how many images for camera calibration?

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of course according to Zhang's paper it seems more samples the better the results. In fact according to the data presented there (if I remember correctly) there are dramatic improvements with 5+ images. However in many tests I got a much lower reprojection error rate (~.2 or .3) when I used 5-10 images versus 20-30. In my view it ought be possible for calibration in a controlled environment to use images taken from a minimal set of fixed orientations to get a reliable result. Instead of the adhoc approach currently. That needs re investigating the mathematical derivation. As far as near or far camera positions relative to the chess board plane: I got my best results (better undistortion) when all the pictures were taken with the camera closest to the plane. Thanks.

But the reprojection error is maybe not the best indicator. If you just use one image, you can get a perfect reprojection error just for this image. It would be interesting to do the standard machine learning approach and divide your images into training and test datasets. You could use some of the images to compute the intrinsic values of your camera. In a second step you try to find find the pattern in the test-images using these intrinsic values via solvePnP. A good calibration would have a small reprojection error in both cases. If you have to little images in the training phase, you could suffer from overfitting which would result in much larger errors in the test phase.