An improved bitwise logic-based trigonometric approximation for holographic computation

One of the main technical challenges in electroholography-based three-dimensional (3D) display systems is accelerating the computation of computer-generated holograms (CGH), which function as electronic recording media for 3D images. Since generating CGH through optical propagation calculations heavily relies on the use of trigonometric functions, reducing the computational cost of these functions is an effective approach to speed up the calculations. Notably, holography can preserve the image quality even when some calculations are performed with low precision.

In this study, we developed a trigonometric function approximation method for holographic computations using a minimal bit-width representation. Specifically, we extended our previous approach — originally designed for specialized computing hardware with a 2-bit input and 1-bit output — to a more expressive model using a $p$-bit input (with $p$ being an arbitrary positive integer) and $(p-1)$-bit outputs for the real and imaginary components. The experimental results showed that the proposed method offers significant advantages in terms of hardware implementation feasibility, compact circuit size, and the quality of the reconstructed 3D images, all while incurring only a modest increase in the computational load.