Approximating a desired temporal impulse response with a pupil function that consists of a series of light pulses

Abstract

A procedure based on the method of stationary phase and that of Fresnel zones, is presented for synthesizing a desired impulse response of a time lens, from a pupil function that consists of a series of properly-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 from the stationary points of the first Fresnel zone. The stationary points are given by the locations where the inverse Fourier transform of the desired impulse response is an extremum. As examples, we consider the generation of wavelet-like responses because previous application of the wavelet transform method to images formed by diffraction has shown that it extracts the presence of signal features such as edges and spikes, more accurately than Fourier filtering.