuscript. Funding: This work was supported by the Natural Science Foundation of China (NSFC) under Grants No. 11674111, No. 62005086, and No. 12150410318. Institutional Review Board Statement: Not applicable. 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Journal

PhotonicsMultidisciplinary Digital Publishing Institute

Published: Feb 23, 2022

Keywords: digital holography; interferometry; phase-shifting; polarization; complex field imaging; quantitative phase imaging

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