bobn2 wrote:

Leo360 wrote:

Yes, I cannot discover a scene precisely but I can find as much as possible conditioned on my observation.

Good. We're agreed there, then.

I am not talking about temperature of the image plane. Where did you get it from. Also, Bob, you deleted the whole paragraph from my post which talks about black-body radiation. Let's hope it was unintentional

No, it was intentional, because it was irrelevant.

Well, you are taking the liberty to edit the words of your conversation partner at will based upon what you deem irrelevant against the objections of the other party who claims that it is. In a civilized discussion both parties should agree that the omission is appropriate. Don't you think so?

What I am saying here is that by observing spectrum of the incoming light from a back-body you can estimate deterministic parameters of the said body like its temperature that governs the radiation process and it happens despite the fact that a photon detector captures finite and fluctuating photon count. More photons you get higher the estimation accuracy of the underlying physical (deterministic) parameter(s).

I have the feeling that you understand exactly what I am saying and our discussion is quickly diverging into a philosophical one.

Yes, I do understand exactly what you are saying, and it has always had a philosophical nature, coming from your statement that the lambda functions were 'the reality'. So, if you maintain that I will argue, because it is a central point. From the point of view of the camera as a capture system, the 'reality' is only the photon events that happen at the sensor. You cannot ever know what is the 'reality' of the scene in front of the lens, if for no other reason than it is not guaranteed that there is only one 'reality' that would generate the same patten of photon events.

Let us get this straight. If one had information on the nature of every light source lighting the scene, and the geometry and material characteristic of every object within the scene we could construct a mathematical model of the light intensities at the image plane. That is exactly what we do with ray tracing in 3D modelling. But that is not the reality on any individual exposure.

Exactly correct. Therefore, whenever we reason about the objects in the scene, we think of all its parameters as conditional probabilities conditioned on our observation (digital image). Better sensors with lesser noise, more resolving power, etc allow for tighter estimates of the scene features. The scene is a fundamental entity and an image is just a representation which can be traced (with some errors) back to the scene.

This is where we diverge again. As I said, for the camera the only reality is the photon events at the sensor. We cannot determine from those, even if we had the perfect sensor (although our perfect sensor allows us to reconstruct an amazing amount about the scene) a unique scene that would have generated those events. So, the nature of that scene remains speculative. The more information we collect at the image plane, the more and more of its properties we can discover.

So they are in probability theory, but with a wider meaning more is revealed. As I said, what is 'expected' is what you expect before the observation (the clue is in the word). The mean is after the wave functions have collapsed, the observation has been made and the reality has been determined.

You are making your own domain language which is different from the common conventions.

No, I am digging beneath the semantics of the common conventions. Why is the term used in probability theory 'expected' and not 'real'? Precisely because the is no underlying hard 'reality', there is an expectation and there are observations. Expectation denotes a 'before' state.

In Quantim Mechanics nobody uses word "mean" to denote the results of individual measurement (collapse of the wave function, if you wish). The Square of the absolute value of the wave function determines the probability (which is calculated before the measurement) to find your quantum system in one of its eigen-states (eigen-vectors of its Hamiltonian) after the measurement. After you completed your measurement the system "collapses" to one of those eigen-states of the system. It does not collapse to a MEAN in any sense of that word.

It collapses to the mean of a single observation.

A single observation collapses a wave function to the specific quantum state (typically one of the eigen-states of its conserved operators like Hamiltonian (Energy) or Momentum or Spin, etc related to the observation). There is no "mean" of a single observation and no one uses this word in this context. It is also strange to hear it from you Bob, who argues that there is no noise in a single pixel

As you make more observations you will gather a mean closer to the expectation (provided the model on which the expectation is based is good). You need to think why these words are used.

Again, let us stay on the subject. You were talking about collapse of a wave function, which is a single event and does not have any statistical properties of its own. When you consider a large ensemble of the identically prepared systems and perform the experiment on the plurality of the systems you can collect the statistics and derive not only the mean but all the higher moments, and, ultimately, the entire probability distribution (wave-function square modulus) from it (at least in theory).

Don't take my word for it, please, check any good QM book. Wikipedia provides a good starting point http://en.wikipedia.org/wiki/Wave_function_collapse .

If I wanted to check any good QM book, I'd dig out my old texts from college days.

This is a good idea. But this particular philosophical aspect of Quantum Mechanics has very little to do with sensors and photography.

Where did I say that photon shot noise originates inside pixels?

I never said that you said that.

Again, you are engaging in creative edition of the previous posts. Below I am including your own sentence which preceded my "ascribing me the words...":

Bob's phrase: "The number of photons registered by it should correspond to the number of photons which hit it. Shot noise is not because pixels are incorrectly counting the number of photons (that is read noise)"

This has been my position all along and I have no I idea how you reached the conclusion that I am taking an opposing point of view which had to be explicitly argued against.

I never said you said that, and the creative quoting that you have just engaged in shows that. I added a clarification in case you were arguing that, but I never ever accused you of arguing that, and I'd hope you'd be honest enough to stop falsely accusing me of doing so.

As Eric pointed out, for the purposes of calculation it gets catered for simply by multiplying the photon count by the QE. As Joofa pointed out, that is an approximation.

This is true for "mean values" (as in "mathematical expectation") not for individual photon counts. So it is true for "lambdas" (in Poisson approximation lambda IS the mean photon count). I think Joofa said exactly the same thing

http://forums.dpreview.com/forums/post/50345602

"The mean value of photoelectrons can be estimated as the mean number of photons multiplied by the QE."

Note Joofa's very correct and proper use of the word 'estimated'.

Again, you are arguing semantics. Bottom line: If you magically know the EXACT photon count hitting the pixel you still cannot predict the number of photo-electrons generated by the pixel. They are Binomially distributed with QE being a probability of photon -> electron conversion. You cannot just say:

"No, it gets catered for simply by multiplying the photon count by the QE. " and get the exact electron count.

One can work out the relevant probability distributions, estimators, their variances, etc. In fact, the model which assumes Poisson photon arrivals and constant iid conversion probability (Binomial distribution of electrons conditioned on photons) is exactly solvable. Today morning I worked it out. If you are interested we can share the notes over a private channel.

Thank you, I would welcome that. Saves me the trouble.

I am trying to figure out how to post here scanned hand-written pages (they are in PDF). Any help is welcome.

No we are not. A 'pattern of photon events' is the observation that occurs, the sampling is the nature of the counting that you do. A discrete photon event counter would not be a sampled system. How you sample does not affect the pattern of photon events.

The act of observing a random process is called sampling from it.

Not really. http://en.wikipedia.org/wiki/Sampling_(statistics). Sampling involves selection of a subset of events according to some selection criteria.

This is population sampling. In the theory of Random Processes (and Random Fields) the words samples and sampling have somewhat different meaning. See http://en.wikipedia.org/wiki/Random_process and search for "sample sequences".

It is not the sampling in ADC sense. Again we are talking semantic differences here.

Semantic differences which are vital to where the discussion started, which is the influence of pixel size on the information yielded. There the right use of 'sampled' is indeed in the ADC sense. So, you are engaging in a confusing overloading of 'sampling'.

Bob,

I can't help but notice that you are trying to pick a fight here and argue about semantics or philosophical foundations of Quantum Mechanics or meaning of words "mean" and "sample" which are clear from context. All of these subjects are great topics for a face-to-face discussion with a bottle of Whiskey but I do not find them interesting in an on-line photography forum. In my professional life I reached a point which I call "Ignorance, Third Degree" (ITD) which means that "I do know what I know and I do know what I don't know". I came to this forum to educate myself about the subjects in photography, image processing, photographic gear where my knowledge is deficient. Also I hope to be able to provide some useful input in the areas of my expertise. But I really am not prepared to waste my time (and yours) on esoteric and annoying bickering about words or concepts of no relevance for the topic at hand.

With all due respect I am signing off from this conversation.

Leo