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Light per unit area of focal plane is determined by the f-ratio alone. Amount of light hitting a sensor there is proportional to the square of the f-ratio. For example, take f/4 vs f/6: the f/4 lens collects (6/4)-squared = 1.5 x 1.5 = 2.25 times more light per detector pixel than an f/6.
Light per unit area (or solid angle) of sky OTOH is proportional to the square of the aperture (diameter) of the lens: double the aperture gives you 4x the light; increase/decrease the aperture by factor N, you'll increase/decrease the number of photons collected from a fixed portion of the sky by factor N x N.
The reason for this perhaps counter-intuitive discrepancy between these two ways of figuring it is that if you increase the aperture but leave the f-ratio unchanged you also increase the image scale (magnification) in proportion to the aperture. So you do get more photons from a fixed bit of sky but they are spread over a larger area in the focal plane.
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