# Fractional cyclic transforms in optics: theory and applications

## Tatiana Alieva, Martin J. Bastiaans, and Maria Luisa Calvo

In this paper we review fractional linear integral transforms, which have been actively used during the last decade in optical information processing. The general algorithm for the fractionalization of the linear cyclic integral transforms is discussed and the main properties of fractional transforms are considered. It is shown that there is an infinite number of continuous fractional transforms related with a given cyclic integral transform.

The optical fractional Fourier transform used for different applications such as adaptive filter design, phase retrieval, encryption, watermarking, etc., is discussed in detail. Other fractional cyclic transforms that can be implemented in optics, such as fractional Hankel, Sine, Cosine, Hartley, and Hilbert transforms, are investigated.

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To: Papers by Martin J. Bastiaans