## Description and simulation of an active imaging technique utilizing two speckle fields: root reconstructors

JOSA A, Vol. 19, Issue 3, pp. 444-457 (2002)

http://dx.doi.org/10.1364/JOSAA.19.000444

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### Abstract

Quasi-monochromatic light will form laser speckle upon reflection from a rough object. This laser speckle provides information about the shape of the illuminated object. Further information can be obtained if two colors of coherent light are used, provided that the colors are sufficiently close in wavelength that the interference is also measurable. It is shown that no more than two intensities of two speckle patterns and their interference are required to produce an unambiguous band-limited image of an object, to within an overall spatial translation of the image, in the absence of measurement errors and in the case where all roots of both fields and their complex conjugates are distinct. This result is proven with a root-matching technique, which treats the electric fields as polynomials in the pupil plane, the coefficients of which form the desired complex object. Several root-matching algorithms are developed and tested. These algorithms are generally slow and sensitive to noise. So motivated, several other techniques are applied to the problem, including phase retrieval, expectation maximization, and probability maximization in a sequel paper [J. Opt. Soc. Am. A **19**, 458 (2002)]. The phase-retrieval and expectation-maximization techniques proved to be most effective for reconstructions of complex objects larger than 10 pixels across.

© 2002 Optical Society of America

**OCIS Codes**

(030.6140) Coherence and statistical optics : Speckle

(100.3010) Image processing : Image reconstruction techniques

(100.5070) Image processing : Phase retrieval

(120.6150) Instrumentation, measurement, and metrology : Speckle imaging

**Citation**

R. B. Holmes, K. Hughes, P. Fairchild, B. Spivey, and A. Smith, "Description and simulation of an active imaging technique utilizing two speckle fields: root reconstructors," J. Opt. Soc. Am. A **19**, 444-457 (2002)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-19-3-444

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### References

- V. I. Tatarskii, Wave Propagation in a Turbulent Medium, translated by R. S. Silverman (McGraw-Hill, New York, 1961).
- K. T. Knox and B. J. Thompson, “Recovery of images from astronomically degraded short-exposure photographs,” Astrophys. J. Lett. 193, L45–L48 (1974).
- A. W. Lohmann, G. Weigelt, and B. Wirnitzer, “Speckle masking in astronomy: triple correlation theory and applications,” Appl. Opt. 22, 4028–4037 (1983).
- J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21, 2758–2769 (1982).
- A. C. S. Readhead, T. S. Nakajima, T. J. Pearson, G. Neugebauer, J. B. Oke, and W. L. W. Sargent, “Diffraction-limited imaging with ground-based optical telescopes,” Astron. J. 95, 1278–1296 (1988).
- J. Hardy, J. Lefebvre, and C. Koliopoulis, “Real time atmospheric compensation,” J. Opt. Soc. Am. 67, 360–369 (1977).
- J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, New York, 1975), pp. 9–68.
- Paul S. Idell, J. R. Fienup, and Ron S. Goodman, “Image synthesis from nonimaged laser-speckle patterns,” Opt. Lett. 12, 858–860 (1987).
- M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, UK, 1999), p. 356.
- R. A. Hutchin, “Sheared coherent interferometric photography: a technique for lensless imaging,” in Digital Image Recovery and Synthesis II, P. S. Idell, ed., Proc. SPIE 2029, 161–168 (1993).
- S. M. Stahl, R. M. Kremer, P. W. Fairchild, K. Hughes, B. A. Spivey, and R. Stagat, “Sheared-beam coherent image reconstruction,” in Applications of Digital Image Processing XIX, A. G. Tescher, ed., Proc. SPIE 2847, 150–158 (1996).
- M. Born and E. Wolf, Principles of Optics, 7th ed., pp. 572–577 (Cambridge U. Press, Cambridge, UK, 1999).
- J. W. Goodman, Statistical Optics (Wiley, New York, 1985), Chap. 5.
- Yu. M. Bruck and L. G. Sodin, “On the ambiguity of the image reconstruction problem,” Opt. Commun. 30, 304–308 (1979).
- H. B. Deighton, M. S. Scivier, and M. A. Fiddy, “Solution of the two-dimensional phase-retrieval problem,” Opt. Lett. 10, 250–251 (1985).
- R. G. Lane, W. R. Fright, and R. H. T. Bates, “Direct phase retrieval,” IEEE Trans. Acoust. Speech Signal Process. ASSP-35, 520–525 (1987).
- D. Israelevitz and J. S. Lim, “A new direct algorithm for image reconstruction from Fourier transform magnitude,” IEEE Trans. Acoust. Speech Signal Process. ASSP-35, 511–519 (1987).
- J. R. Fienup, “Reconstruction of a complex-valued object from the modulus of its Fourier transform using a support constraint,” J. Opt. Soc. Am. A 4, 118–123 (1987).
- R. G. Lane and R. H. T. Bates, “Automatic multidimensional deconvolution,” J. Opt. Soc. Am. A 4, 180–188 (1987).
- J. R. Fienup and C. C. Wackerman, “Phase-retrieval stagnation problems and solutions,” J. Opt. Soc. Am. A 3, 1897–1907 (1986).
- C. C. Wackerman and A. E. Yagle, “Use of Fourier domain real-plane zeros to overcome a phase retrieval stagnation,” J. Opt. Soc. Am. A 8, 1898–1904 (1991).
- C. C. Wackerman and A. E. Yagle, “Phase retrieval and estimation with use of real-plane zeros,” J. Opt. Soc. Am. A 11, 2016–2026 (1994).
- P. J. Bones, C. R. Parker, B. L. Satherley, and R. W. Watson, “Deconvolution and phase retrieval with use of zero sheets,” J. Opt. Soc. Am. A 12, 1842–1857 (1995).
- T. J. Schulz, “Multiframe blind deconvolution of astronomical images,” J. Opt. Soc. Am. A 10, 1064–1073 (1993).
- R. H. T. Bates, B. K. Quek, and C. R. Parker, “Some implications of zero sheets for blind deconvolution and phase retrieval,” J. Opt. Soc. Am. A 7, 468–479 (1990).
- P. Chen, M. A. Fiddy, A. H. Greenaway, and Y. Wang, “Zero estimation for blind deconvolution from noisy sampled data,” in Digital Image Recovery and Synthesis II, P. S. Idell, ed., Proc. SPIE 2029, 14–22 (1993).
- D. C. Ghiglia, L. A. Romero, and G. A. Mastin, “Systematic approach to two-dimensional blind deconvolution by zero-sheet separation,” J. Opt. Soc. Am. A 10, 1024–1036 (1993).
- B. R. Hunt, T. L. Overman, and P. Gough, “Image reconstruction from pairs of Fourier transform magnitude,” Opt. Lett. 23, 1123–1125 (1998).
- B. Ya Zeldovich, Principles of Phase Conjugation (Springer-Verlag, New York, 1985), Chap. 3.
- M. S. Scivier and M. A. Fiddy, “Phase ambiguities and the zeros of multidimensional band-limited functions,” J. Opt. Soc. Am. A 2, 693–697 (1985).
- E. P. Wallner, “Optimal wave-front correction using slope measurements,” J. Opt. Soc. Am. 73, 1771–1776 (1983).
- J. D. Downie and J. W. Goodman, “Optimal wave-front correction with segmented mirrors,” Appl. Opt. 28, 5326–5332 (1989).
- R. G. Paxman, T. J. Schulz, and J. R. Fienup, “Joint estimation of object and aberrations by using phase diversity,” J. Opt. Soc. Am. A 9, 1072–1085 (1992).
- R. Holmes, K. Hughes, P. Fairchild, B. Spivey, and A. Smith, “Description and simulation of an active imaging technique utilizing two speckle fields: iterative reconstructors,” J. Opt. Soc. Am. A 19, 458–471 (2002).
- R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plan pictures,” Optik 35, 237–246 (1972).
- V. S. R. Gudimetla and J. F. Holmes, “Probability density function of the intensity for a laser-generated speckle field after propagation through the turbulent atmosphere,” J. Opt. Soc. Am. 72, 1213–1218 (1982), and references therein.
- M. H. Lee, J. F. Holmes, and J. R. Kerr, “Statistics of speckle propagation through the turbulent atmosphere,” J. Opt. Soc. Am. 66, 1164–1172 (1976).
- G. Parry, “Speckle patterns in partially coherent light,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, New York, 1975), Eq. 3.19.
- P. S. Idell and A. Webster, “Resolution limits for coherent optical imaging: signal-to-noise analysis in the spatial frequency domain,” J. Opt. Soc. Am. A 9, 43–56 (1992).
- R. B. Holmes, B. Spivey, and A. Smith, “Recovery of images from two-color, pupil-plane speckle data using object-plane root-matching and pupil-plane error minimiziation,” in Digital Image Reconstruction and Synthesis IV, P. S. Idell and T. J. Schulz, eds., Proc. SPIE 3815, 70–89 (1999).

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