Image FFT and Lens MTF: Evaluating Final Image Quality

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Discussion Overview

The discussion revolves around the evaluation of final image quality on a detector using the Fourier Transform (FFT) of an object and the Modulation Transfer Function (MTF) of a lens. Participants explore the implications of object size on frequency representation and the effects of MTF on image clarity, focusing on both theoretical and practical aspects of image processing in optical systems.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions how the multiplication of the FFT of an object and the lens MTF accounts for changes in object size and frequency representation.
  • Another participant suggests that reducing the object size leads to larger spatial frequencies, which may result in increased blurring due to the constant MTF.
  • A participant expresses uncertainty about handling frequency information when applying the lens MTF or Optical Transfer Function (OTF) to the transformed object image.
  • One participant references Goodman's book to explain the relationship between the point spread function, OTF, and the object field, outlining different cases for incoherent and coherent imaging.
  • Another participant raises a concern about the necessity of sampling the object at a sufficient pixel count to match the maximum frequency before applying convolution.
  • A later reply indicates that the participant has resolved their confusion regarding the topic.

Areas of Agreement / Disagreement

Participants express varying levels of understanding regarding the relationship between object size, frequency representation, and the application of MTF. There is no consensus on the best approach to handle frequency values in relation to sampling and convolution.

Contextual Notes

Participants mention specific parameters such as the lens MTF cut-off at 20 lp/mm and the dimensions of the viewed object (600x600 mm), indicating that these factors may influence the discussion but are not fully resolved.

Neels
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Hi, I am trying to determine the final image on a detector having a 600x600 mm viewed object and the known MTF of a lens. So when I FFT the object, thus creating frequencies -128/600 : 128/600 for a 256x256 image, how does the multiplication of the transformed object and the MTF "keep track" of the frequencies or the size of the input object? Because I can change the object to 60x60 mm and that would not affect the multiplication. How then do I evaluate the correctness of the final IFFTed image? thanks
 
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Neels said:
Hi, I am trying to determine the final image on a detector having a 600x600 mm viewed object and the known MTF of a lens. So when I FFT the object, thus creating frequencies -128/600 : 128/600 for a 256x256 image, how does the multiplication of the transformed object and the MTF "keep track" of the frequencies or the size of the input object? Because I can change the object to 60x60 mm and that would not affect the multiplication. How then do I evaluate the correctness of the final IFFTed image? thanks

If I understand you correctly, shrinking the object scale will result in larger spatial frequencies- the FT has a scale factor essentially corresponding to object size (or feature size, if you prefer). Because the MTF is constant (in your case), the smaller the object, the more attenuated those larger spatial frequencies are, resulting in more pronounced blurring.
 
Thanks Andy - yes, I understand that there will be more pronounced blurring, but if I FFT the object image I don't know how to handle the frequency information when the transform is multiplied with the lens MTF or OTF.
 
Neels said:
Thanks Andy - yes, I understand that there will be more pronounced blurring, but if I FFT the object image I don't know how to handle the frequency information when the transform is multiplied with the lens MTF or OTF.

Goodman's book has all the information you need. In brief, calling 'h' the point spread function and H the OTF (|H| is the MTF), 'o' the object field and 'O' the transform of object field, 'i' the image *intensity* and 'I' the transform of i, and letting '×'/'⊗' represent the convolution/autocorrelation integral, there are two cases, depending on whether or not the imaging system is phase-sensitive:

Incoherent imaging: i = |h|2×|o|2; I = [H⊗H][O⊗O]
Coherent imaging: i = |h×o|2; I = HO⊗HO

Does that help?
 
Yes, but I guess my issue is more about the frequency values that apply - I have a measured lens MTF with a cut-off at 20 lp/mm. The object I am viewing is 600x600 mm - so do I need to sample (i.e. use nr of pixels) on the object to get the same order of max frequency before I perform the ⊗?
 
Neels said:
Yes, but I guess my issue is more about the frequency values that apply - I have a measured lens MTF with a cut-off at 20 lp/mm. The object I am viewing is 600x600 mm - so do I need to sample (i.e. use nr of pixels) on the object to get the same order of max frequency before I perform the ⊗?

I don't understand your question.
 
I believe I have complicate things a bit - but managed to sort it out. Thanks
 
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