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 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.

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 present a DST-based Gerchberg-Saxton search algorithm for generating binary-phase holograms. The new algorithm is shown to give an order of magnitude speed improvement for a small reduction in image quality.

Recent experimental work has demonstrated the potential to combine the merits of diffractive and onchip photonic information processing devices in a single chip by making use of planar (or slab) waveguides.Researchers have adapted key results of 3D Fourier optics to 2D, by analogy, but rigorous derivations in planar contexts have been lacking. Here, such arguments are developed to show that diffraction formulas familiar from 3D can be adapted to 2D under certain mild conditions on the operating speeds of the devices in question. Equivalents to the Rayleigh-Sommerfeld diffraction (RS) formulas in 2D are provided and a Radiation Condition of validity proved. The equivalence of the first 2D RS formula with an angular spectrum formulation is demonstrated. Finally Fresnel approximations are derived starting from the RS formulation and that of the angular spectrum. In addition to serving those working with slab waveguides, this letter provides analytical tools to researchers in any field where 2D diffraction is encountered, including the study of surface plasmon polaritons, surface waves, 3D diffraction with line-sources or corresponding symmetries, and the optical, acoustic and crystallographic properties of 2D materials.