Abstract

Spatio-temporal phase modulation with a phase-only liquid-crystal spatial light modulator (SLM) plays an important role in the optics and photonics community. SLMs are generally affected by either or both spatial and temporal phase fluctuations, depending on driver electronics, thereby reducing the quality of a generated beam. In this study, to reduce phase fluctuations, we present an optical-based linear phase superimposition method with spatial bandpass filtering. We experimentally investigate the method’s effectiveness, particularly for holographic data storage applications. Experimental results show that the presented method is useful in robustly generating phase distributions against fluctuations, regardless of the SLM driving scheme.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Tailoring the phase of light brings attractive benefits in the optics and photonics community, such as three-dimensional display [1,2], imaging [38], laser processing [9], manipulation [10], communication [11,12], beam shaping [13,14], and data storage [1517]. There are several optical devices for tailoring the phase of light, such as diffractive optical elements [18,19], holographic optical elements [20,21], metasurfaces [22], and spatial light modulators (SLMs) [23]. Among them, phase-only liquid-crystal (LC) SLMs enable spatially and dynamically flexible phase modulation with a high quantization level, and they are commercially available [2426]. In terms of driver electronics, SLMs may be categorized as either analog or digital [23,26]. Both driving schemes are affected by either or both spatial and temporal phase fluctuations, which reduce the quality of modulated beams, as reported in several previous works [2731]. These are caused by the deformation of the substrate layer, non-uniformity of an LC layer, unevenness of the imposed electric field in each pixel, and the fluctuation of imposed electric fields. In general, for the reduction of spatial phase fluctuations, an accurate calibration step is required in advance [3235], whereas for temporal phase fluctuations, the pulse modulation width of imposed electric fields should be optimized [36,37]. In addition, cooling LC molecules is another effective approach [38]. In addition to the aforementioned fluctuations, SLMs have other limitations [39], including the generation of an undesirable zeroth-order beam [40], a fringing field effect [41,42], suppression of high-frequency components [43], and Fabry–Perot effects [44].

Although it is preferable to adequately address the aforementioned limitations to achieve high-quality phase modulation, these effects are negligible, depending on the application. However, holographic data storage, which we have studied [45,46], is heavily affected by these limitations. Holographic data storage encodes digital data onto optical fields, such as amplitude [4547], phase [4851], and polarization [52,53], and records these optical parameters as a volume hologram in a photopolymer [54] or photorefractive crystal materials. Previous studies on holographic data storage have shown the possibility of achieving a storage capacity of 1–2 TBs in a 5-inch disc [46,55]. These previous studies encoded digital data onto only the amplitude of light. Phase encoding is attractive to further increase its storage capacity. Similar to the field of coherent communication, phase encoding improves the coding rate, enabling multilevel recording in holographic data storage systems. Based on this concept, many researchers have proposed phase-recording geometries [4851,5659]. The degree of a multilevel phase is affected by many factors, such as spatial light modulations, materials, detection, and environmental disturbance. An accurate phase modulation with an SLM is necessary to increase the degree of multilevel recording. However, as mentioned above, SLMs are affected and limited by various factors, in particular, spatial and temporal phase fluctuations.

In this study, we aim to develop an accurate phase modulation technique that is robust to spatial and temporal phase fluctuations while focusing on the application of holographic data storage. Spatial phase fluctuations, which we aim to reduce, are caused by the non-uniformity of LC and substrate layers, unevenness of the imposed electric field in each pixel, and the fringing field effect. In contrast, temporal phase fluctuations are caused by fluctuations of the imposed electric field. Previously, the phase fluctuation reduction was mainly achieved via accurate calibrations and electrical or LC solutions. In contrast, we present an optical solution based on a linear phase superimposition technique with spatial bandpass filtering in this study. By digitally superimposing a linear phase pattern onto the desired phase pattern on an SLM, the desired optical field can be obtained as the main diffraction order of the linear phase, whereas undesirable components affected by fluctuations are scattered or directed to some other directions. Thus, by extracting only the desirable order via spatial bandpass filtering, a high-quality optical field can be obtained. The introduction of the linear phase has frequently been used to avoid the undesirable zeroth-order beam in the field of kinoforms [60] and Fourier-transform-based computer-generated holograms [61]. However, previous works have not directly investigated the reduction effect of phase fluctuations by phase measurement. Moreover, the generation of optical fields was previously restricted to the Fourier plane of an SLM. In contrast, we experimentally investigated the effect of introducing the linear phase on the conjugate plane of an SLM. Furthermore, we experimentally evaluated the effect of linear phase superimposition on both analog and digital SLMs.

The remainder of this study is organized as follows. In Section 2, we describe the reduction method for reducing the effect of either or both spatial and temporal phase fluctuations on SLMs by introducing linear phase superimposition, along with spatial bandpass filtering. In Section 3, we experimentally evaluate the effectiveness of the reduction method using analog and digital SLMs. Finally, we provide our conclusion in Section 4.

2. Linear phase superimposition

Figure 1 shows a schematic of the linear phase superimposition technique with spatial bandpass filtering. The setup consists of a single-phase-only SLM and a 4f geometry with an aperture. In the preparation process of a phase pattern to be displayed on the SLM, a linear phase pattern is developed in a computer. The linear phase pattern in a pixelated form is represented as

$${\phi _l}(m,n) = \bmod \left\{ {\frac{\pi }{2}(im + jn),\,2\pi } \right\},$$
where m and n denote the vertical and horizontal pixel indexes of the SLM, respectively. i and j determine the arbitrary signs of m and n, namely, +1 or −1, respectively, according to the direction of the phase slope. Figure 2(a) depicts an enlarged typical linear phase pattern for better comprehension. Phase values change along the diagonal direction of the image. This direction is useful in avoiding the deterioration of the quality of the generated light caused by overlapping the sinc-shaped side lobes of the undesired zeroth-order beam onto the Fourier spectrum of the desired phase distribution. The linear phase has a single Fourier spectrum component, which acts as a spatial frequency carrier to carry the signal component of the desired phase distribution. Note that the above linear phase is represented in a pixelated form, and its Fourier spectrum consists of multiple peaks because of its stair-like distribution, as shown in Fig. 2(b). However, there is a single peak in the Nyquist area of the SLM indicated by the broken square in Fig. 2(b). Hence, the pixelated linear phase can be considered to consist of a single spatial frequency by filtering out the outer region of the Nyquist area. The linear phase pattern ${\phi _l}(m,n)$ is superimposed onto the desired phase distribution ${\phi _d}(m,n)$ to be generated, or
$${\phi _{slm}}(m,n) = \bmod \{{{\phi_l}(m,n) + {\phi_d}(m,n),\,2\pi } \}.$$

 figure: Fig. 1.

Fig. 1. Schematic of a linear phase superimposition technique with spatial bandpass filtering for generating a high-quality phase distribution by reducing the effect of phase fluctuations on a phase-only SLM

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 figure: Fig. 2.

Fig. 2. Details of the linear phase pattern introduced to an SLM—(a) enlarged view of a typical linear phase pattern, and (b) its Fourier spectrum; the broken line shows the Nyquist size is of a phase-only SLM

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 figure: Fig. 3.

Fig. 3. Experimental setup for the evaluation on the effect of linear phase superimposition

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 figure: Fig. 4.

Fig. 4. Generation of the target phase for experimental evaluation—(a) phase distribution of a phase data page consisting of four-phase values; (b) phase signal on a complex plane or constellation diagram; (c) Fourier spectrum; and (d) linear phase superimposition onto the phase data page

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The SLM displays this phase pattern ${\phi _{slm}}(m,n)$ instead of directly displaying ${\phi _d}(m,n)$. The SLM with a pixel pitch of d modulates the phase distribution of a plane wave with a wavelength of $\lambda $ according to Eq. (2). The modulated light is Fourier-transformed using a lens with a focal length of f. The focal plane of the lens has an aperture. The center of the aperture corresponds to the peak position of the linear phase shown in Fig. 2(b) and thus is located at $({\lambda f{{({4d} )}^{ - 1}}, - \lambda f{{({4d} )}^{ - 1}}} )$. These signs depend on i and j in Eq. (1). The aperture allows the passage of spatial frequency components carried by the linear phase. However, it blocks other frequency components. When the SLM is affected by phase fluctuations, the linear phase is modified. This produces undesirable frequency components on the Fourier plane, which are blocked by the aperture. Thus, the effect of phase fluctuations can be suppressed. Afterward, the filtered light is once more Fourier transformed by a subsequent lens. At the conjugate plane of the SLM, light with the desired phase distribution can be obtained by reducing the effect of phase fluctuations on the SLM. Note that the obtained light at the conjugate plane contains a continuous linear phase. This linear phase changes the propagation direction of the light. In holographic data storage, the effect of fluctuations on the linear phase can be digitally compensated for during the decoding process because the linear phase pattern is a priori known. Alternatively, the linear phase can be optically removed by shifting the second lens according to the center position of the aperture.

3. Experimental evaluation

3.1 Optical setup and evaluation procedure

We conducted experiments to verify the effectiveness of linear phase superimposition. Figure 3 shows an experimental setup for the evaluation. Similar to Fig. 1, the experimental setup consists of a single-phase-only SLM and 4f geometry. In addition, the setup includes a tilted mirror and complementary metal-oxide-semiconductor (CMOS) sensor, enabling single-shot measurement of the phase distributions of beams generated from the SLM in the off-axis Michelson interferometer using Fourier fringe analysis [62]. As a light source, we used a He–Ne laser with a wavelength of 633 nm. Although a short wavelength, such as 405 nm, would have been preferable to increase the capacity of holographic data storage [46], we used the He–Na laser because of its stability and high optical transmittance, and it has a high sensitivity image sensor, enabling high accuracy phase detection. Moreover, the size of Fourier spectra of beams is large due to the long wavelength, which is preferable for precise evaluation with less misalignment. The laser beam was collimated with a spatial filter and lens. The resulting plane wave was divided into two beams. One beam is propagated to a tilted mirror, which acted as a reference beam for phase measurement. The other beam is modulated with a phase-only SLM. For SLMs, we used analog and digital SLMs to evaluate the applicability and generality of linear phase superimposition. The analog SLM has 1272 × 1024 pixels and a pixel pitch of 12.5 µm, whereas the digital one has 1920 × 1080 pixels and a pixel pitch of 8 µm. The target phase distribution in this evaluation was set as a phase data page, which is a two-dimensional data array for holographic data storage, as shown in Fig. 4(a). It consists of periodically arrayed four-phase values, 0, $\pi /2$, $\pi $, and $3\pi /2$, as shown by the constellation diagram in Fig. 4(b). Owing to the periodicity of the test phase pattern, its Fourier transform consists of some separated peaks, as shown in Fig. 4(c). Note that in an actual holographic storage system, phase arrays are typically arranged at random to represent arbitrary digital data. However, we used the above periodic phase data page because the limited four-phase step and periodicity of the test phase pattern enable us to easily evaluate the effect of phase fluctuations and linear phase superimposition, as will be described below. The number of pixels of the phase distribution shown in Fig. 4 is 256 × 256. To avoid the fringing field effect on the SLM and robustly evaluate the quality of modulated beams, each phase data are oversampled or represented by 16 × 16 pixels. Thus, the number of phase data, termed symbol, on the phase data page is 256 (=16 × 16). The upper right 6 × 2 symbols of Fig. 4(a), indicated by the broken square, serves as a pilot phase signal to calibrate the overall phase shift caused by the accumulation of unknown constant phases. A linear phase pattern was superimposed onto the phase data page to produce the phase pattern, as shown in Fig. 4(d) is created by superimposing a linear phase pattern on the phase data page. The SLM modulated the incident plane wave’s phase distribution according to the resulting phase pattern. The modulated beam by the SLM and reference beam reflected from the tilted mirror were imaged to the conjugate the plane located at the CMOS sensor that has 2048 × 2048 pixels and a 6.5-µm pixel pitch despite having a 4f geometry with the aperture. Note that in holographic data storage, a recording material is placed behind the aperture to record the hologram of a Fourier spectrum of a data page. However, we did not use a recording material in this experimental setup because the goal of this study is to evaluate the phase quality of the SLM. On the CMOS sensor, the modulated and reference beams interfered with each other, resulting in an off-axis interference pattern, which was captured by the CMOS sensor. Because the SLM has a frame rate of 60 Hz, the effect of fluctuations will be different, depending on the CMOS sensor’s exposure time. To verify this point, we changed the CMOS sensor’s exposure time to 50, 20, and 1 ms. By applying the Fourier fringe analysis to the captured interference pattern [62], the amplitude and phase distributions of the beam generated by the SLM can be measured at a single exposure. The detected phase distribution contains the superimposed linear phase. Moreover, it is generally affected by the wavefront aberration of the experimental setup and the non-uniformity of the substrate of the SLM. To digitally eliminate these components, we captured an additional interference pattern for calibration. During the calibration, the SLM displayed a linear phase without the target phase distribution. Hence, the phase information on the linear phase and the wavefront aberration can be obtained via Fourier fringe analysis. Only the phase distribution of the beam generated by the SLM can be evaluated by substituting these components from the phase data page's interference pattern. For comparison, the phase data page without linear phase superimposition was displayed on the SLM. Moreover, the above calibration process for wavefront aberration was also applied. In this case, the phase distribution may be affected by either or both the spatial and temporal phase fluctuations. The generated light was measured in the same manner, as described above. Note that the aperture in the 4f geometry of this experimental setup removes only the high diffraction order beams of the SLM caused by its pixelation. This does not act as spatial bandpass filtering required for the presented method because a narrow aperture will also block the reference beam reflected from the tilted mirror, preventing the interference of beams; thus, phase distributions can be accurately measured. For the effect of the aperture for spatial bandpass filtering, we digitally implemented spatial bandpass filtering with a virtual aperture in a computer following the abovementioned optical experiments. This is possible because the complex amplitude distribution has already been obtained using Fourier fringe analysis. In the following subsection, we provide the experimental results for evaluating the effectiveness of linear phase superimposition on analog and digital SLMs. Note that we do not aim to compare the performance of analog and digital SLMs. We are interested in investigating the applicability and generality of linear phase superimposition, regardless of the SLM scheme. Several studies, e.g., [23,29,63], have compared analog and digital SLMs.

3.2 Evaluation of linear phase superimposition on analog SLMs

Figure 5 shows experimental results for the analog SLM without linear phase superimposition. Figures 5(a)–(c) show the measured complex (amplitude and phase) distributions using Fourier fringe analysis at each exposure time. Note that there are variations at the boundaries of the amplitude distributions in Figs. 5(a)–(c), where the phases are abruptly changing. This is caused by spatial frequency filtering through the aperture. Alternatively, in holographic data storage, this is known as inter-pixel interference [15]. From the complex amplitude distribution in Figs. 5(a)–(c), we numerically obtained the corresponding Fourier spectra, as shown in Figs. 5(d)–(f) to compare them with the ideal Fourier spectrum shown in Fig. 4(c). In Fig. 4(c), there is no zeroth-order peak. In contrast, in Figs. 5(d)–(f), there is a weak peak in the center of the spectrum image. This is mainly caused by the fringing field effect and the limited fill factor of the SLM. Because of the presence of the undesired zeroth-order beam, the generated light may deteriorate. To verify phase quality, we plotted the complex amplitude values on a complex plane or constellation diagram, as shown in Figs. 5(g)–(i). This plot is useful for verifying and discussing the variations in amplitude and phase. Note that the plotted data were obtained by averaging the complex amplitude values within each phase data symbol, which corresponds to the decoding process in holographic data storage. The number of phase data symbols is 256, including the pilot signal in Fig. 4(a). Hence, the number of plotted complex amplitude values is also 256, as shown in Figs. 5(g)–(i). The quality and variation of complex amplitude values were evaluated in terms of modulation error ratio (MER), which is given by

$$\textrm{MER}\;\textrm{[dB] = }10\,{\log _{10}}\left( {\frac{{\sum\nolimits_{k = 1}^N {{{|{{O_k}} |}^2}} }}{{\sum\nolimits_{k = 1}^N {{{|{{O_k} - {C_k}} |}^2}} }}} \right),$$
where ${O_k}$ and ${C_k}$ denote the complex amplitude of the original and measured signals, respectively. N denotes the number of phase data symbols in the phase data page shown in Fig. 4(a). This metric is often used to evaluate signal quality in a communication system. The higher the MER, the better the phase distribution. In terms of MER evaluation, the detected phase may contain an overall phase shift as a result of the accumulation of unknown constant phases, resulting in a small MER. We compensated for the undesirable phase shift by measuring it while comparing the original and detected pilot phase signals. Generally, analog SLMs are robust to temporal phase fluctuations [23,63,64]. As shown in Figs. 5(g), 5(h), and 5(i), the phase variation and MERs are relatively constant, regardless of the exposure time. However, the phase variation is larger than the original signal shown in Fig. 4. This may be caused by the spatial phase fluctuation as well as the interference from the zeroth-order beam. Depending on the pixel position and phase level, the phase may spatially fluctuate. Note that this spatial fluctuation does not include the effect of the constant non-uniformity of the substrate layer because it was removed through calibration in advance, as described above. The MER increases with the increase in the exposure time, possibly due to the reduction of small time-dependent fluctuation caused by time averaging.

 figure: Fig. 5.

Fig. 5. Evaluation results of an analog SLM without linear phase superimposition—(a)–(c): Measured amplitude and phase distributions at exposure times of 50, 10, and 1 ms, respectively; (d)–(f): Fourier spectra of the measured distributions of (a)–(c); (g)–(i): constellation diagrams of (a)–(c); in the constellation diagrams, the maximum amplitude is normalized as one for the evaluation of signal variation

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Figure 6 shows the experimental results for linear phase superimposition. Similar to Fig. 5, we evaluated the Fourier spectrum and the variation of the measured complex amplitude values. Comparing the constellation diagrams and MERs between Figs. 5(g)–(i) and Figs. 6(g)–(i), we found that linear phase superimposition improves the quality of phase distributions. MERs at exposure times of 50, 20, and 1 ms are improved from 14.3, 13.8, and 13.1 to 19.5, 19.7, and 18.3, respectively. This may have been caused by the removal of fluctuating light components through the aperture. In addition, as shown in Figs. 6(d)–(f), there is no zeroth-order beam, which is also removed by the aperture. Thus, the above results show that linear phase superimposition is effective for reducing the spatial fluctuation in analog SLMs.

 figure: Fig. 6.

Fig. 6. Evaluation results of analog SLM with linear phase superimposition—(a)–(c): measured amplitude and phase distributions at exposure times of 50, 10, and 1 ms, respectively; (d)–(f): Fourier spectra of the measured distributions of (a)–(c); and (g)–(i): constellation diagrams of (a)–(c)

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3.3 Evaluation of linear phase superimposition on digital SLMs

Similar to Figs. 5 and 6, we experimentally evaluated the performance of linear phase superimposition on the digital SLM. Figure 7 shows the experimental results without linear phase superimposition. Unlike the analog SLM, the digital one mainly suffers from temporal phase fluctuations, rather than spatial fluctuation [23,63]. Figure 7 shows this effect. At the exposure time of 1 ms, the amplitude distribution shown in Fig. 7(c) is relatively uniform; however, its phase is different from the original, which is caused by temporal fluctuations. Note that for the exposure time of 1 ms, the phase distribution is easily and rapidly changed depending on the timing of the shutter and the pulse signal imposed on the LC of the SLM. The low-quality phase distribution can be confirmed from the small MER of 0.951 in Fig. 7(i). The effect of averaging the time improves phase quality as exposure time increases. Inversely, the amplitude distribution tends to be affected, as shown in Figs. 7(a) and 7(b), because it is reduced depending on the phase values, which can also be confirmed from the constellation diagrams shown in Figs. 7(g) and 7(h). In particular, the amplitude with a phase of $3\pi /2$ is the lowest. Because digital SLMs use pulse width modulation of the electric field to represent different phase values, the fluctuations of the LC molecules differ depending on the phase values. Thus, the above difference in amplitudes is caused by the difference in temporal fluctuations, depending on the phase values [30,31,36,65]. Long exposure time with temporal phase fluctuation reduces the contrast of the interference pattern during measurement, reducing the amplitude. The amplitude reduction rate increases as the extent of temporal fluctuation increases. The amplitude variations can also be explained by the presence of the high-intense zeroth-order beam, as shown in Figs. 7(d) and 7(e). The zeroth-order beam transforms into a plane wave on the phase data plane by Fourier transform. This plane wave is coherently added to the phase data page. This interference effect leads to the variation in amplitude.

 figure: Fig. 7.

Fig. 7. Evaluation results of digital SLM without linear phase superimposition—(a)–(c): measured amplitude and phase distributions at exposure times of 50, 10, and 1 ms, respectively; (d)–(f): Fourier spectra of the measured distributions of (a)–(c); and (g)–(i): constellation diagrams of (a)–(c)

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Figure 8 shows the results using linear phase superimposition. As shown in Figs. 8(a) and 8(b), there is less variation in the amplitude distribution unlike in Figs. 7(a) and 8(b). In addition, the zeroth-order beam is removed, as shown in Figs. 8(d) and 8(e). In contrast, the improvement is limited at the exposure time of 1 ms as shown in Figs. 8(c), 8(f), and 8(i). This can be explained as follows. The presented method using linear phase superimposition cannot directly reduce temporal fluctuations. However, it indirectly mitigates the effect of temporal fluctuation by removing the affected beam. Thus, at a short exposure time with the digital SLM, the linear phase pattern is also affected by temporal fluctuation. Although the effect of linear phase superimposition at the exposure time of 1 ms is limited, as shown in Figs. 8(c) and 8(i), MERs are increased by linear phase superimposition. The MERs at the exposure times of 50, 20, and 1 ms are increased from 7.16, 6.88, and 0.951 to 20.0, 18.1, and 2.77, respectively. Thus, linear phase superimposition is also effective in digital SLMs. Note that the use of linear phase superimposition in the digital SLM converts temporal phase fluctuations into temporal intensity fluctuations. In holographic data storage, temporal phase fluctuation momentarily deforms holograms during data recording, which corresponds to a multiplexed recording of different holograms. In contrast, temporal intensity fluctuations change the brightness of holograms during data recording. This means that the hologram shape is almost constant during data recording, and the deformation effect is mitigated. Thus, intensity fluctuations are more acceptable than phase fluctuations in digital SLMs.

 figure: Fig. 8.

Fig. 8. Evaluation results of digital SLM with linear phase superimposition—(a)–(c): measured amplitude and phase distributions at exposure times of 50, 10, and 1 ms, respectively; (d)–(f): Fourier spectra of the measured distributions of (a)–(c); and (g)–(i): constellation diagrams of (a)–(c)

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4. Conclusions

We presented a linear phase superimposition method with spatial bandpass filtering to generate the desired phase distribution for phase-only LC SLMs that is robust to either or both spatial and temporal phase fluctuations. The presented method is effective for both analog and digital SLM schemes. In particular, the presented method is not a direct solution to improve the fluctuation problem of SLMs. Rather, the presented method mitigates the effect of fluctuations by reducing the amount of light affected by the fluctuations. The drawback of this method is the reduction of the spatial bandwidth product (SBP) of SLMs. Because the presented method requires spatial bandpass filtering using the aperture, the spectrum of a generated light should be restricted. Therefore, there is a tradeoff between the quality of the phase and SBP. The appropriate aperture size for spatial bandpass filtering varies depending on the target phase distribution. The abovementioned point should be investigated in detail.

For holographic data storage applications, reducing the SBP reduces the number of phase data symbols on a single data page. Thus, it is necessary to represent a single-phase data symbol with multiple pixels of the SLM. This decreases the data transfer rate compared with the ideal case in which every single pixel of the SLM represents a single-phase data symbol. However, with the presented method, the quality of the phase can be improved, and this is effective in improving the degree of the phase level. In terms of storage capacity, the effect of reducing the SBP may be limited. Because the illumination pattern onto a recording material in holographic data storage is the Fourier spectrum of a data page, representing a single-phase data symbol with multiple pixels of the SLM reduces the beam spot on a recording medium. Thus, recording density or storage capacity is relatively robust to the decrease in the SBP. Moreover, because the presented method improves phase quality, increasing the degree of the phase level improves storage capacity. Therefore, linear phase superimposition would improve the performance of holographic data storage systems.

In this study, we discussed the effectiveness of linear phase superimposition through experiments. To further optimize the quality of the phase and reveal the above tradeoff relationship in detail, we need to theoretically investigate the effectiveness of linear phase superimposition depending on the driving SLM scheme. This point is beyond the scope of this study. Despite the drawback, i.e., the reduction of the SBP, linear phase superimposition is an effective approach to generate high-quality phase distribution from SLMs.

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this study are not publicly available at this time but may be obtained from the authors upon reasonable request.

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25. Z. Zhang, A. M. Jeziorska-Chapman, N. Collings, M. Pivnenko, J. Moore, B. Crossland, D. P. Chu, and B. Milne, “High quality assembly of phase-only liquid crystal on silicon (LCOS) devices,” J. Disp. Technol. 7(3), 120–126 (2011). [CrossRef]  

26. Z. Zhang, Z. You, and D. Chu, “Fundamentals of phase-only liquid crystal on silicon (LCOS) devices,” Light: Sci. Appl. 3(10), e213 (2014). [CrossRef]  

27. R. J. Beck, J. P. Parry, J. D. Shephard, and D. P. Hand, “Compensation for time fluctuations of phase modulation in a liquid-crystal-on-silicon display by process synchronization in laser materials processing,” Appl. Opt. 50(18), 2899–2905 (2011). [CrossRef]  

28. H. Yang and D. P. Chu, “Phase flicker in liquid crystal on silicon devices,” JPhys Photonics 2(3), 032001 (2020). [CrossRef]  

29. J. Strauß, T. Häfner, M. Dobler, J. Heberle, and M. Schmidt, “Evaluation and calibration of LCoS SLM for direct laser structuring with tailored intensity distributions,” Phys. Procedia 83, 1160–1169 (2016). [CrossRef]  

30. J. P. Yang, F. Y. Wu, P. S. Wang, and H. P. Chen, “Characterization of the spatially anamorphic phenomenon and temporal fluctuations in high-speed, ultra-high pixels-per-inch liquid crystal on silicon phase modulator,” Opt. Express 27(22), 32168–32183 (2019). [CrossRef]  

31. I. Moreno, A. Lizana, A. Marquez, C. Iemmi, E. Fernandez, J. Campos, and M. J. Yzuel, “Time fluctuations of the phase modulation in a liquid crystal on silicon display: characterization and effects in diffractive optics,” Opt. Express 16(21), 16711–16722 (2008). [CrossRef]  

32. D. Marco, A. Vargas, M. D. M. Sanchez-Lopez, and I. Moreno, “Measuring the spatial deformation of a liquid-crystal on silicon display with a self-interference effect,” Opt. Lett. 45(16), 4480–4483 (2020). [CrossRef]  

33. S. Reichelt, “Spatially resolved phase-response calibration of liquid-crystal-based spatial light modulator,” Appl. Opt. 52(12), 2610–2618 (2013). [CrossRef]  

34. D. Engström, M. Persson, J. Bengtsson, and M. Goksör, “Calibration of spatial light modulators suffering from spatially varying phase response,” Opt. Express 21(13), 16086–16103 (2013). [CrossRef]  

35. R. Li and L. Cao, “Progress in phase calibration for liquid crystal spatial light modulators,” Appl. Sci. 9(10), 2012 (2019). [CrossRef]  

36. Y. Tong, M. Pivnenko, and D. Chu, “Improvements of phase linearity and phase flicker of phase-only LCoS devices for holographic applications,” Appl. Opt. 58(34), G248–G255 (2019). [CrossRef]  

37. H. Yang and D. P. Chu, “Phase flicker optimisation in digital liquid crystal on silicon devices,” Opt. Express 27(17), 24556–24567 (2019). [CrossRef]  

38. J. Garcia-Marquez, V. Lopez, A. Gonzalez-Vega, and E. Noe, “Flicker minimization in an LCoS spatial light modulator,” Opt. Express 20(8), 8431–8441 (2012). [CrossRef]  

39. T. Haist and W. Osten, “Holography using pixelated spatial light modulators—part 1: theory and basic considerations,” J. Micro/Nanolithogr., MEMS, MOEMS 14(4), 041310 (2015). [CrossRef]  

40. J. Liang, S. Y. Wu, F. K. Fatemi, and M. F. Becker, “Suppression of the zero-order diffracted beam from a pixelated spatial light modulator by phase compression,” Appl. Opt. 51(16), 3294–3304 (2012). [CrossRef]  

41. U. Efron, B. Apter, and E. Bahat-Treidel, “Fringing-field effect in liquid-crystal beam-steering devices: an approximate analytical model,” J. Opt. Soc. Am. A 21(10), 1996–2008 (2004). [CrossRef]  

42. M. Persson, D. Engstöom, and M. Goksör, “Reducing the effect of pixel crosstalk in phase only spatial light modulators,” Opt. Express 20(20), 22334–22343 (2012). [CrossRef]  

43. M. Agour, C. Falldorf, and C. von Kopylow, “Digital pre-filtering approach to improve optically reconstructed wavefields in opto-electronic holography,” J. Opt. 12(5), 055401 (2010). [CrossRef]  

44. J. L. Martinez, I. Moreno, M. del Mar Sanchez-Lopez, A. Vargas, and P. Garcia-Martinez, “Analysis of multiple internal reflections in a parallel aligned liquid crystal on silicon SLM,” Opt. Express 22(21), 25866–25879 (2014). [CrossRef]  

45. T. Muroi, Y. Katano, N. Kinoshita, and N. Ishii, “Dual-page reproduction to increase the data transfer rate in holographic memory,” Opt. Lett. 42(12), 2287–2290 (2017). [CrossRef]  

46. Y. Katano, T. Muroi, N. Kinoshita, and N. Ishii, “Prototype holographic data storage drive with wavefront compensation for playback of 8 K video data,” IEEE Trans. Consum. Electron. 63(3), 243–250 (2017). [CrossRef]  

47. S. Hirayama, K. Fujimura, S. Umegaki, Y. Tanaka, and T. Shimura, “Theoretical study of a surface collinear holographic memory,” Photonics 6(2), 70 (2019). [CrossRef]  

48. S. Honma and H. Funakoshi, “A two-step exposure method with interleaved phase pages for recording of SQAM signal in holographic memory,” Jpn. J. Appl. Phys. 58(SK), SKKD05 (2019). [CrossRef]  

49. Y. W. Yu, Y. C. Chen, K. H. Huang, C. Y. Cheng, T. H. Yang, S. H. Lin, and C. C. Sun, “Reduction of phase error on phase-only volume-holographic disc rotation with pre-processing by phase integral,” Opt. Express 28(19), 28573–28583 (2020). [CrossRef]  

50. X. Lin, Y. Huang, Y. Li, J. Liu, J. Liu, R. Kang, and X. Tan, “Four-level phase pair encoding and decoding with single interferometric phase retrieval for holographic data storage,” Chin. Opt. Lett. 16(3), 032101 (2018). [CrossRef]  

51. M. Tokoro and R. Fujimura, “Single-shot detection of four-level phase modulated signals using inter-pixel crosstalk for holographic data storage,” Jpn. J. Appl. Phys. 60(2), 022004 (2021). [CrossRef]  

52. T. Nobukawa, T. Fukuda, D. Barada, and T. Nomura, “Coaxial polarization holographic data recording on a polarization-sensitive medium,” Opt. Lett. 41(21), 4919–4922 (2016). [CrossRef]  

53. T. Ochiai, D. Barada, T. Fukuda, Y. Hayasaki, K. Kuroda, and T. Yatagai, “Angular multiplex recording of data pages by dual-channel polarization holography,” Opt. Lett. 38(5), 748–750 (2013). [CrossRef]  

54. J. T. Sheridan, R. K. Kostuk, A. F. Gil, Y. Wang, W. Lu, H. Zhong, Y. Tomita, C. Neipp, J. Francés, S. Gallego, I. Pascual, V. Marinova, S. H. Lin, K. Y. Hsu, F. Bruder, S. Hansen, C. Manecke, R. Meisenheimer, C. Rewitz, T. Rölle, S. Odinokov, O. Matoba, M. Kumar, X. Quan, Y. Awatsuji, P. W. Wachulak, A. V. Gorelaya, A. A. Sevryugin, E. V. Shalymov, V. Yu Venediktov, R. Chmelik, M. A. Ferrara, G. Coppola, A. Márquez, A. Beléndez, W. Yang, R. Yuste, A. Bianco, A. Zanutta, C. Falldorf, J. J. Healy, X. Fan, B. M. Hennelly, I. Zhurminsky, M. Schnieper, R. Ferrini, S. Fricke, G. Situ, H. Wang, A. S. Abdurashitov, V. V. Tuchin, N. V. Petrov, T. Nomura, D. R. Morim, and K. Saravanamuttu, “Roadmap on holography,” J. Opt. 22(12), 123002 (2020). [CrossRef]  

55. M. Hosaka, T. Ishii, A. Tanaka, S. Koga, and T. Hoshizawa, “1 Tbit/inch2 recording in angular-multiplexing holographic memory with constant signal-to-scatter ratio schedule,” Jpn. J. Appl. Phys. 52(9S2), 09LD01 (2013). [CrossRef]  

56. J. Liu, H. Horimai, X. Lin, Y. Huang, and X. Tan, “Phase modulated high density collinear holographic data storage system with phase-retrieval reference beam locking and orthogonal reference encoding,” Opt. Express 26(4), 3828–3838 (2018). [CrossRef]  

57. M. Bunsen and S. Tateyama, “Detection method for the complex amplitude of a signal beam with intensity and phase modulation using the transport of intensity equation for holographic data storage,” Opt. Express 27(17), 24029–24042 (2019). [CrossRef]  

58. J. Hao, K. Wang, Y. Zhang, H. Li, X. Lin, Z. Huang, and X. Tan, “Collinear non-interferometric phase retrieval for holographic data storage,” Opt. Express 28(18), 25795–25805 (2020). [CrossRef]  

59. T. Nobukawa and T. Nomura, “Multilevel recording of complex amplitude data pages in a holographic data storage system using digital holography,” Opt. Express 24(18), 21001–21011 (2016). [CrossRef]  

60. I. Moreno, J. Campos, C. Gorecki, and M. J. Yzuel, “Effects of amplitude and phase mismatching errors in the generation of a kinoform for pattern recognition,” Jpn. J. Appl. Phys. 34(Part 1, No. 12A), 6423–6432 (1995). [CrossRef]  

61. H. Zhang, J. Xie, J. Liu, and Y. Wang, “Elimination of a zero-order beam induced by a pixelated spatial light modulator for holographic projection,” Appl. Opt. 48(30), 5834–5841 (2009). [CrossRef]  

62. M. Takeda, “Fourier fringe analysis and its application to metrology of extreme physical phenomena: a review [Invited],” Appl. Opt. 52(1), 20–29 (2013). [CrossRef]  

63. H. M. Chen, J. P. Yang, H. T. Yen, Z. N. Hsu, Y. Huang, and S. T. Wu, “Pursuing high quality phase-only liquid crystal on silicon (LCoS) devices,” Appl. Sci. 8(11), 2323 (2018). [CrossRef]  

64. J. L. Martínez, P. García-Martínez, and I. Moreno, “Microscope system with on axis programmable Fourier transform filtering,” Opt. Lasers Eng. 89, 116–122 (2017). [CrossRef]  

65. F. J. Martinez, A. Marquez, S. Gallego, M. Ortuno, J. Frances, A. Belendez, and I. Pascual, “Averaged Stokes polarimetry applied to evaluate retardance and flicker in PA-LCoS devices,” Opt. Express 22(12), 15064–15074 (2014). [CrossRef]  

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  60. I. Moreno, J. Campos, C. Gorecki, and M. J. Yzuel, “Effects of amplitude and phase mismatching errors in the generation of a kinoform for pattern recognition,” Jpn. J. Appl. Phys. 34(Part 1, No. 12A), 6423–6432 (1995).
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  61. H. Zhang, J. Xie, J. Liu, and Y. Wang, “Elimination of a zero-order beam induced by a pixelated spatial light modulator for holographic projection,” Appl. Opt. 48(30), 5834–5841 (2009).
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  62. M. Takeda, “Fourier fringe analysis and its application to metrology of extreme physical phenomena: a review [Invited],” Appl. Opt. 52(1), 20–29 (2013).
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  63. H. M. Chen, J. P. Yang, H. T. Yen, Z. N. Hsu, Y. Huang, and S. T. Wu, “Pursuing high quality phase-only liquid crystal on silicon (LCoS) devices,” Appl. Sci. 8(11), 2323 (2018).
    [Crossref]
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2021 (2)

C. M. Chia, S. Vyas, T. H. Wu, J. A. Yeh, and Y. Luo, “Multi-plane confocal microscopy with multiplexed volume holographic gratings [Invited],” Appl. Opt. 60(10), B141–B150 (2021).
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M. Tokoro and R. Fujimura, “Single-shot detection of four-level phase modulated signals using inter-pixel crosstalk for holographic data storage,” Jpn. J. Appl. Phys. 60(2), 022004 (2021).
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2020 (7)

J. T. Sheridan, R. K. Kostuk, A. F. Gil, Y. Wang, W. Lu, H. Zhong, Y. Tomita, C. Neipp, J. Francés, S. Gallego, I. Pascual, V. Marinova, S. H. Lin, K. Y. Hsu, F. Bruder, S. Hansen, C. Manecke, R. Meisenheimer, C. Rewitz, T. Rölle, S. Odinokov, O. Matoba, M. Kumar, X. Quan, Y. Awatsuji, P. W. Wachulak, A. V. Gorelaya, A. A. Sevryugin, E. V. Shalymov, V. Yu Venediktov, R. Chmelik, M. A. Ferrara, G. Coppola, A. Márquez, A. Beléndez, W. Yang, R. Yuste, A. Bianco, A. Zanutta, C. Falldorf, J. J. Healy, X. Fan, B. M. Hennelly, I. Zhurminsky, M. Schnieper, R. Ferrini, S. Fricke, G. Situ, H. Wang, A. S. Abdurashitov, V. V. Tuchin, N. V. Petrov, T. Nomura, D. R. Morim, and K. Saravanamuttu, “Roadmap on holography,” J. Opt. 22(12), 123002 (2020).
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Y. W. Yu, Y. C. Chen, K. H. Huang, C. Y. Cheng, T. H. Yang, S. H. Lin, and C. C. Sun, “Reduction of phase error on phase-only volume-holographic disc rotation with pre-processing by phase integral,” Opt. Express 28(19), 28573–28583 (2020).
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D. Marco, A. Vargas, M. D. M. Sanchez-Lopez, and I. Moreno, “Measuring the spatial deformation of a liquid-crystal on silicon display with a self-interference effect,” Opt. Lett. 45(16), 4480–4483 (2020).
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J. Hao, K. Wang, Y. Zhang, H. Li, X. Lin, Z. Huang, and X. Tan, “Collinear non-interferometric phase retrieval for holographic data storage,” Opt. Express 28(18), 25795–25805 (2020).
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H. Yang and D. P. Chu, “Phase flicker in liquid crystal on silicon devices,” JPhys Photonics 2(3), 032001 (2020).
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N. Yoneda, Y. Saita, and T. Nomura, “Motionless optical scanning holography,” Opt. Lett. 45(12), 3184–3187 (2020).
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M. Meem, S. Banerji, C. Pies, T. Oberbiermann, A. Majumder, B. Sensale-Rodriguez, and R. Menon, “Large-area, high-numerical-aperture multi-level diffractive lens via inverse design,” Optica 7(3), 252–253 (2020).
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2019 (10)

T. Nobukawa, Y. Katano, T. Muroi, N. Kinoshita, and N. Ishii, “Bimodal incoherent digital holography for both three-dimensional imaging and quasi-infinite-depth-of-field imaging,” Sci. Rep. 9(1), 3363 (2019).
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J. Rosen, A. Vijayakumar, M. Kumar, M. R. Rai, R. Kelner, Y. Kashter, A. Bulbul, and S. Mukherjee, “Recent advances in self-interference incoherent digital holography,” Adv. Opt. Photonics 11(1), 1–66 (2019).
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J. P. Yang, F. Y. Wu, P. S. Wang, and H. P. Chen, “Characterization of the spatially anamorphic phenomenon and temporal fluctuations in high-speed, ultra-high pixels-per-inch liquid crystal on silicon phase modulator,” Opt. Express 27(22), 32168–32183 (2019).
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R. Li and L. Cao, “Progress in phase calibration for liquid crystal spatial light modulators,” Appl. Sci. 9(10), 2012 (2019).
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Y. Tong, M. Pivnenko, and D. Chu, “Improvements of phase linearity and phase flicker of phase-only LCoS devices for holographic applications,” Appl. Opt. 58(34), G248–G255 (2019).
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H. Yang and D. P. Chu, “Phase flicker optimisation in digital liquid crystal on silicon devices,” Opt. Express 27(17), 24556–24567 (2019).
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G. Lazarev, P. J. Chen, J. Strauss, N. Fontaine, and A. Forbes, “Beyond the display: phase-only liquid crystal on Silicon devices and their applications in photonics [Invited],” Opt. Express 27(11), 16206–16249 (2019).
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M. Bunsen and S. Tateyama, “Detection method for the complex amplitude of a signal beam with intensity and phase modulation using the transport of intensity equation for holographic data storage,” Opt. Express 27(17), 24029–24042 (2019).
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S. Hirayama, K. Fujimura, S. Umegaki, Y. Tanaka, and T. Shimura, “Theoretical study of a surface collinear holographic memory,” Photonics 6(2), 70 (2019).
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S. Honma and H. Funakoshi, “A two-step exposure method with interleaved phase pages for recording of SQAM signal in holographic memory,” Jpn. J. Appl. Phys. 58(SK), SKKD05 (2019).
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2018 (6)

2017 (5)

M. Wang, L. Zong, L. Mao, A. Marquez, Y. Ye, H. Zhao, and F. Vaquero Caballero, “LCoS SLM study and its application in wavelength selective switch,” Photonics 4(4), 22 (2017).
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P. Genevet, F. Capasso, F. Aieta, M. Khorasaninejad, and R. Devlin, “Recent advances in planar optics: from plasmonic to dielectric metasurfaces,” Optica 4(1), 139–152 (2017).
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J. L. Martínez, P. García-Martínez, and I. Moreno, “Microscope system with on axis programmable Fourier transform filtering,” Opt. Lasers Eng. 89, 116–122 (2017).
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T. Muroi, Y. Katano, N. Kinoshita, and N. Ishii, “Dual-page reproduction to increase the data transfer rate in holographic memory,” Opt. Lett. 42(12), 2287–2290 (2017).
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Y. Katano, T. Muroi, N. Kinoshita, and N. Ishii, “Prototype holographic data storage drive with wavefront compensation for playback of 8 K video data,” IEEE Trans. Consum. Electron. 63(3), 243–250 (2017).
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2016 (7)

T. Nobukawa, T. Fukuda, D. Barada, and T. Nomura, “Coaxial polarization holographic data recording on a polarization-sensitive medium,” Opt. Lett. 41(21), 4919–4922 (2016).
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T. Nobukawa and T. Nomura, “Multilevel recording of complex amplitude data pages in a holographic data storage system using digital holography,” Opt. Express 24(18), 21001–21011 (2016).
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J. Strauß, T. Häfner, M. Dobler, J. Heberle, and M. Schmidt, “Evaluation and calibration of LCoS SLM for direct laser structuring with tailored intensity distributions,” Phys. Procedia 83, 1160–1169 (2016).
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J. Wang, “Advances in communications using optical vortices,” Photonics Res. 4(5), B14–B28 (2016).
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T. W. Clark, R. F. Offer, S. Franke-Arnold, A. S. Arnold, and N. Radwell, “Comparison of beam generation techniques using a phase only spatial light modulator,” Opt. Express 24(6), 6249–6264 (2016).
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K. Wakunami, P. Y. Hsieh, R. Oi, T. Senoh, H. Sasaki, Y. Ichihashi, M. Okui, Y. P. Huang, and K. Yamamoto, “Projection-type see-through holographic three-dimensional display,” Nat. Commun. 7(1), 12954 (2016).
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M. Yamaguchi, “Light-field and holographic three-dimensional displays [Invited],” J. Opt. Soc. Am. A 33(12), 2348–2364 (2016).
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2015 (2)

X. Li, Y. Cao, N. Tian, L. Fu, and M. Gu, “Multifocal optical nanoscopy for big data recording at 30 TB capacity and gigabits/second data rate,” Optica 2(6), 567–570 (2015).
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T. Haist and W. Osten, “Holography using pixelated spatial light modulators—part 1: theory and basic considerations,” J. Micro/Nanolithogr., MEMS, MOEMS 14(4), 041310 (2015).
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2014 (5)

J. L. Martinez, I. Moreno, M. del Mar Sanchez-Lopez, A. Vargas, and P. Garcia-Martinez, “Analysis of multiple internal reflections in a parallel aligned liquid crystal on silicon SLM,” Opt. Express 22(21), 25866–25879 (2014).
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F. J. Martinez, A. Marquez, S. Gallego, M. Ortuno, J. Frances, A. Belendez, and I. Pascual, “Averaged Stokes polarimetry applied to evaluate retardance and flicker in PA-LCoS devices,” Opt. Express 22(12), 15064–15074 (2014).
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J. Zhang, M. Gecevicius, M. Beresna, and P. G. Kazansky, “Seemingly unlimited lifetime data storage in nanostructured glass,” Phys. Rev. Lett. 112(3), 033901 (2014).
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S. Hasegawa and Y. Hayasaki, “Holographic vector wave femtosecond laser processing,” Int. J. Optomechatronics 8(2), 73–88 (2014).
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Z. Zhang, Z. You, and D. Chu, “Fundamentals of phase-only liquid crystal on silicon (LCOS) devices,” Light: Sci. Appl. 3(10), e213 (2014).
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2013 (7)

2012 (4)

2011 (3)

R. J. Beck, J. P. Parry, J. D. Shephard, and D. P. Hand, “Compensation for time fluctuations of phase modulation in a liquid-crystal-on-silicon display by process synchronization in laser materials processing,” Appl. Opt. 50(18), 2899–2905 (2011).
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Z. Zhang, A. M. Jeziorska-Chapman, N. Collings, M. Pivnenko, J. Moore, B. Crossland, D. P. Chu, and B. Milne, “High quality assembly of phase-only liquid crystal on silicon (LCOS) devices,” J. Disp. Technol. 7(3), 120–126 (2011).
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C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photonics Rev. 5(1), 81–101 (2011).
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2010 (1)

M. Agour, C. Falldorf, and C. von Kopylow, “Digital pre-filtering approach to improve optically reconstructed wavefields in opto-electronic holography,” J. Opt. 12(5), 055401 (2010).
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2009 (1)

2008 (1)

2007 (1)

T. Inoue, H. Tanaka, N. Fukuchi, M. Takumi, N. Matsumoto, T. Hara, N. Yoshida, Y. Igasaki, and Y. Kobayashi, “LCOS spatial light modulator controlled by 12-bit signals for optical phase-only modulation,” Proc. SPIE 6487, 64870Y (2007).
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2004 (1)

1995 (1)

I. Moreno, J. Campos, C. Gorecki, and M. J. Yzuel, “Effects of amplitude and phase mismatching errors in the generation of a kinoform for pattern recognition,” Jpn. J. Appl. Phys. 34(Part 1, No. 12A), 6423–6432 (1995).
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Aburakawa, Y.

Agour, M.

M. Agour, C. Falldorf, and C. von Kopylow, “Digital pre-filtering approach to improve optically reconstructed wavefields in opto-electronic holography,” J. Opt. 12(5), 055401 (2010).
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Aieta, F.

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M. Woerdemann, C. Alpmann, M. Esseling, and C. Denz, “Advanced optical trapping by complex beam shaping,” Laser Photonics Rev. 7(6), 839–854 (2013).
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Arnold, A. S.

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J. T. Sheridan, R. K. Kostuk, A. F. Gil, Y. Wang, W. Lu, H. Zhong, Y. Tomita, C. Neipp, J. Francés, S. Gallego, I. Pascual, V. Marinova, S. H. Lin, K. Y. Hsu, F. Bruder, S. Hansen, C. Manecke, R. Meisenheimer, C. Rewitz, T. Rölle, S. Odinokov, O. Matoba, M. Kumar, X. Quan, Y. Awatsuji, P. W. Wachulak, A. V. Gorelaya, A. A. Sevryugin, E. V. Shalymov, V. Yu Venediktov, R. Chmelik, M. A. Ferrara, G. Coppola, A. Márquez, A. Beléndez, W. Yang, R. Yuste, A. Bianco, A. Zanutta, C. Falldorf, J. J. Healy, X. Fan, B. M. Hennelly, I. Zhurminsky, M. Schnieper, R. Ferrini, S. Fricke, G. Situ, H. Wang, A. S. Abdurashitov, V. V. Tuchin, N. V. Petrov, T. Nomura, D. R. Morim, and K. Saravanamuttu, “Roadmap on holography,” J. Opt. 22(12), 123002 (2020).
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X. Quan, M. Kumar, O. Matoba, Y. Awatsuji, Y. Hayasaki, S. Hasegawa, and H. Wake, “Three-dimensional stimulation and imaging-based functional optical microscopy of biological cells,” Opt. Lett. 43(21), 5447–5450 (2018).
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K. Curtis, L. Dhar, A. J. Hill, W. L. Wilson, and M. R. Ayres, Holographic Data Storage: From Theory to Practical Systems (Wiley, 2010).

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G. Nehmetallah and P. P. Banerjee, “Applications of digital and analog holography in three-dimensional imaging,” Adv. Opt. Photonics 4(4), 472–553 (2012).
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J. T. Sheridan, R. K. Kostuk, A. F. Gil, Y. Wang, W. Lu, H. Zhong, Y. Tomita, C. Neipp, J. Francés, S. Gallego, I. Pascual, V. Marinova, S. H. Lin, K. Y. Hsu, F. Bruder, S. Hansen, C. Manecke, R. Meisenheimer, C. Rewitz, T. Rölle, S. Odinokov, O. Matoba, M. Kumar, X. Quan, Y. Awatsuji, P. W. Wachulak, A. V. Gorelaya, A. A. Sevryugin, E. V. Shalymov, V. Yu Venediktov, R. Chmelik, M. A. Ferrara, G. Coppola, A. Márquez, A. Beléndez, W. Yang, R. Yuste, A. Bianco, A. Zanutta, C. Falldorf, J. J. Healy, X. Fan, B. M. Hennelly, I. Zhurminsky, M. Schnieper, R. Ferrini, S. Fricke, G. Situ, H. Wang, A. S. Abdurashitov, V. V. Tuchin, N. V. Petrov, T. Nomura, D. R. Morim, and K. Saravanamuttu, “Roadmap on holography,” J. Opt. 22(12), 123002 (2020).
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J. Zhang, M. Gecevicius, M. Beresna, and P. G. Kazansky, “Seemingly unlimited lifetime data storage in nanostructured glass,” Phys. Rev. Lett. 112(3), 033901 (2014).
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C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photonics Rev. 5(1), 81–101 (2011).
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J. T. Sheridan, R. K. Kostuk, A. F. Gil, Y. Wang, W. Lu, H. Zhong, Y. Tomita, C. Neipp, J. Francés, S. Gallego, I. Pascual, V. Marinova, S. H. Lin, K. Y. Hsu, F. Bruder, S. Hansen, C. Manecke, R. Meisenheimer, C. Rewitz, T. Rölle, S. Odinokov, O. Matoba, M. Kumar, X. Quan, Y. Awatsuji, P. W. Wachulak, A. V. Gorelaya, A. A. Sevryugin, E. V. Shalymov, V. Yu Venediktov, R. Chmelik, M. A. Ferrara, G. Coppola, A. Márquez, A. Beléndez, W. Yang, R. Yuste, A. Bianco, A. Zanutta, C. Falldorf, J. J. Healy, X. Fan, B. M. Hennelly, I. Zhurminsky, M. Schnieper, R. Ferrini, S. Fricke, G. Situ, H. Wang, A. S. Abdurashitov, V. V. Tuchin, N. V. Petrov, T. Nomura, D. R. Morim, and K. Saravanamuttu, “Roadmap on holography,” J. Opt. 22(12), 123002 (2020).
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J. Rosen, A. Vijayakumar, M. Kumar, M. R. Rai, R. Kelner, Y. Kashter, A. Bulbul, and S. Mukherjee, “Recent advances in self-interference incoherent digital holography,” Adv. Opt. Photonics 11(1), 1–66 (2019).
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S. Ngcobo, I. Litvin, L. Burger, and A. Forbes, “A digital laser for on-demand laser modes,” Nat. Commun. 4(1), 2289 (2013).
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I. Moreno, A. Lizana, A. Marquez, C. Iemmi, E. Fernandez, J. Campos, and M. J. Yzuel, “Time fluctuations of the phase modulation in a liquid crystal on silicon display: characterization and effects in diffractive optics,” Opt. Express 16(21), 16711–16722 (2008).
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R. Li and L. Cao, “Progress in phase calibration for liquid crystal spatial light modulators,” Appl. Sci. 9(10), 2012 (2019).
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Capasso, F.

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H. M. Chen, J. P. Yang, H. T. Yen, Z. N. Hsu, Y. Huang, and S. T. Wu, “Pursuing high quality phase-only liquid crystal on silicon (LCoS) devices,” Appl. Sci. 8(11), 2323 (2018).
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J. T. Sheridan, R. K. Kostuk, A. F. Gil, Y. Wang, W. Lu, H. Zhong, Y. Tomita, C. Neipp, J. Francés, S. Gallego, I. Pascual, V. Marinova, S. H. Lin, K. Y. Hsu, F. Bruder, S. Hansen, C. Manecke, R. Meisenheimer, C. Rewitz, T. Rölle, S. Odinokov, O. Matoba, M. Kumar, X. Quan, Y. Awatsuji, P. W. Wachulak, A. V. Gorelaya, A. A. Sevryugin, E. V. Shalymov, V. Yu Venediktov, R. Chmelik, M. A. Ferrara, G. Coppola, A. Márquez, A. Beléndez, W. Yang, R. Yuste, A. Bianco, A. Zanutta, C. Falldorf, J. J. Healy, X. Fan, B. M. Hennelly, I. Zhurminsky, M. Schnieper, R. Ferrini, S. Fricke, G. Situ, H. Wang, A. S. Abdurashitov, V. V. Tuchin, N. V. Petrov, T. Nomura, D. R. Morim, and K. Saravanamuttu, “Roadmap on holography,” J. Opt. 22(12), 123002 (2020).
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Y. Tong, M. Pivnenko, and D. Chu, “Improvements of phase linearity and phase flicker of phase-only LCoS devices for holographic applications,” Appl. Opt. 58(34), G248–G255 (2019).
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Z. Zhang, Z. You, and D. Chu, “Fundamentals of phase-only liquid crystal on silicon (LCOS) devices,” Light: Sci. Appl. 3(10), e213 (2014).
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H. Yang and D. P. Chu, “Phase flicker in liquid crystal on silicon devices,” JPhys Photonics 2(3), 032001 (2020).
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H. Yang and D. P. Chu, “Phase flicker optimisation in digital liquid crystal on silicon devices,” Opt. Express 27(17), 24556–24567 (2019).
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Z. Zhang, A. M. Jeziorska-Chapman, N. Collings, M. Pivnenko, J. Moore, B. Crossland, D. P. Chu, and B. Milne, “High quality assembly of phase-only liquid crystal on silicon (LCOS) devices,” J. Disp. Technol. 7(3), 120–126 (2011).
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Collings, N.

Z. Zhang, A. M. Jeziorska-Chapman, N. Collings, M. Pivnenko, J. Moore, B. Crossland, D. P. Chu, and B. Milne, “High quality assembly of phase-only liquid crystal on silicon (LCOS) devices,” J. Disp. Technol. 7(3), 120–126 (2011).
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J. T. Sheridan, R. K. Kostuk, A. F. Gil, Y. Wang, W. Lu, H. Zhong, Y. Tomita, C. Neipp, J. Francés, S. Gallego, I. Pascual, V. Marinova, S. H. Lin, K. Y. Hsu, F. Bruder, S. Hansen, C. Manecke, R. Meisenheimer, C. Rewitz, T. Rölle, S. Odinokov, O. Matoba, M. Kumar, X. Quan, Y. Awatsuji, P. W. Wachulak, A. V. Gorelaya, A. A. Sevryugin, E. V. Shalymov, V. Yu Venediktov, R. Chmelik, M. A. Ferrara, G. Coppola, A. Márquez, A. Beléndez, W. Yang, R. Yuste, A. Bianco, A. Zanutta, C. Falldorf, J. J. Healy, X. Fan, B. M. Hennelly, I. Zhurminsky, M. Schnieper, R. Ferrini, S. Fricke, G. Situ, H. Wang, A. S. Abdurashitov, V. V. Tuchin, N. V. Petrov, T. Nomura, D. R. Morim, and K. Saravanamuttu, “Roadmap on holography,” J. Opt. 22(12), 123002 (2020).
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Z. Zhang, A. M. Jeziorska-Chapman, N. Collings, M. Pivnenko, J. Moore, B. Crossland, D. P. Chu, and B. Milne, “High quality assembly of phase-only liquid crystal on silicon (LCOS) devices,” J. Disp. Technol. 7(3), 120–126 (2011).
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M. Woerdemann, C. Alpmann, M. Esseling, and C. Denz, “Advanced optical trapping by complex beam shaping,” Laser Photonics Rev. 7(6), 839–854 (2013).
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K. Curtis, L. Dhar, A. J. Hill, W. L. Wilson, and M. R. Ayres, Holographic Data Storage: From Theory to Practical Systems (Wiley, 2010).

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J. Strauß, T. Häfner, M. Dobler, J. Heberle, and M. Schmidt, “Evaluation and calibration of LCoS SLM for direct laser structuring with tailored intensity distributions,” Phys. Procedia 83, 1160–1169 (2016).
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Engstöom, D.

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M. Woerdemann, C. Alpmann, M. Esseling, and C. Denz, “Advanced optical trapping by complex beam shaping,” Laser Photonics Rev. 7(6), 839–854 (2013).
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Data availability

Data underlying the results presented in this study are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Figures (8)

Fig. 1.
Fig. 1. Schematic of a linear phase superimposition technique with spatial bandpass filtering for generating a high-quality phase distribution by reducing the effect of phase fluctuations on a phase-only SLM
Fig. 2.
Fig. 2. Details of the linear phase pattern introduced to an SLM—(a) enlarged view of a typical linear phase pattern, and (b) its Fourier spectrum; the broken line shows the Nyquist size is of a phase-only SLM
Fig. 3.
Fig. 3. Experimental setup for the evaluation on the effect of linear phase superimposition
Fig. 4.
Fig. 4. Generation of the target phase for experimental evaluation—(a) phase distribution of a phase data page consisting of four-phase values; (b) phase signal on a complex plane or constellation diagram; (c) Fourier spectrum; and (d) linear phase superimposition onto the phase data page
Fig. 5.
Fig. 5. Evaluation results of an analog SLM without linear phase superimposition—(a)–(c): Measured amplitude and phase distributions at exposure times of 50, 10, and 1 ms, respectively; (d)–(f): Fourier spectra of the measured distributions of (a)–(c); (g)–(i): constellation diagrams of (a)–(c); in the constellation diagrams, the maximum amplitude is normalized as one for the evaluation of signal variation
Fig. 6.
Fig. 6. Evaluation results of analog SLM with linear phase superimposition—(a)–(c): measured amplitude and phase distributions at exposure times of 50, 10, and 1 ms, respectively; (d)–(f): Fourier spectra of the measured distributions of (a)–(c); and (g)–(i): constellation diagrams of (a)–(c)
Fig. 7.
Fig. 7. Evaluation results of digital SLM without linear phase superimposition—(a)–(c): measured amplitude and phase distributions at exposure times of 50, 10, and 1 ms, respectively; (d)–(f): Fourier spectra of the measured distributions of (a)–(c); and (g)–(i): constellation diagrams of (a)–(c)
Fig. 8.
Fig. 8. Evaluation results of digital SLM with linear phase superimposition—(a)–(c): measured amplitude and phase distributions at exposure times of 50, 10, and 1 ms, respectively; (d)–(f): Fourier spectra of the measured distributions of (a)–(c); and (g)–(i): constellation diagrams of (a)–(c)

Equations (3)

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ϕ l ( m , n ) = mod { π 2 ( i m + j n ) , 2 π } ,
ϕ s l m ( m , n ) = mod { ϕ l ( m , n ) + ϕ d ( m , n ) , 2 π } .
MER [dB] =  10 log 10 ( k = 1 N | O k | 2 k = 1 N | O k C k | 2 ) ,