Problem: How can we model a linear thermal temperature gradient of an interferometer cavity in ZEMAX?



This question was posed by an interferometer expert in one of the online optics fourms. He wanted an analytical or modeling solution to this problem. I thought that I could model this in ZEMAX and took a quick look at the gradient index surface types and incorrectly decided it could not be done. So I came up with another way using non-sequential ray-tracing.

I would make rectangular volume objects and lay them all on top of each other to create a linear thermal gradient in the interferometer cavity. I mentioned this method, and a fellow ZEMAX user (Dave Schaack) mentioned that I could use a Gradient4 type surface in sequential zemax to model this problem. I looked up Gradient4 in the manual and sure enough it had the capability, I just missed it when I read the manual too fast before – message: read the manual carefully before you make assumptions!

The key to putting in a vertical thermal gradient into the airspace between the point source and the mirror is to use the Gradient4 type surface.  This type of gradient index enables one to create a linear or quadratic type index variation along one, two, or three axis.  This can be understood by looking at the refractive index equation for the Gradient4 surface:

^{n(x, y, z) = n₀ + n_x1*x + n_x2*x2 + n_y1*y + n_y2*y2 + n_z1*z + n_z2*z2}

By using only the terms in y the required gradient can be easily produced.