Need help solving nonhomogenous Sellmeier curve equations in Matlab?

  • Thread starter hrky
  • Start date
  • Tags
    Curve Fit
In summary, the speaker has five experimental values for refractive index at different wavelengths and wants to use a Sellmeier fit formula to find A1, A2, A3, A4, and A5 parameters. They are seeking help on which function to use in Matlab to solve the system of five equations. Another person suggests using the SOLVE command and the multivariable Newton Raphson technique. The speaker then confirms that they have successfully solved the Sellmeier fit.
  • #1
hrky
3
0
I have five, very precise, experimental values of refractive index for five different wavelengths and would like to draw the Sellmeier fit of the form:

n^2=A1+A2/(1-A3/lambda^2) + A4/(1-A5/lambda^2)

So, to find A1, A2, A3, A4 and A5 parameters I need to solve the system of five equations. Those equations are nonhomogenous. I would like to use Matlab program to solve that, but I don’t know which function and which form to use…Anybody already solved this? Thanks!
 
Physics news on Phys.org
  • #2
To solve numerically, you could use the multivariable Newton Raphson technique.

In Matlab, I'd guess you need the SOLVE command. Here's the online help documentation
 
Last edited:
  • #3
thx!

Thanks! Sellmeier is now solved:cool:
 

1. What is the Sellmeier curve?

The Sellmeier curve is a mathematical model that describes the relationship between refractive index and wavelength for a specific material. It is often used to determine the optical properties of a material, such as glass, and is commonly used in the design of optical components.

2. How is the Sellmeier curve used in fitting optical components?

The Sellmeier curve is used in the fitting process by providing a set of coefficients that can be used to calculate the refractive index of a material at a given wavelength. These coefficients are determined through experimental data and can be used to accurately predict the refractive index for a specific material.

3. What factors affect the accuracy of the Sellmeier curve?

Several factors can affect the accuracy of the Sellmeier curve, including the quality and amount of experimental data used to determine the coefficients, the temperature and pressure of the material, and any impurities present in the material.

4. How do I determine the Sellmeier coefficients for a specific material?

The Sellmeier coefficients can be determined through experimentation, typically using a spectrometer or interferometer to measure the refractive index at different wavelengths. Once enough data points have been collected, they can be fit to the Sellmeier curve equation to determine the coefficients.

5. Can the Sellmeier curve be used for all materials?

No, the Sellmeier curve is only applicable to materials that exhibit a linear relationship between refractive index and wavelength. Some materials, such as metals, do not follow this relationship and therefore cannot be accurately fit with the Sellmeier curve.

Similar threads

Solve this system of linear equations
    • Precalculus Mathematics Homework Help
Replies
7
Views
1K
Fitting VS Control Point?
    • General Math
Replies
2
Views
1K
Any way to do this using simple matrix math?
    • Calculus and Beyond Homework Help
Replies
1
Views
1K
I Questions about Density Parameter and Critical Density
    • Cosmology
Replies
6
Views
917
Engineering Optical Fibres: Wavelength for Zero net Dispersion
    • Engineering and Comp Sci Homework Help
Replies
3
Views
819
MATLAB Partial Differential Equation - solve with Matlab
    • MATLAB, Maple, Mathematica, LaTeX
Replies
1
Views
1K
Very tricky line of people problem
    • Calculus and Beyond Homework Help
Replies
8
Views
1K
Help me solve this integral for the equation of motion
    • Introductory Physics Homework Help
Replies
19
Views
665
MATLAB Help naming matrices in matlab
    • MATLAB, Maple, Mathematica, LaTeX
Replies
4
Views
2K
How to Design FP resonator from Bragg mirror in Matlab?
    • Advanced Physics Homework Help
Replies
2
Views
3K

Hot Threads

Recent Insights

Back
Top