Fast computation method for a Fresnel hologram using three-dimensional affine transformations in real space

Calculating computer-generated holograms takes a tremendous amount of computation time. We propose a fast method for calculating object lights for Fresnel holograms without the use of a Fourier transform. This method generates object lights of variously shaped patches from a basic object light for a fixed-shape patch by using three-dimensional affine transforms. It can thus calculate holograms that display complex objects including patches of various shapes. Computer simulations and optical experiments demonstrate the effectiveness of this method. The results show that it performs twice as fast as a method that uses a Fourier transform.