Optics folks!

[Jbryant61]

Hi.

do any of the optics folks have any mathcad examples showing how to obtain the PSF from the MSF?

thanks
Jason

[GuyB]

On 8/11/2009 12:14:47 PM, Jbryant61 wrote:
>Hi.
>
>do any of the optics folks
>have any mathcad examples
>showing how to obtain the PSF
>from the MSF?
>
>thanks
>Jason

I assume that PSF is point spread function.

I don't know what you mean by MSF, however.

- Guy

[ptc-1368288]

>I don't know what you mean by MSF, however.<<br> _______________________

Hard to tell. There is so much and so different and so proprietary obscure about MTF, that maybe MSF is a kind of disambiguation just invented to confuse even more... like my sky hook I have lost long time ago.

Jean

[PhilipOakley]

Do you mean PSF <-> MTF, the latter is modulation transfer function, which is usually seen at the effective transfer function of vertical bar patterns.

The ideal is sinewave bars (at an orientation of your choice;-).

There are lots of potentially confounding issues and 'practicalities' as you have already seen.

Convert the psf to an lsf [line spread function](i.e. do a vertical sum across the psf), then do a basic fft (the half size one) to get the MTF.

Philip Oakley

[Jbryant61]

>Convert the psf to an lsf
>[line spread function](i.e. do
>a vertical sum across the
>psf), then do a basic fft (the
>half size one) to get the MTF.
>
>Philip Oakley


Hi,yes this is correct I mean't psf -> MTF.

Thanks for getting me started. When you say do a vertical sum, do you mean a line scan thru' the centroid?

BTW, I do feel guilty asking all these optics questions in a mathcad Forum. But to be honest, the amount of experience here is amazing and using Mathcad for this is extremely fun(and I prefer it to Matlab!)

Jason

[PhilipOakley]

On 8/13/2009 2:55:26 PM, Jbryant61 wrote:
>
>>Convert the psf to an lsf
>>[line spread function](i.e. do
>>a vertical sum across the
>>psf), then do a basic fft (the
>>half size one) to get the MTF.
>>
>>Philip Oakley
>
>
>Hi,yes this is correct I
>mean't psf -> MTF.
>
>Thanks for getting me started.
>When you say do a vertical
>sum, do you mean a line scan
>thru' the centroid?
Nope, you sum down each column of the psf, so that
the peak gets 'sharper', which is what happens if
you image an edge. (actually a perfectly narrow
line - an impulse function)

so then you can do the fft of that edge/line, you
have the fft of the impulse, which is the
frequency spectrum, etc.

>
>BTW, I do feel guilty asking
>all these optics questions in
>a mathcad Forum. But to be
>honest, the amount of
>experience here is amazing and
>using Mathcad for this is
>extremely fun(and I prefer it
>to Matlab!)
So do I... MatLab has its place, but gets over
hyped. It is more of an efficient implementation
tool. And it is still stuck in the old
hack/compile/run/see mistake/hack cycle.

>
>Jason



Philip Oakley C.Eng
philipoakley@iee.org

[ptc-1368288]

On 8/11/2009 12:14:47 PM, Jbryant61 wrote:
>Hi.
>
>do any of the optics folks
>have any mathcad examples
>showing how to obtain the PSF
>from the MSF?
>
>thanks
>Jason
_______________________

PSF is a function, an exploitable and exploited function. MTF is an overall global conclusive characteristic of an optical system a "function like". So, no Mathcad work sheet can relate intelligibly an onion and a dice. That's my understanding, otherwise you would have had a returned work sheet ... is it ?

Jean

[GuyB]

On 8/11/2009 12:14:47 PM, Jbryant61 wrote:
>Hi.
>
>do any of the optics folks
>have any mathcad examples
>showing how to obtain the PSF
>from the MSF?

You cannot obtain the PSF from the MTF.

Very quickly, the point spread function (PSF) is a real function of position. If you take the Fourier transform of the PSF you get a complex function of spatial frequency. At the risk of creating more confusion by introducing another name, the Fourier transform of the PSF is called the optical transfer function, or OTF. To recover the PSF you take the inverse Fourier transform of the OTF.

At each spatial frequency the OTF has an amplitude & phase. However, by definition the modulation transfer function (MTF) is just the amplitude of the OTF.

With only the MTF to go by, you can't reproduce the the original PSF because you have only half the information you'd need to invert the Fourier transform.

You could invent some form of the phase function and compute a guesstimate for the PSF, but there's no real way to know what it should be without more information.

Try it - create your own PSF and compute an MTF. Then, try inverting it back to a PSF with some arbitrary phase relationship (constant phase, linear phase, etc.) All you need to know to do this is how to take the Fourier transform and the inverse Fourier transform of some data - presumably you can do that by now. You'll see what you can and cannot expect to achieve,

- Guy

[PhilipOakley]

Whilst Guy is correct, you can also make assumptions so that you can get an approximation of what the psf might be.
The usual approximation would be perfect rotational symmetry.

Philip Oakley

[GuyB]

On 8/14/2009 4:34:23 AM, philipoakley wrote:
>Whilst Guy is correct, you can
>also make assumptions so that
>you can get an approximation
>of what the psf might be.
>The usual approximation would
>be perfect rotational
>symmetry.
>
>Philip Oakley

Excellent point. If you assume radial symmetry you can write an expression that directly computes the PSF from the MTF. (Eqn. (18) [sic - should have been (16)] in the enclosed sheet.)

- Guy

[Jbryant61]

Thankyou Philip & Guy.

I'm looking forward to diving into your worksheet.

I've never really thanked you for showing me the Hankel transform - it speeded up my worksheet tremendously - so thanks!

Jason

[Jbryant61]

BTW - there is no eq. (18)!

[GuyB]

On 8/14/2009 5:58:06 PM, Jbryant61 wrote:
>BTW - there is no eq. (18)!


Apologies - eq. (16). Typo in the collab post.

- Guy

[ptc-1368288]

BTW, Guy
Thanks, saved in the tool box.

Jean