Introduction to Digital Holography

Author(s): Leonid Yaroslavsky and Jaakko Astola

DOI: 10.2174/978160805079610901010008

Holographic Transforms in Digital Computers

Pp: 8-36 (29)

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Abstract

SHS investigation development is considered from the geographical and historical viewpoint. 3 stages are described. Within Stage 1 the work was carried out in the Department of the Institute of Chemical Physics in Chernogolovka where the scientific discovery had been made. At Stage 2 the interest to SHS arose in different cities and towns of the former USSR. Within Stage 3 SHS entered the international scene. Now SHS processes and products are being studied in more than 50 countries.

Abstract

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.

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