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| Bob May |
 Posted: Mon Nov 21, 2005 2:05 pm |
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Anybody got the right way to go from refractive indices to the Sellmeier
coefficients? The only way that I've seen with a Google is that they are
derived empirically (!) for a glass.
Either that or how do you enter refractive indices into OSLO? I found the
private glass library entry form but when I enter a set of values for the
glass, the program blows up when raytracing. There are 3 entries for
refractive indices and 3 for wavelengths and I guess that I need the order
of the colors and the form of the numbers. I think I know that the
wavelengths should be in microns (0.58756 for Nd for example) but there are
many other questions that aren't answeered in either the help section or the
Reference Manual (PDF).
I'm trying to put a real glass melt indices into OSLO so that I can finalize
a telescope design.
--
Why do penguins walk so far to get to their nesting grounds? |
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| Guest |
| Posted: Mon Nov 21, 2005 9:03 pm |
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On 11/21/05 11:05 AM, in article
IqGdnf49zMq0hx_enZ2dnUVZ_tqdnZ2d@nethere.com, "Bob May" <bobmay@nethere.com>
wrote:
[quote:6a87159a35]Anybody got the right way to go from refractive indices to the Sellmeier
coefficients? The only way that I've seen with a Google is that they are
derived empirically (!) for a glass.
Either that or how do you enter refractive indices into OSLO? I found the
private glass library entry form but when I enter a set of values for the
glass, the program blows up when raytracing. There are 3 entries for
refractive indices and 3 for wavelengths and I guess that I need the order
of the colors and the form of the numbers. I think I know that the
wavelengths should be in microns (0.58756 for Nd for example) but there are
many other questions that aren't answeered in either the help section or the
Reference Manual (PDF).
I'm trying to put a real glass melt indices into OSLO so that I can finalize
a telescope design.
--
Why do penguins walk so far to get to their nesting grounds?
There is an extensive literature on least square fitting. I believe that[/quote:6a87159a35]
Microsoft Excel has suitable capability.
Bill
-- Ferme le Bush |
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| Steve Eckhardt |
| Posted: Tue Nov 22, 2005 9:40 am |
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In article <IqGdnf49zMq0hx_enZ2dnUVZ_tqdnZ2d@nethere.com>, bobmay@nethere.com
says...
[quote:3139433a4e]
Anybody got the right way to go from refractive indices to the Sellmeier
coefficients? The only way that I've seen with a Google is that they are
derived empirically (!) for a glass.
Either that or how do you enter refractive indices into OSLO? I found the
private glass library entry form but when I enter a set of values for the
glass, the program blows up when raytracing. There are 3 entries for
refractive indices and 3 for wavelengths and I guess that I need the order
of the colors and the form of the numbers. I think I know that the
wavelengths should be in microns (0.58756 for Nd for example) but there are
many other questions that aren't answeered in either the help section or the
Reference Manual (PDF).
I'm trying to put a real glass melt indices into OSLO so that I can finalize
a telescope design.
--
Why do penguins walk so far to get to their nesting grounds?
[/quote:3139433a4e]
Help me understand your question. Do you want to calculate the refractive
index at a wavelength, or do you want to fit coefficients to get an equation
for your melt indices?
If it's the former, you can just plug in the wavelength and compute.
If it's the latter, you can't do it with just three data. The problem is that
you are trying to solve for more than three unknowns with only three
equations. If you really need the Sellmeier coefficients, first fit the
Conrady formula (which has only three coefficients) and compute the refractive
index at about a dozen wavelengths. Then fit the Sellmeier coefficients to
these. You can do a sanity check by having Excel or Mathcad plot the curve
for the catalog data beside the new data. The curve for the melt data should
be almost a displaced version of the original.
--
Best regards,
Steve Eckhardt
skeckhardt at mmm dot com |
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| Jim Klein |
| Posted: Tue Nov 22, 2005 10:24 am |
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"Bob May" <bobmay@nethere.com> wrote:
[quote:14a8917bdc]Anybody got the right way to go from refractive indices to the Sellmeier
coefficients? The only way that I've seen with a Google is that they are
derived empirically (!) for a glass.
Either that or how do you enter refractive indices into OSLO? I found the
private glass library entry form but when I enter a set of values for the
glass, the program blows up when raytracing. There are 3 entries for
refractive indices and 3 for wavelengths and I guess that I need the order
of the colors and the form of the numbers. I think I know that the
wavelengths should be in microns (0.58756 for Nd for example) but there are
many other questions that aren't answeered in either the help section or the
Reference Manual (PDF).
I'm trying to put a real glass melt indices into OSLO so that I can finalize
a telescope design.
[/quote:14a8917bdc]
There are six Sellmeir coefficients so you will need at least six and
probably more like 12 index/wavelength pairs to get a good least
squares fit. Furthermore, the Sellmeir equation is not linear with
respect to the coefficients, as is the old Schott equation, so a
simple least squares regression fit does not work. You need a damped
least squares fit as described in Numerical Recipies. This requires
first and second derivatives (a Hessian matrix). It is more than
simple programming and Excel can do it. ZEMAX can do it.
You will need at least six index/wavelength pairs or the coefficients
will be meaningless at any wavelengths except the wavelengths you
start with.
Sincerley,
Jim Klein |
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| Bob May |
| Posted: Tue Nov 22, 2005 3:01 pm |
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Nope, it is to put the melt index values into OSLO.
Remember that in the real world, the glass you get isn't the same as the
numbers that the program uses to calculate the curves for a lens design.
One of the last things to do with a lens design is to put in the real world
indices and recalculate the lens for those glasses otherwise the real world
lens won't be anywhere near as good as the theory indicates.
--
Why do penguins walk so far to get to their nesting grounds? |
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| Bob May |
| Posted: Tue Nov 22, 2005 3:08 pm |
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THanks to all of you for your repli9es.
My math isn't great so going and doing a damped least squares or any other
type calculation isn't in my future.
I had hoped that there would be a straightforward formula that would spit
out the numbers but that isn't in the books, it seems.
The basic problem, as I stated was to enter some real world glass indices
into ISLO so that I could recalculate the lenses in a design so I could
actually build the lens. The design is quite sensitive to changes as
diffraction limited performance is desired across the whole image and the
lens is large (13") so the diffreaction limit is very small.
I had a private email from Richard which explained how to enter the RI for
the glass. OSLO apparently demands the RI in a particular order and that
order isn't obvious. It wants Nd, NF and then NC for the three index
points. The yellow, blue, red order just doesn't seem to be ordered to me.
--
Why do penguins walk so far to get to their nesting grounds? |
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| Richard F.L.R.Snashall |
| Posted: Tue Nov 22, 2005 4:44 pm |
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Bob May wrote:
[quote:7ceadd90b0]THanks to all of you for your repli9es.
My math isn't great so going and doing a damped least squares or any other
type calculation isn't in my future.
I had hoped that there would be a straightforward formula that would spit
out the numbers but that isn't in the books, it seems.
[/quote:7ceadd90b0]
Just in case you change your mind (I forgot to give you this URL
earlier):
http://users.rcn.com/rflrs/glasgen.htm
The damping is crude, but I've used it with some success. |
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| redbelly |
| Posted: Tue Nov 22, 2005 5:52 pm |
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Jamie wrote:
[quote:7a4a9260c2]I doubt that Excel can handle this one as the least squares fit for
Sellmeier Coef.s is rather difficult.
[/quote:7a4a9260c2]
FYI, you can download an Excel template to do nonlinear regression:
http://faculty.washington.edu/ambrown/
You'll need to have the "Solver" feature of Excel installed (accessed
by clicking on "Tools"). Brown's method uses Solver to maximum the r^2
value of the fit by adjusting the parameters in the fitting function.
Mark |
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| James R (Jim) Lynch III |
| Posted: Thu Nov 24, 2005 7:45 pm |
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Take a look at:
"Melt-dependent refractive index interpolation for optical glasses",
Langenbach, Eckhard; AA(Fisba Optik AG)
Publication: Proc. SPIE Vol. 3737, p. 57-64, Design and Engineering of
Optical Systems II, Fritz Merkle; Ed.
Publication Date: 08/1999
His Formula "Lin dN(N)" works best according to his paper
N' = N + a*N + b = N*(1+a) + b
N' - N = a*N + b
dN = a*N + b
http://www.fisba.ch/english/fe/index.htm
Down, near the end of the page, the link "spie3737.pdf 67KB" will allow you
to download the paper in PDF format.
It is possible to implement this method using whatever interpolation formula
the glass manufacturer uses for the nominal glass indices (Cauchy-Laurent or
Sellmeier). You then fit the differences in index versus wavelength, N(melt
sheet) - N(nominal), to the simple, line equation above. Most scientific,
programmable calculators can fit the data to a linear equation and give you
the a and b coefficients.
It works quite well
James R (Jim) Lynch III |
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