I think the scattering medium is indeed assumed to be frozen in time. This would be the case for any solid of course, but also for a sufficiently homogeneous fo

I think the scattering medium is indeed assumed to be frozen in time. This would be the case for any solid of course, but also for a sufficiently homogeneous fog. I assume you are only inverting the statistical average of the scattering medium properties, so as long as those are frozen in time it's sufficient.