You need to calibrate your camera to use pixel coordinate as angular coordinate. One of the important steps is to define optical axis position and another one define camera distortion properties. After that you will be able to use relatively simple geometrical relations.

(1) Take care that fish eye lens have a high level of distortion. Because of that you need to characterize your system for distortion. The simplest way is to use defined grid pattern at distance higher than few tens of the lens focal length. The grid pattern could be plane surface or , better, spherical surface. Comparing grid properties and image you will be able to define lens distortion correction.

(2) Using similar plane grid on the optical bench where your camera is mounted there is a way to define where is optical axis penetrate your camera sensor plane.

A simple optical fact that any point on lens optical axis stay on axis after refraction can be used to determine the optical axis point (pixel) in the image. try to define your grid that will allow you to track the position of the selected points in the image. Take the image of the grid at few distances on optical bench, analyze images and try to find which one of the points on the grid keep nearly constant position in all images. The related pixel is then on optical axis.

Good luck.

Dear Branko,

Point (1)

I know about this method of taking a photo of a regular grid to compute the lens distortion. Matlab has a routine that automatically analyzes the image and gives the angles of each pixel.

=> However, that angular mapping will be biased if we don't point the camera perpendicular to the grid (i.e. the optical axis being perpendicular to the grid). Hence first, I have to know the optical axis. Then, from the experimental point of view, how do you to guarantee that it will be perpendicular to the external physical grid? Do you have a suggestion?

Point (2)

I'm not sure I understood your suggestion. If I move the grid further away and the optical axis is not perpendicular to the grid plane, the pixel at the optical axis will view something else. Right?

Do you have a paper or book that explain this idea?

Thanks

Henrique

You are right. regarding grid image and fixed point. But if you use designated points to track their coordinates than you can. define optical center coordinates. For more detail see extract from related procedure given in file attached.

In addition you can see document at the link.

https://www.ri.cmu.edu/pub_files/pub2/willson_reg_1993_1/willson_reg_1993_1.pdf

Unfortunately, I can not send you the original document because it is related to proprietary product camera calibration fixture and procedures.

Hope that this can help you more.

Good luck,

Katia Mendes sent me this links to me as a private message. As they are are quite useful, for the benefit of others reading this thread:

https://www.theeminentcodfish.com/gopro-calibration/

Beekmans et al, 2016, "Cloud photogrammetry with dense stereo for fisheye cameras"