Field Autocorrelation
For a complex electric field, the field autocorrelation function is defined by
The Wiener-Khinchin theorem states that the Fourier transform of the field autocorrelation is the spectrum of, i.e., the square of the magnitude of the Fourier transform of . As a result, the field autocorrelation is not sensitive to the spectral phase.
The field autocorrelation is readily measured experimentally by placing a slow detector at the output of a Michelson interferometer. The detector is illuminated by the input electric field coming from one arm, and by the delayed replica from the other arm. If the time response of the detector is much larger than the time duration of the signal, or if the recorded signal is integrated, the detector measures the intensity as the delay is scanned:
Expanding reveals that one of the terms is, proving that a Michelson interferometer can be used to measure the field autocorrelation, or the spectrum of (and only the spectrum). This principle is the basis for Fourier transform spectroscopy.
Read more about this topic: Optical Autocorrelation
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