Overcoming the Challenges of Image Restoration

3. Overcoming the Challenges of Image Restoration Ronald Magarin University of Hawaii - Institute for Astronomy Mentor: Doug Hope Advisor: Stuart Jefferies

4. Problem of Image Restoration Advanced Electro-Optical System (AEOS) Images obtained at AEOS Hubble Space Telescope (HST)

5. Planar wavefront Distorted wavefront Atmospheric blur Point source Turbulence region Telescope Pupil Point Spread Function (PSF)

6. Images obtained by telescope PSF with four equal Overlapping image intensity speckles PSF with two equal intensity speckles Overlapping images Atmospheric PSF many different Many overlapping intensity speckles images PSF with single speckle Blurred object

7. Removing atmospheric blur from telescope images Actual object being imaged Image obtained from ground-based telescope

8. Methods Multi-frame Blind Deconvolution (MFBD) Algorithm • Multi-frame – use multiple images • Blind Deconvolution - estimate both PSF and object • Dependant on: • number of frames • turbulence strength • noise in the data • knowledge about the telescope pupil size • estimate PSF’s using Zernike polynomials Main Focus • Pupil size • What if you use the wrong pupil? • How does it affect the restoration • Can you reliably get speckles?

9. Results

10. Pupil size effects on PSF estimates Wrong Pupil Truth PSF Correct Pupil Incorrect telescope pupil size affects estimates of speckles (intensity at locations) in the PSF.

11. Conclusions • For mild turbulence we were able to estimate the correct pupil size from the data by running restorations for a variety of pupil sizes • In strong turbulence one needs a large number of Zernike polynomials to accurately model speckles in PSF • Important information for an MFBD algorithm is the size of the telescope pupil that was used to obtain the data • Use of incorrect pupil size in MFBD degrades the estimation of PSF’s • Poor estimation of PSF’s limits the estimation of fine detail in the object

12. Culture and Clarity

13. Acknowledgements Center for Adaptive Optics Scott Seagroves, Hilary O’Bryan, Lisa Hunter and the CfAO instructors University of Hawaii - Institute for Astronomy Douglas Hope, Stuart Jefferies, J.D. Armstrong and Jeff Khun Maui Community College Mark Hoffman and Wallette Pellegrino Maui Economic Development Board Isla Yap and Leslie Wilkins National Science Foundation “Uncle” Charlie Maxwell Funding provided through a Research Experiences for Undergraduates (REU) Supplement to the Center for Adaptive Optics, a National Science Foundation Science and Technology Center (STC), AST-987683

14. Sources • http://www.ctio.noao.edu/~atokovin/tutorial/intro.html • http://www.jhu.edu/~signals/ • http://www.de.afrl.af.mil REFERENCES: • “Imaging Through Turbulence”, Michael C. Roggemann, Byron Welsh • “Digital Image Processing”, Second Edition, Rafael C. Gonzalez, Richard E. Woods • “The Fourier Transform and its Applications”, Third Edition, Ronald N. Bracewell

15. Pupil size effects on object estimates Wrong Pupil Truth Object Correct Pupil Conclusion: Incorrect telescope pupil size affects estimates (intensity at locations) the object.

16. Data

17. Questions • Is there a relation to the pupil size and the accuracy of the restoration? • What other factors change the result of the restoration? • How can this information be used in the future?