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[task #13565] Add non-linear warpings.


From: Sachin Kumar Singh
Subject: [task #13565] Add non-linear warpings.
Date: Sun, 15 Mar 2020 18:32:20 -0400 (EDT)
User-agent: Mozilla/5.0 (X11; Ubuntu; Linux x86_64; rv:73.0) Gecko/20100101 Firefox/73.0

Follow-up Comment #1, task #13565 (project gnuastro):

This
<https://www.researchgate.net/publication/224599781_Lens_Distortion_Correction_Using_Ideal_Image_Coordinates?enrichId=rgreq-b4da5c700a5e5ffef071dce621b851fc-XXX&enrichSource=Y292ZXJQYWdlOzIyNDU5OTc4MTtBUzoyMTAzMzI5NzE3MzcwOTBAMTQyNzE1ODY5NjM4MQ%3D%3D&el=1_x_2&_esc=publicationCoverPdf>
paper gives a very nice method to correct optical distortion, which can also
fix the sky distortion problem. The Wikipedia
<https://en.wikipedia.org/wiki/Distortion_(optics)#Software_correction> page
also suggest a similar way but its a bit complex. In all these methods there
is the distortion coefficient(k) is required. Now this
<https://www.researchgate.net/publication/224616900_Analytically_solving_radial_distortion_parameters?enrichId=rgreq-7e7d3714b9411375c6b1542e20c7c42c-XXX&enrichSource=Y292ZXJQYWdlOzIyNDYxNjkwMDtBUzozNzczMjE3OTUxNDU3MzBAMTQ2Njk3MTkzNDQwOA%3D%3D&el=1_x_2&_esc=publicationCoverPdf>
paper provides an analytical way to find the coefficient. But it's complex to
implement(thoughts?). We can just ask the user to provide these coefficients
based on their own calibrations.
  
For celestial coordinate mapping this Wikipedia section
<https://en.wikipedia.org/wiki/Celestial_coordinate_system#Converting_coordinates>
provides good transformations required. I think we might need to use and/or
modify the `wcs' library for its implementation.

For weak lensing this <https://arxiv.org/pdf/1109.3410.pdf> paper seems to
pose many challenges on its implementation, so we can let go of this for the
time being.


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