APPROXIMATING A DESIRED TEMPORAL IMPULSE-RESPONSE WITH A PUPIL FUNCTION THAT CONSISTS OF A SERIES OF LIGHT-PULSES

A procedure based on the method of stationary phase and that of Fresne l zones, is presented for synthesizing a desired impulse response of a time lens, from a pupil function that consists of a series of properl y-spaced light pulses of equal heights. The temporal impulse response is given by the Fourier transform of the temporal pupil function. The number and relative separations of the light pulses are determined fro m the stationary points of the first Fresnel zone. The stationary poin ts an given by the locations where the inverse Fourier transform of th e desired impulse response is an extremum. As examples, we consider th e generation of wavelet-like responses because previous application of the wavelet transform method to images formed by diffraction has show n that it extracts the presence of signal features such as edges and s pikes, more accurately than Fourier filtering. (C) 1998 Elsevier Scien ce B.V.