| Re: IDL FFT (spec -> interferogram) [message #30108 is a reply to message #30034] |
Mon, 08 April 2002 11:36   |
Paul van Delst
Messages: 364
Registered: March 1997
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Senior Member |
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Robert Stockwell wrote:
>
> Paul van Delst wrote:
>
>> But one doesn't always want the power spectrum. Usually (in my field at least) one wants the
>> complex valued spectrum where the imaginary component is known and happily zero. (Don't know if
>> Randall wants that tho')
>
>> paulv
>
> isn't that the same thing? ( real eq complex with imag=0)
> If the interferrogram is indeed the autocorrelation function,
> then the power spectrum is all you have, you cannot deduce
> any phase info.
First off, I think I slipped up on the terminology. When I saw "power spectrum" I thought
|spectrum|^2, but you are correct in that the autocorrelation function of the electric field is
the interferogram. What would be the flux density (power spectrum in your terminology) is what
I usually call "the spectrum". So I thought you meant the square of what I call the spectrum
and....well you see where I screwed up. Ehem.
> Having said that, it is conceivable that one can create a
> complex interferrogram (for instance, combining two different
> channels etc), but in the "usual" (i.e. that I am familiar with),
> an interferrogram is an scalar autocorrelation function.
However -- and I'm sure you know all this -- in practice, when you compute the flux density
spectrum from the interferogram, you are not guaranteed to get a spectrum where the imaginary
part is zero. If the interferogram is perfectly symmetric, sure. In practice, however, IFGs are
typically asymmetric and this causes the imaginary part to be non-zero. Assuming the IFG
measurement is relatively quick (what you're observing hasn't changed) the IFG asymmetry is due
to not knowing where the zero path difference (ZPD) occurs (or the lag of the autocorrelation
is zero). By calculating the phase "error" it's possible to determine the correct ZPD and
obtain a spectrum with zero (or close to numerical precision).
That's also a reason why, in my examples that Randall mentioned, I'm doing all the spectrum
folding and what not - I simulate double-sided interferograms rather than single-sided ones.
Then any gross asymmetry is relatively easy to correct for.
So, with apologies for the ramble, you're absolutely correct - I was just thinking of
situations with interferometers which I've had to deal with, phase correcting the spectra and
all.
paulv
--
Paul van Delst Religious and cultural
CIMSS @ NOAA/NCEP purity is a fundamentalist
Ph: (301)763-8000 x7274 fantasy
Fax:(301)763-8545 V.S.Naipaul
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