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Simulating Atmospheric Strehl
Trex Enterprises
Mentor: Ben Wheeler
Ryan Nora
Summer 2005
Some Background on Strehl
 Strehl is a mathematical relationship attached
to an image.
 Strehl is commonly used to measure the
performance of an optical system.
Strehl = maximum intensity of the distorted wavefront
maximum intensity of the perfect wavefront
The Value of Strehl
 A perfect optical setup with no atmospheric
distortions would give a Strehl of 1.0 .
 Realistically, any optical setup with a Strehl of 0.8
would be considered diffraction limited.
 Here are some corrected Strehl values of telescopes
across the globe:
UH Int. Astronomy (IR) = .4 @ .7 um
ESO/France (IR) = .13 @ 1.25 um and .65 @ 2.2 um
*This information is from Adaptive Optics for Astronomical Telescopes, J. Hardy, 1998
The Project
 To simulate atmospheric distortions in a
wavefront and calculate its Strehl.
 Modeled after the AEOS telescope.
 Broken into two simulations to calculate
Strehl.
Simulation Setup
Energy Distribution Background
1
0.04
0.8
0.02
0.6
0
0.4
-0.02
0.2
-0.04
-0.02
-0.04
-0.02
0
0.02
Airy Disk
-0.01
0.01
0.04
Intensity Plot
0.02
Ideal System
Important Steps in calculating the energy
distribution of the ideal system:
 Define the amount of light entering the
system
 Find which frequencies are present
 Convert amplitude to intensity
Energy Distribution of Ideal System
0.01
0.005
30
100
20
0
80
10
60
0
0
-0.005
40
20
40
20
60
80
-0.01
-0.01
-0.005
0
0.005
Diffraction Pattern
0.01
100
Intensity
0
Distorted System
Important Steps in calculating the energy
distribution of the distorted system:
 Define the amount of light entering the
system
 Generate distorted wavefront
 Find which frequencies are present
 Convert amplitude to intensity
Simulating the Atmosphere
0.0005
1
0
0.5
-0.0005
-1
0
-0.5
-0.5
0
2
0.5
1
1
-1
1
0
-1
-2
0.5
-1
0.0001
1
0.0005
0
1
0
0.5
-0.0005
-1
0
-0.5
0.5
-0.5
0
0.5
-0.0001
0.5
-1
0
1
-0.5
-0.5
0
0
-0.5
-1
-0.5
0
0.5
1
-1
1
-1
Zernike coefficients generated from the Kolmogorov
turbulence spectrum were used to build the
distortions in the wavefront.
* This relationship is from Noll’s paper on Zernikes.
Energy Distribution of the Distorted System
40
20
1
100
0
0.5
80
0
-20
60
20
40
40
-40
60
20
80
-40
-20
0
20
Wavefront
40
100
Intensity
Calculating Strehl
Strehl = maximum intensity of the distorted wavefront
maximum intensity of the perfect wavefront
By creating the aberrations in the
simulated wave front similar to what the
atmosphere distorts waves in real life, I
have calculated an atmospheric Strehl of:
~ 0.03
Conclusion
The amount of
distortion caused by the
atmosphere shows us
the need to create an
Adaptive Optics system
to minimize the
atmospheric distortions,
and allow us to collect
better data.
200
150
100
50
0
0
50
100
150
200
Many Mahalos to:
Center for Adaptive
Trex Enterprises
Ben Wheeler
Dr. Mike Flannigan
Optics
Malika Bell
Maui Community
College
Lisa Hunter
Mark Hoffman
Liz Espinoza
Wallette Pellegrino
This project is supported by the National Science Foundation Science
and Technology Center for Adaptive Optics, managed by the
University of California at Santa Cruz under cooperative agreement
No. AST - 9876783.