As Nancy suggests, these are just mathematical work-arounds, when it may be better to put the effort into creating a more uniform illumination source. But where is the fun in that
Ah, but the rewards ...
Nancy, I trust that your translucent illumination is radially symmetric, but why would it not be brighter in the center, where the scattering angle is smallest? If you place the sun off-center, do you still get the same result?
A diffuser like Nancy describes is a more or less
Lambertian diffuser. Personally, I use 2 sheets of opaline glass taped together at the edges, to avoid yellowing after a long time of light exposure and temperature changes. As long as the light that reaches the surface of the diffuser is relatively uniform, the out of focus (infinity focused lens) image of that diffuser, held flush to the lens barrel/hood, is very uniform.
That should leave the lens vignetting and light fall-off as the only variable, then modified a bit by the sensor's pixel shading, but that's mostly constant for lenses with a similar exit pupil position.
I use such a diffuser plate for creating a Lens Cast Correction (LCC) file for Capture-One, which then corrects the slightly different sensor response for different colors, and the vignetting and light fall-off, as the angle of incidence gets more oblique towards the corners of the sensor.
Cheers,
Bart