Re: Michael Reichmann reasoning for AA filters?

In article <1192887107.282629.95650@xxxxxxxxxxxxxxxxxxxxxxxxxxx>, acl <achilleaslazarides@xxxxxxxxxxx> writes
On Oct 20, 1:24 pm, Kennedy McEwen <r...@xxxxxxxxxxxxxxxxxx> wrote:
In article <_o-dnbPbVMtI2YTanZ2dnUVZ_judn...@xxxxxxxxxxxx>, David J.
Littleboy <davi...@xxxxxxx> writes



>That doesn't work very well because diffraction causes more loss in the pass
>band than a good AA filter (the MTF curve for diffraction is a straight line
>from 100% at 0 lp/mm to 0% at 1600/(f number), but what you want for an AA
>filter is a step function).

Actually, the diffraction MTF for a circular aperture is not quite a
straight line, it flattens off significantly towards the cut-off. The
diffraction MTF is the autocorrelation of the pupil.

Is that so? Then if I take the pupil to be described by a step
function between 0 and 1 (radially), the MTF would be $(1-f)^2$ (err..
I hope, at least) with f in the inverse of the length units in which
the radius is 1. But the inverse fourier transform of that isn't an
airy function, so this can't be the mtf... Or I misunderstood what you
said. Or screwed up some integral.

I think you have gone wrong before the integral...
Remember you are calculating the common area between two overlapped circles.

Without going round the houses, the function you are looking for is:
MTF(u)=(2.a - sin(2.a))/pi where
cos(a) = w.u.f
w = wavelength
u = spatial frequency
f = f/#
--
Kennedy
Yes, Socrates himself is particularly missed;
A lovely little thinker, but a bugger when he's pissed.
Python Philosophers (replace 'nospam' with 'kennedym' when replying)
.

Relevant Pages

  • Re: Michael Reichmann reasoning for AA filters?
    ... filter is a step function). ... straight line, it flattens off significantly towards the cut-off. ... diffraction MTF is the autocorrelation of the pupil. ...
    (rec.photo.digital)
  • Re: Michael Reichmann reasoning for AA filters?
    ... filter is a step function). ... straight line, it flattens off significantly towards the cut-off. ... diffraction MTF is the autocorrelation of the pupil. ...
    (rec.photo.digital)
  • Re: Michael Reichmann reasoning for AA filters?
    ... filter is a step function). ... straight line, it flattens off significantly towards the cut-off. ... diffraction MTF is the autocorrelation of the pupil. ...
    (rec.photo.digital)
  • Re: Lens-sensor Resolution Calculations Made Easy
    ... high frequency noise is filtered ... increasing MTF and resolution. ... My impression has been that some lenses trade-off having a higher MTF at low-middle spatial frequencies versus a lower MTF near the system's Nyquist limit, where the AA filter is going to limit MTF in any case - i.e. you might want to design a lens differently for "digital", or at least look at the MTF curve with a different view that for a film camera. ...
    (rec.photo.digital.slr-systems)
  • Re: Olympus shocker! E-5, no AA filter!!
    ... need to sharpen under most circumstances, AA filter or no AA filter? ... the lens you are using has an MTF ... If the image processing chain you use doesn't include that correction, you may need to sharpen every time. ...
    (rec.photo.digital.slr-systems)