Fixed-Point Accuracy Analysis of 2D FFT for the Creation of Computer Generated Holograms

Computer Generated Holograms (CGHs) are fundamental to the creation of holographic display and are responsible for carrying the phase or amplitude information of a particular optical field. The standard approaches for CGH generation on personal computers all involve multiple forward and inverse 2-dimensional fast Fourier Transforms (2D FFTs). This common method is not fast enough for a real-time application. Producing CGHs via configurable hardware may reduce the computational burden. To reduce overhead, fixed-point arithmetic is usually implemented; however, this sacrifices the precision of the algorithm. Care needs to be taken when applying fixed-point operations.In this paper, we present a radix-2 error propagation model to analyses the 2D FFT based on three different rounding methods and we also show the simulation results on selection of appropriate rounding methods.