Phase Measurement of Guided-Mode Resonance Device Using Digital Micromirror Device Gratings
Phase Measurement of Guided-Mode Resonance Device Using Digital Micromirror Device Gratings
Chiang, Min-Xu;Tongpakpanang, Jaturon;Kuo, Wen-Kai
2021-04-23 00:00:00
hv photonics Communication Phase Measurement of Guided-Mode Resonance Device Using Digital Micromirror Device Gratings Min-Xu Chiang, Jaturon Tongpakpanang and Wen-Kai Kuo * Graduate Institute of Electro-Optical and Materials Science, National Formosa University, Yunlin 63208, Taiwan; MinXu.Chiang@auo.com (M.-X.C.); d0677104@gm.nfu.edu.tw (J.T.) * Correspondence: wkkuo@nfu.edu.tw Abstract: This paper reports on the measurement system of the phase difference between s- and p-polarization components of the light passing through a guided-mode resonance (GMR) device using a digital micromirror device (DMD) gratings as a digital phase-shifting device. The phase of the non-zeroth order diffraction beams of the grating pattern displayed on the DMD can exhibit a phase change when the grating pattern is shifted. Two nearest different diffraction orders of p-polarized and s-polarized beams can be used as the reference and measurement beams, respectively, and are combined to implement the phase-shifting interferometry (PSI). The phase difference between the s- and the p-polarization components of the incident light passing through the GMR device can be obtained by applying the four-step phase-shift algorithm to the DMD-based PSI system. Experimental results show that this measurement system has a phase detection limit of 1 and was able to obtain the abrupt phase difference curve of the GMR device versus the incident angle. Keywords: guided-mode resonance; digital micromirror; phase-shifting interferometry Citation: Chiang, M.-X.; 1. Introduction Tongpakpanang, J.; Kuo, W.-K. Phase A guided-mode resonance (GMR) device consists of a waveguide layer and grating Measurement of Guided-Mode structure, and incident light can be coupled to the waveguide layer by the grating high Resonance Device Using Digital diffraction orders. Because of the grating, the propagation wave inside the waveguide Micromirror Device Gratings. layer slowly leaks out of the waveguide guide, and when the incident light wavelength is Photonics 2021, 8, 136. https:// at the resonance wavelength, the leakage wave interferes with the non-diffraction wave doi.org/10.3390/photonics8050136 to produce nearly 0% transmittance and 100% reflectivity as a filter response [1]. This resonance angle is highly sensitive to the refractive index (RI) of material on the grating Received: 29 March 2021 surface; therefore, the GMR device can be used as a label-free biosensor [2]. Among the Accepted: 22 April 2021 GMR sensor interrogation methods, the phase-based interferometric approach has been Published: 23 April 2021 proved to have a better detection resolution [3,4]. In our previous works, heterodyne interferometry based on an electro-optic modulator was presented [5] and subsequently, Publisher’s Note: MDPI stays neutral phase-shift interferometry (PSI) based on two liquid-crystal (LC) retardation plates was with regard to jurisdictional claims in also proposed [6]. Our results showed that the phase-detection sensitivity of the RI change published maps and institutional affil- on the grating surface of the GMR device can be better than 5000 /RIU. Since the PSI is an iations. image-type detection, it can achieve parallel (multi-channel) sensing and has great potential for high-throughput screening. In this paper, we propose using a digital micromirror device (DMD) to replace the LC device in our previous work to implement the PSI system. The LC device in the PSI needs a calibration process to obtain an accurate analog driving voltage. Copyright: © 2021 by the authors. The DMD-based spatial light modulator (SLM) can display shifting grating patterns to Licensee MDPI, Basel, Switzerland. achieve four digital phase-shifting, 0, /2, , and 3/2, without the calibration process. A This article is an open access article PSI system implemented by an electrically addressed liquid-crystal-based SLM has been distributed under the terms and proposed [7]. Here, the DMD-SLM is proposed to substitute the LC-SLM because the DMD- conditions of the Creative Commons SLM has a better reflectivity and higher operation speed [8,9]. We propose to use the DMD- Attribution (CC BY) license (https:// SLM to facilitate digital phase-shifting in the PSI system using proper micro-mirror patterns creativecommons.org/licenses/by/ without the need for the accurate analog driving voltage in the LC device. We also propose 4.0/). Photonics 2021, 8, 136. https://doi.org/10.3390/photonics8050136 https://www.mdpi.com/journal/photonics Photonics 2021, 8, x FOR PEER REVIEW 2 of 10 use the DMD-SLM to facilitate digital phase-shifting in the PSI system using proper micro- Photonics 2021, 8, 136 2 of 10 mirror patterns without the need for the accurate analog driving voltage in the LC device. We also propose a method to use this DMD-SLM-based PSI system to perform the phase measurement of the GMR device. Besides, because of mature batch-type production tech- a method to use this DMD-SLM-based PSI system to perform the phase measurement of nologies, DMD chips have become cost-effective and more attractive for many applica- the GMR device. Besides, because of mature batch-type production technologies, DMD tions. The diffraction properties of the DMD-SLM are different from the LC-SLM. We will chips have become cost-effective and more attractive for many applications. The diffraction first investigate diffraction patterns of the DMD with different grating patterns and then properties of the DMD-SLM are different from the LC-SLM. We will first investigate describe how to utilize the DMD-SLM in the PSI system. Subsequently, fabrication and diffraction patterns of the DMD with different grating patterns and then describe how simulation of the GMR device will be briefly reviewed. Finally, we will demonstrate the to utilize the DMD-SLM in the PSI system. Subsequently, fabrication and simulation of measurement results of the phase difference between the s- and p-polarization of the GMR the GMR device will be briefly reviewed. Finally, we will demonstrate the measurement sensor using this DMD-based PSI system. results of the phase difference between the s- and p-polarization of the GMR sensor using this DMD-based PSI system. 2. DMD Grating and Its Diffraction Pattern A schematic of the setup for observation of the diffraction patterns of a DMD grating 2. DMD Grating and Its Diffraction Pattern is illustrated in Figure 1. A He-Ne laser with a wavelength of 632.8 nm was normally in- A schematic of the setup for observation of the diffraction patterns of a DMD grating cident to the DMD surface through a hole in a black-color paper plate that was 1 m away is illustrated in Figure 1. A He-Ne laser with a wavelength of 632.8 nm was normally from the DMD surface, and light spots of the reflective diffraction beams could be ob- incident to the DMD surface through a hole in a black-color paper plate that was 1 m served on the paper plate. Because the DMD was a two-dimensional (2D) grating pattern, away from the DMD surface, and light spots of the reflective diffraction beams could diffraction spots along the vertical and horizontal directions were expected to be ob- be observed on the paper plate. Because the DMD was a two-dimensional (2D) grating served. The schematic of all the DMD pixels in the static state (without applying voltage) pattern, diffraction spots along the vertical and horizontal directions were expected to be is as shown in Figure 2a, in which all micromirrors were parallel to the substrate. The observed. The schematic of all the DMD pixels in the static state (without applying voltage) pitch (period) of the 2D gratings is equal to the width of a pixel cell as indicated in Figure is as shown in Figure 2a, in which all micromirrors were parallel to the substrate. The pitch 2a [10]. Its diffraction spot image is shown in Figure 2b. Multiple order diffraction light (period) of the 2D gratings is equal to the width of a pixel cell as indicated in Figure 2a [10]. spots were observed, and the zeroth-order light reflected through the hole in the paper Its diffraction spot image is shown in Figure 2b. Multiple order diffraction light spots plate. The DMD 2D array pixels can be mathematically treated as a convolution of the were observed, and the zeroth-order light reflected through the hole in the paper plate. rectangle (“rect”) and the comb (“comb”) functions. Let the Fourier transforms of the “rect” The DMD 2D array pixels can be mathematically treated as a convolution of the rectangle and the “comb” functions be “Sinc” and “Comb” functions, respectively. Therefore, the (“rect”) and the comb (“comb”) functions. Let the Fourier transforms of the “rect” and the diffraction patterns of the DMD can be calculated as the multiplication of the “Sinc” and “comb” functions be “Sinc” and “Comb” functions, respectively. Therefore, the diffraction “Comb” functions [11]. In Figure 2b, the center (peak intensity) of the 2D “Sinc” envelope patterns of the DMD can be calculated as the multiplication of the “Sinc” and “Comb” function is the zero-other reflected spot position (hole), and the “Comb” spots near the functions [11]. In Figure 2b, the center (peak intensity) of the 2D “Sinc” envelope function hole have a higher intensity. The location of the “Sinc” envelope peak is dependent on is the zero-other reflected spot position (hole), and the “Comb” spots near the hole have a the incident angle and tilted angle of the micromirror [12]. According to the grating equa- higher intensity. The location of the “Sinc” envelope peak is dependent on the incident tion, spacing D between two nearest diffraction order spots is inversely proportional to angle and tilted angle of the micromirror [12]. According to the grating equation, spacing D the gratin between two g penear riod. est diffraction order spots is inversely proportional to the grating period. Figure 1. Schematic of setup for observation of the diffraction patterns of a DMD. Figure 1. Schematic of setup for observation of the diffraction patterns of a DMD. When proper voltages are applied, the micromirror can be tilted to +12 or 12 along When proper voltages are applied, the micromirror can be tilted to +12° or −12° along its diagonal, corresponding to the ON- or OFF-state, respectively. The schematic of all the its diagonal, corresponding to the ON- or OFF-state, respectively. The schematic of all the micromirrors in the ON-state is shown in Figure 2c. The grating structure becomes the micromirrors in the ON-state is shown in Figure 2c. The grating structure becomes the brazed-type, and its period is indicated as L ; its corresponding diffraction spot image is brazed-type, and its period is indicated as Λ1; its corresponding diffraction spot image is shown in Figure 2d. The tilted micromirrors cause the center peak of the “Sinc” envelope to shown in Figure 2d. The tilted micromirrors cause the center peak of the “Sinc” envelope shift from the hole to a new location along the 45 line. In this figure, the hole in the paper plate is labeled O as the reference point. When all the micromirrors are in the OFF-state, the schematic and its diffraction spot image are as shown in Figure 2e,f, respectively. The center peak of the “Sinc” envelope is shifted to the opposite side. Photonics 2021, 8, x FOR PEER REVIEW 3 of 10 to shift from the hole to a new location along the 45° line. In this figure, the hole in the Photonics 2021, 8, 136 paper plate is labeled O as the reference point. When all the micromirrors are in the OFF- 3 of 10 state, the schematic and its diffraction spot image are as shown in Figure 2e and 2f, re- spectively. The center peak of the “Sinc” envelope is shifted to the opposite side. (a) (b) (c) (d) (e) (f) Figure 2. (a) Schematic of all micromirror pixels in the static state, and (b) its diffraction spot im- Figure 2. (a) Schematic of all micromirror pixels in the static state, and (b) its diffraction spot image. age. (c) Schematic of all micromirror pixels in ON-state (tilted + 12°), and (d) its diffraction spot (c) Schematic of all micromirror pixels in ON-state (tilted + 12 ), and (d) its diffraction spot image. image. (e) Schematic of all micro-mirror pixels in OFF-state (tilted − 12°), and (f) its diffraction spot (e) Schematic of all micro-mirror pixels in OFF-state (tilted 12 ), and (f) its diffraction spot image. image. Next, two modulated DMD patterns were investigated. Figure 3a shows the schematic Next, two modulated DMD patterns were investigated. Figure 3a shows the sche- of a DMD pattern with a period of one line ON-state (white stripe) and one line OFF-state matic of a DMD pattern with a period of one line ON-state (white stripe) and one line (black stripe). In this configuration, the grating period indicated as L was two DMD pixel OFF-state (black stripe). In this configuration, the grating perio d indicat ed as Λ2 was two widths. Because of the two opposite-tilted angles (+12 and 12 ) of the micromirrors, two DMD pixel widths. Because of the two opposite-tilted angles (+12° and −12°) of the micro- symmetric diffraction spot images were observed on two sides of the center along the 45 mirrors, two symmetric diffraction spot images were observed on two sides of the center line, as shown in Figure 3b. Because the line grating period L was double that of L in 2 1 along the −45° line, as shown in Figure 3b. Because the line grating period Λ2 was double Figure 2c, the distance between the two nearest order diffraction spots along the horizontal that of Λ1 in Figure 2c, the distance between the two nearest order diffraction spots along direction became half of that in Figure 2c. Because there was no pattern modulation along the horizontal direction became half of that in Figure 2c. Because there was no pattern the other vertical direction, the distance between the two nearest diffractive spots along the modulation along the other vertical direction, the distance between the two nearest dif- vertical direction was the same as that in Figure 2c. To implement the digital four-phase fractive spots along the vertical direction was the same as that in Figure 2c. To implement shifting, a DMD pattern with a period of L having four-pixel width, including two ON- the digital four-phase shifting, a DMD pattern with a period of Λ3 having four-pixel width, state (white stripe) and two OFF-state (black stripe) line pixels, was required. Its schematic including two ON-state (white stripe) and two OFF-state (black stripe) line pixels, was and corresponding diffraction spot image are shown in Figure 3c,d, respectively. Because required. Its schematic and corresponding diffraction spot image are shown in Figure 3c the grating pitch L was twice L , the distance between two diffraction spots along the 3 2 and 3d, respectively. Because the grating pitch Λ3 was twice Λ2, the distance between two horizontal direction became only half of that in Figure 3b. The phase difference between diffraction spots along the horizontal direction became only half of that in Figure 3b. The the two nearest order diffraction lights could be changed by shifting this DMD line pattern phase difference between the two nearest order diffraction lights could be changed by to implement the phase shifting in a PSI system. The number of reflecting mirrors and their periods did not affect the performance of the PSI system. The mirror period will change the diffraction angle only. Photonics 2021, 8, x FOR PEER REVIEW 4 of 10 shifting this DMD line pattern to implement the phase shifting in a PSI system. The num- Photonics 2021, 8, 136 4 of 10 ber of reflecting mirrors and their periods did not affect the performance of the PSI system. The mirror period will change the diffraction angle only. (a) (b) (c) (d) Figure 3. (a) Schematic of the DMD pattern with a period of 1 ON-state and 1 OFF-state line pixel, Figure 3. (a) Schematic of the DMD pattern with a period of 1 ON-state and 1 OFF-state line pixel, and (b) its diffraction spot pattern. (c) Schematic of DMD grating pattern with a period of 2 ON- and (b) its diffraction spot pattern. (c) Schematic of DMD grating pattern with a period of 2 ON-state state and 2 OFF-state line pixels, and (d) its diffraction pattern. and 2 OFF-state line pixels, and (d) its diffraction pattern. 3. DMD-Based PSI System 3. DMD-Based PSI System Figure 4 shows the optical setup of the proposed DMD-based PSI system. Here, we Figure 4 shows the optical setup of the proposed DMD-based PSI system. Here, used a com we used mercia a commer lly avai cially lable DLP available Light DLP Cra LightCrafter fter display display 2000 ev 2000 aluatevaluation ion module module (DLPDLC (DLPDLCR R 2000EV2000EVM, M, Texas Instrument Texas Instr s)uments), , comprisicomprising ng a DLP 20a 00 DLP DMD chi 2000 p DMD with a res- chip with a resolution of 640 480. This is a development kit for micro-projectors and can be controlled olution of 640 × 480. This is a development kit for micro-projectors and can be controlled via a Beaglebone Black platform. In our system, a He–Ne laser was used as the light source, via a Beaglebone Black platform. In our system, a He–Ne laser was used as the light and two polarizers, P and P , were used to vary the incident light intensity. P was rotated source, and two polarizers, P0 and P1, were used to vary the incident light intensity. P1 was 0 1 1 45 to yield output light having both p- and s-polarized components. The output light rotated 45° to yield output light having both p- and s-polarized components. The output passed through a Wollaston prism (WP) and split into an s-polarized beam (red line) and light passed through a Wollaston prism (WP) and split into an s-polarized beam (red line) a p-polarized beam (green line) at a separation angle of 15 . The p-polarized beam was and a p-polarized beam (green line) at a separation angle of 15°. The p-polarized beam directly incident on the DMD chip, while the s-polarized beam passed two mirrors (M was directly incident on the DMD chip, while the s-polarized beam passed two mirrors 2 and M ) before being incident on the DMD chip. These two mirrors were used to adjust (M2 and M3) before be 3 ing incident on the DMD chip. These two mirrors were used to ad- the zeroth-order reflected beam (solid red line) of the s-polarized light to coincide with the just the zeroth-order reflected beam (solid red line) of the s-polarized light to coincide first-order reflected beam (dashed green line) of the p-polarized incident light. The angle with the first-order reflected beam (dashed green line) of the p-polarized incident light. difference q between these two incident beams was equal to the difference between the The angle difference θ between these two incident beams was equal to the difference be- zeroth- and the first-order reflected beams of the p-polarized light. The phase difference tween the zeroth- and the first-order reflected beams of the p-polarized light. The phase between these two coincided beams could be controlled by the four-line pattern displayed difference between these two coincided beams could be controlled by the four-line pattern on the DMD chip. This coincided beam was then passed through an aperture (AP) and displayed on the DMD chip. This coincided beam was then passed through an aperture analyzer (A) and became a measurement beam in the PSI system. After this beam passed (AP) and analyzer (A) and became a measurement beam in the PSI system. After this beam through the GMR device, the resulting interferograms were generated and captured by a passed through the GMR device, the resulting interferograms were generated and cap- web camera (WebCAM) (Phillips 900nc). A lens (L) was used to adjust the image size of tured by a web camera (WebCAM) (Phillips 900nc). A lens (L) was used to adjust the im- the interferograms. Diffraction spot patterns of these two reflected beams before and after age size of the interferograms. Diffraction spot patterns of these two reflected beams be- coinciding are shown in Figure 5a,b, respectively. The intensity difference between the s- fore and after coinciding are shown in Figure 5a and 5b, respectively. The intensity differ- and p-polarized beams could be adjusted by rotating the analyzer to have the best contrast ence between the s- and p-polarized beams could be adjusted by rotating the analyzer to of the interferogram. The final enlarged interferogram is shown in Figure 5c. have the best contrast of the interferogram. The final enlarged interferogram is shown in Figure 5c. Photonics 2021, 8, 136 5 of 10 Photonics 2021, 8, x FOR PEER REVIEW 5 of 10 Photonics 2021, 8, x FOR PEER REVIEW 5 of 10 Figure 4. The optical setup of the proposed digital PSI based on the DMD. Figure 4. The optical setup of the proposed digital PSI based on the DMD. Figure 4. The optical setup of the proposed digital PSI based on the DMD. (a) (b) (c) (a) (b) (c) Figure 5. Diffraction spot patterns of the s- and the p-polarized reflected beams (a) before and (b) after coinciding align- Figure 5. Diffraction spot patterns of the s- and the p-polarized reflected beams (a) before and (b) after coinciding align- Figure 5. Diffraction spot patterns of the s- and the p-polarized reflected beams (a) before and (b) after coinciding alignment. ment. (c) The final enlarged interferogram. ment. (c) The final enlarged interferogram. (c) The final enlarged interferogram. A set of four-step patterns displayed on the DMD-SLM is shown in Figure 6. The A set of A set of f four our- -step step pa patterns tterns di displayed splayed on the DMD- on the DMD-SLM SLM i is s shown shown i in n Figure Figure 6 6.. The The black- and white-stripe colors correspond to two lines of OFF- and ON-states, respec- black black- - an and d w white-stripe hite-stripe c colors olors corr correspond espond to to two two l lines inof es of OFF- OFF- and and ON-sta ON-states, rtes, respe espectively c-, tively, on the DMD chip as illustrated in Figure 3c. Each subsequent pattern had one pixel tively, on the DMD chip as illustrated in Figure 3c. Each subsequent pattern had one pixel on the DMD chip as illustrated in Figure 3c. Each subsequent pattern had one pixel shifting shifting to achieve a phase shift of π/2. Therefore, four digital phase shifts, 0, π/2, π, and shift to achieve ing to ac a phase hieve a phase shift of shift of /2. Ther π/2 efor . Therefore e, four digital , four d phase igital ph shifts, ase sh 0, ifts, 0, /2, π , and /2, π3 , and /2, 3π/2, could be achieved by sequentially displaying these four patterns on the DMD-SLM. 3 could π/2, cou be achieved ld be achiby eved by s sequentially equenti displaying ally displa these ying these four patterns four paon tterns on the DMD- the DMD-SLM. Befor SLM. e Before performing the GMR sensor measurements, system repeatability was investigated. performing the GMR sensor measurements, system repeatability was investigated. The Before performing the GMR sensor measurements, system repeatability was investigated. The GMR device was replaced by a null glass substrate and four interferograms corre- GMR device was replaced by a null glass substrate and four interferograms corresponding The GMR device was replaced by a null glass substrate and four interferograms corre- sponding to the four patterns of Figure 6 were obtained, as shown in Figure 7. Because to the four patterns of Figure 6 were obtained, as shown in Figure 7. Because the action of sponding to the four patterns of Figure 6 were obtained, as shown in Figure 7. Because the action of the micromirrors was flipped, not stationary, this could have a time-averag- the micromirrors was flipped, not stationary, this could have a time-averaging effect on the the action of the micromirrors was flipped, not stationary, this could have a time-averag- ing effect on the laser intensity and reduce the speckle in the interferogram. In each inter- laser intensity and reduce the speckle in the interferogram. In each interferogram image, a ing effect on the laser intensity and reduce the speckle in the interferogram. In each inter- ferogram image, a red square area (10 × 10 pixels) was selected, as indicated in the figure, red square area (10 10 pixels) was selected, as indicated in the figure, and their average ferogram image, a red square area (10 × 10 pixels) was selected, as indicated in the figure, and their average gray values were used to obtain the average intensity values used in the gray values were used to obtain the average intensity values used in the PSI system. The and their average gray values were used to obtain the average intensity values used in the PSI system. The phase difference between the s- and p-polarized lights could be calculated phase difference between the s- and p-polarized lights could be calculated with the 4-step PSI system. The phase difference between the s- and p-polarized lights could be calculated with the 4-step phase-shifting algorithm [13]. The same condition was repeatedly meas- phase-shifting algorithm [13]. The same condition was repeatedly measured 8 times, and with the 4-step phase-shifting algorithm [13]. The same condition was repeatedly meas- hence, ured 8 times, eight phase and henc values e, eight phase were calcul values ated; the were c results alcul ar ate ed; t shown he re in sult Figur s are e sho 8. The wn in upper Fig- ured 8 times, and hence, eight phase values were calculated; the results are shown in Fig- ure 8. The upper curve (black) represents the 32 average intensity gray values of the eight ure 8. The upper curve (black) represents the 32 average intensity gray values of the eight Photonics 2021, 8, 136 6 of 10 Photonics 2021, 8, x FOR PEER REVIEW 6 of 10 Photonics 2021, 8, x FOR PEER REVIEW 6 of 10 Photonics 2021, 8, x FOR PEER REVIEW 6 of 10 curve (black) represents the 32 average intensity gray values of the eight sets, whereas the sets, whereas the red curve (red) represents the calculated phase values. The variation of sets, whereas the red curve (red) represents the calculated phase values. The variation of sets, whereas the red curve (red) represents the calculated phase values. The variation of red curve (red) represents the calculated phase values. The variation of the phase values the phase values was within 1° and hence, the system detection limit could be estimated the phase values was w ithin 1° and hence, the system detection limit could be esti mated the phase v was within alues was w 1 and hence, ithin the 1° and h system enc detection e, the system detecti limit couldobe n limi estimated t could be to be esti 1ma . te This d to be 1°. This detection limit may be further improved by enhancing the stiffness of the to be 1°. This detection limit may be further improved by enhancing the stiffness of the todetection be 1°. Thlimit is det may ection be li further mit may impr be oved further by improved by enh enhancing the stifa fness ncing t of h the e st PSI iffnsystem. ess of the PSI system. PSI system. PSI system. Step 4 Step 4 Step 4 Step 3 Step 3 Step 3 Step 2 Step 2 Step 2 Step 1 Step 1 Step 1 Figure 6. Four-step patterns displayed on the DMD-SLM. Each subsequent step pattern with one Figure 6. Four-step patterns displayed on the DMD-SLM. Each subsequent step pattern with one Figure 6. Four-step patterns displayed on the DMD-SLM. Each subsequent step pattern with one Figure 6. Four-step patterns displayed on the DMD-SLM. Each subsequent step pattern with one pixel shifting corresponding to a phase shift of π/2 in the first order diffraction beam. pixel shifting corresponding to a phase shift of /2 in the first order diffraction beam. pixel shifting corresponding to a phase shift of π/2 in the first order diffraction beam. pixel shifting corresponding to a phase shift of π/2 in the first order diffraction beam. Figure 7. Four-step interferograms (1~4) of the null glass substrate corresponding to the four-step Figure 7. Four-step interferograms (1~4) of the null glass substrate corresponding to the four-step Figure 7. Figure 7. Four-step interferog Four-step interferograms rams (1~4) of (1~4) t of he null gl the nullass glass substrate corresponding to the substrate corresponding to the four-step four-step patterns in Figure 6. A selected square area (10 × 10 pixels, in a red-color line) for calculating PSI in patterns in Figure 6. A selected square area (10 × 10 pixels, in a red-color line) for calculating PSI in patterns in Figure 6. A selected square area (10 × 10 pixels, in a red-color line) for calculating PSI in patterns in Figure 6. A selected square area (10 10 pixels, in a red-color line) for calculating PSI in the same position for each interferogram. the same position for each interferogram. the same position for each interferogram. the same position for each interferogram. Figure 8. Stability test results for the experimental setup. Figure 8. Stability test results for the experimental setup. Figure 8. Stability test results for the experimental setup. Figure 8. Stability test results for the experimental setup. 4. GMR Device Measurement Results 4. GMR Device Measurement Results 4. GMR Device Measurement Results 4. GMR Device Measurement Results Finally, the setup was used to measure the phase difference between the s- and p- Finally, the setup was used to measure the phase difference between the s- and p- Finally, the setup was used to measure the phase difference between the s- and p- Finally, the setup was used to measure the phase difference between the s- and p- polarized light beams passing through the GMR device. Under the resonance condition, polarized light beams passing through the GMR device. Under the resonance condition, polarized light beams passing through the GMR device. Under the resonance condition, polarized light beams passing through the GMR device. Under the resonance condition, the angular transmission phase of the GMR device had a large phase change known as the angular transmission phase of the GMR device had a large phase change known as the angular transmission phase of the GMR device had a large phase change known as the angular transmission phase of the GMR device had a large phase change known as Goos-Hänchen (GH) shift [14,15]. The resonance angles of the GMR device for the s- and Goos-Hänchen (GH) shift [14,15]. The resonance angles of the GMR device for the s- and Goos-Hänchen (GH) shift [14,15]. The resonance angles of the GMR device for the s- and Photonics 2021, 8, 136 7 of 10 Photonics 2021, 8, x FOR PEER REVIEW 7 of 10 Photonics 2021, 8, x FOR PEER REVIEW 7 of 10 Goos-Hänchen (GH) shift [14,15]. The resonance angles of the GMR device for the s- and p-polarized light beams were different, and the proposed DMD-based PSI system was able p-polarized light beams were different, and the proposed DMD-based PSI system was able to measure the phase difference between the resonance angle and non-resonance angle. The p-polarized light beams were different, and the proposed DMD-based PSI system was able to measure the phase difference between the resonance angle and non-resonance angle. schematic of the tested GMR device is shown in Figure 9a; the device is similar to the one to measure the phase difference between the resonance angle and non-resonance angle. The schematic of the tested GMR device is shown in Figure 9a; the device is similar to the in our previous report [6]. The device was fabricated on a glass substrate and comprised a The schematic of the tested GMR device is shown in Figure 9a; the device is similar to the one in our previous report [6]. The device was fabricated on a glass substrate and com- TiO thin-film layer with a thickness d of 325 nm, a SiO grating layer with a period L of 2 2 one in our previous report [6]. The device was fabricated on a glass substrate and com- prised a TiO2 thin-film layer with a thickness d of 325 nm, a SiO2 grating layer with a 555 nm, and modulation depth h of 65 nm. The grating structure was fabricated by using prised a TiO2 thin-film layer with a thickness d of 325 nm, a SiO2 grating layer with a period Λ of 555 nm, and modulation depth h of 65 nm. The grating structure was fabri- the nanoimprinting sol-gel method. A photograph of the completed GMR sensor is shown period Λ of 555 nm, and modulation depth h of 65 nm. The grating structure was fabri- cated by using the nanoimprinting sol-gel method. A photograph of the completed GMR in Figure 9b. cated by using the nanoimprinting sol-gel method. A photograph of the completed GMR sensor is shown in Figure 9b. sensor is shown in Figure 9b. Air (n =1.0) Air Λ h Air (n =1.0) Air TiO (n =2.298) 2 ti TiO (n =2.298) 2 ti SiO (n =1.5) 2 s SiO (n =1.5) 2 s Glass substrate (n =1.515) Glass substrate (n =1.515) (a) ( b) (a) (b) Figure 9. (a) Schematic and (b) photo of the GMR sensor. Figure 9. (a) Schematic and (b) photo of the GMR sensor. Figure 9. (a) Schematic and (b) photo of the GMR sensor. The GMR device was simulated using commercially available finite-difference time- The GMR device was simulated using commercially available finite-difference time- The GMR device was simulated using commercially available finite-difference time- domain (FDTD) software. The GMR device was investigated with the condition that the domain (FDTD) software. The GMR device was investigated with the condition that the domain (FDTD) software. The GMR device was investigated with the condition that the p-polarized component of the incident light satisfy the phase-matching condition. The in- p-polarized component of the incident light satisfy the phase-matching condition. The p-polarized component of the incident light satisfy the phase-matching condition. The in- cident light entered at the substrate of the GMR device and the sensor surface was air (n incident light entered at the substrate of the GMR device and the sensor surface was air cident light entered at the substrate of the GMR device and the sensor surface was air (n = 1.0). In simulation, complex refractive n = 2.298 and extinction coefficient k = 0.005 of the (n = 1.0). In simulation, complex refractive n = 2.298 and extinction coefficient k = 0.005 = 1.0). In simulation, complex refractive n = 2.298 and extinction coefficient k = 0.005 of the TiO2 thin-film layer were used. The extinction coefficient was used to model the loss due of the TiO thin-film layer were used. The extinction coefficient was used to model the TiO2 thin-film layer were used. The extinction coefficient was used to model the loss due to all non-ideal effects. The simulation results for the transmissivity versus the scanning loss due to all non-ideal effects. The simulation results for the transmissivity versus the to all non-ideal effects. The simulation results for the transmissivity versus the scanning incident angle are shown in Figure 10a. The resonance p-polarization and the non-reso- scanning incident angle are shown in Figure 10a. The resonance p-polarization and the incident angle are shown in Figure 10a. The resonance p-polarization and the non-reso- nance s-polarization are indicated as the red and black lines, respectively, and the reso- non-resonance s-polarization are indicated as the red and black lines, respectively, and the nance s-polarization are indicated as the red and black lines, respectively, and the reso- nance angle of p-polarization is 18.8°. The transmission phases of the GMR device are resonance angle of p-polarization is 18.8 . The transmission phases of the GMR device are nance angle of p-polarization is 18.8°. The transmission phases of the GMR device are shown in Figure 10b. The resonance transmission phase (p-polarization, red) had an ab- shown in Figure 10b. The resonance transmission phase (p-polarization, red) had an abrupt shown in Figure 10b. The resonance transmission phase (p-polarization, red) had an ab- rupt change near the resonance angle, while the non-resonance phase (s-polarization, change near the resonance angle, while the non-resonance phase (s-polarization, black) had rupt change near the resonance angle, while the non-resonance phase (s-polarization, black) had a smooth change due to the incident angle change. The phase difference be- a smooth change due to the incident angle change. The phase difference between the p- black) had a smooth change due to the incident angle change. The phase difference be- tween the p- and the s-polarization component is also shown in Figure 10b. This phase and the s-polarization component is also shown in Figure 10b. This phase difference can be tween the p- and the s-polarization component is also shown in Figure 10b. This phase difference can be measured by the proposed DMD-based PSI system. measured by the proposed DMD-based PSI system. difference can be measured by the proposed DMD-based PSI system. (a) (b) (a) (b) Figure 10. Simulation results for the (a) transmittance, (b) phase curves, and phase difference be- Figure 10. Simulation results for the (a) transmittance, (b) phase curves, and phase difference be- tween, the polarization components of the incident light. Figure 10. Simulation results for the (a) transmittance, (b) phase curves, and phase difference tween, the polarization components of the incident light. between, the polarization components of the incident light. Photonics 2021, 8, 136 8 of 10 Photonics 2021, 8, x FOR PEER REVIEW 8 of 10 For the measurements, the GMR device was mounted on a rotation stage as indicated For the measurements, the GMR device was mounted on a rotation stage as indicated in Figure 4, and the incident angle was varied from 16 to 18.5 with an interval of 0.05 in Figure 4, and the incident angle was varied from 16° to 18.5° with an interval of 0.05° by rotating the stage. Five selected sets of four-step interferograms (I ~I ) (in a red-color by rotating the stage. Five selected sets of four-step interferograms (I 11~I4 4) (in a red-color rectangle line) corresponding to four incident angles, 17 , 17.25 , 17.5 , 17.75 , and 18 , rectangle line) corresponding to four incident angles, 17°, 17.25°, 17.5°, 17.75°, and 18°, are are shown in Figure 11, and each set of the four-step interferograms was used to calculate shown in Figure 11, and each set of the four-step interferograms was used to calculate phase values by applying the 4-step phase-shifting algorithm to the selected square area, phase values by applying the 4-step phase-shifting algorithm to the selected square area, as shown in Figure 7. The five sets of interferograms were selected to demonstrate the as shown in Figure 7. The five sets of interferograms were selected to demonstrate the variation of the grayscale values due to the resonance angle. The average intensities of variation of the grayscale values due to the resonance angle. The average intensities of the the interferograms decreased from 17 to 17.25 as the incident angle was approaching the interferograms decreased from 17° to 17.25° as the incident angle was approaching the resonance angle, reached the minimum at the resonance angle of 17.5 , and then increased resonance angle, reached the minimum at the resonance angle of 17.5°, and then increased from 17.75 to 18 as the incident angle was leaving the resonance angle. from 17.75° to 18° as the incident angle was leaving the resonance angle. Figure 11. Five selected sets of 4-step interferograms (I1~I4) (in a red-color rectangle line) corre- Figure 11. Five selected sets of 4-step interferograms (I ~I ) (in a red-color rectangle line) correspond- 1 4 sponding to 5 incident angles, 17°, 17.25°, 17.5°, 17.75°, and 18°. Average intensities of the interfer- ing to 5 incident angles, 17 , 17.25 , 17.5 , 17.75 , and 18 . Average intensities of the interferograms ograms decreased from 17° to 17.25°, reached a minimum at the resonance angle of 17.5°, and then decreased from 17 to 17.25 , reached a minimum at the resonance angle of 17.5 , and then increased increased from 17.75° to 18°. from 17.75 to 18 . The calculated 50 phase values (red) and 200 (50 × 4) intensities (gray) of the selected The calculated 50 phase values (red) and 200 (50 4) intensities (gray) of the se- areas in all interferograms versus the incident angle are shown in Figure 12. The obtained lected areas in all interferograms versus the incident angle are shown in Figure 12. The phase curve corresponded to the phase difference between s- and p-polarization compo- obtained phase curve corresponded to the phase difference between s- and p-polarization nents and agreed with the simulation in Figure 10b. The black line is the average trans- components and agreed with the simulation in Figure 10b. The black line is the average mitted intensity and corresponds to the transmissivity in Figure 10a. The resonance angle transmitted intensity and corresponds to the transmissivity in Figure 10a. The resonance can be found as 17.5°, and the phase curve exhibited an abrupt change near the resonance angle can be found as 17.5 , and the phase curve exhibited an abrupt change near the angle. The simulation results have a larger resonance angle and phase dynamic range than resonance angle. The simulation results have a larger resonance angle and phase dynamic the measured values; these discrepancies may be due to the parameters of the fabricated range than the measured values; these discrepancies may be due to the parameters of the GMR device, which were not the same as those used in the simulation model. In Table 1, fabricated GMR device, which were not the same as those used in the simulation model. In this system is compared with other phase measurement studies of the GMR device. Table 1, this system is compared with other phase measurement studies of the GMR device. Table 1. Comparison of some studies on phase measurement of the GMR device. Features This Work Ref. [3] Ref. [4] Ref. [5] Ref. [6] Cost Low High Fair High Fair Multi-Channel Yes Yes Yes No Yes Digital-PSI Yes No No No No Noise 1 0.3 0.3 0.1 10 Photonics 2021, 8, 136 9 of 10 Photonics 2021, 8, x FOR PEER REVIEW 9 of 10 Figure 12. The total calculated phase values and successive intensities in the selected area of the Figure 12. The total calculated phase values and successive intensities in the selected area of the recorded interferograms versus the incident angle. recorded interferograms versus the incident angle. Table 1. Comparison of some studies on phase measurement of the GMR device. 5. Conclusions A PSI system using the DMD-SLM as a phase shifter was developed and applied to Features This Work Ref. [3] Ref. [4] Ref. [5] Ref. [6] measure the phase difference of a GMR device. The DMD grating pattern can be designed Cost Low High Fair High Fair and used to digitally shift the phase of a first-order diffraction beam by one pixel width in Multi-Channel Yes Yes Yes No Yes the displayed grating pattern without calibrating the driving voltage as needed in an LC Digital-PSI Yes No No No No phase retarder. The experimental setup could achieve phase difference measurements with Noise 1° 0.3° 0.3° 0.1° 10° a repeatability of 1 , and this value may be further improved by elevating the stability of the optical system. The proposed system successfully yielded the transmitted abrupt phase 5. Conclusions curve of the GMR device and could be applied to several phase difference measurements. A PSI system using the DMD-SLM as a phase shifter was developed and applied to Author Contributions: Conceptualization, W.-K.K.; methodology, M.-X.C.; writing—original draft measure the phase difference of a GMR device. The DMD grating pattern can be designed preparation, J.T.; writing—review and editing, W.-K.K.; visualization, J.T.; supervision, W.-K.K.; and used to digitally shift the phase of a first-order diffraction beam by one pixel width project administration, W.-K.K.; funding acquisition, W.-K.K. All authors have read and agreed to the in the displayed grating pattern without calibrating the driving voltage as needed in an published version of the manuscript. LC phase retarder. The experimental setup could achieve phase difference measurements wit Funding: h a repe This atabil resear ity o chf was 1°, a funded nd this by va the lue Ministry may be of fScience urther improved and Technology by elev , Taiwan, ating grant the st number abil- 107-2221-E-150-023, 108-2221-E-150-026, and 109-2221-E-150-07. ity of the optical system. The proposed system successfully yielded the transmitted abrupt phase curve of the GMR device and could be applied to several phase difference meas- Institutional Review Board Statement: Not applicable. urements. Informed Consent Statement: Not applicable. Author Contributions: Conceptualization, W.-K.K.; methodology, M.-X.C.; writing—original draft Data Availability Statement: Not applicable. preparation, J.T.; writing—review and editing, W.-K.K.; visualization, J.T.; supervision, W.-K.K.; Acknowledgments: The authors thank Everwide Chemical Co., Ltd. of Taiwan for the free UV-cured project administration, W.-K.K.; funding acquisition, W.-K.K. All authors have read and agreed to glue that was used to fabricate GMR devices. the published version of the manuscript. Conflicts of Interest: The authors declare no conflict of interest. Funding: This research was funded by the Ministry of Science and Technology, Taiwan, grant num- ber 107-2221-E-150-023, 108-2221-E-150-026, and 109-2221-E-150-07. References Institutional Review Board Statement: Not applicable. 1. Wang, S.S.; Magnusson, R. Theory and applications of guided-mode resonance filter. Appl. Opt. 1993, 32, 2606–2613. [CrossRef] [PubMed] Informed Consent Statement: Not applicable. 2. Kim, W.J.; Kim, B.K.; Kim, A.; Huh, C.; Ah, C.S.; Kim, K.H.; Hong, J.; Park, S.H.; Song, S.; Song, J.; et al. Response to cardiac Data Availability Statement: Not applicable. markers in human serum analyzed by guided-mode resonance biosensor. Anal. Chem. 2010, 82, 9686–9693. [CrossRef] [PubMed] 3. Sahoo, P.K.; Sarkar, S.; Joseph, J. High sensitivity guided-mode-resonance optical sensor employing phase detection. Sci. Rep. Acknowledgments: The authors thank Everwide Chemical Co., Ltd. of Taiwan for the free UV- 2017, 7, 7607. [CrossRef] [PubMed] cured glue that was used to fabricate GMR devices. 4. Barth, I.; Conteduca, D.; Reardon, C.; Krauss, T.F. Common-path interferometric label-free protein sensing with resonant dielectric Conflicts of Interest: The authors declare no conflict of interest nanostructures. Light Sci. Appl. 2020, 9, 96. [CrossRef] [PubMed] 5. Kuo, W.K.; Huang, N.C.; Weng, H.P.; Yu, H.H. Tunable phase detection sensitivity of transmitted-type guided-mode resonance References sensor in a heterodyne interferometer. Opt. Express. 2014, 22, 22968–22973. [CrossRef] 6. Kuo, W.K.; Syu, S.H.; Lin, P.Z.; Yu, H.H. Tunable sensitivity phase detection of transmitted-type dual-channel guided-mode 1. Wang, S.S.; Magnusson, R. Theory and applications of guided-mode resonance filter. Appl. Opt. 1993, 32, 2606–2613. resonance sensor based on phase-shift interferometry. Appl. Opt. 2016, 55, 903–907. [CrossRef] [PubMed] 2. 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