Since the ADC digitizes a DC voltage, I can not accept that the sensor does not generate signals.
You seem to have gone off at a tangent: DC talks about pixels with not a hint of 'proportion of the photo' nor of 'spatial frequency'. I know you are not given to straw man arguments but I suppose a little obfuscation doesn't hurt?
Please cut the attitude. Yes, the shot noise per pixel will be higher -- no one says or implies otherwise.
The natural and implicit conditions are viewing the photo at the same size from the same distance.
Always, since that is how we view photos.
Sorry, comment withdrawn - was supposed to have been gentle sarcasm. My bad.
Aha! Now it is clear. So, for example, what is the effect of down-sampling the larger image to the same size as the smaller? Is that 1.2% above reduced by sqrt(2) to 0.85% assuming a simple bi-linear reduction?
Thanks for the explanations which goes a long way to explaining the differing assertions in this thread.
Ah. No worries!
I keep embedding Lee Jay's photo which really tells the whole story, and tells it well:
That page is dated 2013. I think you'll find that those authors did not discover that photon shot noise is 'an inherent property of light'. That was already a well known fact (I don't know who 'discovered' it, but it was already being talked about by Emil Martinec and many others when I joined these forums in 2007).
Schottky wasn't talking about image sensors. He was talking about electron shot noise in semiconductors, we're talking about photon shot noise. The statistics are the same, the carrier is different.
All that is true, except that the shot noise recorded by the sensor isn't exactly the shot noise in the photons, because there is another random process going on, the conversion of photons to electrons. Current sensors have about a 50% conversion rate (if the photon makes its way through the CFA) and that also is random.
Either way, the photoelectrons counted by a pixel still follow the Poisson Distribution. Chris (cpw) did a derivation of that a while back, but I don't have the link handy.
It's not a phrase that I like very much. For a start, I'm not sure what 'state' means when applied to nature as you are applying it - the 'state' seems to depend on how you observe it.
Most peer reviewed physics journals are all about weasly ways of appearing different. One of the things that you need to realise about Jayne's 'state of nature' is that it is not a 'state of nature' - it is a conceptual abstraction - a 'state of nature' is an infinite set of integers. here is your basic problem. At some stage, when the GUT is finally constructed, we might be able to determine that there is a singular 'state of nature' corresponding to some observed phenomenon. In that sense it is a useful abstraction, but what it isn't, is how the universe functions. It is a model of how it functions.
I'd agree that.
Given some priors, it can. that's how noise reduction works, which definitely does improve signal to noise ratio, though at other costs.
Sure, but I'm not sure what that applies to here.
Indeed there aren't. And in relation to this wider discussion, there has been no process descried by which 'downsampling' would improve SNR.
Yes, they do - but the Poisson distribution is in part down to what's going on in the pixel, as we know. Apply the same stimulus to two sensors identical apart from quantum efficiency, you get a different distribution. Or, another thought experiment - suppose one made a photon gun which could shoot a known number of photons into each pixel (can't think of how the technology would work, because you can't count the photons without collapsing their wave function) even then, you'd see a Poisson distribution, unless the sensor had 100% QE.
It is quite simple. Sensors (at least, pixels) are photon counters. They basically suffer from two kinds of inaccuracy. One is non-linearity - if you know what it is, it can be corrected, the other is electronic noise, which is independent of the reading. That inaccuracy is called read noise. When it comes to a sensor, there is a third inaccuracy, which is that the scale factor (output to photons) is not exactly the same for every pixel. This inaccuracy is called 'Pixel Response Non-Uniformity' or 'PRNU'. Again, it can be corrected if every pixel is characterised and individual correction applied. Often it runs in rows and columns, and a simpler option which most cameras adopt is characterising line by line and column by column and applying those corrections. But really, there is no reason to suspect that large pixels are more accurate photon counters than small ones, unless they fail to be engineered such that read noise is proportional to full well capacity.
There are two competing theses. Thesis one is that the major noise in photos is photon shot noise, which depends on the number of photons counted and not on the 'accuracy' of the pixel. The second thesis is that the major noise in photos is pixel inaccuracy. In effect what they are saying is that read noise dominates shot noise. It's demonstrably untrue, but that doesn't stop the case being argued with some passion.
Ted, two things.
blog.kasson.com
Rats! Quite right, Jim.
I was thinking that bi-linear was kind of like simple averaging but, judging by the amount of humble pie I've already eaten today, that's probably wrong too.Second, the reduction of noise upon binlinear interpolation downsampling is not a simple function of sampling ratio, as is indicated by this graph, which has no AA filtering:
In the case of 2:1 downsampling, the noise is indeed reduced by a factor of 2.
I thought Bart was the only guy on the planet that does that! ;-)
Helps, Jim. Thanks.For a Gaussian AA filter with sigma equal to 0.2 times the ratio of input width in pixels over output width in pixels, the noise reduction looks like this:
In downsampling you have the opportunity to trade off reducing noise and preserving detail. Lanczos 3 is often thought to be a reasonable compromise.
With more aggressive AA filtering, we get this:
And now, as the reduction ratio gets near 0.2, or 5, depending no how you look at it, the reduction in noise is as predicted by formulae like the image size normalization algorithm used by DxO.
Does that help, or just muddy the water?
When I generated those graphs, I was surprised, too.
Caught me! You may have noticed I used Bart's suggested Gaussian sigmas (see below). Thanks to Detail Man for pointing me to Bart's downsampling page:
Thanks, Ted.
Correct me if I'm wrong, but wasnt this when the area was 4X? So a factor of 2 would be the quadrature. Was it not really 2 then?
Me too! So which filter is the closest to quadrature then? Sorry, I have had time to read through all your good work.
Pardon me for correcting the mess DPR editor made of your post!
By 2:1 downsampling, I mean measured linearly. So that's four pixels that become one. Quadrature says half the noise: sqrt(4) = 2. Binlinear interpolation gives you half the noise. But change the ratio a bit -- up or down -- and bilinear interpolation s not as good at reducing noise. That's what the graph without the AA filter says.
I'm assuming you mean which resamping algorithm, not which filter. If that's the case, bilinear interpolation.
A smart man (probably the same one) sent it to me, too. Still - it's useful for other people to have the link too.
