Optical interferometry with pulsed fields

Abstract

The problem of predicting and interpreting the results of interferometric optical experiments involving pulse trains is addressed. Specifically, a cyclostationary field arising from the modulation of a stationary, stochastic source is considered in the classical Young's experiment. It is shown that the effects of modulation may be identical to unrelated statistical interference effects.

Propagation of spatial coherence in fast pulses

“…The interferogram produced in such an experiment also can be used to determine the approximate coherence time (and thus the bandwidth) of the impinging field. For cyclostationary plane waves, it has been shown that in a Young's interferometer the meaning of the interferogram is changed and there is some ambiguity in connecting the results to the source parameters [7]. Specifically, it was shown that the smaller of the pulse duration, T, and the coherence time, c , sets the width of the primary peak in the interferograms.…”

“…In works on nonstationary fields [6,7,20], the emphasis has been on sources that are spatially fully coherent and of infinite extent. Such sources produce polychromatic plane waves.…”

“…When the assumption of stationarity does not hold, the correlation functions that describe the field become two-time or two-frequency correlation functions, and the Wiener-Khintchine-Einstein theorem no longer holds. For these reasons and others, the timeaveraged measurements made with an interferometer or a spectrometer have a more complicated relationship with the nonstationary sources that generated them [6][7][8] than in the stationary case. Some sort of prior knowledge is necessary to make unambiguous estimates of the statistical properties of the sources based on the measured data.…”

“…These values all affect the statistical properties of the cyclostationary field. Based on the relative scales of these three quantities, there are three qualitatively distinct regimes into which most realizable systems fall [7]:…”

“…Opt. 55, 1541(2008], where only the temporal correlations of pulsed fields were considered in a Young's interferometer. The meaning of the interferograms is addressed for measurements taken in the near, Fresnel, and far zones of the source.…”