It was necessary to determine the field of view of the intended camera, so that the joint in the integration sphere was not within the view. (At this stage, we are still undecided whether the camera will have a lens to focus the image, or whether it will be removed to aid the uniformity of light distribution onto the CMOS sensor.) The field of view was determined experimentally with the following set up:
Screen shots like the one below (at 400mm in this case) were taken at several distances away from a measured target. The centre point is at the mid height of the camera, where the sensor is, and the camera was mounted perfectly vertically.
With some geometry and a little CAD manipulation, we were able to calculate a 64 degree field of view. Before any smart people complain that the calculation is wrong, we have mirrored the similar triangles relative to the camera position. A fixed target size would clearly get smaller further away from the camera, not larger. Plotting this on the overall CAD model, we could confirm that the joint would not be seen.