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Diffraction, Fresnel Transform, Fractional Fourier Transform, Cosine Transform, Sine Transform.

Two novel transforms, related together and called Sine and Cosine Fresnel Transforms, as well as their optical implementation are presented. Each transform combines both backward and forward light propagation in the framework of the scalar diffraction approximation. It has been proven that the Fresnel transform is the optical version of the fractional Fourier transform. Therefore the former has the same properties as the latter. While showing properties similar to those of the Fresnel transform and therefore of the fractional Fourier transform, each of the Sine and Cosine Fresnel transforms provides a real result for a real input distribution. This enables saving half of the quantity of information in the complex plane. Because of parallelism, optics offers high speed processing of digital signals. Speech signals should be first represented by images through special light modulators for example. The Sine and Cosine Fresnel transforms may be regarded respectively as the fractional Sine and Cosine transforms which are more general than the Cosine transform used in information processing and compression.