# Calculating required amount of lumen for camera sensor satuation

I am stuck on this problem at work - I hope some of you can help me further. I work with underwater vision and am trying to find way or methodology to get a somewhat estimate of the required light from a lamp underwater to illuminate an object at a distance of 4 meter.

The following parameters are set in stone:

Sensor:

• QSat = 12.6 ke-
• Pixelsize = 4.5 x 4.5 µm
• FOV: 101 deg H, 76 deg V
• Qe = 40 %
• Exposure time = 4 ms

LEDs:

• White light - the color temperature is 6200K
• Max power = 15W
• 200 lumen / W
• FWHM = 120 deg

So far we may emit the propagation in water and assume much is ideal. I have taken two approaches on cracking this.

# 1

Convert QSat to Coloumb to further convert to ampere, taking the pixel and inspected area in consideration and thereby figuring out how much power needs to be reflected from the object. However, here I am stuck in trying to relate required reflected power [W] of the object to something that will let me scale the chosen LED, i.e. relating W to lumen.

I do have 200 lumen / W available but that does not seem to work as the W would just disappear and I will be left with lumen, saying that 1 W required is equal to 200 lumen, but what if the parameter of the light had 100 lumen / W - then it would have been 100 lumen. That does not add up.

# 2

I tried calculating the required photon flux [photons / (s x m^2)] and ended up with a number in the order of 200e15 which I guess it quite alright. I am just failing again to relating that to something with lumen such that I can figure out how many LEDs I need to saturate the image.

I hope someone really good with physics can help me out here. Thanks alot!