Content area
Liquid-crystal spatial light modulators are used in solving a broad range of contemporary problems in science and engineering. With the help of these modulators, it is possible to control the amplitude, phase, and direction of propagation of the coherent optical radiation in optical data-processing systems. However, the influences of the characteristics of time dynamics of liquid-crystal spatial light modulators on the performance of information optical systems, including diffraction neural networks, are studied quite poorly. We present the results of investigation of the time dynamics of phase modulation of an SLM-200 (Santec, Japan) liquid-crystal spatial light modulator. In our experiments, we used computer-synthesized binary phase-diffraction optical elements, and measured the characteristics of time dynamics of the optical modulator: 125 msec is the rise time of diffraction efficiency in the case of displaying of optical diffraction elements on the screen and 61.9 msec is the time of decay when switching the frames. For these characteristics, we can guarantee the formation of a variable optical field at a frame display frequency of 2 Hz with an interference level of—17.1 dB. As the frame display frequency increases, we observe the appearance of unavoidable interframe interferences, which, in turn, restrict the efficient performance of the information system. The obtained results can be used in the design of high-performance systems of optical data processing and diffraction neural networks.
Introduction
At present, the field of investigations of artificial neural networks is actively developed, numerous types of neural-network architectures are known, and the methods for their analysis are available [1]. Artificial neural networks can be used to solve practical problems in various fields, such as medicine [2], telecommunications [3], computer vision [4], natural language processing [5], and 3D visualization [6]. However, contemporary digital neural networks impose high computational, power, and energy requirements restricting the growth of efficiency [7, 8]. For the most part, this explains rapid development of the optical neural networks characterized both by high energy efficiency [9] and a high degree of parallelization of the computational operations [10]. As one of the classes of optical neural networks, we can mention diffraction neural networks in which diffraction is used as the main principle for the realization of synapses [11].
The efficiency of diffraction neural networks directly depends on the characteristics of the applied optoelectronic components. In the analyzed case, these components are spatial light modulators (SLM), which directly reflect the diffraction optical elements (DOEs), the layers of neurons in the neural networks. Among the parameters of optical modulators, the strongest influence on the efficiency characteristics of the diffraction neural networks is exerted by the space resolution, maximum frame rate, and the time dynamics of modulation [12].
The aim of the present study is to measure various characteristics of the time dynamics of an SLM-200 (Santec, Japan) liquid-crystal SLM, such as the time of increase in the diffraction efficiency, the time of its drop corresponding to the change in DOE, and the level of interframe noise, as well as to analyze the applicability of liquid-crystal modulators in the schemes of diffraction neural networks.
Spatial modulators in diffraction neural networks
The optical neural networks (ONN) can be regarded as the collection of methods intended for the hardware implementation either of separate computational stages or of the entire architectures of artificial neural networks based on the application of the optical systems of data transmission and processing in the form of light signals and images.
Optical technologies are mainly used in the construction of neural networks for the operations of matrix multiplication (actually, of connecting neurons in different layers with each other), integration, nonlinear activation, convolution of matrices, and training [11]. There are different approaches to the construction of the ONN systems based on different optical effects used for the realization of synapses and adjusting their weight matrices. These effects include, in particular, propagation of radiation [13], light scattering [14], energy exchange between the light waves in closely located waveguides [15], interference [1], and diffraction [17, 18, 19–20].
Various implementations of the ONN include different degrees and ways of integration optical systems into the architectures of neural networks. Among other networks, we can mention (as promising) the neural networks based on diffraction regarded as a fundamental principle for establishing the inter-neuron connections via the control over the amplitude, phase, and direction of the coherent radiation [10, 17]. The information on the weight matrices of synapses is introduced in these systems by means of the DOE, which may have the form either of phase plates with complex microscopic surface topography [17] or of holographic optical elements [11]. To improve the universality and convenience of the real-time rearrangement of the system, it is customary to use computer-synthesized holograms displayed in SLM [21, 22]. To synthesize holograms (in fact, to perform training of the neural network), it is customary to apply iterative phase-restoration algorithms, e.g., the random trajectory search method [23] or the Gerchberg-Saxton algorithm [24].
Proposed scheme for measuring the parameters of modulation
The declared characteristics of the studied SLM-200 liquid-crystal SLM are as follows: a resolution of 1920×1200 (2.1 megapixels); pixels 7.8 × 7.8 μm in size; the number of grayscale levels is 1024 (10 bits), and the nominal frame rate is equal to 60 Hz.
In the present work, to measure the variable dynamic characteristics of the SLM-200 liquid-crystal SLM, we use an experimental scheme similar to that described in [12]. As a source of radiation, we used a Cobolt Samba-200 (HÜBNER Photonics GmbH, Germany) continuous single-frequency diode-pumped solid-state laser with a power of 5 mW and a central emission wavelength of 532 nm. To remove the side diffraction maxima, the laser beam was additionally attenuated by an optical filter. The divergent beam obtained after space filtering illuminated the beam-splitting cube and the SLM standing behind it.
At the center of the SLM microdisplay, three models of phase binary out-off-axis focusing DOE 1024×1024 readings in size were displayed , in turn at a frequency f = 2 Hz. The applied DOE have different angles of deviation of the focus from the principal optical axis of the system, which guarantees the possibility of formation of three spatially separated focused light spots in the plane of the photosensor matrix of the camera. The holograms were computed by using an iterative search method with random trajectory for a spherically divergent reading beam [25].
To record reconstructed images, we used a Flare 48 MP CoaXPress digital camera (Vieworks, South Korea) configured to record images in the ROI (region of interest) mode. The characteristics of the camera are as follows: a resolution of 7920×6004 (48 megapixels); pixels 4.6 × 4.6 μm in size; the full frame recording rate is 30 Hz; the ROI 400×128 pixels in size, and the frame frequency in the ROI mode equal to 1 kHz.
We performed two series of measurements; each series contained 1500 images and was equivalent to one complete cycle of sequential switchings of three DOE. Examples of images of the light spots for each DOE are shown in Fig. 1. The time dependence of the diffraction efficiency is shown in Fig. 2.
[See PDF for image]
Fig. 1
Images of the light spots for a liquid crystal modulator with three focusing diffraction optical elements
[See PDF for image]
Fig. 2
Time dependences of the diffraction efficiency η of the first 1, second 2 and third 3 DOE
By using the obtained dependences, we measured the times of increase Ti and decrease Td for the diffraction efficiency levels η1 = 10; 90% and η2 = 25; 75% of the maximum value. At a frequency f = 2 Hz of updating the SLM frames, we estimated the mean level of interframe interference as the ratio of the area of overlapping of the neighboring switchings to the average area under the plot of diffraction efficiency for a single DOE switching. An example of the dynamics of a single DOE switching is shown in Fig. 3. The measured characteristics are presented in Table 1. The measurement errors are estimated according to the standard deviation S with regard for the confidence probability P = 0.68.
[See PDF for image]
Fig. 3
Dynamics of a single switching of DOE
Table 1. Measured characteristics of the time dynamics of an SLM-200 liquid-crystal modulator
Characteristics | Measurement conditions | Mean value | S |
|---|---|---|---|
Ti, msec | η1 | 125.0 | 3.0 |
η2 | 61.4 | 0.4 | |
Td, msec | η1 | 61.9 | 0.9 |
η2 | 32.2 | 0.4 | |
Fp, dB | f | −17.1 | 0.3 |
The results obtained for the times Ti and Td according to the diffraction efficiency levels η1 reveal an improvement in the time dynamics of the SLM-200 Santec model compared, e.g., with the dynamics of the HoloEye Pluto‑2 [12] and HoloEye GAEA‑2 [26] models. In addition, the SLM-200 model is characterized by a lower level of interframe noise as compared with the Pluto‑2 model. Nevertheless, both the Pluto‑2 model and the SLM-200 model are unsuitable for the high-precision formation of the optical fields with the maximum frame rate declared by the manufacturer, i.e., 60 Hz.
The restrictions imposed on the speed of liquid-crystal radiation modulators negatively affect their applicability in the optical neural networks, which manifests itself in a decrease in the maximum speed of processing of the input images and a decrease in the rate of rearrangement of weights in separate layers of the network.
In addition, to attain the maximum possible efficiency of operation, the liquid-crystal modulators of the commonly used models should be illuminated by normally incident light beams, which may lead to the repeated modulation of the reflected radiation and the formation of noise. This phenomenon should be additionally taken into account in the design of multilayer neural networks with several liquid-crystal modulators.
At the same time, liquid-crystal modulators offer some other possibilities for application in diffraction neural networks caused by their slow response, namely, rapid layer prototyping and reproduction of the frozen layers of preliminarily trained neural networks by DOE.
The micromirror SLM can be regarded as a possible alternative to liquid-crystal devices in the diffraction neural networks. At present, the specific features of their application and their influence on the efficiency of neural networks require additional research. In particular, the influence of the type of modulation (amplitude or phase) on the efficiency of the system, as well as the approaches to the design of multilayer networks with two or more micromirror modulators are now studied quite poorly.
Conclusions
The results of measurements of the characteristics of the time dynamics of phase modulation for the SLM-200 liquid-crystal SLM, i.e., the durations of rise of the leading edge and decrease in the trailing edge of the response and the level of interframe noise at a frequency of 2 Hz, confirmed the limitation of speed of operation of the diffraction neural networks. The impossibility of accurate and high-speed formation of the diffraction optical fields may reduce the efficient speed of response in numerous key operations, including the data input in the system or rearrangement of the weighting matrices. In addition, certain specific features of the construction of liquid-crystal SLM create a risk of undesirable repeated modulation of radiation in the case where multiple devices are used within a single optical system. In general, these circumstances should be taken into account in the design of high-performance multilayer optical neural networks based on liquid-crystal SLM. Micro-mirror modulators may become an alternative to the liquid-crystal SLMs. However, they require additional investigations.
Funding
The present work was financially supported by the Russian Science Foundation (RSF), Project No. 23-12-00336.
Author Contribution
R. S. Starikov, E. Yu. Zlokazov, and E. K. Petrova conceived this research and designed the experiments. A. A. Volkov and T. Z. Minikhanov performed the experiments and analysis. R. S. Starikov and A. A. Volkov participated in the design and interpretation of the data. E. Yu. Zlokazov, A. A. Volkov, and A. V. Shifrina wrote the paper and participated in its revisions. All authors read and approved the final manuscript.
Conflict of interest
The authors declare that they have no potential conflict of interest in relation to the study in the present paper.
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
References
1. LeCun, Y; Bottou, L; Bengio, Y; Haffner, P. Gradient-based learning applied to document recognition. Proc. Ieee; 1998; 86,
2. Amisha, PM. M. Pathania, and V. K. Rathaur, “Overview of artificial intelligence in medicine,”; 2019; pp. 2328-2331. [DOI: https://dx.doi.org/10.4103/jfmpc.jfmpc_440_19]
3. Jiang, C; Zhang, H; Zh, YRH; Kw-Ch, C; Hanzo, L. Machine learning paradigms for next-generation wireless networks. Ieee Wirel. Comm.; 2017; 24,
4. Wei, H; Laszewski, M; Kehtarnavaz, N. Deep learning-based person detection and classification for far field video surveillance,” 2018 IEEE 13th Dallas Circuits and Systems Conf. (DCAS); 2018; pp. 1-4. [DOI: https://dx.doi.org/10.1109/DCAS.2018.8620111]
5. Collobert, R; Weston, J. “A unified architecture for natural language processing: Deep neural networks with multitask learning.” Proc. of the 25th Internat. Conf. on Machine Learning; 2008; pp. 160-167. [DOI: https://dx.doi.org/10.1145/1390156.1390177]
6. Rymov, D; Svistunov, A; Starikov, R; Shifrina, A; Rodin, V; Evtikhiev, N; Cheremkhin, P. “3D-CGH-Net: customizable 3D-hologram generation via deep learning,” Optics Lasers Eng ; 2025; [DOI: https://dx.doi.org/10.1016/j.optlaseng.2024.108645]
7. Kim, NS; Austin, T; Baauw, D; Mudge, T; Flautner, K; Hu, JS. Leakage current: Moore’s law meets static power. Computer; 2003; 36,
8. Dennard, RH; Gaensslen, FH; Hwa-Nien, Y; Rideout, VL; Bassous, E; LeBlanc, AR. Design of ion-implanted MOSFET’s with very small physical dimensions. Ieee J. Solid-state Circuits; 1974; 9,
9. Hamerly, R; Bernstein, L; Sludds, A; Soljačić, M; Englund, D. Large-scale optical neural networks based on photoelectric multiplication. Phys. Rev. X; 2019; 9,
10. Mengu, D; Luo, Y; Rivenson, Y; Ozcan, A. Analysis of diffractive optical neural networks and their integration with electronic neural networks. Ieee J. Sel. Top. Quantum Electron.; 2019; 26,
11. Xu, R; Lu, P; Xu, F; Shi, Y. A survey of approaches for implementing optical neural networks. Opt. Laser Technol.; 2021; [DOI: https://dx.doi.org/10.1016/j.optlastec.2020.106787]
12. Minikhanov, TZ; Yu. Zlokazov, E; Starikov, RS; Cheremkhin, PA. Phase modulation time dynamics of the liquid-crystal space-time light modulator. Izmerit. Tekh.; 2024; 73,
13. Goodman, JW; Dias, A; Woody, L. Fully parallel, high-speed incoherent optical method for performing discrete Fourier transforms. Opt. Lett.; 1978; 2,
14. Dong, J; Gigan, S; Krzakala, F; Wainrib, G. Scaling up echo-state networks with multiple light scattering; 2018; Statistical Signal Processing Workshop (SSP), IEEE: pp. 448-452. [DOI: https://dx.doi.org/10.1109/SSP.2018.8450698]
15. Feldmann, J; Youngblood, N; Wright, CD; Bhaskaran, H; Pernice, WH. All-optical spiking neurosynaptic networks with self-learning capabilities. Nature; 2019; 569,
16. Shen, Y; Harris, NC; Skirlo, S; Prabhu, M; Baehr-Jones, T; Hochberg, M; Sun, X; Zhao, Sh; Larochelle, H; Englund, D; Soljačić, M. Deep learning with coherent nanophotonic circuits. Nature Photon; 2017; 11,
17. Lin, X; Rivenson, Y; Yardimci, NT; Luo, Y; Jarrahi, M; Ozcan, A. All-optical machine learning using diffractive deep neural networks. Science; 2018; 361,
18. Chen, H; Feng, J; Jiang, M; Wang, Y; Lin, J; Tan, J; Jin, P. Diffractive deep neural networks at visible wavelengths. Engineering; 2021; 7,
19. Zhou, T; Lin, X; Wu, J; Chen, Y; Xie, H; Li, Y; Fan, J; Wu, H; Fang, L; Dai, Q. Large-scale neuromorphic optoelectronic computing with a reconfigurable diffractive processing unit. Nat. Photon.; 2021; 15,
20. Bernstein, L; Sludds, A; Panuski, C; Trajtenberg-Mills, S; Hamerly, R; Englund, D. Single-shot optical neural network. Sci. Adv.; 2023; 9,
21. Deng, Z; Qing, D-K; Hemmer, PR; Zubairy, MS. Implementation of optical associative memory by a computer-generated hologram with a novel thresholding scheme. Opt. Lett.; 2005; 30,
22. Zuo, Y; Li, B; Zhao, Y; Jiang, Y; Chen, Y-C; Chen, P; Jo, G-B; Liu, J; Du, S. All-optical neural network with nonlinear activation functions. Optica; 2019; 6,
23. Evtikhiev, NN; Krasnov, VV; Ryabcev, IP; Rodin, VG; Starikov, RS; Cheremkhin, PA. Measuring of the modulation of the phase liquid-crystal light modulator Santec SLM-200 and analysis of its applicability for the reconstruction of images from diffraction elements. Izmerit. Tekh.; 2021; 5, pp. 4-8. [DOI: https://dx.doi.org/10.32446/0368-1025it.2021-5-4-8]
24. G.-z. Yang,; B.-z, D; B.-y, G; J.-y, Z; Ersoy, OK. Gerchberg-Saxton and Yang-Gu algorithms for phase retrieval in a nonunitary transform system: a comparison; 1994; 2 pp. 209-218. [DOI: https://dx.doi.org/10.1364/AO.33.000209]
25. Ovchinnikov, A; Krasnov, V; Cheremkhin, P; Rodin, V; Savchenkova, E; Starikov, R; Evtikhiev, N. What binarization method is the best for amplitude inline Fresnel holograms synthesized for divergent beams using the direct search with random trajectory technique?. J. Imaging; 2023; 9,
26. Minikhanov, TZ; Yu. Zlokazov, E; Krasnov, VV; Derevenickaia, DD. Research of the dynamic characteristics of the phase LC STLM HoloEye PLUTO 2 VIS-016 and HoloEye GAEA-2 VIS-036. Proc. of the XXXII Internat. School-Symp. on Holography, Coherent Optics, and Photonics, St. Petersburg; 2022; pp. 195-197.
© Springer Science+Business Media, LLC, part of Springer Nature 2025.