Mathcad 15 cfft help (Converting MTF to PSF)

[Jbryant61]

Hi, I am trying to convert an MTF of an optical system by taking the magnitude of the fourier transform. I have attempted this but the result doesn't look like it should.   I cannot see any obvious mistake.

I appreciate any help,

thanks

Jason

[LucMeekes]

I don't know what an MTF of an optical system is, and I could make a guess of what PSF means...

But I have a few points that may be of help to you:

1.

You chose to use the cfft() function, not the fft(), not the FFT() and also not the CFFT() function.

Did you review each of of these functions to find the one most suitable to your application?

2.

You did a curve fit to your initial points, and from that created more points. Usually there is no point in doing that, unless you have a specific purpose. Such kind of data creation will certainly NOT increase the accuracy of your result.

Success!
Luc

[Jbryant61]

Hi.

psf = point spread function

mtf = modulation transfer function.

psf is used in the spatial domain to indicate the smallest object an imaging system can deliver.  The MTF is the equivalent but in the frequency domain.   The beauty of working with MTF's is the response from different components (optics, detector etc) can be obtained by cascading the MTF's.    

The psf is the magnitude of the FT of the MTF.  But something doesn't appear right in my implication of this.

Regards

Jason

[Fred_Kohlhepp]

I'm not sure, like Luc I'm in uncharted waters.  But a quick google search turned up

"

Formally, the OTF is defined as the FFT of the (PSF, that is, the of the optics, the image of a point source). As a Fourier transform, the OTF is complex-valued; but it will be real-valued in the common case of a PSF that is symmetric about its center. The MTF is formally defined as the magnitude (absolute value) of the complex OTF.

"

So your claim that the PSF is the FFT of the MTF sounds backwards. . . .

[Jbryant61]

Hi, so using icfft instead of cfft doesn't change anything.

[Fred_Kohlhepp]

I'm not surprised.  If we believe Wikipedia (if it's on the internet it must be right!) the MTF is the amplitude of the OTF, so trying for an inverse FFT of that would be a challenge.

I've done a bit more research, http://www.montana.edu/jshaw/documents/18%20EELE582_S15_OTFMTF.pdf does a pretty fair (from a layman's view) job of showing the relationships.  Comparing your MTF to one of theirs shows a similar construct: