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Consider a low-light, high-ISO, short-exposure shot. We all know the image will be noisy. I understand that the image noise is dominated by the photon counting noise (shot noise) that is caused by photons being discrete particles and because there'd be so few of them per pixel. This excellent question discusses this.

To me, the simplistic view of an image sensor is a photon counting device. Each incoming photon with the right wavelength for the particular pixel causes its internal counter to "+1", until the saturation value is reached. Say, 16383 for 14-bit sensors.

As I read more, I understand that things are not quite that simple - not every photon gets counted (QE), then there's this analog amplifier part that introduces a "few electrons of noise". So my question is how much noise in this scenario is contributed by the photon counting noise, and how much is due to sensor imperfections?

Put another way - if we dial down the ISO low enough, so that sensor imperfections account for just the last bit of the 14-bit digital value of the "counter", how many photons on average need to strike that pixel to cause a +1 increase? Obviously, if we get this ratio to just "1", we'd get our perfect photon counting device, and clearly we aren't there yet, but with the commercially-available sensors in 2017, how close are we?

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  • While this question might start an interesting discussion it does not have an objective answer in terms of photography that will be true a year of more from now. It is probably better suited for a photography discussion forum than it is for this site's question and answer format.
    – user50888
    Nov 16, 2017 at 18:13
  • You are correct, I'll update it to state I'm considering current sensors.
    – anrieff
    Nov 16, 2017 at 18:18
  • ...Each incoming photon with the right wavelength for the particular pixel causes its internal counter to "+1" Not really. Sensors are monochromatic. Every photon that gets through the Bayer filter causes a +1. And some photons from all visible wavelengths make it through all three of the colored filters on Bayer masked sensors. Just look at the response curves of any Bayer masked sensor. RAW files store 3 colors per pixel, or only one?
    – Michael C
    Nov 16, 2017 at 20:23
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    @MichaelClark, that's exactly what I mean by "with the right wavelength". Also note that there are RGB sensors that don't utilise a Bayer filter, so your statement is not universally true.
    – anrieff
    Nov 16, 2017 at 20:57
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    I'm voting to close this question as off-topic because it's asking a question about state of the art engineering or physics, rather than photography.
    – StephenG - Help Ukraine
    Nov 17, 2017 at 2:47

2 Answers 2

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Obviously, if we get this ratio to just "1", we'd get our perfect photon counting device, and clearly we aren't there yet, but with the commercially-available sensors in 2017, how close are we?

The LinCam has 1000x1000 pixel resolution with a temporal resolution of 50ps (2.5 gigasamples per second precision).

LINCam25 and LINCam40

Such cameras are used for Time-Resolved Super-Resolution Fluorescence Studies of Biological Structures, a method where fluorescent chemicals are injected into plants or humans and then cell activity can be viewed.

PicoQuant's wide range of products for photon counting includes several high-end modules for time-correlated single photon counting (TCSPC) and event timing, single photon sensitive detectors and specialized analysis software for the evaluation of (time-resolved) fluorescence measurements and quantum correlations.

Some of the available single photon detectors (not an image, just a pixel) feature detection efficiency maximum of 40 to 50% at 400 to 550 nm. Indeed they do rely on receipt of a single photon to measure the time it occurred after the stimulus as multiple photons (or missing photons) affect the measurements in Fluorescent Lifetime Imaging (FLIM).

While the technology continues to improve such cameras have been available for many years, Stanford Computer Optics was founded in 1989. Their Image Intensified CCD Camera and EMCCDs (electron multiplying) operate efficiently, the photon being detected is brighter than the residual noise (with sufficient cooling).

Quantum Efficiency Chart

These cameras (and single pixel detectors) are designed to count single photons accurately and without error, like all electrical devices sometimes they miss a photon and sometimes there's an error in the count - averaging the results with multiple frames can accumulate enough information to produce a histogram showing the count and occurrence frequency.

For an explanation of the math behind counting photons and the effects of noise see http://www.andor.com/learning-academy/ccd,-emccd-and-iccd-comparisons-difference-between-the-sensors or http://www.andor.com/learning-academy/electron-multiplying-ccd-cameras-the-technology-behind-emccds where Andor claims:

"In the limit of when there is less than 1 electron falling on a pixel in a single exposure the EMCCD can be used in Photon counting mode. In this mode a threshold is set above the ordinary amplifier readout and all events are counted as single photons. In this mode with a suitable high gain a high fraction of the incident photons (>90%) can be counted without being affected by the Noise factor effect.".

An EMCCD can multiply it's input by over 10K times, dividing by the same value gives you an accurate count of the photons.

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  • Thanks, this answers my question - if speciality sensors can count photons accurately, that is good enough for me. Do you think it's reasonable to assume that consumer sensors will also be at this level of precision soon?
    – anrieff
    Nov 17, 2017 at 15:20
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    Currently you should expect to pay over $20K for EMCCD, so you can see 1 or 2 photons (per pixel / per frame); if you're expecting several times as many photons then sCMOS is far less expensive - check out used equipment prices: photometrics.com/products/demoproducts - most "consumers" don't live in a cave and have many photons floating around. Standing in a forest during a power failure would blind an EMCCD Camera resulting in a white screen and no image. Chances are there will not be a 'consumer' (cheap and drop-proof) EMCCD Camera this decade, sCMOS will replace it.
    – Rob
    Nov 18, 2017 at 6:55
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If you mean, "how much closer to an ideal can we get practicaly/technologicaly?", no one can a priori answer the question. We have no way of knowing what technological breakthroughs will be made in the future. There is, of course, a theoretic limit (which we will likely never reach.)

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  • My question was specifically what % of the noise comes from theoretical limits. Of course, reducing the other (sensor-induced) noise to 0 is very likely impossible.
    – anrieff
    Nov 24, 2017 at 13:49

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