Comment by foldr | Hacker News Reader

Comment by foldr | Hacker News Reader

The size of the sensor isn't as important as people think it is. What really matters is the diameter of the aperture (the absolute diameter, not the f number). Consider a cone of light for a given angle of view hitting a small sensor close to the aperture and a large sensor further from the aperture:

         o < aperture of a given diameter
        /\
       /  \
       ----    < small sensor (less area, more light per unit area)
      /    \
     /      \
     --------  < large sensor (more area, less light per unit area)

If you compare typical shooting apertures for DLSRs and camera phones, they're not radically different. Say you are shooting a 50mm lens at f8 on a DSLR. That's an aperture of 6.25mm. A typical smartphone camera will have an aperture of around 3-4mm. In this scenario, then, the DLSR is getting about 3 times more light (or ~1.5 stops).

Of course you can use much wider apertures on DSLRs, but their use is more limited given the shallow depth of field that results. If you're shooting e.g. landscapes, then you're probably not going to use apertures much wider than f8 anyway.

This is related to the conservation of Etendue [1] in an optical system, which is basically a statement of conservation of power: you rightly point out that radiant flux is determined by the source and constant – and for that reason, the primary numerical aperture or f-number of the lens is ultimately what really matters – assuming, as you point out, that you want to use the narrower DoF that arises (in which case SNR scales as the square root of sensor area).

However, sensors get noise from different sources: and while you're right to point out that you might be up against photon shot noise, read noise goes down with pixel area: so, as long as pixel area scales with sensor area, and that scaling is performed by uniformly scaling the pixel, the larger sensor is intrinsically "a little bit better". Quoting shamelessly again from wikipedia [2]

> The read noise is the total of all the electronic noises in the conversion chain for the pixels in the sensor array. To compare it with photon noise, it must be referred back to its equivalent in photoelectrons, which requires the division of the noise measured in volts by the conversion gain of the pixel. This is given, for an active pixel sensor, by the voltage at the input (gate) of the read transistor divided by the charge which generates that voltage, CG = V_{rt}/Q_{rt}. This is the inverse of the capacitance of the read transistor gate (and the attached floating diffusion) since capacitance C = Q/V. Thus CG = 1/C_{rt}.

As capacitance is proportional to area, pixel area matters here – read noise is proportional to it linearly. In low-light conditions, read noise dominated most cellphone sensors (mostly for the above).

[1] https://en.wikipedia.org/wiki/Etendue [2] https://en.wikipedia.org/wiki/Image_sensor_format#Read_noise

That is a good point that I hadn't considered, thanks.

Are smaller sensors also faster to read, given the lower capacitance? I wonder if that might give them an advantage when it comes to stacking and averaging images to reduce noise.

> I wonder if that might give them an advantage when it comes to stacking and averaging images to reduce noise.

That's another good question and (as ever) the devil is in the engineering detail. I work with noise professionally (well, with signal in a low SNR environment, where the SNR per acquisition of interest is definitely << 1...) and those sorts of questions are good to ask but depend a lot on the exact noise stats: your approach requires that the average value of the noise is the same in both cases (read-out N times, digitally average; vs read-out once vs "analogue" averaging). In practice, because the distributions differ of different noise sources and images are positive semi-definite, I doubt this is true. The advantage of stacking is that helps with motion (a lot) and also helps with a finite dynamic range instrument (i.e. you don't blow it and can do gain compression).

> Are smaller sensors also faster to read, given the lower capacitance?

This Stanford paper with a model of a CMOS sensor [1] is rather old but quite a good explanation of where the readout time comes from; the capacitance across the active area is C_{pd} but the minimum read-out time is dominated by the capacitance of the readout bias, C_T, across the ADC line. As a result it scales by transistor feature size (fig 5) independent of the sensor area. Of course, as 'moar megapixelz' came along, this got higher and other designs were explored to mitigate it – a paper from Rochester [2] states that removing it buggers up the noise statistics unless you do "clever things" (which they describe in detail).

> That is a good point that I hadn't considered, thanks.

I should procrastinate more productively, but thank you!

[1] https://isl.stanford.edu/~abbas/group/papers_and_pub/tcas1.p... [2] https://sci-hub.se/10.1109/ISCAS.2008.4541803

>The advantage of stacking is that helps with motion (a lot)

Yeah, that was my assumption that I didn't articulate very clearly. For the same total exposure time, you wouldn't intuitively expect an average of multiple short exposures to be much different from a single long exposure (all depends on the mathematical details, as you say). But of course if you have a good alignment algorithm, you can often in practice use a much longer total exposure time. Then, to state the obvious, you can use a lower ISO and get less noise.

Is it the case that C_T is independent of C_{pd}? Looking at the (obviously rather idealized) circuit diagram, it seems odd that their values would be entirely independent in a realistic design. I guess I am basing my intuition on the simpler case of reading a single photodiode, where it is undoubtedly the case that the larger capacitance of a larger photodiode makes it more difficult to achieve a high bandwidth. Perhaps 'read time' as such is not the issue. But being able to scale up the individual photodiodes without sacrificing bandwidth seems a big magical.

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