- Home
- User Articles
- How To Model a Gradient Index version of a Sellmeier1 Glass using the Gradient 5 Surface
- Home
- Glass and Refractive Index
- How To Model a Gradient Index version of a Sellmeier1 Glass using the Gradient 5 Surface
How To Model a Gradient Index version of a Sellmeier1 Glass using the Gradient 5 Surface
- By Brian Bauman
- Published 22 June 2009
- User Articles , Glass and Refractive Index
- Unrated
Calculating Gradient 5 Dispersion Constants
The Gradient 5 surface type has parameters to model variations of the refractive index in r and z. Other gradient surface types can model these variations as well, but what makes Gradient 5 different is that it includes dispersion parameters which mimic the often-used Sellmeier 1 formula. The dispersion formula for the Gradient 5 surface type is:
while the dispersion given by the Sellmeier 1 formula is:
If one is modeling a Sellmeier 1 glass that also has r and/or z variations (say, because of temperature gradients), then only the first K term and the first L term are necessary, since the Sellmeier K and L parameters do not vary with the index at the reference wavelength. In other words, the only terms needed for the Gradient 5 surface will be K11, K21, K31, L11, L21, and L31. Note that the convention that I’m using here is that K’s and L’s with one index are Sellmeier constants, and those with two indices are Gradient 5 constants.
The Li1’s are defined in the same way as the Li terms in the Sellmeier formula, which makes sense because the index formulae should have singularities at the same wavelengths (assuming small changes in index). However, the Ki1’s (which generally indicate the strength of the absorption line) are not defined the same way as the Ki terms in the Sellmeier formula. If one evaluates the Sellmeier formula for a wavelength λ and a wavelength λref, takes the difference between the expressions, and compares to the Gradient 5 formula, one finds that:
with the other Kij and Lij terms being zero.
One item to note is that it does not matter what wavelength is used as λref as long as the Ki1’s are calculated using the same wavelength, and that same wavelength is used in finding the base index n0 in the Gradient 5 surface type.
If one has a glass that is not described by a Sellmeier 1 formula, then one can use the index fitting feature (Tools > Catalogs > Glass Fitting) to generate a Sellmeier 1 model. More information on the Glass Fitting Tool may be found in the article entitled “Fitting Index Data in ZEMAX”.
while the dispersion given by the Sellmeier 1 formula is:
If one is modeling a Sellmeier 1 glass that also has r and/or z variations (say, because of temperature gradients), then only the first K term and the first L term are necessary, since the Sellmeier K and L parameters do not vary with the index at the reference wavelength. In other words, the only terms needed for the Gradient 5 surface will be K11, K21, K31, L11, L21, and L31. Note that the convention that I’m using here is that K’s and L’s with one index are Sellmeier constants, and those with two indices are Gradient 5 constants.
The Li1’s are defined in the same way as the Li terms in the Sellmeier formula, which makes sense because the index formulae should have singularities at the same wavelengths (assuming small changes in index). However, the Ki1’s (which generally indicate the strength of the absorption line) are not defined the same way as the Ki terms in the Sellmeier formula. If one evaluates the Sellmeier formula for a wavelength λ and a wavelength λref, takes the difference between the expressions, and compares to the Gradient 5 formula, one finds that:
with the other Kij and Lij terms being zero.
One item to note is that it does not matter what wavelength is used as λref as long as the Ki1’s are calculated using the same wavelength, and that same wavelength is used in finding the base index n0 in the Gradient 5 surface type.
If one has a glass that is not described by a Sellmeier 1 formula, then one can use the index fitting feature (Tools > Catalogs > Glass Fitting) to generate a Sellmeier 1 model. More information on the Glass Fitting Tool may be found in the article entitled “Fitting Index Data in ZEMAX”.