All-optical wavelet transform realization and use for imaging, image processing, and increased depth of focus

We realize optical wavelet transforms by two methods. In the first, we image an object through an array of lenses having various diameters. This results in images of the object at different resolutions (according to the imaging lens). We show that a weighted combination of these images may realize the wavelet transform coefficients. In the second method we use the fact that defocus aberrations affect the resolution of the image. Imaging an object in high resolution (with a large-diameter lens) while focusing on different planes enables us to perform a wavelet transformation when the object is two-dimensional. After realizing the wavelet transform optically, we show how the suggested optical configurations can be used for image processing, for compression, and for extending the depth of focus of the imaged object. All required processing operations have very low computational complexity.