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Camera with auto-focus and 3D reconstruction

Hi, I'm using some very simple web cam, during the chessboard calibration I got every time very different intrinsic matrix(especially the part with focal lengths), is it because the camera has auto-focus? If I take the pictures of multiple chessboard position the undistorted image is afterward more distorted then the original, how can it be? Is it possible the auto-focus is disturb somehow the distortion parameters calculation? When I want to calculate projection matrix I need non-variable focus length, needn't I?

But I don't understand how such a camera can have auto-focus, when the there is need to screw the lens to make the picture sharp? I thought auto-focus is moving some lens to focus??

And second question is if I want to make a laser scanner. I need to somehow calculate the homography to laser plane is it right? So probably I can directly find the laser line on the chessboard during the calibration. But do I need to measure the distance of the chessboard or can I somehow calculate the distance from the chessboard? Do I need chessboard 3D coordinates to calculate the extrinsic matrix?

Thanks for your time