Vertical Temperature Gradient in Interferometer Cavity

Hi,

let's assume we are testing a perfect concave spherical mirror with an
interferometer. The optical axis is horizontal. What happens if there is a
linear vertical temperature gradient in the light path? Does it produce
astigmatism or coma? How can these errors be calculated?
It's well known that a nonlinear temperature gradient produces astigmatism
and other errors, for example if there is a layer of warm air in the closed
tube of a SC telescope.
But my question is only about a linear vertical temperature gradient. I
typically have about a 0.4K/m gradient above my table, and the distance from
the interferometer to the mirror can be up to 4m. Is there any affordable
raytracer that can simulate this case? Or even better, is there an
analytical solution?

Thanks,
Michael


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