A close double in bad seeing

This is a double star closer than the speckle diameter. In the poster frame the double nature of the star is not visible, but if one clicks on the animated gif, there will be moments in which the star can be split despite it is closer than the diameter of the turbulent image.

Yet another slow motion movie of speckles

This is anoher movie. The "taylor screen" in this case has been produced by inverse fourier transform and should be of better quality (in the sense it is closer to the statistical properties the wavefront should have, as described by Fried, Statistics of a geometric representation of wavefront distortion, JOSA 55-11, 1965).

The time step corresponds to the motion of the taylor screen of 1% of the diameter (~1ms in typical conditions).

See also http://autocostruttori.blogspot.com/ (in the comments there is the code fragment that produces the movie)

Simulation of bad seeing

This video shows another realistic simulation of a star image seen with a telescope under very bad seeing conditions. I do not know the exact value of the turbulence scale (the Fried's parameter), but, judging the number nd size of speckles, it can be estimated to be one tenth or less than the scope diameter.
The step between frames correspond to a lateral displacemnt of the wavefront which amounts to 1% of the scope diameter (e.g. for 1 meter and wind speed of 10 m/s it is 1 cm and 1 ms). If played at 25 fps, the movie is ~40 times slower than reality.
An interesting aspect is the way the single speckles change. They both move and vary in intensities, but the latter is quicker. The speckle pattern looks more like swarm of bubbles appearing and fading than a moving set of spots. Is that true or an artifact? Here is a slow motion movie of Eps aql.
http://en.wikipedia.org/wiki/Image:Eps_aql_movie_not_2000.gif

Realistic simulation of atmospheric seeing

These movies (click to animate) show a simulation of atmospheric seeing. To provide realistic time flow, the frames have been computed according to the “Taylor” hypotesis (http://www.mpia.de/AO/INSTRUMENTS/FPRAKT/AOonLargeTelescopes.pdf) which assumes that the the turbulent wavefront moves in front of the telescope carried by winds.
For the sake of precision, if we assume that the phase fluctuation to be a function of space (x) and time (t):

then, as in all transport phenomena, we can derive time dependencies as:

The left hand side term is the deformation of the wave front due to rearrangement of the eddies in the flow, the terms to the extreme right is the transport of the wave front caused by fluid flow at speed u, and the first term after the equal sign is the wave front fluctuation seen by the scope pointing at the sem direction (x is considered scalar for simplicity). The Taylor hypothesis means that the thwo terms at the right side of the equation are considered dominant, whereas the rearrangement of the eddies is slower. That means that the scope sees a wave front sliding in front of it.
The R source code does exactly that: 1) first a wave front in the form of a long strip is generated, 2) then it is passed in front of the aperture.
Every time frame the wave front moves 4% of the diameter of the scope. This means that for a scope the size of 500 mm the wave front moves 20 mm every frame. If we assume a typical wind speed of 10 m/s that means the time step is 2ms, or 500 frames per second (20 times slower than reality when reproduced at 25 fps).
The two movies differ for the amount of bad seeing. It is interesting to note the motion and rearrangement of the speckles, and at the same time, the slow wandering of the whole pattern due to largest scale wave front tilt.


The R source code -----------------

size <- 51
t <- turb(size*11,size*3)
p <- pupil(size)
step <- 2
nsteps <- floor((size*10)/step)
star <- star.test(p,size=40,pad=4,draw=FALSE)
zmax <- max(star)
gamma <- 2.2

GDD("turbulence", type="gif", width=400, height=400)

for (i in 1:nsteps) {
tt <- t[((i-1)*step+1):((i-1)*step+size),(size*1):(size*2)]
rms <- sd(as.vector (tt))*20
p$set.turb2(tt,rms)
star <- star.test(p,size=40,pad=4,draw=FALSE)
image ((star/zmax)^(1/gamma), zlim=c(0,1), col=gray256, asp=1, bty='n', axes=FALSE)
}

dev.off()