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Re: difference between HeavisidePi and UnitBox

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  • Subject: [mg100653] Re: difference between HeavisidePi and UnitBox
  • From: Anatoly <anatoly.bourov at>
  • Date: Wed, 10 Jun 2009 05:35:17 -0400 (EDT)
  • References: <gvq08j$moo$> <gvtmcu$gc6$>

Great, thanks for the Davis link, I will definitely try to follow up.

My typical application has been a 4F imaging system -- FourierTransform
[rect[x]], then multiply by the pupil function, another rect, then
InverseFourierTransform back into space domain.

I've tried using both HeavisidePi and the UnitBox to represent the
rect, both seem to have problems

I start having severe problems when I use multiple scaled
HeavisidePi.  As a matter of fact, as soon as I shift and scale it,
FourierTransform cannot calculate a result.

With the UnitBox as the object, the results are a bit better, but then
I cannot use a sum expression to represent the 5-bar pattern, I have
to specify them explicitly.  Not a big deal, and in the end things
seem to work out.

That is until I add an off-axis source, or defocus into the system.
With an off-axis source the input is UnitBox[x] E^(I x s) -- and here
the most curious thing happens. In this form everything is fine, but
when I use UnitBox[x] E^(-I x s) I get two extra DiracDeltas in the
FourierTransform with different signs.  But I am side-tracked.

For this kind of application, FourierTransform[UnitBox], multiply by
UnitBox, InverseFourierTransform, am I using the right function?
Should I spend more time with HeavisidePi?

Thanks again for the discussion guys, I feel slightly less lost

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