How many photons?

[alanrockwood]

How many photons need to be absorbed by a silver halide crystal to form a developable center?

I think I many have seen the figure of 2 floating around in some discussions, but I don't remember for sure.

I'm pretty sure it's not a single hard and fast number, and it probably depends on a number of factors, but I would be interested in at least a rough or typical number.

The reason for wanting to know is that I am toying with some simplified mathematical models for simulating an exposure/density curves, including Poisson statistics in the model.

 

[markjwyatt]

Your number of 2 photons is supported in Tadaaki, Tani, Photographic Sensitivity Theory and Mechanisms, Oxford University Press, 1995 on page 106. The discussion is around "Lowe's hypothesis", a Figure 4.20 is relevant. The source reference that used to support that is R.K. Hailstone, et. al., J. Imaging Sci, 32 150(1988).

 

[Helge]

What is really interesting about that, is that silver halide is not inherently low quantum efficiency then, as often postulated.
Only the way it’s coated, distributed and developed limits its efficiency.
Many of those factors being controllable, makes it interesting for the inclined hobbyist.

 

[Nicholas Lindan]

I've seen two, but I think that may be more a theoretical lower limit and is sensitive to location and timing. From what I have read it seems somewhere around 8-12 may be needed to form a really permanent latent image.

A sigmoid, usually the 'logistic function' (as it is easily computable), makes a reasonable approximation to an HD curve. Two sigmoids joined by a straight line gives independent control of the toe, shoulder and linear segment of the HD curve.

 

[markjwyatt]

If you read the text in Tadaaki, the two photons was for "hydrogen hyper-sensitized and sulfur plus gold sensitized fine AgBr grains". I suspect the average film is not treated to such a degree. So I suspect what @Nicholas Lindan is saying is more likely for "real" photography. But I think for the OP's perspective it may serve as a rational minimum for modeling.

 

[Nicholas Lindan]

I think for the OP's perspective it [2 photons] may serve as a rational minimum for modeling.

No doubt. The statistics should come out the same - just multiply the horizontal axis by however many photons you think are needed.

 

[Alan Johnson]

Quantum Efficiency Considerations in the Comparison of Analog and Digital Photography (imaging.org)
Quantum efficiency for silver halide is estimated at a few percent for reasons given.

 

[wiltw]

OMG, my eyes are starting to glaze...in in my stunned state I start to wonder how many Photons emitted from a Phaser which is set on Stun vs. a Phaser set on Kill

 

[Helge]

Quantum Efficiency Considerations in the Comparison of Analog and Digital Photography (imaging.org)
Quantum efficiency for silver halide is estimated at a few percent for reasons given.

Notice who wrote the paper.
It’s an hatchet job to kill film, from someone with strong interests in pushing CCD sensors.
It indirectly references Birds study from the late sixties. Which was good research, but was then somewhat out of date and done as real research.
While at the same time glossing over the factors that take electronic sensors real QE down several pegs.

There is a tonne of papers like that from the mid nineties to the mid 00s.

 

[markjwyatt]

OMG, my eyes are starting to glaze...in in my stunned state I start to wonder how many Photons emitted from a Phaser which is set on Stun vs. a Phaser set on Kill

If stun= N /sqm, I would imagine kill is 10^5-10^7 time N. I will let a subject matter expert state what=N.

 

[Helge]

If you read the text in Tadaaki, the two photons was for "hydrogen hyper-sensitized and sulfur plus gold sensitized fine AgBr grains". I suspect the average film is not treated to such a degree. So I suspect what @Nicholas Lindan is saying is more likely for "real" photography. But I think for the OP's perspective it may serve as a rational minimum for modeling.

Almost all colour film is sulfur and gold sensitized. And has been so for decades.

Two electron sensitization is a stab at doing storage-able hydrogen hypering.

Gas hypering is possible (especially if you realize that you don’t need or want a pressure chamber and water purging stage when not doing it for reciprocity failure), so is preflashing and latensification.

 

[wiltw]

If stun= N /sqm, I would imagine kill is 10^5-10^7 time N. I will let a subject matter expert state what=N.

I suppose the conversion between Newtons and Photons is an exercise which is left for the student?!

 

[markjwyatt]

I suppose the conversion between Newtons and Photons is an exercise which is left for the student?!

Ha! N = some integer in this case.

 

[wiltw]

Ha! N = some integer in this case.

Oh, lower case 'n', not upper case 'N'! So we are left with another unknown to solve for.

 

[Maris]

Counting photons is not so easy. Years ago when I was doing thermoluminescence studies on mineral grains I used a photomultiplier tube that could register the arrival of a single photon. BUT quantum indeterminacy meant that the signal of the arrival of a single photon was just better than 50% true. To be sure of getting one with good probability then two would have to be counted and to be really really sure then the count had to be three. I don't know how the old photo-chemists managed it.

 

[Vaughn]

I just always assumed 4. Seems like a nice number. It is how I describe why reciprosity failure (RF) happens. During long exposures, the shadow areas are impatiently waiting for enough photons to activate any of the grains of silver crystals hanging around in them, while the mid-tones and highlights are happily buzzing right along as if everything was normal.

 

[Sirius Glass]

Any software engineer would tell us that it is good practice is to do things in even powers of 2.

 

[markjwyatt]

Any software engineer would tell us that it is good practice is to do things in even powers of 2.

or powers of 8 or 16.

 

[ic-racer]

Quanta theory would seem to indicate ONE photon. I can't seem to see how it would be more, unless they were arriving simultaneously. The 'photoelectric effect' (yes, not what we are discussing here) is certainly obeying quanta theory.

Planck thought his concept of quanta was just a mathematical "trick" to get theory to match experiment. But Einstein extended Planck's quanta to light itself. (Planck had assumed that just the vibrations of the atoms were quantized.) Light, Einstein said, is a beam of particles whose energies are related to their frequencies according to Planck's formula. When that beam is directed at a metal, the photons collide with the atoms. If a photon's frequency is sufficient to knock off an electron, the collision produces the photoelectric effect. As a particle, light carries energy proportional to the frequency of the wave; as a wave it has a frequency determined by the particle's energy. Einstein won the 1921 Nobel Prize in physics for this work. But it was just the beginning

.

 

[Vaughn]

Perhaps it takes a wave of photons....

Edited to add a quote from Werner Heisenberg..."Atoms are not things."

 

[Sirius Glass]

Quanta theory would seem to indicate ONE photon. I can't seem to see how it would be more, unless they were arriving simultaneously. The 'photoelectric effect' (yes, not what we are discussing here) is certainly obeying quanta theory.

.

PE said that one photon causes too much noise aka fog, and therefore two photons was the design goal. Hence sticking to even powers of 2.

 

[RalphLambrecht]

How many photons need to be absorbed by a silver halide crystal to form a developable center?

I think I many have seen the figure of 2 floating around in some discussions, but I don't remember for sure.

I'm pretty sure it's not a single hard and fast number, and it probably depends on a number of factors, but I would be interested in at least a rough or typical number.
I don't think photons can be counted.
The reason for wanting to know is that I am toying with some simplified mathematical models for simulating an exposure/density curves, including Poisson statistics in the model.

 

[Helge]

Recombination can be “fixed”. The main problem with most of those solutions is storage.
Distribution of halide crystals could also be improved by various means, but would require completely redesigned coating machines.

Those are two main detractors in taking QE of film emulsions down.

The main things “holding film back” is distribution from the manufacturer, and development.

Photographic developer is like a single ended tube amp a wonderful amplifier, but not a powerful one.
Though again like tubes the distortion is less objectionable when pushed to the limit.

Companding that would be the natural solution, is also hard with the common techniques.
Various compensation schemes being the best attempt at rectifying the hysteresis (RF) and limited amplification range of the developer.

Working on mechanical, optical or chemical ways of rectifying this, would bring film up to very high QE.

 

[Nicholas Lindan]

Yes, 1 photon of sufficient energy will knock an electron out of a silver-halide molecule, reducing the silver to its metallic state. However, there is now a naked halide atom and a wandering electron along with the metallic silver atom. In time the electron wanders back to the silver atom and the halide atom and the three form a silver-halide molecule again.

If enough metallic silver atoms are formed in a close enough space in a short enough time the aggregate of silver will become stable forming a long-lasting latent image grain. Why this is so seems to still be a matter of debate.

The recombination of a lone silver atom, a halide atom and a free electron after a single photon hit is what gives rise to low intensity reciprocity failure. If the next photon hits the grain after the first silver-halide molecule split apart by the first photon has had time to recombine then the grain is back to where it started from and a stable latent image never forms. As the inter-arrival time of the photons is a statistical phenomenon, if enough time passes with a low photon flux eventually enough photons will arrive in a short enough time to form a stable latent image.

A highly energetic photon, a gamma ray or cosmic ray, will form a cascade that knocks many electrons free forming a stable latent image. This is why film will fog in the freezer. Kodak stored its unexposed film stock in deep mines to keep the cosmic ray flux to a minimum.

 

[ic-racer]

Thank you Nicholas.