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
Turbulence Layer in Atmosphere
Atmosphere (no turbulence)
PSF
What’s measured by the detector is the PSF 2

3. D/r0 = 5, approximately 52 = 25 speckles

4. Image Formation D/r0 = 5, Weak Turbulence D/r0 = 25, Strong Turbulence
Insert picture of HST convolved with a PSF for Dr025, which yields a distorted image of HST. Explain that D is the diameter (telescopic pupil) and r0 is the size of the wavefront, where it is coherent. A large ratio of D to r0 implies strong turbulence.

5. 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 5

6. Modeling the PSF 1st basis - Zernike Polynomials
1st Zernike
2nd Zernike
10th Zernike
100th Zernike 6

7. Modeling the PSF 2nd basis – Disc Harmonics
1st Disc Harmonic
2nd Disc Harmonic
10th Disc Harmonic
100th Disc Harmonic 7

8. 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. 8

9. Dr025 Number of Parameters Vs. Error1
Zernike Modes
Disc Harmonics
Boxcar Convolution
0.9
0.8
0.7
0.6
Error
0.5
0.4
0.3
0.2
0.1
Number of Parameters

10. Zernikes Vs. True PSF for High Turbulence D/r0 = 25

11. Disc Harmonics Vs. True PSF for High Turbulence D/r0 = 25

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
Number of Parameters

13. Zernikes Vs. True PSF for Higher Turbulence D/r0 = 50

14. Disc Harmonics Vs. True PSF for Higher Turbulence D/r0 = 50

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
Number of Parameters 15

16. Zernikes Vs. True PSF for High Turbulence D/r0 = 100

17. Disc Harmonics Vs. True PSF for Extreme Turbulence D/r0 = 100

18. Real World Image Restorations
Astronomical observation
Criminal Investigations
Medical Imaging (i.e., Digital X-ray, MRIs, CT scans, Ultrasound, mammography, etc)

19. Thank you for everything! ALL PAU!!!
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 ) 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 and from the University of Hawaii. 19