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Lots of people say that full frame sensors receive more light than cropped sensors. I have never found a proof of this claim so I tried to do the computation by myself, and proved the contrary! Could you tell me if I am wrong ?

We want to compare the same frame with the same depth of field. I'm not concerned by the quantity of photons by photosite, which is unrelated to sensor size but to the density of pixels. I have neglected effects like vignetting or angle effect on the edge of the micro-lens array. Here is my simple reasoning :

If you want the same angle of view α~2arctan(size/2f) with a full-frame sensor and a crop sensor with crop ratio c, you have to multiply the focal length by approximately c. Now, in order to maintain the same depth of field, the f-number N have to be divided by c. If we measure the "amount of light" with the well defined Illuminance Ev provided by the same frame of the same scene (so the luminance is fixed), we have Ev ~ f/N.

Putting all together, Ev_crop = Ev_ff x c², so the cropped sensor receive more light than the full frame sensor !

For those who are interested in the price of two equivalent systems, one with a FF+50mm+135mm and the other with Crop+35mm+85mm, see this example.

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EV is a measure of illuminance, which is defined in the link you provided as "luminous flux incident on a surface, per unit area". You are correct in stating that when if you keep field of view, depth of field and subject brightness constant:

Ev_crop = Ev_ff x c²

however since:

Area_crop = Area_ff / c²

and

Light(total) = EV x Area

we arrive at

Light_crop = Light_ff

In other words your APS-C system will collect more light per unit area of the sensor, however by virtue of a larger sensor a FF system will collect the same amount of light in total.


However, when comparing systems in any practical sense you have to take lens availability into account. For a given full frame lens there may not exist a lens for APS-C with focal length c times shorter and f number c times lower.

From 135mm and up you can generally achieve equality in light gathering, let c = 1.6:

135mm f/2.0 -> 135/1.6 = 84.3, 2.0/1.6 = 1.25 -> 85mm f/1.2
500mm f/4.5 -> 500/1.6 = 312.5, 4.5/1.6 = 2.8 -> 300mm f/2.8

In the normal to short tele range the best you can hope for is to maintain the same f-stop, which means projecting the same amount per unit area onto the sensor, meaning the larger sensor gathers more light total.

     FF         APS-C
85mm f/1.2 -> 50mm f/1.2
50mm f/1.4 -> 30mm f/1.4

At the wide end lenses for full frame can be significantly faster, giving the full frame system more light per unit area and more area for a significantly greater light gathering ability:

     FF         APS-C
24mm f/1.4 -> 14mm f/2.8
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Do full frame sensors gather more light than crop sensors?

Lots of people say that full frame sensors receive more light than cropped sensors. I have never found a proof of this claim so I tried to do the computation by myself, and proved the contrary! Could you tell me if I am wrong?

The question doesn't contain enough information to allow a definitive answer. Intuitively, if you put the same lens with the same settings on both cameras, and if the distance from the lens to the sensor is the same in both cases, then the full frame sensor will collect more light because the sensor is larger and therefore covers more of the circle of light projected by the lens.

You say that you want to compare 'the same frame', but that's tricky because you then have to change parameters other than the sensor (lens focal length, distance to sensor, or distance to subject), and in doing so you're effectively compensating for the difference in sensor size.

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When you are worrying about getting a pinch more light, the DOF is secondary so the statement is of course assuming that you shoot wide open, or at least the same aperture (if stopped down a bit more for sharpness). And you say you deliberately discount pixel size, but if you compare same generation aps-c to FF cameras, the FF's have larger pixels:

Current:

  • 5D mark III (FF): 6.25um
  • 7D (top of the line crop): 4.3um

Past:

  • 5D mark I (FF): 8.2um
  • 30D (top of the line crop): 6.4um
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Canon's White Paper on Full Frame sensors for DSLR cameras clearly states that the larger pixels on a Full Frame sensor gather FIVE Times as much light that an APS-C sized sensor is capable of capturing. (see page 5). The Illustrations that Canon provide demonstrate much larger sensor cells and how they gather More light in Less exposure time.

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    Can you provide a link to the Canon Paper? Is something wrong with the explanation of the accepted answer? You are talking about the "pixels" of the sensor, not about the whole sensor. – Olivier Jan 1 '17 at 17:01
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Sorry but from what I understand there is no difference in light collection from full to crop sensor. You just have less "image" at the same distance.

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Take a lens designed for full frame. Of the photons entering the lens, 'x' amount of output light is hitting the full frame sensor. Now put that same lens on a crop sensor (let's assume a 1.6 crop factor), so now the output light is spread over a larger area than the crop sensor itself, with a factor of 0.6 lost light creating the image. Still at this point the same number of photons are actually hitting the sensor as the equivalent reduced area on a full frame sensor. Assuming the sensor pixels are the same size, then same exact exposure. But, this is why crop sensor lenses are made. They are designed to only spread the light over the smaller crop sensor, and with same stated f-stop (really t-stop rating) are exactly the same in light output to the sensor.

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