Does any body use the Schneider Digital centre filter?
Does it work?
Does it do a better job than PS?
How do you get it if you do not speak German?
Can you get an analog (glass) center filter for the Apo-Digitar 47 XL?
A glass centre filter will in theory produce a better approximation, and in practice probably as well. The reason is that one attenuates the photons at the center of the image circle, which requires an increase of exposure which in turn will get more photons at the edges/corners. More photons = higher signal to noise (S/N) ratio. However, glass filters introduce an optical element that's foreign to the lens design, so it's not going to be a totally free lunch.
A digital filter has it's share of issues. From a S/N ratio point of view it will be a sub-optimal. What's more, depending on the lens it's going to require per aperture value settings,
and it has to be applied to Raw not-gamma-corrected data for the best results (it's at least computationally more efficient).
Lenses exhibit 2 types of darkening towards the corners, as seen by the image sensor array / film. First is the vignetting potentially caused by the tubular design of a compounded (multiple element) lens. When light strikes the 'tube' at an angle other than the optical axis, there may come an angle where the light will no longer be a circular cone of light, but it'll become somewhat elliptical in diameter and thus restrict light. This will disappear when stopping down the aperture far enough, hence the dependency on aperture value.
The other component is light fall-off, which is due to the incident angle of the light (and travel distance or magnification factor) towards the corners. This is only minorly influenced by the aperture.
Since the light striking the sensor does so while in linear gamma space, it's most effectively dealt with in linear gamma space (RAW). A lens filter will automatically do (most) of that, although it cannot take the aperture value into account. An LLC taken at the aperture used for the actual shot will be able to correct the uneven lighting (including sensor inefficiencies), but it can't compensate for the difference in photon count (= S/N ratio). It also requires to have an input about lens shift if applicable, because that will cause a decentered vignetting/light fall-off.
Cheers,
Bart