Time-delay detection of short pulses by Fresnel and Fourier transformations

The Fresnel transform of a signal, when used as a preprocessing step to a subsequent spectrum analysis, helps to detect the time delay between short-pulse signals. Light from the short pulses disperses spatially as it propagates through free space to create an interference pattern. As the pulses move through an acousto-optic cell, a point photodetector produces a signal whose temporal frequency is directly proportional to the time delay between the pulses. When this signal is fed to a spectrum analyzer, the frequency domain represents a time-delay domain.