Simulating a Fabry Perot Interferometer

[CasualDays]

I am making an attempt at simulating interference patterns of a Fabry Perot interferometer.

I have fully derived the transmission function and the coefficient of finesse.

T=[tex]\frac{I0 T^{2}}{(1-R)^2}[/tex] + [tex]\frac{1}{1+FSin^2(\frac{\delta}{2})}[/tex]

Where F=[tex]\frac{4R}{(1-R)^2}[/tex] and [tex]\delta[/tex] = [tex]\frac{2\pi}{\lambda}[/tex] 2 n l Cos([tex]\vartheta[/tex])

n=index of refraction of material between two half silvered mirrors
l=thickness of material between mirrors

I guess my question is..How does one draw an interferogram from the transmission equation?

For some reason, it just does not click with me on how you can see a circular ring from a difference in wavelength. I don't really understand which of the variables to assign arbitrary values too, and which to graph if you will.

I need help graphing the interferogram in Mathematica. I just want it to work!

 

[CasualDays]

I tried using Density Plot with this equation,letting theta approach zero, and tried varying t and I0 but still no luck.

For some reason, it doesn't seem very common to create fringe patterns digitally, or at least, I haven't really found any good info on it.

Probably help if I'd taken optics.. :D

 

[sir-pinski]

Drawing an interferogram from the transmission equation can be a bit tricky, but here are some steps that may help:

1. Assign values to the variables: In order to graph the interferogram, you will need to assign values to the variables in the transmission equation. The values you choose will depend on the specific setup of your interferometer. For example, you can choose a specific value for the thickness of the material between the mirrors (l) and the index of refraction of that material (n).

2. Choose a range of values for the wavelength (lambda): The wavelength of the light being used in the interferometer will also affect the interferogram. You can choose a range of values for lambda and plot the interferogram for each value to see how it changes.

3. Plot the transmission function: Using the values you assigned to the variables, you can plot the transmission function T as a function of wavelength (lambda). This will give you a general idea of how the transmission changes with different wavelengths.

4. Plot the interferogram: Now, to plot the interferogram, you will need to use the coefficient of finesse (F) and the phase difference (delta) in the transmission equation. You can plot the interferogram as a function of the phase difference (delta) for different values of F.

5. Use Mathematica: Mathematica has built-in functions for plotting graphs and functions. You can use the "Plot" function to plot the transmission function and the interferogram. Make sure to specify the range of values for the variables and to label your axes correctly.

6. Experiment with different values: Once you have plotted the interferogram, you can experiment with different values for the variables to see how it affects the interferogram. This will help you understand the relationship between the variables and the resulting interference pattern.

Overall, understanding the simulation of a Fabry Perot interferometer takes practice and experimentation. By assigning values to the variables and plotting the transmission function and interferogram, you can gain a better understanding of how the interference patterns are generated. Don't be afraid to play around with different values and ask for help if you get stuck. With some patience and practice, you will be able to successfully simulate a Fabry Perot interferometer.