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Supposing I have an unknown lens of which I don't know f/# and focal length. I want to estimate the total amount of light that my lens can collect which, I believe, is given by the solid angle that my aperture subtends with the object plane. Is it correct to measure the size of the aperture by imaging (using a camera with a lens) the size of the entrance pupil of my unknown lens? That could be done by placing a ruler next to the unknown lens and moving it to be at the same focal plane as the entrance pupil. From the size of the entrance pupil, can I then calculate the solid angle with the usual maths?

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Ok, so trying to understand our disconnect and I think maybe I get what you are thinking now. Are you saying you want to place a ruler in front of the lens that is an unknown and focus on it so that you can look down the unknown lens and see how much of the ruler crosses over the entrance pupil? If so, you also need the distance to the ruler, though I'm not sure exactly where you would measure from. This would then allow for the field of view to be calculated, though you'd need a pretty big ruler to be able to get it in focus since it would have to be out past the minimum focus distance. –  AJ Henderson Oct 14 '13 at 17:18
    
You'd also have to be very careful to keep it in line with the focal plane so as to avoid getting a measurement that was too big. –  AJ Henderson Oct 14 '13 at 17:19

3 Answers 3

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If you don't know the focal length or the aperture, there is no way to figure it out. The amount of light that a lens is going to let in depends on the field of view of the lens as well as the size of the entrance. You don't know enough for the field of view, so you can't know how much light it gathers.

enter image description here

An alternative method that would work would be to make an area light source of a known size and place it a known distance from the lens. You could then measure the size of the circle project by the lens. This would allow you to determine the focal length and field of view, then you can perform the rest of your calculation to determine the speed of the lens.

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mmm. If I have an ideal isotropic point source that emits photons, why would I need to know the focal length of the lens? Isn't the size of the aperture enough to determine the solid angle S? The light gathered would then be S/4Pi, where 4Pi is the solid angle of a sphere. Am I missing something? –  maupertius Oct 14 '13 at 14:43
    
@maupertius - maybe I misunderstood your question, but it sounded like the only measurement you had is the size of the entrance pupil (the front element), the distance from the front element to the sensor doesn't matter because a lens is a complex optic system, not a simple, single lens system. The actual focal length does not have to match up with the length of the lens, so the field of view can not be determined from the measurement of the length of the lens or the measurement of the front element. –  AJ Henderson Oct 14 '13 at 14:46
    
Sorry, I think I was mixing the terms 'aperture' and 'entrance pupil' which I believe they are related. What I meant is that I estimate the size of the aperture by measuring the size of the entrance pupil. From there I then calculate the amount of light collected. –  maupertius Oct 14 '13 at 15:02
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@maupertius - and the reason your point light source breaks down is because the pixel captures more than a simple point. It captures an area and the field of view defines that area. If you have a fixed field of light, then the larger the area that the pixel gets light from, the more light makes it to that pixel. –  AJ Henderson Oct 14 '13 at 15:30
2  
Seems like it might help to point out that the entrance pupil is not the front element, but rather the image of the aperture as seen through the front element. Even so, AJHenderson is correct in that you need more than just the diameter of the entrance pupil to determine light gathered -- you also need focal length. Imagine, for example, that your point light source is way off to the side; light from that source will enter a fisheye lens, but won't enter a telephoto lens. –  William Shakespeare Oct 14 '13 at 16:21

Rough.
Works as a 1st estimate (sample of 1).

  • Set lens to max aperture.

  • Focus an object at infinity onto a sheet of paper.

  • Measure from focused image to reference plane on lens - say seating plane on camera body.
    Use reference plane that best advice suggests is effective lens "centre".
    See example below

  • Look through lens and measure maximum aperture OR diameter that best advice suggests should be used.

Trial: Nikkor 50mm, f/1.8

Measured diameter of optical path looking into lens ~= 28mm
Using f = Focal_length / aperture

f reference plane

1.78 lens to body seating plane 2.5 front element surface 1.5 rear element surface.

Trying this with a number of lenses of known aperture may give a guide as to how accurate this method is and which measurement planes and diameters should be used. And may not :-).

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The lens aperture is usually specified as an f-number, the ratio of focal length to effective aperture diameter.

A 50mm lens with a 50mm effective aperture has a f-number of 1.0

If your lens is a 100mm lens, if it's front element (the entrance pupil, effective aperture of the lens) measures 35mm then its maximum aperture is f/2.8

In theory the aperture blades, which are not perfectly rounded, will slightly reduce the amount of light that passes through the lens, introducing a tiny error in the calculation, I am not a mathematician but I guess the error is microscopic enough to be ignored.

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Yes. However in my case I do not know neither the focal length nor the f-number, so what I'm really asking is whether is possible to calculate the light gathering power by measuring the size of the entrance pupil. I can neglect the error cause by the blades. –  maupertius Oct 14 '13 at 14:02
    
How about mounting your camera on a tripod and using a zoom lens and compare the focal length of the two lens to try to guess the focal length of your unknown lens? It should work and you should get a reasonably accurate calculation. –  Gapton Oct 14 '13 at 14:05
    
That's a good idea, but I would like to leave it as a sort of validation step. What I want would like to prove is whether information on the amount of light collected can be obtained by the exclusive knowledge of the entrance pupil size. –  maupertius Oct 14 '13 at 14:11

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