why fx focal length is changing when I calibrating the camera.
for example 1st calibration 786 and 2nd calibration is 811.is it normal ? and what difference between focal length given by the manufacture and our calibrated focal length
Why fx should be equal to manufacture fx ?
If you take a ruler and measure something you will also get slightly different results each time. The more calibration images you take, the closer the fx value to some asymptotic value will be (provided the calibration images are not corrupted). The focal length given by the manufacturer is the physical focal length (could be 35 mm equivalent focal length). When calibrating your camera you get focal length in pixels as explained for example here: https://answers.opencv.org/question/1...
In my experience the focal length shouldn't change by that much from one calibration to the next (unless you are changing the lens focus between runs). When I do multiple calibrations on the same camera/lens, I think the focal length changes by (maybe) as much as 5 pixels across multiple runs. How many images are you using for your calibrations, and what is the reprojection error you are getting? Depending on the lens and camera, I would shoot for 1 pixel RMS error or less, and really I would like to see 0.5 or less. If you are getting high reproj error, that's a sign that the calibration isn't very accurate, and it isn't too surprising that parameters could shift around from one calib to the next when minimizing the error. How stable is your image center?