Large reflector/diffuser light propagation (calculating light ‘fall-off’/’throw’/’propagation’/’photometric values’ from large soft reflectors) in the optical near field (where the inverse square law does not truly apply) is often considered unquantifiable due to the number of variables involved.
This simply is not true.
While one does need to consider a larger number of variables compared to the inverse square law, in our situation it can be simplified due to our use of light in photography. Here is a brief explanation of the algorithm I’ve written.
1, 2 or however many light sources can be illuminating the reflector. It is assumed these light sources are at an acute angle to the normal of the reflector.
The reflectance value of muslin is approximately 95%/0.95. It then models the reflecting soft surface as being composed of many point sources, m*n (the amount of point sources scale with the size of the reflector), whose total light output is the same as the total luminous flux of the original light sources (minus losses) If the total luminous flux of the sheet is L, then the luminous flux of a single point source is L/(m*n).
These point sources emit light isotopically at a solid angle of 2pi steradians (only in front of the surface). The algorithm computes the luminance at some point z on the axis perpendicular (the normal) to the reflector passing through its centre. To this end, it simply needs to find the luminance produced at this point by each point source and then sum these values to get the total luminance.
Note that the number of point sources, m*n, can become arbitrarily large. However, for m*n => 50 the approximation is almost perfect (note there are approximately 7*7 (49) point sources per m**2 so this algorithm is accurate for sources larger than 3’ x 3’).
To the left is the soft light propagation calculator.
To RUN click the big green button.
Wait for it to initialise.
Enter your values.
I’ll quickly note the following –
The algorithm assumes the reflector is Lambertian – I find most industry-standard soft reflectors/diffusers near enough to Lambertian that the error is minor.
The algorithm calculates light propagation along normal (perpendicular to the source) – If your subject or test is off normal apply lamberts cosine law.