Transcript Modeling Images through Strong Turbulence

Image Restoration in Strong
Atmospheric Turbulence
Trent Kyono
Institute for Astronomy
Mentor: Douglas Hope
How to Model a Point Spread
Function (PSF)
Point Source
Wave-front (planar)
Phase
Turbulence
Atmosphere
Layer
(nointurbulence)
Atmosphere
PSF
What’s measured
by the detector is
the PSF
D/r0 = 5, approximately 52 = 25 speckles
D/r0 = 50, approximately 502 = 2500 speckles
D/r0 = 25, approximately 252 = 625 speckles
D/r0 = 100, approximately 1002 = 10000 speckles
Image Formation
D/r0 = 5, Weak Turbulence
D/r0 = 25, Strong Turbulence
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
Modeling the PSF
1st basis - Zernike Polynomials
1st Zernike
2nd Zernike
10th Zernike
100th Zernike
Modeling the PSF
2nd basis – Disc Harmonics
1st Disc Harmonic
10th Disc Harmonic
2nd Disc Harmonic
100th Disc Harmonic
Modeling the PSF
3rd 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.
Dr025 Number of Parameters Vs. Error
1
Zernike Modes
Disc Harmonics
Boxcar Convolution
0.9
0.8
0.7
Error
0.6
0.5
0.4
0.3
0.2
0.1
0
0
2000
4000
6000
8000
10000
Number of Parameters
12000
14000
Zernikes Vs. True PSF for High
Turbulence D/r0 = 25
Zernike
True
Disc Harmonics Vs. True PSF for
High Turbulence D/r0 = 25
Disc Harmonics
True
Dr050 Number of Parameters Vs. Error
1.4
Zernike Modes
Disc Harmonics
Boxcar Convolution
1.2
1.0
Error
0.8
0.6
0.4
0.2
0
0
2000
4000
6000
8000
10000
Number of Parameters
12000
14000
Zernikes Vs. True PSF for Higher
Turbulence D/r0 = 50
Zernike
True
Disc Harmonics Vs. True PSF for
Higher Turbulence D/r0 = 50
Disc Harmonics
True
Dr0100 Number of Parameters Vs. Error
1.8
Zernike Modes
Disc Harmonics
Boxcar Convolution
1.6
1.4
Error
1.2
1
0.8
0.6
0.4
0.2
0
0
2000
4000
6000
8000
10000
Number of Parameters
12000
14000
Zernikes Vs. True PSF for High
Turbulence D/r0 = 100
Zernike
True
Disc Harmonics Vs. True PSF for
Extreme Turbulence D/r0 = 100
Disc Harmonics
True
Real World Image Restorations
•Astronomical observation
•Criminal Investigations
•Medical Imaging (i.e., Digital X-ray,
MRIs, CT scans, Ultrasound,
mammography, etc)
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
Can’t 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.