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Perspectives on Image-Based Wavefront Sensing

Perspectives on Image-Based Wavefront Sensing

Robert A. Gonsalves

Tufts University, Medford, MA 02155

bobg@http://www.wendangku.net/doc/9c0765c2bb4cf7ec4afed03e.html

Abstract: We review the development and uses of image-based wavefront sensing. We discuss

the tools (phase retrieval, phase diversity), some successes (Hubble fix, curvature sensing, solar

research), and some future applications (control of the JWST, human vision, video cameras).

1. The foundation

The first method for image-based wavefront sensor was image sharpening [1], which mimics how we see - our brain processes the images we receive and controls the focus of our eyes. It is still used for automatic focusing of consumer products. In the 1970’s the Shack-Hartman wavefront sensor, which is not image-based, worked so well that image-based techniques were orphans. Some researchers, however, continued developing the tools, namely phase retrieval [2-11], phase diversity [8,9] and curvature sensing [10,11].

Phase retrieval algorithms can be divided into two groups. The first is the Iterative Transform Algorithm (ITA)

[2-7], in which the wavefront (phase in the pupil) is estimated, iteratively, by imposing physical constraints in the spatial and spatial frequency domains. The other algorithm is Model-Based Phase Retrieval (MBPR) [5,7-9], in which a weighted sum of basis functions for the wavefront is manipulated so that a model for the data fits the observed data. Phase diversity [7-9] uses one or more diverse images. It was developed to resolve the “twin” solution of a symmetric pupil and to allow phase retrieval algorithms to be used with extended objects. Curvature sensing uses a form of phase diversity and the transport equation for intensity [10] to estimate the wavefront [11].

2. The Hubble Fix

In July of 1990 NASA announced that there was a devastating and unknown flaw in the Hubble Telescope’s optics. The tools were in place and the researchers were ready to help. The research teams [12-15] arrived at essentially the same prescription for the fix. In December of 1993 astronauts Story Musgrave and Jeff Hoffman inserted the mechanical/optical fix. At second light, the image was dramatically improved. This success gave image-based wavefront sensing and phase retrieval, in particular, instant credibility.

3. Current and Future Applications

Current and future applications include solar research, in which an extended source and large signal-to-noise ratio make phase diversity a natural and successful way to image the sun [16], with most effort placed in post-processing, not adaptive control of the telescope; curvature sensing in ground-based telescopes[11], which has been used on the Mauna Kea telescope in Hawaii and elsewhere, particularly at IR wavelengths; control of the JWST [17-19], in

which a modified version of the ITA will perform initial commissioning and maintenance of the 18-segment primary mirror; vision research [20], in which researchers are finding better ways to examine, characterize and correct our eyes by using image-based wavefront sensing and MEMS technology; and commercial video cameras which have the capabilities (adaptive optics, multi-wavelength sensors, on-board processors) to use this technology.

4. References

[1] R Muller, A Buffington, "Real-time correction of atmospherically degraded telescope images through image sharpening," JOSA 64, (1974)

[2] P Hirsch et al., “Method of making an object-dependant diffuser,” US Patent 3,619,022 (1971)

[3] R Gerchberg, W Saxton, "Phase determination from image and diffraction plane pictures in an electron-microscope," OPTIK 34 (1971)

[4] D Misell, "A method for the solution of the phase retrieval problem in electro–microscopy,” J. Phys. D. 6 (1973)

[5] R Gonsalves, “Phase retrieval from modulus data,” JOSA, 66 (1976)

[6] J Fienup, "Reconstruction of an object from the modulus of its Fourier transform," Opt Lett 3 (1978)

[7] R Gonsalves and A Devaney, “Wavefront sensing by phase retrieval,” US Patent 4,309,602 (1982)

[8] R Gonsalves, “Phase retrieval and diversity in adaptive optics,” Opt. Eng., 21 (1982)

[9] R Paxman, J Fienup, "Image-reconstruction for misaligned optics using phase diversity," JOSA A 3 (1986)

[10] M Teague, "Image formation in terms of the transport equation," JOSA A 2 (1985)

[11] F Roddier, “Curvature sensing and compensation: a new concept in adaptive optics,” Appl Opt 27 (1988)

[12] R Gonsalves, S Ebstein, “Image inversion analysis of the Hubble Space Telescope OTA,” Final Report, JPL Contract 958891 (1991)

[13] J Fienup et al., “Image inversion analysis of the Hubble Space Telescope,” in Final Report, JPL Contract 958892 (1991)

[14] C Roddier, F Roddier, "Combined approach to Hubble Space Telescope wave-front distortion analysis," JPL Contract 958893 (1991)

[15] R Lyon et al., “Hubble Space Telescope phase retrieval parameter estimation,” Proc. SPIE 1567 (1991)

[16] M L?fdahl, G Scharmer, "Wavefront sensing and image restoration from focused and defocused solar images,"Ast Asphy 107 (1994)

[17] D Redding et al., “Wavefront sensing and control for a Next Generation Space Telescope,” Proc. SPIE 3356 (1988)

[18] DS Acton et al., “James Webb Space Telescope wavefront sensing and control algorithms,” Proc. SPIE 5487 (2004)

[19] B Dean et al., “Phase retrieval algorithm for JWST flight and testbed telescope,” Proc. SPIE 6265 (2006)

[20] N Doble, D Williams, “Application of MEMS technology for adaptive optics in vision science,” IEEE J. Quan Electr, 10 (2004)

Perspectives on Image-Based Wavefront Sensing

? 2008 OSA / Solar 2008

? 2008 OSA / FiO/LS/META/OF&T 2008