Larry, I've had that hypothesis (in the back of my mind) for a while.
Your question made me thinking in more detail about it.
On one hand the argument for why that should be possible is as follows:
If the noise is due to the statistical uncertainty (Sqrt(N)) for the
number of counts (N) on the detector (pixel in this case), and the number
of counts scales with the area of the single detector (pixel), then by
combining the output of the equivalent number of the detectors (or more
exactly, areal coverage), we should obtain a comparable level of the
noise to that of a large detector of the same area.
(For simplicity, let's neglect for now the "wasted" area between the
smaller pixels that is not occupied by the pixel.)
However, that doesn't cover other (numerous) sources of noise that scale
differently (or even don't scale at all) with the sensor size.
Dissertations are written on very careful analysis of those.
(If you are interested, - look e.g. at these class notes:
https://classes.yale.edu/04-05/enas627b/lectures/EENG427l09bnoise.pdf )
But I can think of two "phenomenological" examples that demonstrate
why the sum of smaller sensors might not be as good as a single large one.
1. A smaller sensor might require a fundamentally different design,
which, in turn, produces a different level of noise (e.g. CMOS vs CCD).
2. If noise is generated at the boundary of the sensor. (This could be
relevant for very high-density/small pixel size sensors)
Then the combined boundary length (circumference) of the M smaller pixels
covering the same area as one large pixel will be Sqrt(M) times larger
then that of that single large pixel.
I am not sure if this type of "boundary" noise is actually
happening/important in today's sensors. It might be that this type of
effects are only relevant for much smaller (e.g.
double-digit-nanometer-scale electronics) devices.
But in any case, - different scaling of different types of noise (noise
sources) and different relative contribution from different sources at
different pixel sizes can create the situation when you might not get a
low-light-level noise from the combined pixels of a high-pixel-density
camera sensor as low as you would get it from an equivalent-pixel-count
lower-pixel-density camera sensor.
Igor
Larry Colen Fri, 09 Oct 2015 14:10:38 -0700 wrote:
That being said, I don't understand why with a bit of math a 42 MP sensor
could not put out 12 MP files with the same noise and DR as the 12 MP
sensor. My feeling is that you could probably come pretty close to the
noise of the 12 MP sensor, while still retaining most of the resolution of
the 12 MP sensor, particularly for high contrast edges.
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