Can you correct field curvature with FFTs?

[NickK]

So I'm thinking.. not completely thought through and untested idea.. as I've been reading up on FIR, IIR and s and z-transforms.. 

Assumption - if deconvolution is normally a correcting phase change in frequency space.

Now if you know the field curvature angle (for each point in the image) - using the angle of stars as a 'psf' (or even dots on a board) to give a set of points and rather than performing a interpolated mesh sampling, creating a reverse phase FFT to apply to each image to flatten the image.

Naturally this is a full image sized FFT that needs to be applied.

So the fun part here is that using convolution association so that you can precalculate:

The desired output would be output image = input image * field curvature *  .... 

But you can precalc ahead of time: myConv = field curvature *  ....  then for each image it's simply output image = input image * precalc

Hmm something to think about..

[michael.h.f.wilkinson]

Field curvature is not linear or shift invariant, and hence the convolution model should not apply

[NickK]

Field curvature is not linear or shift invariant, and hence the convolution model should not apply

Well that shoots down that idea

I was thinking how does the FFT work with the variation over 2D.. but I was going to think about that today whilst doing the other jobs.

[michael.h.f.wilkinson]

Convolution/FFT based shemes really work in linear, shift-invariant spaces. If you can transform the image such that the degradation fits that model, you are fine, otherwise, not so much