Seeing wavefront moddeling?

[vlaiv]

I was playing around with simulation of seeing effects and have very viable model in reproducing seeing effect - apart from one thing - creating seeing wavefront disturbance.

Here is quick breakdown of technique used:

I created "aperture" and random seeing disturbance:

Aperture is wavefront intensity with 1 being in aperture circle and 0 elsewhere.

Next I took very small image (24x24) and created Gaussian noise on that and then enlarged it to 512x512 image - this gives rather nice looking wavefront error (although probably away from accurately representing seeing wavefront):

This image should be interpreted as phase of wavefront.

Next step would be to compose two images - real and imaginary by combining phase and magnitude (which is simply sin(phase)*aperture and con(phase)*aperture):

Here it is side by side:

And of course, last step would be to find FFT of this complex wavefront representation and look at power spectrum of it:

This image has been gamma corrected to better visually represent star as it would look when observed.

It gives rather "credible" looking seeing distorted star. Depending on "granulation" of wave front and intensity of phase shift (first is controlled by size of base gaussian noise image and how much it is enlarged / it's relative size compared to aperture, and second is controlled by sigma of gaussian noise - it is phase shift at anyone point in radians) we can get different seeing levels like this:

(fine fluctuations in wavefront - like when using large telescope)

Or very decent seeing - second ring defined but broken in few places.

However, I'm sure that above generated seeing wavefront is not accurate representation of seeing wavefront. It probably has different power spectrum than average seeing that we encounter.

Does anyone know or have an idea how "accurate" seeing wavefront can be obtained (in terms of phase). Further more, how would one go about it's time dependence. I was thinking along the terms of multiple layers moving in different directions where one can define some sort of cell and combining those in some way.

Much like if I were to make multiple images with gaussian noise and then slowly shift them and morph them and somehow combine them?

I know that ultimate solution would be to do something silly like running simulation of Navier Stokes equations for 20km of atmosphere or similar - but let's go with next best thing, shall we?

 

 

[andrew s]

Found a paper "more realistic description of wave front distortions by atmospheric turbulence " try googling it .

Regards Andrew