by Din » Wed Oct 03, 2018 8:22 am
Martin wrote: ↑Wed Oct 03, 2018 5:24 am
The smaller the grains the more image modulation is of the phase type. Maybe someone with better insights into Raleigh and Mie scattering theory could elucidate on this.
Well, roughly, Rayleigh scattering is predominant for small particle size, roughly 10% of λ. Rayleigh scattering is direction independent, and scatters both in the forward (the direction of the incident) light and the backward light. Also, because Rayleigh scattering is independent of the direction of incident light, scattering occurs for both transmission and reflection holograms in random directions within the emulsion. It's also heavily dependent on the wavelength of light, being proportional to the fourth power of the frequency, and so to the fourth power of the inverse wavelength. That is R ~ (1/λ)⁴. So, particles of about, less than, 50nm will strongly Rayleigh scatter, and the scattering is more intense for lower, blue shifted, wavelengths. So, as the colour changes from red to yellow, scattering increases. The scattering ratio, ie the ratio of intensities of scattered light, is:
R(y)/R(r) = [λ(r)/λ(y)]⁴ = [630/590]⁴ ~ 1.4
That is, the yellow will scatter about one and a half times more.
Mie scattering dominates as the wavelength increases to about λ. Mie scattering is not λ dependent, but it is directionally dependent, being stronger in the forward direction (in the direction of the incoming light). It's also much stronger than Rayleigh scattering, which is why, by the way, you can see a small white cloud against a large expanse of blue sky - the water molecules in the cloud are far larger than the nitrogen molecules in the air. In terms of the direction dependency, Mie scattering will scatter towards the viewer in transmission holography, and away from the viewer in reflection holography. However, given the range of particle sizes in terms of these fine grain materials, i'd say Rayleigh scattering is probably more influential in terms of noise. Remeber also that the efficiency of a hologram is not equal to the brightness of a hologram. There are scotopic issues. Roughly, if V(λ) is the efficiency of light reception at λ, then, for blue against yellow:
V(450)/V(590) ~ 0.038/0.757 ~ 0.05
That is, yellow is about 20 times brighter than blue for the same luminosity (efficiency of hologram)
Martin wrote: ↑Wed Oct 03, 2018 5:24 am
The smaller the grains the more image modulation is of the phase type.
One thing I have to point out: the image modulation is not the same as the index modulation. The index modulation is determined by the density of developed grains, since it's the index difference between developed and undeveloped grains, that is, by the ratio of the density of the light parts to the dark parts of the planes in the emulsion. As I've mentioned elsewhere, all emulsions in the last 40 years have been volume holograms due to the fact that emulsions are in the range ~ 8 - 10 microns, giving a Q factor ~ 100 (a Q factor <~ 10 will give an amplitude hologram). Therefore index modulation must be considered as a volume effect, which is dependent on the slant of the Bragg planes.
Image modulation, ie the MTF of the image, is most probably determined by the the noise in the reconstruction in a display hologram and the scattering from the model itself during recording. The early model for efficiency in holography, pre-Kogelnik, was based on the MTF of the hologram, but, I think, they did not consider holographic noise in using MTF as a measure of efficiency. Today, I think MTF will be based o the amount of scatter within the emulsion.
[quote=Martin post_id=70014 time=1538562268 user_id=2364]
The smaller the grains the more image modulation is of the phase type. Maybe someone with better insights into Raleigh and Mie scattering theory could elucidate on this.
[/quote]
Well, roughly, Rayleigh scattering is predominant for small particle size, roughly 10% of λ. Rayleigh scattering is direction independent, and scatters both in the forward (the direction of the incident) light and the backward light. Also, because Rayleigh scattering is independent of the direction of incident light, scattering occurs for both transmission and reflection holograms in random directions within the emulsion. It's also heavily dependent on the wavelength of light, being proportional to the fourth power of the frequency, and so to the fourth power of the inverse wavelength. That is R ~ (1/λ)⁴. So, particles of about, less than, 50nm will strongly Rayleigh scatter, and the scattering is more intense for lower, blue shifted, wavelengths. So, as the colour changes from red to yellow, scattering increases. The scattering ratio, ie the ratio of intensities of scattered light, is:
R(y)/R(r) = [λ(r)/λ(y)]⁴ = [630/590]⁴ ~ 1.4
That is, the yellow will scatter about one and a half times more.
Mie scattering dominates as the wavelength increases to about λ. Mie scattering is not λ dependent, but it is directionally dependent, being stronger in the forward direction (in the direction of the incoming light). It's also much stronger than Rayleigh scattering, which is why, by the way, you can see a small white cloud against a large expanse of blue sky - the water molecules in the cloud are far larger than the nitrogen molecules in the air. In terms of the direction dependency, Mie scattering will scatter towards the viewer in transmission holography, and away from the viewer in reflection holography. However, given the range of particle sizes in terms of these fine grain materials, i'd say Rayleigh scattering is probably more influential in terms of noise. Remeber also that the efficiency of a hologram is not equal to the brightness of a hologram. There are scotopic issues. Roughly, if V(λ) is the efficiency of light reception at λ, then, for blue against yellow:
V(450)/V(590) ~ 0.038/0.757 ~ 0.05
That is, yellow is about 20 times brighter than blue for the same luminosity (efficiency of hologram)
[quote=Martin post_id=70014 time=1538562268 user_id=2364]
The smaller the grains the more image modulation is of the phase type.
[/quote]
One thing I have to point out: the image modulation is not the same as the index modulation. The index modulation is determined by the density of developed grains, since it's the index difference between developed and undeveloped grains, that is, by the ratio of the density of the light parts to the dark parts of the planes in the emulsion. As I've mentioned elsewhere, all emulsions in the last 40 years have been volume holograms due to the fact that emulsions are in the range ~ 8 - 10 microns, giving a Q factor ~ 100 (a Q factor <~ 10 will give an amplitude hologram). Therefore index modulation must be considered as a volume effect, which is dependent on the slant of the Bragg planes.
Image modulation, ie the MTF of the image, is most probably determined by the the noise in the reconstruction in a display hologram and the scattering from the model itself during recording. The early model for efficiency in holography, pre-Kogelnik, was based on the MTF of the hologram, but, I think, they did not consider holographic noise in using MTF as a measure of efficiency. Today, I think MTF will be based o the amount of scatter within the emulsion.