Hologram calculation in sparse Fourier bases using fixed-point operations, and its circuit architecture

Abstract

Creating computer-generated holograms (CGHs) is computationally costly, and many high-speed calculation algorithms have been proposed to address this problem. Recently, a calculation method using sparse point spread functions (PSFs) in the short-time Fourier transform (STFT) domain has been proposed. Since the PSFs are sparse in the STFT domain, only a small fraction of STFT coefficients need to be calculated. Further, in order to obtain the STFT coefficient, fast Fourier transform is generally necessary, but this new method can obtain the STFT coefficient by analytical means. This means that the number of calculations required can be greatly reduced. This paper describes the implementation of an STFTbased CGH calculation algorithm on a field-programmable gate array. All operations in this algorithm were implemented using fixed point arithmetic. Since this algorithm includes a trigonometric function and an error function, we used look-up tables (LUTs) to reduce calculation costs. We have devised a dedicated circuit architecture that allows parallel operations. As a secondary effect, a central processing unit was able to generate holograms using the STFT-based CGH calculation algorithm with fixed point arithmetic and LUTs, faster than by using floating point arithmetic.