Number of photons comparison

Assume two systems: (See below)



In the first one there is no lens, just a simple detector. In the second case there is a lens system with a particular focal length and f#. I am trying to see what is the impact of lens in terms of total photons hitting the detector.

In the first system there is no lens so the total number of photons is proportional to the area of the detector. In the second system there is a lens I assume the number of photons hitting the detector is different. There are optical losses and also size of the aperture of the lens makes a difference.

So, I am trying to gauge what is the difference?

Assuming optical transmission is T, the lens aperture area is A, detector area is D. My guess is the number of photons difference is as follows:

Assume total number of photons for detector only case is X, and Y for with the lens. My guess is

Y= T*X*A/D

Is this correct? Does focal length or f# make any difference?

frankqt said:

Assuming optical transmission is T, the lens aperture area is A, detector area is D. My guess is the number of photons difference is as follows:

Assume total number of photons for detector only case is X, and Y for with the lens. My guess is

Y= T*X*A/D

Is this correct? Does focal length or f# make any difference?

Click to expand...

If I'm reading correctly: captured photons ratio of lens vs. bare detector = lens aperture area / detector area? 10x the surface, 10x times as many photons captured (ignoring T, that is)? Sounds about right.

The "about" is key here. How the light is distributed from object to detector vs. from object to lens, might matter. So relative size, shapes & distances too. And whether all photons that pass through the lens, are focused to hit the detector (-> focal length!). Remember most lenses won't focus different wavelenghts exactly the same (nothing is perfect), so strictly speaking focal length could be wavelength-dependent. And X times more photons on detector might not be detected as exactly X times more photons (non-linear sensitivity, small temperature effects etc).

I'm guessing surface ratios would be a good -rough- estimate. To get more exact results: measure.