Wigner distribution function display: a supplement to ambiguity function display using a single 1-D input

Optical realization of the ambiguity function of real two-dimensional light sources

We propose a setup that can generate the sectional ambiguity function of a two-dimensional real light source. The setup is easy to implement; the theoretical analysis and experimental results are given.

Implementation of the spatial and the temporal cross-ambiguity function for waveguide fields and optical pulses

On the basis of space-time duality, we propose experimental setups to implement the cross-ambiguity function optically in space and time in one and two dimensions. In space the cross-ambiguity is shown to be related to the coupling efficiency between butt-joined optical waveguides. In time it is related to the spectrogram or the frequency-resolved optical gating techniques for the characterization of optical pulses.

Two-dimensional optical filtering of 1-D signals

One-dimensional signals have complementary attributes, their space and spatial frequency properties. Recently, another signal representation was introduced in optics, the Wigner distribution (WD) function, which allows the simultaneous display of the two attributes of a 1-D signal. In this paper optical implementation of a generalized space-spatial frequency (GSF) function is discussed. Special cases of the GSF representations are the WD, the radar ambiguity function (AF), the energy distribution function, the various pseudo-WD functions, the spectrogram, the local frequency and the local Doppler frequency spectrum. The GSF representation allows the simultaneous filtering of both the spatial and the spatial frequency content of a 1-D signal. The 2-D filtering of a 1-D signal allows sidelobe reduction of the WD and AF of quasi-periodic 1-D signals, display of the instantaneous spatial frequency content of a 1-D signal, space-spatial frequency excision of a desired portion of a 1-D signal as well as the usual matched filter detection. Experimental results using coherent space-integrating techniques for the realization of different GSF are presented.