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Old May 2nd 2019, 07:30 AM   #1
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Spectra of an interference pattern

If we analyze the spectra of an interference pattern, will it have components related to the original wave? In other words, is it possible to recover/regenerate the original wave from one that experienced interference?
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Old May 2nd 2019, 07:45 AM   #2
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Spectra implies a range of different wavelengths (frequencies).

Different wavelengths will interfere at different positions,
this is the reason behind the rainbow colours in (for example) a soap bubble or oil film.

Your interference pattern will become an interference rainbow.

You can "recover/regenerate the original wave from one that experienced interference"
If you have knowledge of the geometry of the situation that generated the interference
(e.g. the spacing of a double slit and the position of the screen with respect to the double slit).

Alternatively you can recover the geometry of the situation that generated the interference
if you know the input wave and the output pattern (e.g. X-ray crystallography).
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Old May 2nd 2019, 08:26 AM   #3
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Thanks. One follow up: if the original wave was just a single frequency, the resulting interference pattern could be expressed as the sum of two waves of the same frequency, but different phases. Could it also be expressed as multiple frequencies of the same phase(i.e. as a Fourier series)?
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Old May 2nd 2019, 08:41 AM   #4
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No, but

The Fourier transform takes a time verses amplitude pattern
and calculates the corresponding frequency verses amplitude pattern.

I think what you are after is a closely related process called <cross correlation>.
This allows you to distinguish the phase difference of two (or more) signals of the same frequency.
The maths is a bit hairy...
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