Effect of Bit-depth in Stochastic Gradient Descent Performance for Phase-only Computer-generated Holography Displays

Abstract

SGD (Stochastic gradient descent) is an emerging technique for achieving high-fidelity projected images in CGH (computergenerated holography) display systems. For real-world applications, the devices to display the corresponding holographic fringes have limited bit-depth depending on the specific display technology employed. SGD performance is adversely affected by this limitation and in this piece of work we quantitatively compare the impact on algorithmic performance based on different bit-depths by developing our own algorithm, Q-SGD (Quantised-SGD). The choice of modulation device is a key decision in the design of a given holographic display systems and the research goal here is to better inform the selection and application of individual display technologies.

Information capacity of phase-only computer-generated holograms for holographic displays

“…Previously, work had been done to investigate the effect of Bit-depth in Stochastic Gradient Descent (SGD) performance for phase-only computer-generated holography displays. 9 This paper extends on previous research onto the Gerchberg-Saxton (GS) 4 algorithms for hologram generation, and investigates the correlation between the quality of the reconstructed image from the hologram and the information entropy of the target image, with an aim to reduce the hologram's entropy during the CGH process, for smaller size holograms.…”

“…However, despite many advancements in liquid crystals and micro mirrors technologies, complex-valued spatial light modulators (SLM) are still not yet available, and the currently available SLM can only achieve either amplitude or phase modulation, among which the phase modulation is usually preferred in holographic projections for its lower zero order and higher energy efficiency due to lower blockage of light. There are many algorithms available to compute good quality phase-only holograms, such as direct binary search, 2 simulated annealing, 3 Gerchberg-Saxton 4 and other optimization based methods; [5][6][7][8][9][10] however, none of them can guarantee to compute a perfect phase hologram for a 3D or even a 2D image, where they always end up with some error between the reconstruction of the hologram and the target scene, especially when the phase holograms are quantized to be able to display on SLM with limited bit depth. An intuition therefore arose that the bit depth of the phase hologram is limiting the reconstruction quality, and that the target scene's entropy seems to denote how difficult it is for phase hologram generation.…”

Multi-depth phase-only hologram optimization using the L-BFGS algorithm with sequential slicing

“…Cross entropy (CE) is adapted as shown in Eq. (12). CE is often used in classification problems, such as language modelling [21].…”

“…With the developments in modern numerical optimization methods and computation power, advances in CGH algorithms can be made. Literature review has found some recent work that compute CGH using numerical optimization methods [8][9][10][11][12], but speed and quality are still the major challenges in multi-depth hologram generation. The most common multi-depth CGH optimization methods either evaluate their loss against the entire multi-depth 3D target, which is time-consuming, or evaluate the hologram for each plane and then sum the holograms, which introduces quality degradation.…”

Multi-Frame Binary-Phase Holograms Batched Optimization

“…The classic phase-retrieval algorithms include direct binary search 1 , simulated annealing 2 and Gerchberg-Saxton 3 . With the developments in modern numerical optimization methods and increase in computational power, phase retrieval with new numerical optimization methods has also been found in the literature such as: gradient descent 4,5 , its stochastic variations [6][7][8] , and its derivative L-BFGS 9,10 . However, all of these are single-frame hologram generation methods.…”