Trent Kyono

1
Image Restoration in Strong Atmospheric Turbulence

• Trent Kyono
• Institute for Astronomy
• Mentor Douglas Hope

2
How to Model a Point Spread Function (PSF)
Point Source
Wave-front (planar)
Phase
Atmosphere (no turbulence)
Turbulence Layer in Atmosphere
PSF
Whats measured by the detector is the PSF
3
D/r0 5, approximately 52 25 speckles
D/r0 25, approximately 252 625 speckles
D/r0 50, approximately 502 2500 speckles
D/r0 100, approximately 1002 10000 speckles
4
Image Formation
D/r0 5, Weak Turbulence
D/r0 25, Strong Turbulence
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Full Imaging Problem

• aka Blind Deconvolution
• Start with a blurred image to try and estimate
  both the actual true image (target) and the
  turbulence (PSF).

Blurred Image
Target
PSF
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Modeling the PSF 1st basis - Zernike Polynomials
1st Zernike
2nd Zernike
10th Zernike
100th Zernike
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Modeling the PSF2nd basis Disc Harmonics
1st Disc Harmonic
2nd Disc Harmonic
100th Disc Harmonic
10th Disc Harmonic
8
Modeling the PSF3rd basis Convolution
For image processing, convolution serves as a
weighted average over a given number of pixels.
The smaller the number of pixels the more
accurate the estimation.
9
Dr025 Number of Parameters Vs. Error
1
Zernike Modes Disc Harmonics Boxcar Convolution
0.9
0.8
0.7
0.6
0.5
Error
0.4
0.3
0.2
0.1
0
0 2000 4000 6000
8000 10000 12000 14000
Number of Parameters
10
Zernikes Vs. True PSF for High Turbulence D/r0
25
Zernike
True
11
Disc Harmonics Vs. True PSF for High Turbulence
D/r0 25
Disc Harmonics
True
12
Dr050 Number of Parameters Vs. Error
1.4
Zernike Modes Disc Harmonics Boxcar Convolution
1.2
1.0
0.8
Error
0.6
0.4
0.2
0
0 2000 4000 6000
8000 10000 12000 14000
Number of Parameters
13
Zernikes Vs. True PSF for Higher Turbulence D/r0
50
Zernike
True
14
Disc Harmonics Vs. True PSF for Higher Turbulence
D/r0 50
Disc Harmonics
True
15
Dr0100 Number of Parameters Vs. Error
1.8
Zernike Modes Disc Harmonics Boxcar Convolution
1.6
1.4
1.2
1
Error
0.8
0.6
0.4
0.2
0
0 2000 4000 6000
8000 10000 12000 14000
Number of Parameters
16
Zernikes Vs. True PSF for High Turbulence D/r0
100
Zernike
True
17
Disc Harmonics Vs. True PSF for Extreme
Turbulence D/r0 100
Disc Harmonics
True
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Real World Image Restorations

• Astronomical observation
• Criminal Investigations
• Medical Imaging (i.e., Digital X-ray, MRIs, CT
  scans, Ultrasound, mammography, etc)

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Big Mahalos

• Lisa Hunter, Scott Seagroves Lynne Raschke
• Aunty Lani Lebron and all the IFA staff
• Instructors Dave Harrington, Ryan Montgomery,
  Isar Mostafaneszhad, Mark Pitts Sarah Sonnet

• Cant forget
• DOUG HOPE
• Thank you for everything!
• ALL PAU!!!

The Akamai Internship Program is funded by the
Center for Adaptive Optics through its National
Science Foundation and Technology Grant
(AST-987683) and by grants to the Akamai
Workforce Initiative from the National Science
Foundation and Air Force Office of Scientific
Research (both administered by NSF, AST-0710699
and from the University of Hawaii.