We agree here.
You are right that tiny pixels have a large effect on this as what little light comes in has to be divided up. But we are basically saying the same thing otherwise: the reason the smartphone camera needs a long exposure to improve SNR is because it is also using a very small aperture diameter, or light collecting area. So there is an interplay. Imagine pouring water through a tiny 1mm wide funnel into a small cup. The bucket next to it with gallons dumping straight in is the full-frame or larger lens. So it's more correct to ask: is the pixel size adequate to achieve reasonable image quality with a small lens that doesn't let in a lot of light.
You are right that functionally, we use the focal ratio or f-stop to modulate depth of field. That is related, but not the same as aperture diameter. A 105mm lens at f/2.8 has a much larger aperture (37.5mm) than a 20mm lens at f/2.8 (7.14mm). The 105mm lens will produce much cleaner images in the same amount of exposure time.
Not quite. The exposure is the same. The exposure setting is focal ratio, not merely aperture. F/2.8 on a 105mm lens has a bigger aperture, but a correspondingly smaller portion of the scene is magnified to fill that area. These offset one another to keep the intensity (photons/area) of illumination on the sensor the same.
Matching the degree of out-of-focus blur confounds the usual dimensionless reciprocal relationships, because, unlike exposure, it does relate to actual aperture size. F/4 on a 100mm lens has a 25mm apparent aperture. To get the same out-of-focus blur on a 50mm lens, one needs f/2. A 200mm lens achieves the same blur at f/8. All these have the same 25mm apparent aperture. (Assuming the same degree of enlargement, not the same target print size.)
But they all have different magnifications, and higher magnifications reduce the light for the longer lenses according to the inverse square law. Thus, to get the same exposure (intensity/time or photons/area/time), one needs a longer shutter opening.
Instead of a longer shutter time, we could simply amplify the received signal more, but that also amplifies the noise and we don’t see an increase in S/N. This is the effect of increasing ISO. It may well keep us in the sensor’s linear range, however, for a practical exposure settings.
Example:
My 645z’s 33x44 51MP sensor is almost exactly like four 13MP APS-C sensors in a 2x2 array. Sensel wells are the same size. It takes twice the focal length to preserve the same framing. Twice the focal length with the same
aperture yields one-quarter the illumination because magnification doubles and light intensity is subject to the inverse square law. But that’s obvious, because the same butter is spread over four times the bread. Fortunately, we work in focal ratios rather than apertures to compensate. The same focal ratio for a lens twice as long means an aperture twice as big in diameter and four times the area, and compensates for the loss from the increase in magnification.
But larger sensels mean each is magnified less for a given display size. So we do stuff more light information into each unit of area of the displayed image. And more sensels mean we can make a larger display at the same resolution. So, more large sensels means bigger prints, or smaller prints with a higher density of tonal information, with better color. It also means noise (including the transfer function distortion caused by lens faults) is reduced relative to image size.
But that’s not because the aperture is bigger, it’s because the sensor is bigger.
Rick “bringing back memories of discussions long ago, long settled” Denney
