# Optimising the choice of lens for collecting scattered light

I want to figure out the “best” lens for collecting light that is being scattered in air. For simplicity, lets say that the scattered light in the volume of interest is homogenous – i.e. the intensity per unit volume is equal and light is scattered equally in all directions, and that I want to collect this scattered light using a lens and deliver it to a sensor with width h. In that case, I have two questions:

1. Presumably there is a “cone”, a volume within which a particular lens can collect light, in other words light from outside this cone can’t be accepted by the lens and be imaged onto the sensor. In that case, what would define the angle of this “cone” – should I think in terms of the Numerical Aperture (the range of angles that can be accepted by the lens), or in terms of the Field of View (which also takes into account the size of the sensor)? I should add that I don’t want to create a sharp image onto the sensor, just use the lens as a bucket that gathers as many photons as possible.

I have a lens with NA = 0.63, focal length 40 mm. Using the NA the 'cone' full angle is approx. 78$$^\circ$$, but using the FOV formula I found here I get a 'cone' full angle of approx. 1.4$$^\circ$$ if I consider the sensor h = 1mm. Very large difference between those two values, and I don't know which is "right"!

1. What about the diameter of the lens? Presumably a larger lens will collect light over a larger area, and thus collect more light? But if there is the choice between a larger diameter lens with a smaller NA/FOV, and a smaller diameter lens with a larger NA/FOV, which is the better choice? Thanks in advance!
• @trula would you be able to elaborate? Why would a larger NA lens, that gathers light over a wider range of angles, not collect more light in this scenario? Sep 24 '21 at 8:18
• Can you consider an integrating sphere to collect the light ? Sep 27 '21 at 8:37