Torsten Bronger wrote:

> Have you tested which degree you need?

No.
I have been trying to see what is needed without experimenting by modifying 
lensfun code, but I failed.

My idea was to use the Fx special effects of ImageMagick to experiment with 
various correction formulas.
But I have not been able to reproduce with ImageMagick the effect of using 
lensfun profiles in darktable.

Pablo D'Angelo vignetting model uses the formula M = 1+k_1 r^2+k_2 r^4+k_3 r^6 
where r is the distance from the center of the image, normalised such that the 
corners are at distance 1 (this is explicit in mod-color.cpp, the distance 1 is 
the "half-diagonal length").
The page 
http://lensfun.sourceforge.net/manual/group__Lens.html#ga3fd9e8dbe500297bdda2d6458745b481
 says that the correction is obtained by multiplying by M, but Pablo D'Angelo 
papers say that is it done by dividing by M, and the fact that existing lens 
profiles include negative values for the k_i suggest that lensfun corrects 
vignetting by dividing by M (which will be less than 1).

I thought that I understood how it works, and that the ImageMagick command 
below will do the same correction as the lens profile below.
        <vignetting model="pa" focal="250" aperture="4" distance="1000" 
k1="0.0" k2="-0.156" k3="-0.711" />
        convert IMGP4694.tiff -fx "Xi=i-w/2; Yj=j-h/2; 
r=hypot(Xi,Yj)/hypot(w/2,h/2); s/(1-0.156*r^4-0.711*r^6)" 
IMGP4694-corrected.tiff

But it is not the case.

> Eventually, I'd like to have flat-field images in Lensfun.  See
> <https://en.wikipedia.org/wiki/Flat-field_correction>.  Proposals in
> this direction are very much welcomed.

I guess that instead of having a (parametric) formula to correct brightness 
depending only on the distance to the center, the correction profile could be a 
low-resolution image that lensfun would scale up to the picture size and use to 
.

Louis

PS: There is another addition to lensfun that would be useful for the owners of 
Pentax bodies: taking into account the position of the optical center. Because 
the sensor may not be centered (due to shake reduction, or composition 
adjustment) and therefore the vignetting intensity is not the same in every 
corner.
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