Fire and dispersion techy help please?

[Garry H (Cut Nut)]

. Garry: I am unaware of this Hodgson thing. Reference, please.

Surley Bruce - if not then you will love it!!!
Visual optics.
He's a Scotsman. One of our member Wink has stayed with him

http://www.google.com.au/search?sou...y+alan+hodgkinson&spell=1&fp=695053830d8c4981

 

[michaelgem]

Michael you writting style is repetitive enough, without forcing us to the exact same passage over and over in your re-quotes that include you earlier quotes.

BTW it is not hard to do.

Spectral fanning occurs from contrast edges in the illumination. These edges do not have to be the special case edge of your single, collimated, beam of white light and its dark immediate surroundings. They could as easily be the edges between the bright sky light and the observer's ear. Both result in spectral fanning from dispersion upon entry at an angle to the gem's facets. The fanned out spectra in both cases, through the mechanism of "spectral splitting"/fractioning, can conceivably then be split diverting one spectral component in a different direction from the other.

Michael
PS Sorry if this appears tedious.

I hear you Garry. As you see from my apology, I knew I went long. And you can also see that I have taken to heart your request that I use the quote capability.

So I have concluded my posting on this subject with the previous final summary post. It includes in blue type my best shot at answering Bruce's question as to why the Ideal Cut came to have a combination of pavilion and crown main angles that reflect light to the observer from close to the contrast edge of observer obstruction.

Remember with the short halves of old cuts that reflections from the large mains dominated the reflection pattern in Morse's time around 1870 and even in Tolkowsky's time 50 years later.

I took relevant parts from several posts to put it all together in one final post, since this would be difficult for anyone else to do even if they were interested. So this last post is a coherent whole and can stand on its own with out reference to previous posts.

I would appreciate hearing from anyone whether or not this final effort succeeded in communicating to them.

Best wishes,

MIchael

 

[Garry H (Cut Nut)]

I took relevant parts from several posts to put it all together in one final post, since this would be difficult for anyone else to do even if they were interested. So this last post is a coherent whole and can stand on its own with out reference to previous posts.

I would appreciate hearing from anyone whether or not this final effort succeeded in communicating to them.

Best wishes,

MIchael

Thanks Michael, and BTW changing the color on your own words makes it look like a quote or comment from someone else. It is additionally confusing.

 

[Garry H (Cut Nut)]

. Let's get back to my original question to Garry: "Why do you think the fire is more pronounced if the stone is cut on the edge of 'Bruce's dark zone'?" Your words do not explain it to me. BLH

Hopefully others find my words more adequate, since they contain the explanation. They also explain the more encompassing general principles of light performance in a diamond, those about contrast brilliance and fire.

In Anton's Rainbow article he says: "The fire from a faceted gem will be completely lost in the light of a dull day under cloudy sky. " This statement is true if the ground is covered in snow and there is no observer causing contrast in the illumination by obstructing part of the cloudy sky's illumination.

His words miss the key point that even in the light of a dull day under cloudy sky I still observe and you can see in these photographs fire in an Ideal cut diamond whose virtual facets pick up fire at the contrast edge in the illumination environment due to the ever-present observer obstruction.

From my article: http://www.acagemlab.com/articles/FirePower.htm

Here is a partial analysis of the mosaic pattern of reflections including the blue fire in the attached two and a quarter carat round brilliant cut diamond.

We are viewing this diamond at a slight tilt from the normal, face-up position. The mosaic pattern of reflections from the octagon shaped table contains slender, needle like reflections from the eight pavilion main facets, which meet at the center of the pavilion at the 'culet'.

The two reflections at two and seven o'clock display blue fire, the two at one and five o'clock are dark, the one at nine-thirty is bright and those at four, eight and eleven are partially bright and partially obscured by other reflections. On both sides of the dark main reflection at one o'clock are triangular reflections of blue fire from the halves.

Looking at the photograph of one of the diamond ring's four prongs, you will see mirrored in that prong the panorama of illumination surrounding this diamond. Using our knowledge of both ray tracing and the interaction of the contrast in illumination with the diamond's dispersion properties, we can point out, from the illumination environment reflected in this prong, where each pavilion main reflection originates in the diamond's surrounding .

The two dark main reflections at one and five o'clock are coming from high angles, where the silhouette of my head and outstretched hand is obscuring the bright sky light.

The bright reflections are coming from the bright sky light between my silhouette and the dark silhouette of the surrounding trees.

The reflections of blue fire are coming from high angles right at the edge of the dark-bright transition from my dark silhouette to the bright skylight.

Following is a useful way to think of the fire producing mechanism, which involves dispersion and contrast (like that from observer obstruction). Another form of fractioning/spectral splitting is involved that retains one end of the spectrum or the other :

Using back-tracing from the aperture of my pupil or the camera's lens, we find that due to dispersion a virtual facet reflects long wavelengths from slightly different spots than shorter wavelengths. For instance, virtual facets emanating blue-fire are reflecting/picking up the red-to-yellow end of spectral wavelengths from slightly higher angles due to less bending or refraction of longer waves. But that is where there is darkness from my silhouette, so that end of the spectrum is actually clipped off (fractioned) leaving the blue end of the spectrum whose shorter wavelengths are refracted and dispersed to a greater degree. Since the virtual facets are reflecting/picking up the blue end of the spectrum from this greater angle where there is white light the blue end of the spectrum comes to our eye as spectral fire.

This is why simple head obstruction most often produces blue fire. The reverse situation can occur around an ear or shirt collar where instead of a dark-bright transition there is a bright-dark one. Then the blue end of the spectrum is clipped leaving yellow to red fire to be observed.

As Bruce, Garry and others have noted, this simple dark/bright or bright/dark contrast transition can only result in the fractioning of one or the other end of the spectrum, which is why contrast of this sort from mechanisms such as head obstruction only result in blue and yellow through red fire, but no green. Dark-bright-dark contrast patterns where the bright area has small angular size as in Bruce's collimated beam of white light are necessary for dispersion in the gem to result in the fractioning out of both ends of the spectrum leaving the more elusive green fire to be observed.

With all this detail I hope it is clearer why I said at the beginning:

Re: can you suggest why dispersion is most noticeable here?

The short answer is: Fire emanates from "virtual facets" that reflect from a spot in the surrounding illumination where there is light/dark contrast. With slight movement a reflection from a virtual facet transitions from bright to dark and in between exhibits fire. So reflections from high contrast areas such as the boundary created by observer obstruction result in the display of fire in virtual facets reflecting from those areas. So, not only is the contrast in the illumination from observer obstruction one key to the Ideal's contrast quality of brilliance, it is a factor in the Ideal's superior fire as well.

That is one reason I say "the same diamond exhibiting superior brilliance in lighting conducive to brilliance will exhibit superior fire in lighting conducive to fire." Observer obstruction is a built in producer of contrast which is important in lighting that is otherwise diffuse like the sky in my silhouette image.

So, one key property of the Ideal cut is that reflections from virtual facets from its mains come from the area where there is contrast in illumination at the outer edge of the observer's head. That fact may be one important reason that first Morse and then subsequent cutters like Tolkowsky and his father empirically found a 41 pavilion and close to a 34 crown to be best.

Michael D Cowing

Michael now you know how to edit, can you please cut this down to what needs to be read.

 

[michaelgem]

Garry,

Re: Michael now you know how to edit, can you please cut this down to what needs to be read.

Too much reduction leaves points open to misinterpretation, but I can remove redundancies.

The blue text is most important.

I'll try to channel Bruce's brevity, and give it a go tomorrow.

Michael

 

[Garry H (Cut Nut)]

Garry,

Re: Michael now you know how to edit, can you please cut this down to what needs to be read.

Too much reduction leaves points open to misinterpretation, but I can remove redundancies.

The blue text is most important.

I'll try to channel Bruce's brevity, and give it a go tomorrow.

Michael

I can introduce you to a woman in Mass et 2You Sus who can really help you Michael. Marcia Yudkin. Get her stuff

 

[beryl]

Michael:
. Upon sufficient thought and reflection (no pun intended), I prefer your term 'spectral-splitting'. Although longer, it is more correct than 'fractioning' since, as Garry pointed-out, you cannot isolate specific components as you can in fractioning petroleum or in fractional crystallization. In fractional crystallization the components occur in sequence but you can pull one out without disturbing the others (if they are there).
. We used this trick to find beryl in pegmatite: because of its progressive cooling from outside to inside a vein, tourmalines crystallize first, then mica, then feldspar, then beryl, and finally quartz in the middle (garnets crystallize just outside the vein, precipitating in the host rock by re-heating). We found and uncovered the Reynolds aquamarine mine in Royalston, Massachusetts, a few miles from here; it is mentioned in Bauer's book as producing the finest in the world (at that time, before the Maxixe mine in Brasil). An interesting side-trip of gemology. Actually this preceded our interest in lapidary and gemology. Our activity at one mine in New Hampshire earned my son and I the nickname 'Beryl Mountain boys' - hence the alias 'beryl'.

 

[adamasgem]

I think it is possible to argue that symmetry has some benefits - but I am unconvinced that enhanced fire is one of them.

I agree and I disagree when it comes to fire.
It depends on the diamond size and the degree of non-symmetry.
A .5ct is going to give different results than a 3ct because of the physical size difference of the first and second order virtual facets due to diamond size.
Normalized to 1ct I agree that the differences with minor optical symmetry deviations on fire is very small and real world irrelevant.

If there is a difference other than contrast patterns/balance it will be in scintillation, which I think there is but haven't come up with a good way to prove it yet.

Karl is right on the money with his comments; size and symmetry......asymmetry (large number of virtual facets) gives internal color mixing and bland, pastel earth tones, and small areas of color, NOT an entire facet of the same color

 

[beryl]

. Another excerpt from “Rainbow in a Colorless Gem”, by Anton Vasiliev. I have been comparing it to the draft I edited in 2002; many of my changes were not implemented and the editor himself changed some things.
. Here is Fig.5 redrawn (omitting confusingly similar Greek characters). Note that angle ‘I’ is not the angle of incidence, as it is called in the text. I verified the formula then and now, using the angle ‘I’ shown, and have also shown the adjacent text. This will acquire significance in the next presentation.

 

[Garry H (Cut Nut)]

I think it is possible to argue that symmetry has some benefits - but I am unconvinced that enhanced fire is one of them.

I agree and I disagree when it comes to fire.
It depends on the diamond size and the degree of non-symmetry.
A .5ct is going to give different results than a 3ct because of the physical size difference of the first and second order virtual facets due to diamond size.
Normalized to 1ct I agree that the differences with minor optical symmetry deviations on fire is very small and real world irrelevant.

If there is a difference other than contrast patterns/balance it will be in scintillation, which I think there is but haven't come up with a good way to prove it yet.

Karl is right on the money with his comments; size and symmetry......asymmetry (large number of virtual facets) gives internal color mixing and bland, pastel earth tones, and small areas of color, NOT an entire facet of the same color

Marty we have had this statement from you before - I posted an example of a strongly doubly refractive gem to show that mixing only occurs in those gems.

Show me one photo or tell me one time you have ever seen a non spectral colour in a diamond (unless maybe the stone had a strong body color, but even then, most fire happens on exit).

 

[Garry H (Cut Nut)]

. Another excerpt from “Rainbow in a Colorless Gem”, by Anton Vasiliev. I have been comparing it to the draft I edited in 2002; many of my changes were not implemented and the editor himself changed some things.
. Here is Fig.5 redrawn (omitting confusingly similar Greek characters). Note that angle ‘I’ is not the angle of incidence, as it is called in the text. I verified the formula then and now, using the angle ‘I’ shown, and have also shown the adjacent text. This will acquire significance in the next presentation.

As you all know, I am not a mathematician, but clearly I must be always smaller than what O can be (but not must be). So therefore this formula explains why there will be more potential dispersion if O is larger?

 

[beryl]

Not so, Garry:
. In this example, angle 'I' would be greater than 'O' if the direction of the ray was reversed, as shown in this modified illustration. Angles 'I' and 'O' are directions, not dispersions. The dispersion at exit is ALWAYS greater than at entry because it is the result of dispersion at entry amplified by more dispersion at exit.
. In this reverse illustration, if angles 'V' and 'I' were equal then angle 'O' would be zero; nevertheless, the DISPERSION at exit would be greater than at entry.
. The formula relates the angle of exit 'O' to the refractive index 'n' and is used, in the ensuing text, to calculate the change in width of the spectral fan according to the change in refractive index, showing how much the 'angular dispersion' increases as the change in refractive index for each color ('dispersivity'?) increases.

 

[beryl]

. In each of the preceding illustrations it is important to realize that the ray directions shown ('I' and 'O') are those of the MEAN ray (near green in white light). Each of these is dispersed so that the various colors diverge at the entry refarction and hit the exit side of the prism at different angles, each then being refracted differently as it exits.

 

[beryl]

. This illustration shows a prism with 0° entry or exit. I have exaggerated the dispersion fans for pictorial purposes.
. Note that when entry is at 0° incidence (right pic) there is theoretically no refraction until exit.
. Anyway, this shows that exit angle 'O' can be less than refracted entry angle 'I' (left pic).
. Gotta run. My alma mater (Moo U) is about to play on TV.

 

[beryl]

. For possible interest I calculated the dispersions in the double prism illustration just above.
. Per 'Dana's Textbook of Mineralogy". 4th Ed., p.635.7, the refractive index 'limits' for blue-green tourmaline are 1.6436, 1.6222. Based on the mean of these RI values (1.632 the mean external angle at C is 73.6858°.
. Using these data I found the following:
.... at left: dispersion after entry = 0.5431°, after exit = 0.8868°,
.... at right: dispersion after entry = 0° .... , after exit = 2.5623°,
so the dispersion of the same mean ray through the same prism is greater if the exit is at the greater angle. In this example it is about about 3 times greater (more than usual).
. These 4-decimal-place data seem silly but minimize round-off errors when numbers have such small differences.

 

[beryl]

ERROR:
. In the two-prism illustration, right one, I forgot to erase 'O'=0°at end A. The exit angle 'O'=72° should be adjacent to point C.
. The price of haste (my team won).

 

[beryl]

. Here is the two-prism illustration corrected and expanded, showing the dispersion data, for the sake of those who want to save this for future reference or instruction. I think it is a 'goodie'; feel free to copy/distribute it.

 

[michaelgem]

This post, while likely seen as redundant to some, may be helpful for others to put it all together:

As you all know, I am not a mathematician, but clearly I must be always smaller than what O can be (but not must be). So therefore this formula explains why there will be more potential dispersion if O is larger?

Not so, Garry:
. In this example, angle 'I' would be greater than 'O' if the direction of the ray was reversed, as shown in this modified illustration. Angles 'I' and 'O' are directions, not dispersions. The dispersion at exit is ALWAYS greater than at entry because it is the result of dispersion at entry amplified by more dispersion at exit.

What Garry is getting at is verification that the exit angle O has a greater influence on the net spectral fanning than does the entry angle E. This is true and is supported by the overall dispersion formula, by Bruce's two prism example, and by Anton in Rainbow... where he says: "Let us consider the observer's eye ... looking at the prism. ... The beam leaving the prism forms a fan-shaped bundle of rays of various colors. Actually, the ray begins to disperse upon entering the prism, but this is much less than at exit. "

Excerpting Bruce: "The (total) dispersion ... is the result of dispersion at entry amplified by more dispersion at exit."

The total dispersion/spectral-fan formula gives equal weight of 1/Cos to both the angle of refraction on entry (I) and the angle of refraction on exit (O). Because the angle of incidence (E) is always greater than the angle of refraction (I), to have the same weight angle E must be greater than angle O.

So the exit angle O has a greater influence on the overall dispersion/spectral-fan than does the entry angle E.

Bruce's 0 degree entry/0 degree exit dual prism case is a good supporting example since it demonstrates that you get more spectral fanning from a given angle of exit when the angle of entry is 0, than you do with the same angle at entry when the angle of exit is 0.

Bruce calculates:
. Using these data I found the following:
.... at left: dispersion after entry = 0.5431°, after exit = 0.8868°,
.... at right: dispersion after entry = 0° .... , after exit = 2.5623°,
so the dispersion of the same mean ray through the same prism is greater if the exit is at the greater angle. In this example it is about about 3 times greater (more than usual).

To summarize and conclude, the dispersion formula shows what Garry was getting at: There is a greater contribution to overall dispersion due to the exit angle than there is due to the entry angle.

Michael D Cowing

 

[beryl]

Michael:
. Why do you find it necessary to clarify what has already been said? Sometimes your wordy clarifications confuse the issue.
. You have altered my illustration without noting, on it, that you have done so = a no-no.

 

[michaelgem]

Michael:
. Why do you find it necessary to clarify what has already been said? Sometimes your wordy clarifications confuse the issue.
. You have altered my illustration without noting, on it, that you have done so = a no-no.

Sorry you are bothered by this post, Bruce.

The answer is in the opening statement: This post, while likely seen as redundant to some, may be helpful for others to put it all together. Also I felt that the correctness of Garry's point needed to be spelled out.

I had originally thought it counter-intuitive that the dispersion on entry due to that angle should have less influence on overall spectral fanning than the dispersion on exit due to that angle.

That is why it was also useful to point out:

"The total dispersion/spectral-fan formula gives equal weight of 1/Cos to both the angle of refraction on entry (I) and the angle of refraction on exit (O). Because the angle of incidence (E) is always greater than the angle of refraction (I), to have the same weight angle E must be greater than angle O.

That is the, what might not be obvious to everyone, mathematical reason that "the exit angle O has a greater influence on the overall dispersion/spectral-fan than does the entry angle E."

As far as altering your illustration, all I did was add the entry angle E, which was necessary to the discussion.

Michael

 

[adamasgem]

I think it is possible to argue that symmetry has some benefits - but I am unconvinced that enhanced fire is one of them.

I agree and I disagree when it comes to fire.
It depends on the diamond size and the degree of non-symmetry.
A .5ct is going to give different results than a 3ct because of the physical size difference of the first and second order virtual facets due to diamond size.
Normalized to 1ct I agree that the differences with minor optical symmetry deviations on fire is very small and real world irrelevant.

If there is a difference other than contrast patterns/balance it will be in scintillation, which I think there is but haven't come up with a good way to prove it yet.

Karl is right on the money with his comments; size and symmetry......asymmetry (large number of virtual facets) gives internal color mixing and bland, pastel earth tones, and small areas of color, NOT an entire facet of the same color

Marty we have had this statement from you before - I posted an example of a strongly doubly refractive gem to show that mixing only occurs in those gems.

Show me one photo or tell me one time you have ever seen a non spectral colour in a diamond (unless maybe the stone had a strong body color, but even then, most fire happens on exit).

Anisotropic effects are caused by strain, but mostly it is numerous small virtual facets that result in mixing of spectral colors, inside or outside the stone, but it is observed... Possibly interferance colors.

Real old pic from archives.. bottom row combined pic with increased saturation. (Better camera doesn't require any saturation increase)

 

[beryl]

. To continue with Anton Vasiliev’s “Rainbow in a Colorless Gem”, where we were a few days ago, hoping to find references which will confirm or add to our understanding of ‘fire’.
. The illustration (Fig.6) below is perhaps more confusing than helpful but is referenced in the adjacent text. I have modified it, replacing Greek and eliminating color-coding of curves: imagine that the labels ‘4/3V, V, 2/3V, 1/3V’ correspond to curves ‘1, 2, 3, 4’ respectively. I used ‘X’ for the critical angle. The tiny text at the bottom says “Angular dispersion of prisms of CZ with various vertex angles ‘V’ vs angle of beam departure ‘O’.”, then “modified by B. L. Harding 2010 Nov 28” (I couldn’t make it larger).

Anton says (edited):
. “With angle ‘O’ increasing toward 90° the angular dispersion increases sharply. Its minimum is near(?) O=0°, which is important because that is the viewing angle normal to the table. By providing angular dispersion of 14°/µm for this case, all rays leaving the crown would have pure colors.” (on p.4.7, he explained this requirement).
. “The sharp increase of dispersion at high angles of exit explains the occurrence of 'fire', though not often, at certain angles, even for poorly-cut gems and those having low dispersion. Special cuts have been suggested for high angles of beam exit but the fire of such rays can only be viewed on a slant. almost along its surface.
. “Line ‘A’ defines minimum possible exit angles ‘O’ for various prism vertex angles ‘V’.
. “The last column of the Table (p.3) shows minimum values of angular dispersion for a prism whose vertex is its critical angle (V=X), listed according to that value (°/µm). Only the top three materials listed here are able to provide perfect fire (they are all synthetics). Green colors can hardly be seen in diamond’s fire.
. Note, in Fig.5, that beams departing at high angles to the prism face are dispersed many times more efficiently than incident beams entering at high angles. In other words, angular dispersion is greater for path ABCD than DCBA.” ..... My 2-prism illustration (above) shows this vividly with an extreme case.
. “Ignorance of this fact can lead to sad mistakes. For example, it devaluates GIA’s fire study (2001). ... One can state that beams with maximum fire, with illumination perpendicular to the table, would correspond to low-colored flashes on its surface being viewed normal to the table !” Obviously this paragraph was added to the original article (2001 vs 1995).

. What does all this say? – that the higher the dispersion the better the fire. We all know that well. I think he may use this math stuff in the text after this; ignore it for now.
. Sorry this was so long, but it all belonged together; I trimmed it as much as I could.

 

[beryl]

As you all know, I am not a mathematician, but clearly I must be always smaller than what O can be (but not must be). So therefore this formula explains why there will be more potential dispersion if O is larger?

Not so, Garry:
. In this example, angle 'I' would be greater than 'O' if the direction of the ray was reversed, as shown in this modified illustration. Angles 'I' and 'O' are directions, not dispersions. The dispersion at exit is ALWAYS greater than at entry because it is the result of dispersion at entry amplified by more dispersion at exit.

. What Garry is getting at is verification that the exit angle O has a greater influence on the net spectral fanning than does the entry angle E.

. That may be what he is getting at but it is not what he said (see quote).

 

[beryl]

Bruce,

It is a combination of reverse and forward ray-tracing which explains why the contrast-areas are important producers of observed fire.

Live long,

. Paul; you have me beat when it comes to brevity!
. This statement has been bugging me since you posted it. Can you explain further? Offline if you prefer.

 

[Garry H (Cut Nut)]

I think it is possible to argue that symmetry has some benefits - but I am unconvinced that enhanced fire is one of them.

I agree and I disagree when it comes to fire.
It depends on the diamond size and the degree of non-symmetry.
A .5ct is going to give different results than a 3ct because of the physical size difference of the first and second order virtual facets due to diamond size.
Normalized to 1ct I agree that the differences with minor optical symmetry deviations on fire is very small and real world irrelevant.

If there is a difference other than contrast patterns/balance it will be in scintillation, which I think there is but haven't come up with a good way to prove it yet.

Karl is right on the money with his comments; size and symmetry......asymmetry (large number of virtual facets) gives internal color mixing and bland, pastel earth tones, and small areas of color, NOT an entire facet of the same color

Marty we have had this statement from you before - I posted an example of a strongly doubly refractive gem to show that mixing only occurs in those gems.

Show me one photo or tell me one time you have ever seen a non spectral colour in a diamond (unless maybe the stone had a strong body color, but even then, most fire happens on exit).

Anisotropic effects are caused by strain, Marty I do not see this in my car windscreen without my polaroid sunny's on? but mostly it is numerous small virtual facets that result in mixing of spectral colors, inside or outside the stone, but it is observed... Possibly interferance colors. Have you ever seen this in any normal lighting situation other than your pinlight model? I never have and never heard anyone report seeing 2nd or 3rd order colors (like those you see in a garage pavement on a wet day) Or doubly refractive stones like this calcite in the smithsonian

Real old pic from archives.. bottom row combined pic with increased saturation. (Better camera doesn't require any saturation increase)

 

[adamasgem]

Anisotropic effects are caused by strain, Marty I do not see this in my car windscreen without my polaroid sunny's on? but mostly it is numerous small virtual facets that result in mixing of spectral colors, inside or outside the stone, but it is observed... Possibly interferance colors. Have you ever seen this in any normal lighting situation other than your pinlight model? I never have and never heard anyone report seeing 2nd or 3rd order colors (like those you see in a garage pavement on a wet day) Or doubly refractive stones like this calcite in the smithsonian

Real old pic from archives.. bottom row combined pic with increased saturation. (Better camera doesn't require any saturation increase)

[/quote]

Gary..... When you see white, you are seeing color mixing; that "white" may come from a continuous spectrum or from a RGB system (three primaries)[as in your camera or TV] (your eyeball converts to RGB type and your brain mixes them again].. You see, or better yet, RESOLVE "fire", because there are large areas(angular spread" of one color reaching your eye. You can see the "fire" in a pinpoint white opal (as opposed to broadflash opal) when you are close to it, but when you move away, the colors mix, and you see white.

The 10,000 plus points of white light (8000Kelvin) is an environment that enables you to discriminate the fire, either DIRECTLY, or through a cameras lens. (what you visually see, is what you photographically get) In a diffuse environment, like you describe (your windshield), it would be very difficuly to resolve "fire".

Resolving (seeing) fire is a combination of the cutting AND the envirionment. I just created the envirionment, based on a natural analog, to be able to compare the cuttings ability to generate fire. The results are what they are, the pastels and muddy earthtones were a surprize to me, and I still think about it; all I KNOW, is that there is a direct relationship between the composite angle set combined with optical symmetry, and the ability to visually RESOLVE fire.
Your calcite example, is, my friend, not applicable.

 

[beryl]

Continuing interpretation of “Rainbow in a Colorless Gem” by Anton Vasiliev ...
. Fig. 7 shows a ‘mirror diagram’ of a typical gem cross-section. I have modified it to eliminate the Greek characters and indicated the imaginary prisms formed by the entry and exit faces.
. Surprise! He doesn’t do anything with the math introduced by Fig.6; just simple geometry here. However. he references the curves of Fig.6 to illustrate a point.
. If you didn’t see the relevance of the simple prisms in Fig.5, Fig.7 will now make it clear by showing the virtual prisms formed by the entry and exit faces; I labeled them ‘prism1, prism2, prism3’.

. To quote Anton (severely edited):
. “We will represent ray reflection with a mirror-type diagram (see Fig.7).
. “... the ray leaves the second reflection at angle d = 4(45*-P) to its original direction within the gem."
. “In traditional cuts there are three paths for the ray through the gem:
…. 1. The ray enters the table and leaves through the table. (in this case the prism vertex angle V1 = d)
…. 2. The ray enters the table and leaves through the bezel (or vice-versa). (in this case the prism vertex angle V2 = B-d)
…. 3. The ray passes through bezel facets only. (in this case the prism vertex angle V3 = 2B-d)
. It is essential to avoid reducing any of these vertex angles too much, otherwise non-colored rays having passed through it would suppress colored beams entering through other prisms with higher vertex angles, which are diminished by Fresnel losses.” ??? . . . Recall that in Fig.6 Anton shows that high vertex angles provide more dispersion than low vertex angles (curve 1 = 4/3X was greater than the others) – BLH.

. “So, we do not pursue the goal of enhancing fire by individual beams . . OR . . by certain fixed position of the light source or of the viewer. We are looking for optimum faceting parameters offering maximum dispersion color for least-colored beams of departure in the most general case. Position of the viewer’s head or location of the light source shall not be fixed.”

He then develops some interesting formulas whereby V1 = V2 = 2/3 X and points-out that, using this ...
. "... vertex V3 (bezel-to-bezel rays) becomes so high that it prevents passage of rays. No transmission occurs; in fact, bezel facets (and the girdle) are never seen through the bezel mains."

then, with these values of V1 and V2 he calculates ...
. “... P=40.9°, B=32.5° for diamond (X=24.4°), which is close to the values P=40.75°, B=34.5° calculated by Tolkowsky.” (Tolkowsky’s calculations are based on false logic; he knew the answers and tried to develop a theory to match them – BLH)
. “The vertex angles (V1, V2) in this model are less than critical angle X for which dispersion values are shown in the Table (page 3). These angles can be increased at the sacrifice of brightness ...”
. Then he does some more math stuff and says ...
. “To increase dispersion, B (slope of bezel mains) can be increased at the sacrifice of the gem’s brightness ...”

. That ends my analysis/clarification of “Rainbow in a Colorless Gem” as it relates to fire. I hope it has clarified some things to some folks.
. Garry: take particular note of the last two quotes – sounds like your TIF to me!

 

[Garry H (Cut Nut)]

"No light/dark contrast edges in the illumination environment, no fire, period. And this sweeping statement includes the concept of fractioning. Over ten years ago I demonstrated this by photographing a diamond inside a white hemisphere. The diamond almost disappeared and displayed no fire."

Michael[/size]

Michael when I play with DiamCalc panorama's and make a total igloo lighting, and then introduce a small dark band - I can make some fire appear. If I make the band a little wider at each end, nothing much changes.\
So I disagree that it is about the "edges". I think it is more about the prescence of darkness which creates a darker VF enabling us to see the fire that would otherwise be drowned out by the brightness.

(BTW you might want to make a comment about the origin of Virtual Facets after you complete your investigation)

 

[Garry H (Cut Nut)]

.

Using back-tracing from the aperture of my pupil or the camera's lens, we find that due to dispersion a virtual facet reflects long wavelengths from slightly different spots than shorter wavelengths. For instance, virtual facets emanating blue-fire are reflecting/picking up the red-to-yellow end of spectral wavelengths from slightly higher angles due to less bending or refraction of longer waves. But that is where there is darkness from my silhouette, so that end of the spectrum is actually clipped off (fractioned) leaving the blue end of the spectrum whose shorter wavelengths are refracted and dispersed to a greater degree. Since the virtual facets are reflecting/picking up the blue end of the spectrum from this greater angle where there is white light the blue end of the spectrum comes to our eye as spectral fire.

This is why simple head obstruction most often produces blue fire. The reverse situation can occur around an ear or shirt collar where instead of a dark-bright transition there is a bright-dark one. Then the blue end of the spectrum is clipped leaving yellow to red fire to be observed.[/color]


Michael D Cowing

Not trying to pick on you Michael, but you know that when we see a spectral effect from an edge, that one side is blue and the other red yellow. Does this effect your point?

 

[Garry H (Cut Nut)]

Anisotropic effects are caused by strain, Marty I do not see this in my car windscreen without my polaroid sunny's on? but mostly it is numerous small virtual facets that result in mixing of spectral colors, inside or outside the stone, but it is observed... Possibly interferance colors. Have you ever seen this in any normal lighting situation other than your pinlight model? I never have and never heard anyone report seeing 2nd or 3rd order colors (like those you see in a garage pavement on a wet day) Or doubly refractive stones like this calcite in the smithsonian

Real old pic from archives.. bottom row combined pic with increased saturation. (Better camera doesn't require any saturation increase)

Gary..... When you see white, you are seeing color mixing; that "white" may come from a continuous spectrum or from a RGB system (three primaries)[as in your camera or TV] (your eyeball converts to RGB type and your brain mixes them again].. You see, or better yet, RESOLVE "fire", because there are large areas(angular spread" of one color reaching your eye. You can see the "fire" in a pinpoint white opal (as opposed to broadflash opal) when you are close to it, but when you move away, the colors mix, and you see white.

The 10,000 plus points of white light (8000Kelvin) is an environment that enables you to discriminate the fire, either DIRECTLY, or through a cameras lens. (what you visually see, is what you photographically get) In a diffuse environment, like you describe (your windshield), it would be very difficuly to resolve "fire".

Resolving (seeing) fire is a combination of the cutting AND the envirionment. I just created the envirionment, based on a natural analog, to be able to compare the cuttings ability to generate fire. The results are what they are, the pastels and muddy earthtones were a surprize to me, and I still think about it; all I KNOW, is that there is a direct relationship between the composite angle set combined with optical symmetry, and the ability to visually RESOLVE fire.
Your calcite example, is, my friend, not applicable.[/quote]

Hi Marty, I stand corrected.
When I increase the number of lights, or as Michael and Bruce suggest, by opening the pupil more, the result in your model does occur.