Computer-generated holography (CGH) is a technique to generate holographic interference patterns. One of the major issues related to computer hologram generation is the massive computational power required. Hardware accelerators are used to accelerate this process. Previous publications targeting hardware platforms lack performance comparisons between different architectures and do not provide enough information for the evaluation of the suitability of recent hardware platforms for CGH algorithms. We aim to address these limitations and present a comprehensive review of CGH-related hardware implementations.

The Kaczmarz algorithm is an iterative method for solving linear equations in the form of Ax = b. It is widely used in computed tomography (CT) and digital signal processing (DSP) but has yet to be adopted in computer-generated holography (CGH). Phase retrieval algorithms such as Gerchberg-Saxton or Fienup are significantly more popular in this field, however, in this paper we propose a unique and alternative approach to projecting a replay field through Discrete Fourier Transform (DFT) matrices and have shown that there are legitimate benefits to implementing this approach. The gradient descent iteration mechanism adopted by Kaczmarz, for instance, provides finer granularity control over the individual pixels in the replay field. We consequently demonstrate the quality of the image is significantly improved when compared to Gerchberg-Saxton.

We implement a novel limited-memory Broyden–Fletcher–Goldfarb–Shanno (L-BFGS) optimisation algorithm with cross entropy (CE) loss function, to produce phase-only computer-generated hologram (CGH) for holographic displays, with validation on a binary-phase modulation holographic projector.

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.

We combine a continuous feedback hardware-in-the-loop approach with a binary-phase SLM and an imaging sensor to produce a computer-generated holography system which is scalable in cost, tolerant to real-world effect and suitable for mass-market adoption.