Holographic Transforms in Digital Computers

This chapter is devoted to discrete representation of diffraction integrals. It expounds principles of the discretization and their applications to derivation of different modifications of Discrete Fourier Transforms, Discrete Fresnel Transforms and Kirchhoff-Rayleigh-Sommerfeld transforms. The chapter is supplemented with appendices that contain relevant mathematical details, description of the new algorithm for signal convolution via fast cosine transform and a summary of discrete diffraction transforms.