So a f/1.8 on a 1" sensor would still gather more light than a f/3.5 on an APS-C?

Bob A L wrote:

Great Bustard wrote:

Aside from DOF and noise, why do we care about the f-number at all? It's not exposure time, because whatever exposure time the 1" sensor can use at f/1.8, the APS-C camera can use at f/3.5.

I don't understand. We care about f-number because, the size of the hole to let light through (f-number) and the shutter speed are the only way we can control the amount of light getting to the sensor.

Yes! So, the next question is why do we care about the amount of light getting to the sensor? The answer is: noise (to include DR, which is directly related to noise) and blown highlights. There are no other reasons we care about how much light is projected on the sensor.

And we use f-numbers because physical size of the hole must vary according to focal length to allow the same amount of light through and f-numbers are derived from calculations that create the same amount of light reaching the sensor at f1.8 regardless of focal length, where the physical size of the aperture will be much different on a 5mm lens than a 500mm lens. And aperture physical size is based on focal length, not sensor size.

OK, let's talk about the three different apertures:

1. Physical aperture (iris): this is the physical size of the maximum opening within the lens.
2. Effective aperture (entrance pupil): this is the image of the physical aperture (iris) when viewed from the front element. For a given scene and exposure time, this is what determines the total amount of light projected on the sensor.
3. Relative aperture (f-number): this is the ratio of the focal length to the diameter of the effective aperture (entrance pupil). For a given scene and exposure time, this is what determines the intensity of the light projected on the sensor.

So, why do we use the relative aperture (f-number) instead of the effective aperture (entrance pupil)? Simple -- for *a given system*, the same f-number will result in the same total amount of light projected on the sensor for a given scene and exposure time, regardless of the focal length. This is quite useful when using a camera.

However, the same relative aperture (f-number) *will not* result in the same total amount of light projected on the sensor for a given scene and exposure time for different formats. Thus, the f-number is not the relevant measure for cross-format comparisons with regards to noise (and DOF).

Bringing it all together, f/1.8 on a lens used in combination with a 1" sensor has a slightly larger effective aperture (entrance pupil) diameter than f/3.5 lens used in combination with an APS-C sensor for a given framing, the net result being 1/3 of a stop more light being projected on the sensor for the same scene and exposure time, along with a slightly more shallow DOF.

Fortunately, we can easily compute the equivalent relative aperture (f-number) between formats in the same way we do for focal length: by multiplying by the equivalence ratio (crop factor), which is the ratio of the sensor diagonals. In the case of 1" and APS-C, that ratio is 28.4 mm / 15.9 mm = 1.8x.  Alternatively, you can use the ratio of the crop factors for each sensor to get the same result:  2.7x (1") / 1.5x (APS-C) = 1.8x.  Either way, then, we see that f/1.8 on 1" is equivalent to f/1.8 x 1.8 = f/3.2 on APS-C -- 1/3 of a stop "faster" than f/3.5 on APS-C.

Thus, just as the equivalent focal length results in the same [diagonal] framing for a scene shot from the same position with different formats, the equivalent f-number results in the same total amount of light projected on the sensor and the same DOF for the same scene and exposure time with different formats, and is computed in the same manner as the equivalent focal length. How cool is that!