Shifting the auto-focus in real-world camera doesn't change the focal length, rotation, or any other camera parameter in pinhole camera model. However, it does shift the image plane and affect the depth of field. How is this possible?
I understand that complex mechanism of real-world camera cannot be easily explained with pinhole camera model. However, I believe that there should be some link between them as we use this simplified model in various real-world computer vision applications.
Short answer: it cannot. The pinhole camera model has no notion of 'focus'.
A more interesting question is, I think, the effect of changing the focusing distance on a pinhole approximation of the lens+camera combination, the approximation itself being estimated, for example, through a camera calibration procedure.
With "ordinary" consumer-type lenses having moderate non-linear distortion, usually one observes significant changes in:
The last item implies a change of the calibrated focal length, and this is sometimes "surprising" for novices, who are taught that a lens's focus and focal length do not mix. To convince yourself that the FOV change is in fact happening, visualize the bounding box of the undistorted image, which is "butterfly"-shaped in the common case of barrel distortion. The pinhole model FOV angle is twice the arctangent of the ratio between the image half-width and the calibrated approximation to the physical focal length (which is the distance between the sensor and the lens's last optical surface). Changing the distortion stretches or squeezes that half-width value.
