Nycturne
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We don’t agree here, as I have pointed out. Total photons captured is a function of aperture (area). F-ratio allows us to determine photons per unit area. Photons per unit area determines your SNR (i.e. dictates brightness / exposure times).
If you use a lens designed for a large-sensor camera on one with a small sensor, the following is indeed what happens, corresponding to your description: You have the same photon flow/unit area, so the smaller sensor captures less light. But that's obvously not how you want to design a camera, since you're throwing away all that precious light.
View attachment 25897
Wikipedia has a good description of this lens mismatch: "Lenses produced for 35 mm film cameras may mount well on the digital bodies [of small-sensor cameras], but the larger image circle of the 35 mm system lens allows unwanted light into the camera body, and the smaller size of the image sensor compared to 35 mm film format results in cropping of the image. [Emphasis mine.] This latter effect is known as field-of-view crop."
Image sensor format - Wikipedia
en.wikipedia.org
Ah, but the smaller sensor in this example still has the same SNR! It is equally as bright. That’s the point of the exercise. Despite all the wasted light, all I’ve lost is FOV.
Yes, you should design lenses appropriate for the sensors, but it’s ultimately irrelevant for the discussion at hand as we get to the second example.
Except, what have you actually created in this diagram, if we assume f-ratio is equal? If I assume I’m not using baffling or other techniques to discard light for the smaller image circle, I’ve probably created two systems with the same effective FOV. So in the small sensor case the actual focal length is shorter. This is important, because it means the aperture is smaller for the same f-ratio. In other words, the total photons captured of an extended object is less for the smaller image circle, but as it covers a smaller area, you wind up with the same light per unit area at the same f-ratio. If you keep aperture constant, the lens for the smaller sensor is going to be noticeably faster due to the smaller focal length (faster f-ratio). This is because the image circle is itself a function of aperture and focal length. Short focal lengths converge the light rays more sharply, which has the effect of shrinking the image circle. Shrinking the aperture does much the same if focal length is held constant. However, two light cones with the same f-ratio always have the same shape from the aperture to the focal plane. And so to vary the image circle size is to vary the focal length so long as f-ratio is constant still leaving us with the same light per unit area.
You can’t just “concentrate more light onto a smaller circle” without also affecting the f-ratio. And so a small, bright, image circle is going to show up as a faster f-ratio.
This is why lenses for smaller sensors are generally more compact for the same use. The smaller image circle means I can use shorter focal lengths and smaller apertures for the same FOV, while maintaining similar f-ratios. It also means you can get faster f-ratios with more manageable apertures.
Now, this isn’t the only way to set an image circle, but other ways of controlling the image circle aren’t exactly relevant for the discussion of brightness/SNR.
Another example here is using a focal reducer on a telescope. It makes the focal ratio faster at the expense of the size of the image circle. The light per unit area increases due to the concentration of the light captured and the f-ratio drops as a result because the focal length drops while aperture remains fixed. This works precisely because aperture is fixed in this scenario.
Historically, larger sensors have been where you go for better low light performance, BTW. But that’s more because the size of the “wells” (pixels) matters when trying to get signal above the sensor noise. Although Sony’s modern sensor line, especially now that back-lit sensors are more common, tend to use the same pixel size across the various sizes, so there is no distinct advantage at the sensor alone (although camera body still plays a role). The A7S in particular is known for low-light prowess because in the early models it used sensors with unusually large pixels. More recently it uses 2x2 binning for the same effect. But I think you are the first person I’ve ever seen claim that smaller sensors are actually better for low light, let alone “far better”.
