# Calculating light level radiating back to camera from rough surface

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!

• Are you sure about the responsivity of your image sensor? 1000 lux means it's the worst sensor available. As for the light's lux: "A flux of 1000 lumens, concentrated into an area of 1 square metre, lights up that square metre with an illuminance of 1000 lux". Wikipedia: Lux. With that beam spread .61 meters gives a one meter diameter spot. The reflectivity (or lack thereof) of the rocks will be the biggest uncertainty. – Rob May 30 '18 at 6:04
• Thanks for the further question. The spec for the cameras "Minimum latency" states: "12 us at 1 klux over the mean of 20 pixels". For clarity, I am trying to do this to then get a feel for what level of lighting is then required in order to achieve this latency (if possible!)... – tiluki May 31 '18 at 11:32