Hi - the Dark field image is the dark current noise level in your field. The flat field image measures the illuminated detector with the angular component of the beam being measured. This curvature is applied to detected image and produces the corrected image. There is a very nice explanation with formula in the attached link.

Flat-field correction - Wikipedia -

https://en.wikipedia.org/wiki/Flat-field_correction

Good luck in your work.

Gain Calculation

Gain = (Flat - Dark) / Mean(Flat - Dark)

Corrected Image Calculation

Corrected Image = (Raw Image - Offset) / Gain

First of all, we have to consider the possibility of averaging a stack of several captures (>10) to eliminate temporal noise. So when I say "image", I mean the average of the stack. In this way, we can minimize the problem of spatial non-uniformity. What we have to do is:

1) to obtain an image in darkness, I'll call it DSNU;

2) to obtain an image in front of a Flat Field at the end of the scale in the dynamic range of the instrument, but making sure that there is no pixel in the image that enters into saturation; I'll call this FF;

3) to obtain PRNU = FF - DSNU;

4) to obtain the average value of PRNU, I'll call it PRNUm;

5) and considering that we already have the reference image, a raw image, which I'll call RAW;

6) finally you can obtain your corrected flat field image (Icorr), assuming a linear behavior throughout the entire dynamic range of the sensor, as follows: Icorr = (RAW-DSNU) x PRNUm / (FF - DSNU).

Regards!