Aloha, my name is Ronald Magarin and I’ve been working with the institute for astronomy working under the guidance of Dr’s Doug Hope and Stuart Jefferies just like in ancient Hawaiian times when the Kahuna po’o would go to Haleakala whether it be in times of worship or spirituality to find insight or clarity my project is about Overcoming the challenges of image restoration.

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

Problem of Image Restoration Advanced Electro-Optical System (AEOS) Here we have a truth object (Hubble) and we are looking at it through the AEOS telescope what we would see is a random blur of the image. This image shows how the blur is randomly changing. The image moves not because of the movement of the satellite or the telescope but because of the moving atmosphere. The problem that we are facing is, it possible to get the truth image back from the frames of the blurred image? So what causes the image to blur? Hubble Space Telescope (HST) Images obtained at AEOS

Atmospheric blur Point Spread Function (PSF) Point source Planar wavefront Turbulence region Distorted wavefront To illustrate the blur, When we have a wavefront, we have light waves that include the information of what the object is. For this case we are looking at a point source (star), so the wavefront is flat. Then we have a Turbulence region which is the earth's atmosphere and is a mixture of hot and cold air. As the wavefront goes through the turbulence region it gets distorted. As you can see, the information from the wavefront has now been lost because it is no longer flat, this information is what we know of as the blurred or aberrated image. Point spread function is what we get when you look at a point source through the turbulence region. Telescope Pupil Point Spread Function (PSF)

Images obtained by telescope This slide shows how the images are blurred, On the left we see a PSF with a single dominant speckle, on the right we see a corresponding image of the object that has been blurred by the PSF, next on the left we see a PSF with two dominant speckles of equal intensity with different locations and on the right we see the corresponding images to that PSF , we can take that further and see a PSF of four dominant speckles of equal intensity and different locations and you can see how the images overlap each other and start to blur. So we take that even further and show how the real PSF of different intensities and locations represent the turbulence and affect the image that we get. PSF with two equal intensity speckles Overlapping images Atmospheric PSF many different Many overlapping intensity speckles images PSF with single speckle Blurred object PSF with four equal Overlapping image intensity speckles

Removing atmospheric blur from telescope images This is slide shows Deconvolution; which is given the data, can you estimate the truth object from the data; meaning can we extract the true image from the randomly blurred image Deconvolution is difficult because of all the noise that we get in the atmosphere and the detection noise. estimate the speckles , their intensity and their location where they are supposed to be D =3.6m r0 = 10m Turbulence strength=0.36m Actual object being imaged Image obtained from ground-based telescope

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?

Results This chart shows the results of using ~100 Zernike polynomials which shows the error in the restoration vs the pupil size. I’ve charted the results of five different pupil sizes each with the turbulence strength of 10 which is in the blue and 20 which is in the green. Both strengths were done using 1000 iterations of the MFBD algorithm. If you look at the errors in the restoration for the mild turbulence, as we get to the correct pupil size the error goes down and when we go past it then the errors start to go back up. If you look at the errors for the restoration for the strong turbulence, as we get to the correct pupil size the error goes down but when we go past it the error keeps going down. We suspect that we didn’t use enough Zernikes.

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.

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

Culture and Clarity Culture & clarity ` Being that I was more into electronics industry… I never thought that I cxould find jobs here in Hawaii that would help me to raise my family and have my family, but after seeing the oppor. And going through the cfao program I realized that I could stay here and have a job in the high tech industry and this showed me a path… gave me clarity what Local attitudes, family bonds, blood & calabash, friends community that is the culture I want my family to have around them.

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 I’d like to thank the CfAO 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

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

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

Data In this slide we show the results from using the MFBD algorithm utilizing about 100 Zernike polynomials. Zernike polynomials are what we are using to model the PSF. It’s like building blocks like Lego’s that represent the PSF. It shows the effects of what happens to the truth object and the PSF when using different pupil sizes. On the left side we have the truth object, in this case we’re looking at the Hubble Space Telescope and on the right side you see the PSF as the pupil size changes you can see the different effects. The top two images have a turbulence strength of 10 and the bottom images have a turbulence strength of 20.

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?