Dammit!

[Manul]

did I understand you correctly, silver halides are a suspension in gelatin, there is a void between the grains, when recording a hologram, the sine wave is fragmentary and is associated with this discreteness. In photopolymers and bichrominated gelatin, the sine wave is continuous, hence the higher brightness of the holograms? But why then
But why then does the theory poorly describe photopolymers rather than silver halides?

[Din]

This is extremely interesting; I'd like to hear your thoughts on this, if possible. As I understand it, this is related to the structural properties of DCG and photopolymers. Are we talking about thick polymer layers over 30 µm, or does the poor performance of classical theory also apply to Bayfol?

I would not say that there is a poor performance of classical theories. I think there's an inadequate performance because the assumptions of the theory are idealised, and not really met in the real world to a greater or lesser amount. Specifically, the theories all seem to assume a sinusoidal modulation, but, as I said earlier, it's very difficult, if not impossible, to actually get a sinusoidal modulation. A Taylor expansion of sin(θ), gives you:

sin(θ) ~ θ - θ³/6

So, the response is linear for small angles, but goes cubic at higher angles. This gives Fourier components that throw energy into unwanted orders. For almost continuous media, such as dcg, the response is mostly sinusoidal, but there is a slight non-sinusoidal modulation. If you measure the spectral response of a dcg hologram, you should get a Dirac delta if the modulation were truly sinusoidal; what you do get is a sharp(ish) peak with side orders (see below for a typical spectral response). The side orders represent the Fourier components due to the non-sinusoidal (actual) modulation. But, the actinic mechanism of dcg is cross-linking (polymerisation) of gelatin molecules which increases the hardness of the emulsion and so increases the index. This means that the increase in index - the modulation - follows the sin curve pretty closely.

For photopolymers, the actinic response is due to charge migration which probably gives a non-sinusoidal modulation because the electron density cannot fall away smoothly following a sin curve since there is a Coulomb repulsion between electrons.

I haven't really thought about thick polymer layers, but, my initial thoughts are that there is probably more of a non-sinusoidal response as the polymer gets thicker. I have the specs for Bayfol HX-102 and Bayfol HX-200, which both state a polymer thickness of ~ 16 u; by contrast, silver halide film is ~ 8u. However, I've not seen any spectral plots for polymers. My wife Joy may be working with thicker polymers and I can ask her this evening since she's working now. Display holographers don't have to worry about these non-sinusoidal effects, since any such modulation will simply end up as noise around the image.

did I understand you correctly, silver halides are a suspension in gelatin, there is a void between the grains, when recording a hologram, the sine wave is fragmentary and is associated with this discreteness. In photopolymers and bichrominated gelatin, the sine wave is continuous, hence the higher brightness of the holograms? But why then
But why then does the theory poorly describe photopolymers rather than silver halides?

Yes, silver halide emulsions are suspensions of grains in gelatin. These grains contain what are called 'specks' of silver halide in them The old Agfa plates used to have a grain size of 40nm (if memory serves). Slavich PFG-03C has an 'ultra-fine grain size" of 10nm. However, there is no information on the grain distribution within the emulsion. If you knew the amount of silver bromide that went into the emulsion, and you knew the emulsion thickness it's possible to calculate the grain distribution. The grain distribution will tell you about the separation of the grains.

I wrote a piece on silver halide emulsions, and I quote from that piece a section about grains and specks:

"All the grains in the emulsion consist largely of Silver Bromide with a few atoms of free,
elemental Silver, called sensitivity specks. These Silver specks contain about
1/10,000,000 of the mass of the whole grain. When a particular grain is exposed to light,
some of the Silver specks on it are ionised by the release an electron. These Silver ions
cause neighbouring Silver from nearby Silver Bromide molecules on the grain to also
reduce to elemental Silver and hence the speck grows to form a larger latent image-speck.
When the speck has grown to a particular size, it provides a point at which the developer
can attack the grain. Grains which have not been exposed to light will still have specks,
but with no ionisation of the specks, they will not grow sufficiently to form development"

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[Manul]

The grain distribution and grain size of Slavich vary from batch to batch. Grain size ranges from 0 to 20 nm, with a Gaussian distribution, peak at 10 nm, and monodispersity up to 40%. Could you please explain how this distribution is calculated? And how it can be taken into account when calculating hologram quality during recording? This is very interesting.

[Din]

The grain distribution and grain size of Slavich vary from batch to batch. Grain size ranges from 0 to 20 nm, with a Gaussian distribution, peak at 10 nm, and monodispersity up to 40%. Could you please explain how this distribution is calculated? And how it can be taken into account when calculating hologram quality during recording? This is very interesting.

The usual method of making silver halide plates is to add AgNO3 to some bromide (eg AgBr) and diffuse it into the gelatin. This forms grains. If you know the grain size, then you can calculate the grain volume. If you know the gelatin coating volume, assuming uniform distribution, you can calculate the number of grains in the volume of the coating, and so calculate the distribution.

[Din]

You may want to get hold of Hans' book ( https://www.amazon.com/Silver-Halide-Re ... 3540586199 ). It contains a lot of good information about silver halide.