Hi Cleon,
I first designed and implemented the DBE tool in the final days of "Good Old Film Astrophotography"
TM. Photographic film is nonlinear —it has been designed to mimic the response to light of human vision— so image calibration in film astrophotography, although certainly not impossible, is a very difficult and inaccurate task, compared with digital imaging. For this reason, one of DBE's primary tasks was vignetting correction, since virtually all film images (with the notable exception of Schmidt camera images) suffered from this problem. Some time after I published the first version of DBE (with PixInsight LE, around 2003) Carlos Milovic devised a clever way to apply a
flat field correction by division through a linearization procedure.
Vignetting is a multiplicative nonuniform illumination effect. It is caused by limitations inherent to most optical systems, the main cause being the fact that the objective's aperture projects varying areas on a flat focal plane as a function of distance to the optical axis. This leads to radial symmetry, so I implemented the ability to replicate DBE samples symmetrically over regular polygons around a user-definable center. With this feature, you can fix vignetting problems easily and efficiently on images where there are not enough free sky areas. You just have to define the center of symmetry, which usually corresponds to the intersection of the optical axis with the focal plane on the image, then define DBE samples on free sky regions and replicate them by enabling axial symmetry. For very difficult cases, this feature also allows you to duplicate DBE samples using horizontal, vertical and diagonal symmetries.
With digital image sensors, vignetting must be corrected through image calibration with accurate flat frames. So DBE's symmetries are now rarely used by astrophotographers (I think). They are more useful in other imaging fields, such as microscopy, where image calibration is not a so usual procedure, and even in some fields of daylight photography.
