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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 63, Iss. 6 — Jun. 1, 1973
  • pp: 647–657

Interferometric technique for recording and restoring images degraded by unknown aberrations

W. T. Rhodes and J. W. Goodman  »View Author Affiliations

JOSA, Vol. 63, Issue 6, pp. 647-657 (1973)

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A method for recording and restoring images that have been degraded by unknown aberrations is described. Several images are recorded with different masks placed in the pupil of the optical system. If these images are Fourier analyzed and certain phases are combined algebraically in the proper manner, the effects of the unknown aberrations can be removed, with an uncertainty concerning the absolute location of the object with respect to the imaging system. Experimental results are reported. The sensitivity of the method is analyzed, and the applicability of the technique in astronomical imaging is considered. The method shows considerable promise for high-resolution imaging of fine-grain structure on the solar surface.

© 1973 Optical Society of America

W. T. Rhodes and J. W. Goodman, "Interferometric technique for recording and restoring images degraded by unknown aberrations," J. Opt. Soc. Am. 63, 647-657 (1973)

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  1. J. R. Meyer-Arendt and C. B. Emmanuel, Optical Scintillation: A Survey of the Literature, Natl. Bur. Std. (U.S.), Tech. Note 225 (U.S. Government Printing Office, Washington, D.C., 1965). The question of the scale of aberrations introduced by the atmosphere arises throughout this paper. Hard experimental data of the kind necessary for definitive statements have not been found in the literature; the ranges over which various approximations in this paper are valid are based largely upon indirect experimental evidence and upon subjective reports made by astronomers. For further discussion, see J. C. Moldon, Imaging of Objects Viewed Through a Turbulent Atmosphere, Ph.D. dissertation, Department of Electrical Engineering, MIT, Cambridge, Mass. (1969), pp. 72–95.
  2. Restoration of Atmospherically DegradedImages, Vols. I–IV, Report of the 1966 Woods Hole Summer Study (National Academy. of Sciences, Washington, D.C., 1967).
  3. B. J. McGlamery, J. Opt. Soc. Am. 57, 293 (1966).
  4. R. C. Jennison, Mon. Not. R. Astron. Soc. 118, 276 (1958).
  5. D. H. Rogstad, Appl. Opt. 7, 585 (1966).
  6. For further discussions of interferometric image formation in the context of a retransformation of the partial-coherence function of the object, seeG. L. Rogers, Proc. Phys. Soc. Lond. 81, 323 (1963).
  7. This section is largely heuristic; it can be placed on a firm mathematical basis by considering the Van Cittert-Zernike theorem as it relates to an incoherent imaging system. See, for example, M. Born and E. Wolf, Principles of Optics, 3rd ed. (Pergamon, London, 1965), pp. 505–518.
  8. Reference 7, p. 510.
  9. F. D. Russell and J. W. Goodman, J. Opt. Soc. Am. 61, 182 (1971).
  10. This portion of the discussion parallels in certain respects the paper by Rogstad (Ref. 5), in which is described a technique for collecting the data electronically, in real time, which may be of interest to the reader.
  11. This notation indicates the normalized vector spacing of the pinholes associated with the particular spatial frequency. Thus (1,0) denotes a pinhole pair spaced one unit in the x direction and zero units in the y direction, and so forth.
  12. A1 may contain, in addition, a term arising from lack of registration in the x direction of the input scan. It is easily shown, however, that this and similar terms drop out of the expressions to follow; indeed, such a term is conveniently viewed as the consequence of a wedge-shaped mass of air in front of the imaging system that simply moves the apparent position of the object in the sky. It is thus conveniently represented by a modification of the aberration phases:ϕ l becomes ϕl′, and so forth. For elaboration on this point, see Ref. 13.
  13. W. T. Rhodes, An Optical Array Technique for the Removal of Atmospheric Aberrations in Astronomical Imaging, Ph.D. disseration, Department of Electrical Engineering, Stanford University, Stanford, Calif. (1971) (available from University Microfilms, Ann Arbor, Mich., Order No. 72-16 780).
  14. J. L. Harris (private communication). If desired, it is possible to sample a small fraction of the light incident upon each subaperture during exposure, and on the basis of these measurements, using the relationship expressed in Eq. (1), to compensate for the component magnitude variations induced by the scintillation. Such a procedure is appropriate so long as the irradiance is essentially constant over each subaperture, a condition probably satisfied for 7.5-cm openings under typical atmospheric conditions. It is also possible to correct component amplitudes by the use of redundant image information. The procedure, similar to that used to correct component phases, places additional constraints on the mask configurations, however, and therefore appears to be of little practical value.
  15. J. F. Walkup, Ph.D. dissertation, Department of Electrical Engineering, Stanford University, Stanford, Calif. (1971) (available from University Microfilms, Ann Arbor, Mich., Order No.72-11 685).
  16. C. W. Allen, Astrophysical Quantities, 2nd ed. (Athlone, London, 1963), pp. 122 and 172.

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