H2O Image

[Johnfp]

I guess your 1.38 might qualify for wet gelatin.
In a 1977 paper Meyerhofer quotes Shankoff with the following figures:

Material................................................................................Refractive Index
1) Gelatin.............................................................................1.5426
2) Gelatin + ammonium dichromate....................................1.5486
3) Gelatin + am. dich. exposed...........................................1.5572
4) Gelatin + am. dich. exposed, developend in IPA............1.5515
5) Gelatin + am. dich. unexposed, developed in IPA .........1.5488

Martin, I find that hard to believe. I checked the web extensively and found that the speed of light in Jello is the very near the same as in water from mulitple sources. It seems it is a popular science project for snells law. I guess we could test this by making some Jello, then put a volume of water on it and see if there is a slight refraction or a great refraction between the two substances angularly.

Also, in the above I find it hard to believe that the gelatin and AmDi exposed and processed has nearly the same index of refraction as unexposed but processed just gelatin and AmDi. Seems to me that if you did the processing not to have air void but just the differential of the two different states of gelatin as indicated above you would not get a hologram at all or very very dim at best. But that is not the case. 1.5515 - 1.5488 = Delta n of .0027. A differnental of .0027 between crossliked and uncrosslinked gelatin seems extreemely small in a processed hologram. Do you think that paper was redone and corrected later?

[Dinesh]

Indicies of refraction
1.0 = Air
1.33 = Water
1.38 = Gelatin
1.5 = Crosslinked Gelatin

The refractive index of anything is not an absolute number. The refractive index of air is not, and cannot be, 1 (if it was, there'd be no such thing as mirages). This is because a refractive index of 1 infers that there is no matter at all which can be affected by light. Air (and any gas) is pretty tenuous at STP, so 1 is an idealisation that's close. The actual refractive index of air depends on several conditions such as the temperature, the humidity, height above sea level and even the speed of the air. The figure of 1 is an idealisation for air with no humidity for zero degrees C and exactly 1 atmosphere.

Also, the index of gelatin, gelatin with dichromate, gelatin in alcohol, crosslinked gelatin etc cannot be an absolute number. This depends on the density of the gelatin (the bloom strength), the chemical composition, the orientation of the electron shells etc etc. When you add dichromate, it depends on the level of hydrolysis of the dichromate, the concentration of the dichromate, the way the dichromate dissolves in the gelatin (which, in turn, depends on the kind of gelatin). Once you put it in alcohol, it now depends on how the alcohol reacts with the gelatin/dichromate matrix and a whole bunch of other factors. The index of the "crosslinked" gelatin depends on how much crosslinking you have (the number of polymerised sites/unit vol), the strength and type of the crosslinked bonds (via the hydroxyl ion, eg).

In a 1977 paper Meyerhofer quotes Shankoff with the following figures:

Material................................................................................Refractive Index
1) Gelatin.............................................................................1.5426
2) Gelatin + ammonium dichromate....................................1.5486
3) Gelatin + am. dich. exposed...........................................1.5572
4) Gelatin + am. dich. exposed, developend in IPA............1.5515
5) Gelatin + am. dich. unexposed, developed in IPA .........1.5488

Since Shankoff mentions these figures to three decimal places, I would assume (hope!) that Shankoff actually carried out measurements. Simply looking up the internet for these figures gives you a (very!) broad average with certain conditions that are not mentioned.

As a tool for getting a vague sense of the thing, these absolute figures from the internet are representative, but trying to model an actual physical phenomenon on these figures will give a distorted picture. I have my own feelings about these kind of exact numbers from the internet, but that's another story....

So we can see, uncrosslinked (1.38) to crosslinked after exposure (1.5) but remembering not all gel is crosslkinked in the exposed areas, some of the Cr is in the IV state wating for the fixing to do more crosslinking. So lets say 33% of the gelatin is crosslinked in the exposed areas (This still may be too high) we get (1.5 - 1.38 = .12 .12 x .20 (20%) = .024 .024 + 1.38 = 1.4) So after exposure we may only have a differential of index of refraction of 1.38 and 1.4 which is .02

The index modulation is not just a subtraction of the index for crosslinked gelatin against uncrossedlinked gelatin. The Bragg structure is sinusoidal, so, if you want just a representative figure, you have to model the Bragg structure as a square sinusoid, for which the average over a large number of cylces is half the amplitude. By the by, this is the number usually given as the "power" of a beam of light, it's proportional to half the amplitude, which assumes that there is a single amplitude - which there usually isn't.

[dcgman]

"Sometimes when I remove a plate out of the water bath I will see a fanit hologram image. Not so much to see the object clearly but a rainbow of sorts along with the a dim outline.

I am guessing that the there is a difference between crosslinked and non crosslinked areas that makes an image."

I have also seen this many times, and I think you are right in that it is caused by the the difference in the crosslinked and non-crosslinked areas.
This image is probably being reconstructed when the gel has swollen by an integral multiple of its original thickness, thus allowing visible light to diffract from fringes which run parallel to the gel surface.

[Dinesh]

This image is probably being reconstructed when the gel has swollen by an integral multiple of its original thickness, thus allowing visible light to diffract from fringes which run parallel to the gel surface.

I don't think that mere swelling alters the reconstruction from a non-visible part of the spectrum into a visible part of the spectrum. The latent image must be in the VIS, since it was recorded by a laser emitting in the VIS. It's possible that the swelling has caused an increase in the bandwidth, thus allowing viewability, however such an image would be largely monocoloured. Tony reports:

Sometimes when I remove a plate out of the water bath I will see a fanit hologram image. Not so much to see the object clearly but a rainbow of sorts along with the a dim outline.

The fact that the image is faint, but rainbow-like seems to indicate surface-relief diffraction. I suppose the real question is: what colour is the "faint hologram image", or is the entire image a rainbow coloured image.

[Jeffrey Weil]

Try this next time you see the effect your describing.

While the plate is wet and you see the reflected dim rainbow image hold the plate up to the light and see if there is a bright transmission image, in transmission mode. That might help the dcg pros here figure it out.

My guess is you'll see one brighter than the reflected one your seeing now.

Jeff W

[Martin]

Martin, I find that hard to believe. I checked the web extensively and found that the speed of light in Jello is the very near the same as in water from mulitple sources. It seems it is a popular science project for snells law. I guess we could test this by making some Jello, then put a volume of water on it and see if there is a slight refraction or a great refraction between the two substances angularly.

You're right, depending on gelatin concentration, the refractive index of WET gelatin comes close to that of water (though not in the case of DRY gelatin).

Also, in the above I find it hard to believe that the gelatin and AmDi exposed and processed has nearly the same index of refraction as unexposed but processed just gelatin and AmDi. Seems to me that if you did the processing not to have air void but just the differential of the two different states of gelatin as indicated above you would not get a hologram at all or very very dim at best.

Yes, from a display holographer's point of view.
Generally, layer thickness also is a factor to be considered. If the layer is sufficiently thick, very small refractive index differences may still become "efficient" - so efficient actually that DE may reach 100% at say 1mm thickness (provided there's little scattering). This correlation may be computed from "Kogelnik" - Dinesh?

But that is not the case. 1.5515 - 1.5488 = Delta n of .0027. A differnental of .0027 between crossliked and uncrosslinked gelatin seems extreemely small in a processed hologram. Do you think that paper was redone and corrected later?

I'd expect these figures to be correct (assuming they did pretty extensive testing at Bell Labs - by the way, the table Meyerhofer quoted is from a paper by Shankoff, Phase Holograms in Dichromated Gelatin, Applied Optics, 1968. It looks like this is the pioneering paper on DCG).

[Dinesh]

Also, in the above I find it hard to believe that the gelatin and AmDi exposed and processed has nearly the same index of refraction as unexposed but processed just gelatin and AmDi. Seems to me that if you did the processing not to have air void but just the differential of the two different states of gelatin as indicated above you would not get a hologram at all or very very dim at best.



Yes, from a display holographer's point of view.
Generally, layer thickness also is a factor to be considered. If the layer is sufficiently thick, very small refractive index differences may still become "efficient" - so efficient actually that DE may reach 100% at say 1mm thickness (provided there's little scattering). This correlation may be computed from "Kogelnik" - Dinesh?

Yes, this is true. The efficiency of a reflection hologram depends on certain conditions, wether it's a pure phase, wether the planes are slanted or not etc. However, in these cases, the parameter of interest is:

((pi*(delta n)*d))/(lambda*cos(theta))
where d is the emulsion thickness, lambda is the spatial frequency of the grating and theta is the incident angle.
So, the efficiency depends as much on the emulsion thickness (d) as it does on the index modulation. Note, it also depends on the recording wavelength, which shows up in the spatial frequency term.

In a slanted grating with loss, the usual type of display hologram, the efficiency is given by a coth function here (http://www.efunda.com/math/hyperbolic/d ... ?name=coth ) shown plotted. Noted that the function falls very fast wrt it's argument, so a small change in any of the arguments (the index modulation or the emulsion thickness) can have a dramatic effect. In an unslanted grating with no loss, the efficiency is a tanh function (shown here: http://www.efunda.com/math/hyperbolic/d ... ?name=tanh ). Note that here, the efficiency maxes out at some value of the arguments and then stays constant. In the real world, of course, the curve will eventually fall to zero due to physical conditions such as over-hardening of the gelatin.

You cannot simply take two numbers as "the index", subtract them and model a real hologram. The actual indices inside the emulsion vary quite a lot from position to position, so the area covered by a real laser beam or reconstruction light covers an area of significant change of both delta n and d. The efficiency is an average over the area of illumination. As for air bubbles in the gelatin, there's still a difference of opinion, I believe, between the so-called 'crack theory' - which says that the emulsion cracks along the Bragg planes, and the 'bubble theory', which says that air bubbles form within the Bragg planes. In the 'crack' scenario, the violent dessication in the hot alcohol promotes the cracking of the emulsion, and in the 'bubble' scenario, the gradual dessication of the various alcohols promotes gradual replacement of the gelatin with air bubbles (or water bubbles).

[Ed Wesly]

Here is a different explanation of the phenomena described, as this also happens in silver halide holograms.

Jeff Blyth (bless his soul, hope you’re doing well, please post!), once described the effect in a holosphere article I believe, and he called it the “Spurious Transmission Image”. The reflection reference beam is weakly reflected inside the recording material, and this is in a contrary to the reference propagating beam direction, interfering with the object light that is also traveling in the same direction, so a transmission hologram is also recorded simultaneously!

Less verbosely and more alliteratively, the internal reflection of the reflection hologram reference beam becomes a transmission hologram reference beam.

Silver halide refection hologram gelatins are swelled many times their replay thickness while wet, so the reflection hologram image is reconstructing out of the visible in that state, but the transmission image is visible, exhibiting pretty thick hologram behavior, maybe even with a Q > 10, as it is very sensitive to angle orientation. And it is very rainbow, as described above.

Next time anyone processes a DCG or AgX reflection hologram, try looking for the spurious transmission image by backlighting the plate while it is wet with water.

[holorefugee]

In a 1977 paper Meyerhofer quotes Shankoff with the following figures:

Material................................................................................Refractive Index
1) Gelatin.............................................................................1.5426
2) Gelatin + ammonium dichromate....................................1.5486
3) Gelatin + am. dich. exposed...........................................1.5572
4) Gelatin + am. dich. exposed, developend in IPA............1.5515
5) Gelatin + am. dich. unexposed, developed in IPA .........1.5488

Since Shankoff mentions these figures to three decimal places, I would assume (hope!) that Shankoff actually carried out measurements. Simply looking up the internet for these figures gives you a (very!) broad average with certain conditions that are not mentioned.

I can measure them to four decimal places easily with a Abbe Bench refractometer. They are not too hard to use.

[dcgman]

[quote="Dinesh] I don't think that mere swelling alters the reconstruction from a non-visible part of the spectrum into a visible part of the spectrum. The latent image must be in the VIS, since it was recorded by a laser emitting in the VIS. It's possible that the swelling has caused an increase in the bandwidth, thus allowing viewability, however such an image would be largely monocoloured. Tony reports:

Sometimes when I remove a plate out of the water bath I will see a fanit hologram image. Not so much to see the object clearly but a rainbow of sorts along with the a dim outline.

The fact that the image is faint, but rainbow-like seems to indicate surface-relief diffraction. I suppose the real question is: what colour is the "faint hologram image", or is the entire image a rainbow coloured image.[/quote]

I've noticed this effect when processing the recording of a purely conformal mirror- where's the surface relief there?