I rephrased the question, see last comment
I'm currently working with a highres line camera scanner and we want to use it for measurements. Therefore we need to be able to calibrate it properly in 2d.
We have an accurate test-pattern made by photolithography. We can assume it to be 'exact'. I have managed to come up with a very robust subpixel circle recognition to find the points of interest so I have no question regarding image recognition.
What is unclear to me at this point is how to use the found image coordinates together with the known spatial correlation in order to come up with a distortion map which ultimately would be used to correct the distortion.
The example shows a cropped subset of a typical image of circles with 400µm xy spacing. The recognition is already done (red circles with blue centercross) leaving out structures that are too close to the edge. Now, how do I calculate a distortion-map from that?
I played around with some algorithms like knnsearch in order to look at the lokal distances and I can see that they vary significantly. I don't want to simply create a coordinate system using arbitrary points and then measure relative distances to that system because I fear that might induce large errors over big distances.
My guess is that using a combined approach of the local information (distances) in combination with the 'far field' (straight lines, orthogonality etc.) should result in the most robst outcome but I'm stuck on how to continue. In the end we want to do many measurements in order to determine the measurement errors caused by vibration and thermal influences i.e.
I'm fairly certain this has been solved (many) times but as a non-expert on the field I just don't know what to search for exactly. I would appreciating any help!