Optical wavelet transform and local scaling properties of fractals

The wavelet transform has recently received much attention in the fractals world due to its ability to characterize the scaling properties of multifractal aggregates. This paper is devoted to the optical version of the wavelet transform, with a special emphasis on instrumental aspects. The optical wavelet transform amounts to a series of distinct bandpass filterings of the optical Fourier spectrum of the system under study. One wavelet component is given by one filtered image of the system. The way in which the intensity at any point depends on the filter size directly gives the local scaling behavior around this point.