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Uncertainty in the Phase Flicker Measurement for the Liquid Crystal on Silicon Devices

Uncertainty in the Phase Flicker Measurement for the Liquid Crystal on Silicon Devices hv photonics Article Uncertainty in the Phase Flicker Measurement for the Liquid Crystal on Silicon Devices 1 2 1 1 , Zhiyuan Yang , Shiyu Wu , Jiewen Nie and Haining Yang * School of Electronic Science and Engineering, Southeast University, Nanjing 210096, China; zhiyuan_yang@seu.edu.cn (Z.Y.); 220201566@seu.edu.cn (J.N.) School of Information Science and Engineering, Southeast University, Nanjing 210096, China; 213181969@seu.edu.cn * Correspondence: h.yang@seu.edu.cn Abstract: Phase flicker has become an important performance parameter for the liquid crystal on silicon (LCOS) devices. Since the phase response of the LCOS device cannot be measured directly, it is usually derived from the intensity response of the modulated light beam when the LCOS device was placed between a pair of crossed polarisers. However, the relationship between the intensity of the beam and the phase response of the LCOS device is periodic. This would lead to uncertainty in the phase flicker measurement. This paper analyses this measurement uncertainty through both simulation and experiments. It also proposed a strategy to minimise the uncertainty. Keywords: liquid crystal on silicon (LCOS) device; phase flicker 1. Introduction Phase-only liquid crystal on silicon (LCOS) devices [1–4] are a versatile and efficient tool to modulate the light field. This technology has a wide range of applications including Citation: Yang, Z.; Wu, S.; Nie, J.; information display [5,6], optical switches [7,8], optical tweezers [9,10], laser pulse shaping Yang, H. Uncertainty in the Phase systems [11], etc. Flicker Measurement for the Liquid Key performance parameters for the LCOS devices include resolutions, pixel sizes, Crystal on Silicon Devices. Photonics reflectivity, diffraction efficiency, etc. Recently, phase flicker, i.e., temporal fluctuation of 2021, 8, 307. https://doi.org/ phase response, has also become a critical parameter. It has been demonstrated that the 10.3390/photonics8080307 reduction of the phase flicker in the LCOS devices was able to improve the image quality in the holographic display systems [12,13]. The crosstalk in the optical switches based on Received: 31 May 2021 the LCOS technology can also be suppressed by using LCOS devices with lower phase Accepted: 28 July 2021 flicker [14]. Published: 1 August 2021 A variety of techniques have been proposed for the phase flicker minimisation. In- creasing the field inversion frequency [15,16] of the driving waveforms minimises the Publisher’s Note: MDPI stays neutral impact of the residual DC unbalance and therefore proves to be an effective way to sup- with regard to jurisdictional claims in press the phase flicker. LCOS devices with slower responses are also associated with published maps and institutional affil- low phase flicker. This can be achieved by reducing the operation temperature of the iations. device, using liquid crystal material with higher viscosity [17,18], or increasing the liquid crystal cell gap [19]. However, it might not be desirable to sacrifice the response speed of the LCOS device for some applications. In the digital LCOS devices, where pulse width modulation (PWM) scheme is used to drive the LC material, the optimisation of the pulse Copyright: © 2021 by the authors. sequences [20,21] is also an effective way to reduce the flicker. This makes the digital LCOS Licensee MDPI, Basel, Switzerland. devices suitable for the phase-only applications. This article is an open access article The phase flicker in the LCOS devices can be measured by polarimetric systems [22,23], distributed under the terms and diffractive systems [24] or interferometric systems [25]. Polarimetric and diffractive setups conditions of the Creative Commons uses photodiode as the detector instead of the CCD or CMOS camera used in the interfero- Attribution (CC BY) license (https:// metric systems. Therefore, polarimetric and diffractive systems are easier to setup and able creativecommons.org/licenses/by/ to deliver more accurate characterisation. As the phase of the light cannot be measured 4.0/). Photonics 2021, 8, 307. https://doi.org/10.3390/photonics8080307 https://www.mdpi.com/journal/photonics Photonics 2021, 8, x FOR PEER REVIEW 2 of 10 Photonics 2021, 8, 307 2 of 10 setup and able to deliver more accurate characterisation. As the phase of the light cannot be measured directly, the temporal phase response of the LCOS devices is derived from the temporal intensity of the modulated light beam in both setups. As the phase flicker in the LCOS dev directly, the temporal ices contin phase ues to decre response ase, the no of the LCOS ise within the cha devices is derived racterisa fr ti om on systems ma the temporal y start to influence the level of phase flicker derived. intensity of the modulated light beam in both setups. As the phase flicker in the LCOS devices In this pa continues per, we a to decr naease, lyse th the e uncertaint noise within y in the phase flicker the characterisation measurement. The systems may start im to - pact influence of the laser sourc the level of phase e instflicker ability and derived. the noises of the photo detector were evaluated In this paper, we analyse the uncertainty in the phase flicker measurement. The through simulation and experiments. Subsequently, we proposed a strategy to reduce the impact of the laser source instability and the noises of the photo detector were evaluated measurement uncertainty. through simulation and experiments. Subsequently, we proposed a strategy to reduce the 2. Pha measur seement Flicker Ch uncertainty aracter .isation System In this work, we used a polarimetric system to characterise the phase response and 2. Phase Flicker Characterisation System flicker of the LCOS device. Figure 1 shows the general architecture of this polarimetric In this work, we used a polarimetric system to characterise the phase response and system. A collimated laser source at 1550 nm was fed into this characterisation system. flicker of the LCOS device. Figure 1 shows the general architecture of this polarimetric The LCOS device was placed between a pair of linear polarisers. The directions of these system. A collimated laser source at 1550 nm was fed into this characterisation system. The two linear polarisers were orthogonal to each other. The polarisation direction of the LCOS device was placed between a pair of linear polarisers. The directions of these two LCOS device was aligned 45° with respect to these polarisers. In this setup, the intensity linear polarisers were orthogonal to each other. The polarisation direction of the LCOS of optical beam at the detector plane can be modulated by the phase depth of the LCOS device was aligned 45 with respect to these polarisers. In this setup, the intensity of optical device. In order to characterise the phase flicker, a high-speed amplified photodiode cir- beam at the detector plane can be modulated by the phase depth of the LCOS device. In cuit was used. order to characterise the phase flicker, a high-speed amplified photodiode circuit was used. Figure 1. Experimental setup based on the crossed polarisers. Figure 1. Experimental setup based on the crossed polarisers. The relationship between the light intensity (I) at the detector plane and the phase The relationship between the light intensity (I) at the detector plane and the phase depth (q) of the LCOS device can be described by: depth (𝜃 ) of the LCOS device can be described by: I = I sin + j (1) (1) 𝐼 𝐼 𝜑 where I0 is the maximum power detected by the photodiode circuit, 𝜑 is a constant that where I is the maximum power detected by the photodiode circuit, j is a constant that is is related to liquid crystal cell gap of the LCOS device. related to liquid crystal cell gap of the LCOS device. One of the key advantages of this polarimetric system is that the LCOS device dis- One of the key advantages of this polarimetric system is that the LCOS device displays play uniform s unifor phase m phase patt patterns during erns dur theing t characterisation. he characterisa This tion. Thi avoids s the avoi impact ds the i of m the pact of fringing the ffield ringing fi effectel[d ef 26].fect [2 However 6]. Howe , the value ver, the of the value of the c constant j o isnstant unknown. 𝜑 is unknown. This could This coul complicate d complicat the phaseer t esponse he phasand e respo flicker nse calculation. and flicker c It alc should ulation. be It noted shouthat ld be n theodif ted t fractive hat thcharacter e diffrac-- isation system is able to eliminate this issue although it would also introduce the fringing tive characterisation system is able to eliminate this issue although it would also introduce field effect. However, the mechanism of the measurement uncertainty is similar in both configurations. Therefore, the analysis will be based on the polarimetric system. 𝑠𝑖𝑛 Photonics 2021, 8, x FOR PEER REVIEW 3 of 10 the fringing field effect. However, the mechanism of the measurement uncertainty is sim- Photonics 2021, 8, 307 3 of 10 ilar in both configurations. Therefore, the analysis will be based on the polarimetric sys- tem. 3. Origin of the Measurement Uncertainty 3. Origin of the Measurement Uncertainty The following analysis will illustrate how the noise within the characterisation sys- The following analysis will illustrate how the noise within the characterisation sys- tem could affect the calculated phase flicker level. The primary sources of noise within the tem could affect the calculated phase flicker level. The primary sources of noise within characterisation system are the laser instability and the white noise of the amplified pho- the characterisation system are the laser instability and the white noise of the amplified todiode circuit. This paper will not differentiate these two types of noises since both of photodiode circuit. This paper will not differentiate these two types of noises since both of them ultimately lead to fluctuation of the detected light intensity over the time even in the them ultimately lead to fluctuation of the detected light intensity over the time even in the absence of the phase flicker in the LCOS device. Therefore, this paper will only focus on absence of the phase flicker in the LCOS device. Therefore, this paper will only focus on how such fluctuation would affect the phase flicker derivation. how such fluctuation would affect the phase flicker derivation. First, we assumed that the characterisation system is without any noise and the LCOS First, we assumed that the characterisation system is without any noise and the LCOS device had a peak-to-peak flicker of 0.06 π for all the phase levels. The light intensity at device had a peak-to-peak flicker of 0.06  for all the phase levels. The light intensity at the photodiode detector was simulated. Figure 2 showed the maximum, minimum and the photodiode detector was simulated. Figure 2 showed the maximum, minimum and average intensity measured by the photodiode circuit at each grey level. In this simulation, average intensity measured by the photodiode circuit at each grey level. In this simulation, the value of 𝜑 was set arbitrarily at 0.16π. In practice, the value of 𝜑 depends on the the value of j was set arbitrarily at 0.16. In practice, the value of j depends on the liquid li crystal quid cry cell stthickness al cell thic of kness the LCOS of the LCOS device an device and the bird t efringence he birefrof ingenc the liquid e of th crystal e liquid material. crystal material. This would not affect the analysis and the conclusion described in the below. This would not affect the analysis and the conclusion described in the below. Figure 2. The simulated power response when there is no noise in the characterisation system. Figure 2. The simulated power response when there is no noise in the characterisation system. Subsequently, the phase flicker at each grey level was calculated based on the Equation (1). Subsequently, the phase flicker at each grey level was calculated based on the Equa- The results were presented in Figure 3. For majority of the grey levels, the calculated phase tion 1. The results were presented in Figure 3. For majority of the grey levels, the calcu- flicker was consistent with the assumed value of 0.06 . However, the calculated flicker lated phase flicker was consistent with the assumed value of 0.06 π. However, the calcu- was smaller than it should be around the grey level of 70 and 172. These regions also lated flicker was smaller than it should be around the grey level of 70 and 172. These re- correspond to turning points of the intensity response shown in Figure 2. In those regions, gions also correspond to turning points of the intensity response shown in Figure 2. In the relationship between the phase level and detected light intensity was not monotonic. those regions, the relationship between the phase level and detected light intensity was This would bring certain degree of uncertainty in the calculation. not monotonic. This would bring certain degree of uncertainty in the calculation. In the following simulation, the impact of the characterisation system noise was considered. First, the noise was assumed to be only 0.5% of the maximum power level detected. Figure 4 shows the maximum and minimum intensity detected at each grey level, which looked very similar to the results shown in Figure 2. The calculated phase flicker is shown in Figure 5 for all the phase levels. The level of the flicker was elevated for all the phase levels. This is expected due to the contribution of the characterisation system noise. However, the calculated phase flickers were raised to ~0.9  for the regions corresponding to the turning points in Figure 4. An extremely low level of noise within the characterisation system led to a ~50% measurement error in this case. Photonics 2021, 8, x FOR PEER REVIEW 4 of 10 Photonics 2021, 8, 307 4 of 10 Photonics 2021, 8, x FOR PEER REVIEW 4 of 10 Figure 3. Calculated phase flicker at each grey level when there is no noise in the characterisation system. In the following simulation, the impact of the characterisation system noise was con- sidered. First, the noise was assumed to be only 0.5% of the maximum power level de- tected. Figure 4 shows the maximum and minimum intensity detected at each grey level, which looked very similar to the results shown in Figure 2. The calculated phase flicker is shown in Figure 5 for all the phase levels. The level of the flicker was elevated for all the phase levels. This is expected due to the contribution of the characterisation system noise. However, the calculated phase flickers were raised to ~0.9 π for the regions corresponding to the turning points in Figure 4. An extremely low level of noise within the characterisa- tion system led to a ~50% measurement error in this case. Figure 3. Calculated phase flicker at each grey level when there is no noise in the characterisation Figure 3. Calculated phase flicker at each grey level when there is no noise in the characterisation system. system. In the following simulation, the impact of the characterisation system noise was con- sidered. First, the noise was assumed to be only 0.5% of the maximum power level de- tected. Figure 4 shows the maximum and minimum intensity detected at each grey level, which looked very similar to the results shown in Figure 2. The calculated phase flicker is shown in Figure 5 for all the phase levels. The level of the flicker was elevated for all the phase levels. This is expected due to the contribution of the characterisation system noise. However, the calculated phase flickers were raised to ~0.9 π for the regions corresponding to the turning points in Figure 4. An extremely low level of noise within the characterisa- tion system led to a ~50% measurement error in this case. Figure 4. The simulated power response when there is noise in the characterisation system. Figure 4. The simulated power response when there is noise in the characterisation system. In order to further analyse the impact of characterisation system noise, we repeated the simulation process described in the above with different configurations. In these simulations, the actual phase flicker of the LCOS device ranged from 0.02 to 0.1 . The noise of the characterisation systems ranged from 0% to 3% of the maximum intensity detected by the photodiode circuit. The calculated worst-case phase flicker under each configuration was shown in Table 1. It can be seen that the noise within the characterisation system was able to elevate the calculated phase flicker significantly. In some extreme cases, the calculated phase flicker was ~7 times higher than the actual phase flicker. The largest calculation errors occurred at the phase levels close to the turning points of the detected intensity curves. These results indicated that an accurate characterisation on the phase Figure 4. The simulated power response when there is noise in the characterisation system. flicker required a detector with extremely low level of temporal noise. On the other hand, the detector should also be fast enough to capture the flicker of the LCOS device. Therefore, a balance between the response speed and the noise level should be achieved. Photonics 2021, 8, 307 5 of 10 Photonics 2021, 8, x FOR PEER REVIEW 5 of 10 Figure 5. Calculated phase flicker at each phase level when there is noise in the characterisation Figure 5. Calculated phase flicker at each phase level when there is noise in the characterisation system. system. Table 1. The calculated worst-case phase flicker under different simulation conditions (unit: ). In order to further analyse the impact of characterisation system noise, we repeated the simulation process described in the above with different configurations. In these sim- Power of the Noise in the Detector Circuitry (%) ulations, the actual phase flicker of the LCOS device ranged from 0.02 to 0.1 π. The noise 0.0 0.2 0.4 0.6 0.8 1.0 1.5 2.0 3.0 of the characterisation systems ranged from 0% to 3% of the maximum intensity detected 0.10 0.1 0.107 0.114 0.121 0.127 0.133 0.147 0.159 0.182 by the photodiode circuit. The calculated worst-case phase flicker under each configura- 0.08 0.08 0.089 0.097 0.105 0.112 0.119 0.134 0.148 0.171 tion was shown in Table 1. It can be seen that the noise within the characterisation system Actual phase flicker () 0.06 0.06 0.072 0.082 0.091 0.1 0.107 0.124 0.139 0.164 was able to elevate the calculated phase flicker significantly. In some extreme cases, the 0.04 0.04 0.056 0.069 0.08 0.089 0.098 0.116 0.132 0.158 calculated phase flicker was ~7 times higher than the actual phase flicker. The largest cal- 0.02 0.02 0.045 0.06 0.072 0.083 0.092 0.111 0.127 0.154 culation errors occurred at the phase levels close to the turning points of the detected in- tensity curves. These results indicated that an accurate characterisation on the phase 4. Experimental Verification flicker required a detector with extremely low level of temporal noise. On the other hand, Experimental verification was carried out in this work. An LCOS device with a the detector should also be fast enough to capture the flicker of the LCOS device. There- rfore, a balanc esolution of 1920 e between the  1200 and response a pixel spe size ed an of 8 d the no m was ise used level sho in our uld be experiment. achieved. The driving scheme for this LCOS device is analogue with a field inversion frequency of >1 kHz. As Table 1. The calculated worst-case phase flicker under different simulation conditions (unit: π). a result, this device exhibits a consistently low phase flicker for all the grey levels. This was similar to our simulation condition, in which the LCOS had a constant peak-to-peak Power of the Noise in the Detector Circuitry (%) flicker across all the grey levels. This LCOS device was designed to operate at 1550 nm 0.0 0.2 0.4 0.6 0.8 1.0 1.5 2.0 3.0 since its primary application is for the telecom optical switches, in which the phase flicker 0.10 0.1 0.107 0.114 0.121 0.127 0.133 0.147 0.159 0.182 is a critical performance parameter. It should be noted that LCOS devices based on the 0.08 0.08 0.089 0.097 0.105 0.112 0.119 0.134 0.148 0.171 digital driving schemes suffer from higher phase flicker. Adjacent grey levels within a Actual phase flicker (π) 0.06 0.06 0.072 0.082 0.091 0.1 0.107 0.124 0.139 0.164 digital LCOS device may exhibit significantly different flickering characteristics due to 0.04 0.04 0.056 0.069 0.08 0.089 0.098 0.116 0.132 0.158 the nature of the digital PWM driving. As the main goal of this experiment is to verify 0.02 0.02 0.045 0.06 0.072 0.083 0.092 0.111 0.127 0.154 the uncertainty of the phase flicker derivation, the use of a digital LCOS device would complicate the analysis. Therefore, an analogue LCOS device was chosen. The 1550 nm 4. Experimental Verification laser source used in our experiments quoted a power instability of <1%. The amplified Experimental verification was carried out in this work. An LCOS device with a reso- photodiode circuit used in this work was Thorlabs PDA50B2. lution of 1920 × 1200 and a pixel size of 8 µm was used in our experiment. The driving Figure 6 shows the measured power response of the LCOS device when it is placed scheme for this LCOS device is analogue with a field inversion frequency of >1 kHz. As a in the characterisation system shown in Figure 1. Based on these results, the phase re- result, this device exhibits a consistently low phase flicker for all the grey levels. This was sponse and the phase flicker at each grey level were calculated. The results were shown in similar to our simulation condition, in which the LCOS had a constant peak-to-peak flicker Figures 7 and 8, respectively. It can be seen from Figure 8 that the calculated phase flicker across all the grey levels. This LCOS device was designed to operate at 1550 nm since its of the LCOS device under the test was ~0.01  for majority of the grey level. However, primary application is for the telecom optical switches, in which the phase flicker is a crit- the calculated phase flicker was significantly elevated for the phase range correspond- ical performance parameter. It should be noted that LCOS devices based on the digital ing to the turning points of the intensity response shown in Figure 6. It can reach as driving schemes suffer from higher phase flicker. Adjacent grey levels within a digital high as ~0.09, which is highly unlikely due to the inherent phase flicker of the LCOS device. Instead, these results were consistent with the pattern observed in our simula- tion. Therefore, the calculated phase flicker was artificially raised by the noise within our characterisation systems. Photonics 2021, 8, x FOR PEER REVIEW 6 of 10 LCOS device may exhibit significantly different flickering characteristics due to the nature of the digital PWM driving. As the main goal of this experiment is to verify the uncertainty of the phase flicker derivation, the use of a digital LCOS device would complicate the analysis. Therefore, an analogue LCOS device was chosen. The 1550 nm laser source used in our experiments quoted a power instability of <±1%. The amplified photodiode circuit used in this work was Thorlabs PDA50B2. Figure 6 shows the measured power response of the LCOS device when it is placed in the characterisation system shown in Figure 1. Based on these results, the phase re- sponse and the phase flicker at each grey level were calculated. The results were shown in Figures 7 and 8, respectively. It can be seen from Figure 8 that the calculated phase flicker of the LCOS device under the test was ~0.01 π for majority of the grey level. How- ever, the calculated phase flicker was significantly elevated for the phase range corre- sponding to the turning points of the intensity response shown in Figure 6. It can reach as high as ~0.09π, which is highly unlikely due to the inherent phase flicker of the LCOS device. Instead, these results were consistent with the pattern observed in our simulation. Photonics 2021, 8, 307 6 of 10 Therefore, the calculated phase flicker was artificially raised by the noise within our char- acterisation systems. Photonics 2021, 8, x FOR PEER REVIEW 7 of 10 Photonics 2021, 8, x FOR PEER REVIEW 7 of 10 Figure 6. The experimental power response of the LCOS device. Figure 6. The experimental power response of the LCOS device. Figure 7. The calculated phase response of the LCOS device based on the experimental results. Figure 7. The calculated phase response of the LCOS device based on the experimental results. Figure 7. The calculated phase response of the LCOS device based on the experimental results. Figure 8. The calculated phase flicker of the LCOS device based on the experimental results. 5. Mitigation Strategy Our simulation and experimental results have demonstrated that the turning points of the intensity response will cause uncertainty in the phase flicker analysis. Unfortu- Figure 8. nately, it is The calculated impossible to av phase fli oid those tc u ker of rning points if t the LCOS de he phase vice b dept ased h of the on the ex LCOS device perimental results. Figure 8. The calculated phase flicker of the LCOS device based on the experimental results. is beyond π. However, the intensity response curve can be shifted by adding an additional waveplate between the first polariser and the LCOS device, as illustrated in Figure 9. The 5. Mitigation Strategy fast axis is aligned 45° with respect to the first polariser, i.e., parallel to the polarisation direction Our simula of the LCOS dev tion aice nd experimenta under the test. In l result this case, the turni s have demo ng poi nstrated th nts within the at the turning points measured intensity response can be shifted by adjusting the retardation of this additional of the intensity response will cause uncertainty in the phase flicker analysis. Unfortu- waveplate. nately, it is impossible to avoid those turning points if the phase depth of the LCOS device is beyond π. However, the intensity response curve can be shifted by adding an additional waveplate between the first polariser and the LCOS device, as illustrated in Figure 9. The fast axis is aligned 45° with respect to the first polariser, i.e., parallel to the polarisation direction of the LCOS device under the test. In this case, the turning points within the measured intensity response can be shifted by adjusting the retardation of this additional waveplate. Photonics 2021, 8, 307 7 of 10 5. Mitigation Strategy Our simulation and experimental results have demonstrated that the turning points of the intensity response will cause uncertainty in the phase flicker analysis. Unfortunately, it is impossible to avoid those turning points if the phase depth of the LCOS device is beyond . However, the intensity response curve can be shifted by adding an additional waveplate between the first polariser and the LCOS device, as illustrated in Figure 9. The fast axis is aligned 45 with respect to the first polariser, i.e., parallel to the polarisation direction Photonics 2021, 8, x FOR PEER REVIEW 8 of 10 of the LCOS device under the test. In this case, the turning points within the measured intensity response can be shifted by adjusting the retardation of this additional waveplate. Figure 9. New experimental setup with an additional waveplate. Figure 9. New experimental setup with an additional waveplate. In order to verify the effectiveness of this proposed method, we carried out the same In order to verify the effectiveness of this proposed method, we carried out the same simulation we did for Figures 4 and 5. Specifically, the LCOS device was assumed to have simulation we did for Figures 4 and 5. Specifically, the LCOS device was assumed to have a peak-to-peak flicker of 0.06  for all the phase levels. The noise caused by the photo a peak-to-peak flicker of 0.06 π for all the phase levels. The noise caused by the photo detector was assumed to be only 0.5% of the maximum power level detected. The simulated detector was assumed to be only 0.5% of the maximum power level detected. The simu- relationship between the grey level and the detected power level was plotted in Figure 10. lated relationship between the grey level and the detected power level was plotted in Fig- It can be seen that the intensity curve was shifted by a quarter period in this case. The ure 10. It can be seen that the intensity curve was shifted by a quarter period in this case. grey levels that were close to the turning points within Figure 4 corresponded to the linear The grey levels that were close to the turning points within Figure 4 corresponded to the region of the curve in this measurement. As shown in Figure 11, the measurement error for linear region of the curve in this measurement. As shown in Figure 11, the measurement those grey levels was significantly reduced in this setup. The residual error was primarily error for those grey levels was significantly reduced in this setup. The residual error was contributed to by the noise within the photo detector. Therefore, multiple measurements primarily contributed to by the noise within the photo detector. Therefore, multiple meas- using waveplates with different retardations should be carried out to ensure that each grey urements using waveplates with different retardations should be carried out to ensure level had been in the linear region of the intensity curve in at least one of the measurements. that each grey level had been in the linear region of the intensity curve in at least one of In this case, we could have an accurate assessment for all the grey levels. the measurements. In this case, we could have an accurate assessment for all the grey levels. Figure 10. The simulated power response with an additional quarter waveplate. Photonics 2021, 8, x FOR PEER REVIEW 8 of 10 Figure 9. New experimental setup with an additional waveplate. In order to verify the effectiveness of this proposed method, we carried out the same simulation we did for Figures 4 and 5. Specifically, the LCOS device was assumed to have a peak-to-peak flicker of 0.06 π for all the phase levels. The noise caused by the photo detector was assumed to be only 0.5% of the maximum power level detected. The simu- lated relationship between the grey level and the detected power level was plotted in Fig- ure 10. It can be seen that the intensity curve was shifted by a quarter period in this case. The grey levels that were close to the turning points within Figure 4 corresponded to the linear region of the curve in this measurement. As shown in Figure 11, the measurement error for those grey levels was significantly reduced in this setup. The residual error was primarily contributed to by the noise within the photo detector. Therefore, multiple meas- urements using waveplates with different retardations should be carried out to ensure that each grey level had been in the linear region of the intensity curve in at least one of Photonics 2021, 8, 307 8 of 10 the measurements. In this case, we could have an accurate assessment for all the grey levels. Photonics 2021, 8, x FOR PEER REVIEW 9 of 10 Figure 10. The simulated power response with an additional quarter waveplate. Figure 10. The simulated power response with an additional quarter waveplate. Figure 11. Calculated phase flicker at each phase level with an additional quarter waveplate. Figure 11. Calculated phase flicker at each phase level with an additional quarter waveplate. 6. Conclusions 6. Conclusions This paper demonstrated that there is a high degree of uncertainty in the phase This paper demonstrated that there is a high degree of uncertainty in the phase flicker flicker calculation in the presence of the noise from the characterisation system. Such calculation in the presence of the noise from the characterisation system. Such noise could noise could significantly elevate the level of the phase flicker, particularly for the phase significantly elevate the level of the phase flicker, particularly for the phase levels corre- levels corresponding to the turning points of the intensity response. Therefore, a precise sponding to the turning points of the intensity response. Therefore, a precise characteri- characterisation of the phase flicker requires a characterisation system with an extremely sation of the phase flicker requires a characterisation system with an extremely low level low level of temporal noises. To mitigate the impact of the noise within the characterisation of temporal noises. To mitigate the impact of the noise within the characterisation system, system, a multi-step measurement strategy was proposed in this paper. This method was a multi-step measurement strategy was proposed in this paper. This method was able to able to avoid the use of data close to the turning points of the intensity response. Therefore, the avoi measur d the use of ement accuracy data close can to the turni be improved. ng poi The nts of the i findings pr ntensi esented ty response. Theref in this work could ore, the also measurement be applicable accur to a other cy cacharacterisation n be improved. The fin methods difor ngs presented in this work c the phase flicker in the LCOS ould also device, including the diffraction based methods, interferometer based methods, etc. be applicable to other characterisation methods for the phase flicker in the LCOS device, including the diffraction based methods, interferometer based methods, etc. Author Contributions: Conceptualization, H.Y.; methodology, H.Y.; validation, Z.Y., S.W. and J.N.; formal analysis, Z.Y., S.W. and J.N.; writing—original draft preparation, Z.Y.; writing—review and editing, Z.Y., S.W. and H.Y.; visualization, Z.Y., S.W. and H.Y.; supervision, H.Y.; funding acquisi- tion, H.Y. All authors have read and agreed to the published version of the manuscript. Funding: This research and APC was funded by Natural Science Foundation of Jiangsu Province (BK20200351); Jiangsu Special Professorship. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. 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Photonics 2021, 8, 307 9 of 10 Author Contributions: Conceptualization, H.Y.; methodology, H.Y.; validation, Z.Y., S.W. and J.N.; formal analysis, Z.Y., S.W. and J.N.; writing—original draft preparation, Z.Y.; writing—review and editing, Z.Y., S.W. and H.Y.; visualization, Z.Y., S.W. and H.Y.; supervision, H.Y.; funding acquisition, H.Y. All authors have read and agreed to the published version of the manuscript. Funding: This research and APC was funded by Natural Science Foundation of Jiangsu Province (BK20200351); Jiangsu Special Professorship. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: The data may be available upon request. Conflicts of Interest: The authors declare no conflict of interest. References 1. Vettese, D. Liquid crystal on silicon. Nat. Photonics 2010, 4, 752. [CrossRef] 2. Zhang, Z.; You, Z.; Chu, D. Fundamentals of phase-only liquid crystal on silicon (LCOS) devices. Light Sci. 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Benicewicz, B.C.; Johnson, J.F.; Shaw, M.T. Viscosity Behavior of Liquid Crystals. Mol. Cryst. Liq. Cryst. 1981, 65, 111–131. [CrossRef] 18. García-Márquez, J.; López-Padilla, E.; González-Vega, A.; Noé-Arias, E. Flicker reduction in an LCoS spatial light modulator. In 22nd Congress of the International Commission for Optics: Light for the Development of the World; International Society for Optics and Photonics: Bellingham, WA, USA, 2011; Volume 8011. 19. Hermanns, A.; Wilson, C.; Patel, J.S.; Grueneberg, K.A.; Nelson, K.S.; Townsend-Booth, A.; Ratna, B.R. Effect of cell thickness on electroclinic liquid crystal response time. In Liquid Crystal Materials, Devices, and Applications VI; International Society for Optics and Photonics: Bellingham, WA, USA, 1998; Volume 3297, pp. 73–80. 20. Yang, H.; Chu, D.P. Phase flicker optimisation in digital liquid crystal on silicon devices. Opt. Express 2019, 27, 24556–24567. [CrossRef] [PubMed] 21. Yang, H.; Chu, D.P. Phase flicker in liquid crystal on silicon devices. J. Phys. Photonics 2020, 2, 32001. [CrossRef] 22. Ramirez, C.; Karakus, B.; Lizana, A.; Campos, J. Polarimetric method for liquid crystal displays characterization in presence of phase fluctuations. Opt. Express 2013, 21, 3182–3192. [CrossRef] [PubMed] Photonics 2021, 8, 307 10 of 10 23. Martínez, F.J.; Márquez, A.; Gallego, S.; Francés, J.; Pascual, I.; Beléndez, A. Retardance and flicker modeling and characterization of electro-optic linear retarders by averaged Stokes polarimetry. Opt. Lett. 2014, 39, 1011–1014. [CrossRef] [PubMed] 24. Zhang, Z.; Yang, H.; Robertson, B.; Redmond, M.; Pivnenko, M.; Collings, N.; Crossland, B.; Chu, D. A Diffraction Based Phase Compensation Method for Phase-Only Liquid Crystal on Silicon (LCOS) Devices in Operation. Appl. Opt. 2012, 51, 3837–3846. [CrossRef] [PubMed] 25. García-Márquez, J.; López, V.; González-Vega, A.; Noé, E. Flicker minimization in an LCoS spatial light modulator. Opt. Express 2012, 20, 8431–8441. [CrossRef] [PubMed] 26. Chiang, K.-H.F.; Wu, S.-T.; Chen, S.-H. Fringing Field Effect of the Liquid-Crystal-on-Silicon Devices. Jpn. J. Appl. Phys. 2002, 41, 4577–4585. [CrossRef] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Photonics Multidisciplinary Digital Publishing Institute

Uncertainty in the Phase Flicker Measurement for the Liquid Crystal on Silicon Devices

Photonics , Volume 8 (8) – Aug 1, 2021

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hv photonics Article Uncertainty in the Phase Flicker Measurement for the Liquid Crystal on Silicon Devices 1 2 1 1 , Zhiyuan Yang , Shiyu Wu , Jiewen Nie and Haining Yang * School of Electronic Science and Engineering, Southeast University, Nanjing 210096, China; zhiyuan_yang@seu.edu.cn (Z.Y.); 220201566@seu.edu.cn (J.N.) School of Information Science and Engineering, Southeast University, Nanjing 210096, China; 213181969@seu.edu.cn * Correspondence: h.yang@seu.edu.cn Abstract: Phase flicker has become an important performance parameter for the liquid crystal on silicon (LCOS) devices. Since the phase response of the LCOS device cannot be measured directly, it is usually derived from the intensity response of the modulated light beam when the LCOS device was placed between a pair of crossed polarisers. However, the relationship between the intensity of the beam and the phase response of the LCOS device is periodic. This would lead to uncertainty in the phase flicker measurement. This paper analyses this measurement uncertainty through both simulation and experiments. It also proposed a strategy to minimise the uncertainty. Keywords: liquid crystal on silicon (LCOS) device; phase flicker 1. Introduction Phase-only liquid crystal on silicon (LCOS) devices [1–4] are a versatile and efficient tool to modulate the light field. This technology has a wide range of applications including Citation: Yang, Z.; Wu, S.; Nie, J.; information display [5,6], optical switches [7,8], optical tweezers [9,10], laser pulse shaping Yang, H. Uncertainty in the Phase systems [11], etc. Flicker Measurement for the Liquid Key performance parameters for the LCOS devices include resolutions, pixel sizes, Crystal on Silicon Devices. Photonics reflectivity, diffraction efficiency, etc. Recently, phase flicker, i.e., temporal fluctuation of 2021, 8, 307. https://doi.org/ phase response, has also become a critical parameter. It has been demonstrated that the 10.3390/photonics8080307 reduction of the phase flicker in the LCOS devices was able to improve the image quality in the holographic display systems [12,13]. The crosstalk in the optical switches based on Received: 31 May 2021 the LCOS technology can also be suppressed by using LCOS devices with lower phase Accepted: 28 July 2021 flicker [14]. Published: 1 August 2021 A variety of techniques have been proposed for the phase flicker minimisation. In- creasing the field inversion frequency [15,16] of the driving waveforms minimises the Publisher’s Note: MDPI stays neutral impact of the residual DC unbalance and therefore proves to be an effective way to sup- with regard to jurisdictional claims in press the phase flicker. LCOS devices with slower responses are also associated with published maps and institutional affil- low phase flicker. This can be achieved by reducing the operation temperature of the iations. device, using liquid crystal material with higher viscosity [17,18], or increasing the liquid crystal cell gap [19]. However, it might not be desirable to sacrifice the response speed of the LCOS device for some applications. In the digital LCOS devices, where pulse width modulation (PWM) scheme is used to drive the LC material, the optimisation of the pulse Copyright: © 2021 by the authors. sequences [20,21] is also an effective way to reduce the flicker. This makes the digital LCOS Licensee MDPI, Basel, Switzerland. devices suitable for the phase-only applications. This article is an open access article The phase flicker in the LCOS devices can be measured by polarimetric systems [22,23], distributed under the terms and diffractive systems [24] or interferometric systems [25]. Polarimetric and diffractive setups conditions of the Creative Commons uses photodiode as the detector instead of the CCD or CMOS camera used in the interfero- Attribution (CC BY) license (https:// metric systems. Therefore, polarimetric and diffractive systems are easier to setup and able creativecommons.org/licenses/by/ to deliver more accurate characterisation. As the phase of the light cannot be measured 4.0/). Photonics 2021, 8, 307. https://doi.org/10.3390/photonics8080307 https://www.mdpi.com/journal/photonics Photonics 2021, 8, x FOR PEER REVIEW 2 of 10 Photonics 2021, 8, 307 2 of 10 setup and able to deliver more accurate characterisation. As the phase of the light cannot be measured directly, the temporal phase response of the LCOS devices is derived from the temporal intensity of the modulated light beam in both setups. As the phase flicker in the LCOS dev directly, the temporal ices contin phase ues to decre response ase, the no of the LCOS ise within the cha devices is derived racterisa fr ti om on systems ma the temporal y start to influence the level of phase flicker derived. intensity of the modulated light beam in both setups. As the phase flicker in the LCOS devices In this pa continues per, we a to decr naease, lyse th the e uncertaint noise within y in the phase flicker the characterisation measurement. The systems may start im to - pact influence of the laser sourc the level of phase e instflicker ability and derived. the noises of the photo detector were evaluated In this paper, we analyse the uncertainty in the phase flicker measurement. The through simulation and experiments. Subsequently, we proposed a strategy to reduce the impact of the laser source instability and the noises of the photo detector were evaluated measurement uncertainty. through simulation and experiments. Subsequently, we proposed a strategy to reduce the 2. Pha measur seement Flicker Ch uncertainty aracter .isation System In this work, we used a polarimetric system to characterise the phase response and 2. Phase Flicker Characterisation System flicker of the LCOS device. Figure 1 shows the general architecture of this polarimetric In this work, we used a polarimetric system to characterise the phase response and system. A collimated laser source at 1550 nm was fed into this characterisation system. flicker of the LCOS device. Figure 1 shows the general architecture of this polarimetric The LCOS device was placed between a pair of linear polarisers. The directions of these system. A collimated laser source at 1550 nm was fed into this characterisation system. The two linear polarisers were orthogonal to each other. The polarisation direction of the LCOS device was placed between a pair of linear polarisers. The directions of these two LCOS device was aligned 45° with respect to these polarisers. In this setup, the intensity linear polarisers were orthogonal to each other. The polarisation direction of the LCOS of optical beam at the detector plane can be modulated by the phase depth of the LCOS device was aligned 45 with respect to these polarisers. In this setup, the intensity of optical device. In order to characterise the phase flicker, a high-speed amplified photodiode cir- beam at the detector plane can be modulated by the phase depth of the LCOS device. In cuit was used. order to characterise the phase flicker, a high-speed amplified photodiode circuit was used. Figure 1. Experimental setup based on the crossed polarisers. Figure 1. Experimental setup based on the crossed polarisers. The relationship between the light intensity (I) at the detector plane and the phase The relationship between the light intensity (I) at the detector plane and the phase depth (q) of the LCOS device can be described by: depth (𝜃 ) of the LCOS device can be described by: I = I sin + j (1) (1) 𝐼 𝐼 𝜑 where I0 is the maximum power detected by the photodiode circuit, 𝜑 is a constant that where I is the maximum power detected by the photodiode circuit, j is a constant that is is related to liquid crystal cell gap of the LCOS device. related to liquid crystal cell gap of the LCOS device. One of the key advantages of this polarimetric system is that the LCOS device dis- One of the key advantages of this polarimetric system is that the LCOS device displays play uniform s unifor phase m phase patt patterns during erns dur theing t characterisation. he characterisa This tion. Thi avoids s the avoi impact ds the i of m the pact of fringing the ffield ringing fi effectel[d ef 26].fect [2 However 6]. Howe , the value ver, the of the value of the c constant j o isnstant unknown. 𝜑 is unknown. This could This coul complicate d complicat the phaseer t esponse he phasand e respo flicker nse calculation. and flicker c It alc should ulation. be It noted shouthat ld be n theodif ted t fractive hat thcharacter e diffrac-- isation system is able to eliminate this issue although it would also introduce the fringing tive characterisation system is able to eliminate this issue although it would also introduce field effect. However, the mechanism of the measurement uncertainty is similar in both configurations. Therefore, the analysis will be based on the polarimetric system. 𝑠𝑖𝑛 Photonics 2021, 8, x FOR PEER REVIEW 3 of 10 the fringing field effect. However, the mechanism of the measurement uncertainty is sim- Photonics 2021, 8, 307 3 of 10 ilar in both configurations. Therefore, the analysis will be based on the polarimetric sys- tem. 3. Origin of the Measurement Uncertainty 3. Origin of the Measurement Uncertainty The following analysis will illustrate how the noise within the characterisation sys- The following analysis will illustrate how the noise within the characterisation sys- tem could affect the calculated phase flicker level. The primary sources of noise within the tem could affect the calculated phase flicker level. The primary sources of noise within characterisation system are the laser instability and the white noise of the amplified pho- the characterisation system are the laser instability and the white noise of the amplified todiode circuit. This paper will not differentiate these two types of noises since both of photodiode circuit. This paper will not differentiate these two types of noises since both of them ultimately lead to fluctuation of the detected light intensity over the time even in the them ultimately lead to fluctuation of the detected light intensity over the time even in the absence of the phase flicker in the LCOS device. Therefore, this paper will only focus on absence of the phase flicker in the LCOS device. Therefore, this paper will only focus on how such fluctuation would affect the phase flicker derivation. how such fluctuation would affect the phase flicker derivation. First, we assumed that the characterisation system is without any noise and the LCOS First, we assumed that the characterisation system is without any noise and the LCOS device had a peak-to-peak flicker of 0.06 π for all the phase levels. The light intensity at device had a peak-to-peak flicker of 0.06  for all the phase levels. The light intensity at the photodiode detector was simulated. Figure 2 showed the maximum, minimum and the photodiode detector was simulated. Figure 2 showed the maximum, minimum and average intensity measured by the photodiode circuit at each grey level. In this simulation, average intensity measured by the photodiode circuit at each grey level. In this simulation, the value of 𝜑 was set arbitrarily at 0.16π. In practice, the value of 𝜑 depends on the the value of j was set arbitrarily at 0.16. In practice, the value of j depends on the liquid li crystal quid cry cell stthickness al cell thic of kness the LCOS of the LCOS device an device and the bird t efringence he birefrof ingenc the liquid e of th crystal e liquid material. crystal material. This would not affect the analysis and the conclusion described in the below. This would not affect the analysis and the conclusion described in the below. Figure 2. The simulated power response when there is no noise in the characterisation system. Figure 2. The simulated power response when there is no noise in the characterisation system. Subsequently, the phase flicker at each grey level was calculated based on the Equation (1). Subsequently, the phase flicker at each grey level was calculated based on the Equa- The results were presented in Figure 3. For majority of the grey levels, the calculated phase tion 1. The results were presented in Figure 3. For majority of the grey levels, the calcu- flicker was consistent with the assumed value of 0.06 . However, the calculated flicker lated phase flicker was consistent with the assumed value of 0.06 π. However, the calcu- was smaller than it should be around the grey level of 70 and 172. These regions also lated flicker was smaller than it should be around the grey level of 70 and 172. These re- correspond to turning points of the intensity response shown in Figure 2. In those regions, gions also correspond to turning points of the intensity response shown in Figure 2. In the relationship between the phase level and detected light intensity was not monotonic. those regions, the relationship between the phase level and detected light intensity was This would bring certain degree of uncertainty in the calculation. not monotonic. This would bring certain degree of uncertainty in the calculation. In the following simulation, the impact of the characterisation system noise was considered. First, the noise was assumed to be only 0.5% of the maximum power level detected. Figure 4 shows the maximum and minimum intensity detected at each grey level, which looked very similar to the results shown in Figure 2. The calculated phase flicker is shown in Figure 5 for all the phase levels. The level of the flicker was elevated for all the phase levels. This is expected due to the contribution of the characterisation system noise. However, the calculated phase flickers were raised to ~0.9  for the regions corresponding to the turning points in Figure 4. An extremely low level of noise within the characterisation system led to a ~50% measurement error in this case. Photonics 2021, 8, x FOR PEER REVIEW 4 of 10 Photonics 2021, 8, 307 4 of 10 Photonics 2021, 8, x FOR PEER REVIEW 4 of 10 Figure 3. Calculated phase flicker at each grey level when there is no noise in the characterisation system. In the following simulation, the impact of the characterisation system noise was con- sidered. First, the noise was assumed to be only 0.5% of the maximum power level de- tected. Figure 4 shows the maximum and minimum intensity detected at each grey level, which looked very similar to the results shown in Figure 2. The calculated phase flicker is shown in Figure 5 for all the phase levels. The level of the flicker was elevated for all the phase levels. This is expected due to the contribution of the characterisation system noise. However, the calculated phase flickers were raised to ~0.9 π for the regions corresponding to the turning points in Figure 4. An extremely low level of noise within the characterisa- tion system led to a ~50% measurement error in this case. Figure 3. Calculated phase flicker at each grey level when there is no noise in the characterisation Figure 3. Calculated phase flicker at each grey level when there is no noise in the characterisation system. system. In the following simulation, the impact of the characterisation system noise was con- sidered. First, the noise was assumed to be only 0.5% of the maximum power level de- tected. Figure 4 shows the maximum and minimum intensity detected at each grey level, which looked very similar to the results shown in Figure 2. The calculated phase flicker is shown in Figure 5 for all the phase levels. The level of the flicker was elevated for all the phase levels. This is expected due to the contribution of the characterisation system noise. However, the calculated phase flickers were raised to ~0.9 π for the regions corresponding to the turning points in Figure 4. An extremely low level of noise within the characterisa- tion system led to a ~50% measurement error in this case. Figure 4. The simulated power response when there is noise in the characterisation system. Figure 4. The simulated power response when there is noise in the characterisation system. In order to further analyse the impact of characterisation system noise, we repeated the simulation process described in the above with different configurations. In these simulations, the actual phase flicker of the LCOS device ranged from 0.02 to 0.1 . The noise of the characterisation systems ranged from 0% to 3% of the maximum intensity detected by the photodiode circuit. The calculated worst-case phase flicker under each configuration was shown in Table 1. It can be seen that the noise within the characterisation system was able to elevate the calculated phase flicker significantly. In some extreme cases, the calculated phase flicker was ~7 times higher than the actual phase flicker. The largest calculation errors occurred at the phase levels close to the turning points of the detected intensity curves. These results indicated that an accurate characterisation on the phase Figure 4. The simulated power response when there is noise in the characterisation system. flicker required a detector with extremely low level of temporal noise. On the other hand, the detector should also be fast enough to capture the flicker of the LCOS device. Therefore, a balance between the response speed and the noise level should be achieved. Photonics 2021, 8, 307 5 of 10 Photonics 2021, 8, x FOR PEER REVIEW 5 of 10 Figure 5. Calculated phase flicker at each phase level when there is noise in the characterisation Figure 5. Calculated phase flicker at each phase level when there is noise in the characterisation system. system. Table 1. The calculated worst-case phase flicker under different simulation conditions (unit: ). In order to further analyse the impact of characterisation system noise, we repeated the simulation process described in the above with different configurations. In these sim- Power of the Noise in the Detector Circuitry (%) ulations, the actual phase flicker of the LCOS device ranged from 0.02 to 0.1 π. The noise 0.0 0.2 0.4 0.6 0.8 1.0 1.5 2.0 3.0 of the characterisation systems ranged from 0% to 3% of the maximum intensity detected 0.10 0.1 0.107 0.114 0.121 0.127 0.133 0.147 0.159 0.182 by the photodiode circuit. The calculated worst-case phase flicker under each configura- 0.08 0.08 0.089 0.097 0.105 0.112 0.119 0.134 0.148 0.171 tion was shown in Table 1. It can be seen that the noise within the characterisation system Actual phase flicker () 0.06 0.06 0.072 0.082 0.091 0.1 0.107 0.124 0.139 0.164 was able to elevate the calculated phase flicker significantly. In some extreme cases, the 0.04 0.04 0.056 0.069 0.08 0.089 0.098 0.116 0.132 0.158 calculated phase flicker was ~7 times higher than the actual phase flicker. The largest cal- 0.02 0.02 0.045 0.06 0.072 0.083 0.092 0.111 0.127 0.154 culation errors occurred at the phase levels close to the turning points of the detected in- tensity curves. These results indicated that an accurate characterisation on the phase 4. Experimental Verification flicker required a detector with extremely low level of temporal noise. On the other hand, Experimental verification was carried out in this work. An LCOS device with a the detector should also be fast enough to capture the flicker of the LCOS device. There- rfore, a balanc esolution of 1920 e between the  1200 and response a pixel spe size ed an of 8 d the no m was ise used level sho in our uld be experiment. achieved. The driving scheme for this LCOS device is analogue with a field inversion frequency of >1 kHz. As Table 1. The calculated worst-case phase flicker under different simulation conditions (unit: π). a result, this device exhibits a consistently low phase flicker for all the grey levels. This was similar to our simulation condition, in which the LCOS had a constant peak-to-peak Power of the Noise in the Detector Circuitry (%) flicker across all the grey levels. This LCOS device was designed to operate at 1550 nm 0.0 0.2 0.4 0.6 0.8 1.0 1.5 2.0 3.0 since its primary application is for the telecom optical switches, in which the phase flicker 0.10 0.1 0.107 0.114 0.121 0.127 0.133 0.147 0.159 0.182 is a critical performance parameter. It should be noted that LCOS devices based on the 0.08 0.08 0.089 0.097 0.105 0.112 0.119 0.134 0.148 0.171 digital driving schemes suffer from higher phase flicker. Adjacent grey levels within a Actual phase flicker (π) 0.06 0.06 0.072 0.082 0.091 0.1 0.107 0.124 0.139 0.164 digital LCOS device may exhibit significantly different flickering characteristics due to 0.04 0.04 0.056 0.069 0.08 0.089 0.098 0.116 0.132 0.158 the nature of the digital PWM driving. As the main goal of this experiment is to verify 0.02 0.02 0.045 0.06 0.072 0.083 0.092 0.111 0.127 0.154 the uncertainty of the phase flicker derivation, the use of a digital LCOS device would complicate the analysis. Therefore, an analogue LCOS device was chosen. The 1550 nm 4. Experimental Verification laser source used in our experiments quoted a power instability of <1%. The amplified Experimental verification was carried out in this work. An LCOS device with a reso- photodiode circuit used in this work was Thorlabs PDA50B2. lution of 1920 × 1200 and a pixel size of 8 µm was used in our experiment. The driving Figure 6 shows the measured power response of the LCOS device when it is placed scheme for this LCOS device is analogue with a field inversion frequency of >1 kHz. As a in the characterisation system shown in Figure 1. Based on these results, the phase re- result, this device exhibits a consistently low phase flicker for all the grey levels. This was sponse and the phase flicker at each grey level were calculated. The results were shown in similar to our simulation condition, in which the LCOS had a constant peak-to-peak flicker Figures 7 and 8, respectively. It can be seen from Figure 8 that the calculated phase flicker across all the grey levels. This LCOS device was designed to operate at 1550 nm since its of the LCOS device under the test was ~0.01  for majority of the grey level. However, primary application is for the telecom optical switches, in which the phase flicker is a crit- the calculated phase flicker was significantly elevated for the phase range correspond- ical performance parameter. It should be noted that LCOS devices based on the digital ing to the turning points of the intensity response shown in Figure 6. It can reach as driving schemes suffer from higher phase flicker. Adjacent grey levels within a digital high as ~0.09, which is highly unlikely due to the inherent phase flicker of the LCOS device. Instead, these results were consistent with the pattern observed in our simula- tion. Therefore, the calculated phase flicker was artificially raised by the noise within our characterisation systems. Photonics 2021, 8, x FOR PEER REVIEW 6 of 10 LCOS device may exhibit significantly different flickering characteristics due to the nature of the digital PWM driving. As the main goal of this experiment is to verify the uncertainty of the phase flicker derivation, the use of a digital LCOS device would complicate the analysis. Therefore, an analogue LCOS device was chosen. The 1550 nm laser source used in our experiments quoted a power instability of <±1%. The amplified photodiode circuit used in this work was Thorlabs PDA50B2. Figure 6 shows the measured power response of the LCOS device when it is placed in the characterisation system shown in Figure 1. Based on these results, the phase re- sponse and the phase flicker at each grey level were calculated. The results were shown in Figures 7 and 8, respectively. It can be seen from Figure 8 that the calculated phase flicker of the LCOS device under the test was ~0.01 π for majority of the grey level. How- ever, the calculated phase flicker was significantly elevated for the phase range corre- sponding to the turning points of the intensity response shown in Figure 6. It can reach as high as ~0.09π, which is highly unlikely due to the inherent phase flicker of the LCOS device. Instead, these results were consistent with the pattern observed in our simulation. Photonics 2021, 8, 307 6 of 10 Therefore, the calculated phase flicker was artificially raised by the noise within our char- acterisation systems. Photonics 2021, 8, x FOR PEER REVIEW 7 of 10 Photonics 2021, 8, x FOR PEER REVIEW 7 of 10 Figure 6. The experimental power response of the LCOS device. Figure 6. The experimental power response of the LCOS device. Figure 7. The calculated phase response of the LCOS device based on the experimental results. Figure 7. The calculated phase response of the LCOS device based on the experimental results. Figure 7. The calculated phase response of the LCOS device based on the experimental results. Figure 8. The calculated phase flicker of the LCOS device based on the experimental results. 5. Mitigation Strategy Our simulation and experimental results have demonstrated that the turning points of the intensity response will cause uncertainty in the phase flicker analysis. Unfortu- Figure 8. nately, it is The calculated impossible to av phase fli oid those tc u ker of rning points if t the LCOS de he phase vice b dept ased h of the on the ex LCOS device perimental results. Figure 8. The calculated phase flicker of the LCOS device based on the experimental results. is beyond π. However, the intensity response curve can be shifted by adding an additional waveplate between the first polariser and the LCOS device, as illustrated in Figure 9. The 5. Mitigation Strategy fast axis is aligned 45° with respect to the first polariser, i.e., parallel to the polarisation direction Our simula of the LCOS dev tion aice nd experimenta under the test. In l result this case, the turni s have demo ng poi nstrated th nts within the at the turning points measured intensity response can be shifted by adjusting the retardation of this additional of the intensity response will cause uncertainty in the phase flicker analysis. Unfortu- waveplate. nately, it is impossible to avoid those turning points if the phase depth of the LCOS device is beyond π. However, the intensity response curve can be shifted by adding an additional waveplate between the first polariser and the LCOS device, as illustrated in Figure 9. The fast axis is aligned 45° with respect to the first polariser, i.e., parallel to the polarisation direction of the LCOS device under the test. In this case, the turning points within the measured intensity response can be shifted by adjusting the retardation of this additional waveplate. Photonics 2021, 8, 307 7 of 10 5. Mitigation Strategy Our simulation and experimental results have demonstrated that the turning points of the intensity response will cause uncertainty in the phase flicker analysis. Unfortunately, it is impossible to avoid those turning points if the phase depth of the LCOS device is beyond . However, the intensity response curve can be shifted by adding an additional waveplate between the first polariser and the LCOS device, as illustrated in Figure 9. The fast axis is aligned 45 with respect to the first polariser, i.e., parallel to the polarisation direction Photonics 2021, 8, x FOR PEER REVIEW 8 of 10 of the LCOS device under the test. In this case, the turning points within the measured intensity response can be shifted by adjusting the retardation of this additional waveplate. Figure 9. New experimental setup with an additional waveplate. Figure 9. New experimental setup with an additional waveplate. In order to verify the effectiveness of this proposed method, we carried out the same In order to verify the effectiveness of this proposed method, we carried out the same simulation we did for Figures 4 and 5. Specifically, the LCOS device was assumed to have simulation we did for Figures 4 and 5. Specifically, the LCOS device was assumed to have a peak-to-peak flicker of 0.06  for all the phase levels. The noise caused by the photo a peak-to-peak flicker of 0.06 π for all the phase levels. The noise caused by the photo detector was assumed to be only 0.5% of the maximum power level detected. The simulated detector was assumed to be only 0.5% of the maximum power level detected. The simu- relationship between the grey level and the detected power level was plotted in Figure 10. lated relationship between the grey level and the detected power level was plotted in Fig- It can be seen that the intensity curve was shifted by a quarter period in this case. The ure 10. It can be seen that the intensity curve was shifted by a quarter period in this case. grey levels that were close to the turning points within Figure 4 corresponded to the linear The grey levels that were close to the turning points within Figure 4 corresponded to the region of the curve in this measurement. As shown in Figure 11, the measurement error for linear region of the curve in this measurement. As shown in Figure 11, the measurement those grey levels was significantly reduced in this setup. The residual error was primarily error for those grey levels was significantly reduced in this setup. The residual error was contributed to by the noise within the photo detector. Therefore, multiple measurements primarily contributed to by the noise within the photo detector. Therefore, multiple meas- using waveplates with different retardations should be carried out to ensure that each grey urements using waveplates with different retardations should be carried out to ensure level had been in the linear region of the intensity curve in at least one of the measurements. that each grey level had been in the linear region of the intensity curve in at least one of In this case, we could have an accurate assessment for all the grey levels. the measurements. In this case, we could have an accurate assessment for all the grey levels. Figure 10. The simulated power response with an additional quarter waveplate. Photonics 2021, 8, x FOR PEER REVIEW 8 of 10 Figure 9. New experimental setup with an additional waveplate. In order to verify the effectiveness of this proposed method, we carried out the same simulation we did for Figures 4 and 5. Specifically, the LCOS device was assumed to have a peak-to-peak flicker of 0.06 π for all the phase levels. The noise caused by the photo detector was assumed to be only 0.5% of the maximum power level detected. The simu- lated relationship between the grey level and the detected power level was plotted in Fig- ure 10. It can be seen that the intensity curve was shifted by a quarter period in this case. The grey levels that were close to the turning points within Figure 4 corresponded to the linear region of the curve in this measurement. As shown in Figure 11, the measurement error for those grey levels was significantly reduced in this setup. The residual error was primarily contributed to by the noise within the photo detector. Therefore, multiple meas- urements using waveplates with different retardations should be carried out to ensure that each grey level had been in the linear region of the intensity curve in at least one of Photonics 2021, 8, 307 8 of 10 the measurements. In this case, we could have an accurate assessment for all the grey levels. Photonics 2021, 8, x FOR PEER REVIEW 9 of 10 Figure 10. The simulated power response with an additional quarter waveplate. Figure 10. The simulated power response with an additional quarter waveplate. Figure 11. Calculated phase flicker at each phase level with an additional quarter waveplate. Figure 11. Calculated phase flicker at each phase level with an additional quarter waveplate. 6. Conclusions 6. Conclusions This paper demonstrated that there is a high degree of uncertainty in the phase This paper demonstrated that there is a high degree of uncertainty in the phase flicker flicker calculation in the presence of the noise from the characterisation system. Such calculation in the presence of the noise from the characterisation system. Such noise could noise could significantly elevate the level of the phase flicker, particularly for the phase significantly elevate the level of the phase flicker, particularly for the phase levels corre- levels corresponding to the turning points of the intensity response. Therefore, a precise sponding to the turning points of the intensity response. Therefore, a precise characteri- characterisation of the phase flicker requires a characterisation system with an extremely sation of the phase flicker requires a characterisation system with an extremely low level low level of temporal noises. To mitigate the impact of the noise within the characterisation of temporal noises. To mitigate the impact of the noise within the characterisation system, system, a multi-step measurement strategy was proposed in this paper. This method was a multi-step measurement strategy was proposed in this paper. This method was able to able to avoid the use of data close to the turning points of the intensity response. Therefore, the avoi measur d the use of ement accuracy data close can to the turni be improved. ng poi The nts of the i findings pr ntensi esented ty response. Theref in this work could ore, the also measurement be applicable accur to a other cy cacharacterisation n be improved. The fin methods difor ngs presented in this work c the phase flicker in the LCOS ould also device, including the diffraction based methods, interferometer based methods, etc. be applicable to other characterisation methods for the phase flicker in the LCOS device, including the diffraction based methods, interferometer based methods, etc. Author Contributions: Conceptualization, H.Y.; methodology, H.Y.; validation, Z.Y., S.W. and J.N.; formal analysis, Z.Y., S.W. and J.N.; writing—original draft preparation, Z.Y.; writing—review and editing, Z.Y., S.W. and H.Y.; visualization, Z.Y., S.W. and H.Y.; supervision, H.Y.; funding acquisi- tion, H.Y. All authors have read and agreed to the published version of the manuscript. Funding: This research and APC was funded by Natural Science Foundation of Jiangsu Province (BK20200351); Jiangsu Special Professorship. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. 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Journal

PhotonicsMultidisciplinary Digital Publishing Institute

Published: Aug 1, 2021

Keywords: liquid crystal on silicon (LCOS) device; phase flicker

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