Problem statement: I have an imaging sensor (“camera”) that has a minimal response specified at 1000 lux. This camera is set up to resolve a rough surface at 1 meter distance. Alongside the camera is a light source, also pointing at the surface. What power output do I need from the light (in lumens) to realistically deliver the minimum response?
Here is a quick sketch:
You can assume the light source is reasonably uniform, and that the surface is equivalent to a gravel river bed - with the same sort of random distribution and grade of rocks. The light is just standard visible/white (e.g. 550nm) and the sensor responds to that.
So, firstly, it’s been a while since I’ve done anything like this with the physical modelling of light. I’m vaguely aware of the differences between photometric and radiometric units (and the inherent dangers in converting to/fro them). I’m also aware (from computer graphic modelling days of yore) of illuminance, luminance, and the need for a reflectance model of the surface (interaction of diffusion, absorption/albedo, specular reflections (assume none) and refraction (assume none)...
So, I had a go myself as follows:
Assume a light source of know lumens (e.g. 7000lm) and uniform beam spread angle (90degrees).
Convert lumens of source to Irradiance (W/m^-2)
Use a Oren-Nayar model for the surface - http://www1.cs.columbia.edu/CAVE/publications/pdfs/Oren_SIGGRAPH94.pdf - factoring in albedo or 0.5, sigma variation of the surface of 30 (justification: roughly the size/absorption/distribution of rocks?) and angle between camera and light of 1.42rad at 1m.
Calculate the average Radiance emitted from the surface from this (W/m^-2/sr)
And, as you can see, I can’t then derive how much of this Radiance would result in hitting the camera (as such). It seems to me that I somehow have to account for the size/distance of the imaging sensor itself?
I appreciate this is perhaps not really the best way go about modelling this - so very grateful to be pointed in the correct direction!