Flat field images are used in astrophotography to rid images of vignetting, dust on sensor plane and to even the general unevenness of light field. Shooting flat field images for longer lenses is relatively easy, one only needs an evenly illuminated featureless object. However, with fisheye lenses and their immense field of view and depth of field, there are certain problems one must solve.
Because the field of view is usually about 180 degrees from corner to in case if diagonal fisheyes and the same 180 degrees from edge of the imaging circle in case of circular fisheyes, one cannot just point the lens to something white and featureless and expect a good result. The lens needs to be quite close to the surface and the surface must be curved or round to cover the whole field of view.
The surface also must be non-reflecting. This can be achieved using white acrylic glass which is then sanded with very fine grit, around one thousand in CAMI grit designation. Coarse sandpaper should not be used to avoid visible streaks.
(Stuff gets reflected into the flat field image.)
Another problem is that the camera and lens casts a shadow on the acrylic glass. One must block the light entering behind the camera, black cloth or black painted flat field box can be used to counter the extra light.
Here's one version of a flat field box for fisheye lenses:
1: inner walls should be painted black, 2: curved acrylic glass sanded matte 3: diffuse light source, be it a window or similar. Top and bottom should also be covered.
For circular fisheyes the acrylic glass should be curved in two dimensions, not just one to cover the field of view. Hot air blower can be used to help making the curvature. Paper should not be used in place of the plexiglass as it is not homogenous enough.
Below is an example of the effect of flat field correction on spherical panorama embedded with Saladoplayer.
Look straight down for the most visible effect. Here's single image, with flat field correction enabled and without:
Flat field correction was done in Raw Therapee. It detects the lens used and loads the corresponding flat field image automatically. If there are multiple falt field images, the images are either stacked or the best one is selected using various criteria.
This article is adapted from post on Pallopanoraamablogi titled "flättiboksi kalansilmälle" and "flättiruutujen vaikutus pallopanoraamoihin".