Simulation of the Effects of Scintillation at Three Frequencies
Diffractive propagation of an electromagnetic wavefront displays the
effects of scintillation - random distortions of the wavefront
amplitude that grow with propagation distance. This effect may be
simulated using a near field Fresnel diffractive propagator, which
simulates propagation by convolving the wavefront with a filter of
unit amplitude and parabolic phase. Because one can only simulate a
finite piece of the wavefront, oscillatory edge effects arise in the
application of this filter, which affect both the amplitude and the
phase of the wavefront.
Here is a movie showing the amplitude of the diffractive wavefront as this
wavefront propagates through free space after encountering a single
turbulent screen.
Aliased scintillation simulation
The Fried parameter for this screen was chosen to be 1.5 meters at 1
micron. This value was chosen to approximate the typical strength of
high-altitude turbulence at good astronomical sites. In the movie,
the wavefront propagates for 20 km in 100 meter steps. The
oscillatory edges drift into the image as the propagation distance
increases. Here is a summary of the simulation parameters.
5 meter wavefront
2 micron radiation
r0 of 1.5 meters at 1 micron
1 cm pixel scale in the wavefront
1 cm pixel scale in the turbulence layer
100 meter distance step
20 km of simulated propagation path
To avoid these edge effects, one must make the wavefront larger than
the aperture and then discard the corrupted edges. The factor that
indicates how much of the image must be discarded grows linearly with
the wavelength of the electromagnetic radiation and the propagation,
and are inversely proportional to the square of the sampling interval.
In the movie below I've padded by the required amount, performed the
propagation, and then clipped the resulting wavefronts to remove the
invalid edges. The resulting wavefronts are 5 meters in size. I have
repeated this exercise for 3 different frequencies - .5, 1, and 2
microns. (This is the order of the wavefronts shown in the movie,
from left to right.) The same realization of the turbulent optical
path differences was used at all three frequencies.
Valid scintillation simulation
My eyeball estimate of the amplitude modulation is about 10 percent at .5 microns,
5 percent at 1 micron, and a few percent at 2 microns.
This simulation was generated using the program scintillation_simulation, which is
provided as part of the arroyo distribution.