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Image Restoration in Strong Atmospheric Turbulence

Trent Kyono Institute for Astronomy Mentor: Douglas Hope. Image Restoration in Strong Atmospheric Turbulence. How to Model a Point Spread Function (PSF). Point Source. Wave-front (planar). Phase. Atmosphere (no turbulence). Turbulence Layer in Atmosphere. PSF.

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Image Restoration in Strong Atmospheric Turbulence

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  1. Trent Kyono Institute for Astronomy Mentor: Douglas Hope Image Restoration in Strong Atmospheric Turbulence

  2. How to Model a Point Spread Function (PSF) Point Source Wave-front (planar) Phase Atmosphere (no turbulence) Turbulence Layer in Atmosphere PSF What’s 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

  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

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

  7. Modeling the PSF2nd basis – Disc Harmonics 1st Disc Harmonic 2nd Disc Harmonic 10th Disc Harmonic 100th 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

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

  19. 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!!! Big Mahalos… 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.

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