Optical implementation of a wavelet transform by the use of dynamic holographic recording in a photorefractive material.

An optical system that employs holographic recording in a photorefractive material is proposed and experimentally demonstrated for the implementation of a wavelet transform of two-dimensional mages. A scaling operation, to derive the family of wavelet filters from a mother wavelet filter, is performed by the use of an optical feedback loop. The selection of a desired wavelet filter from the family and the correlation for a wavelet transformation are made by the use of a holographic recording in a photorefractive material. The principle of operation of the system relies on the frequency detuning introduced inside the loop and the subsequent variation in the holographic grating diffraction. Experimental results on wavelet-filter selection and wavelet transformation are presented. This nonlinear optical wavelet-transform system is advantageous for pattern recognition applications.