# Computer-Generated Holography Methods for Data Page Reconstruction Using Phase-Only Medium
## 1 Introduction  
Holographic data storage systems [1; 2; 3; 4; 5], coherent diffractive image correlators [6; 7; 8; 9], optical encryption schemes [10; 11; 12; 13], optical-digital Fourier processors [14], and diffractive neuroprocessors [15; 16; 17; 18; 19] require the formation of coherent optical fields with a given complex amplitude distribution in space. These systems provide optical-digital processing of analyzed digital signals. The signal is optically transformed, registered by a digital camera, and subsequently digitally post-processed using a computer. In the case of coherent diffractive image correlators, an input digital encoded image or a complex invariant filter [9] can be considered as such a signal. In the case of optical holographic memory systems, the signal is a data page [1; 2], which can be either amplitude or complex-modulated [20]. For optical encryption, this is the key image [10]. In the case of diffractive neuroprocessors, the signal is the weight matrix of the convolutional layer of the neural network [21; 22]. In contrast to the images for visual observation, these images have increased requirements for the accuracy of their formation. This is because their distortion leads to the loss of encoded information and the incorrect performance of the optical-digital system. Electro-optical spatial light modulators are widely applied for information signal generation [23; 24; 25; 26; 27]. They provide high-speed input of digital information into the optical system. However, current devices cannot independently control both the amplitude and the phase of the optical field in space. The maximum spatial resolution of 10 megapixels can be obtained using phase-only liquid crystal on silicon (LCoS) spatial light modulators [28]. These types of spatial light modulators (SLMs) are widely applied to form a complex impulse response using computer-generated holography methods [29]. Another practical example of phase computer-generated holograms (CGH) of data page implementation is the HDS system, which uses a data recorder device based on a single beam incoherent projection scheme [30; 31]. Fourier CGH fringe patterns are displayed on a screen of amplitude LCoS SLM and projected onto a photosensitive carrier. Using phase medium and anamorphic optics allowed us to record and reconstruct binary data pages from multiplexed holograms using a reader device based on a coherent optical scheme [31; 32]. The throughput of optoelectronic information processing systems mentioned above is defined not only by the frame rate of SLM used for CGH introduction into the optical scheme but also by the speed of CGH calculation. Therefore, the problem of fast-calculating the CGH fringe pattern is relevant. Fourier CGHs are attractive for application along with phase-only SLMs, as this type of CGH requires only one fast Fourier transformation in object beam calculation algorithms and provides a high space-bandwidth product limited to one-half of the total number of SLM pixels. Different methods allow the encoding of a complex wavefront of the object beam onto a phase of the CGH fringe pattern. Well-known iterative methods, such as those that are based on the Gerchberg-Saxton algorithm [33], or optimization methods, such as optimal projection [34] or direct search with random trajectory [35], are not capable of satisfying the requirement of high-speed CGH calculation. The most promising methods for fast synthesis of the phase Fourier CGH fringe pattern are bipolar intensity [29] and double-phase coding methods [36; 37; 38]. The advantage of both methods is the direct analytical calculation of a hologram. A large number of iterations and solutions to optimization tasks are not required. Though both methods require only several matrices of element-wise addition or multiplication, the calculation complexity of these methods linearly depends on the number of elements in the matrices. There is no information about the advantages of using one or another method for holographic memory data page reconstruction purposes.