Abstract

It is often possible to reduce the requirements on an imaging system by placing greater demands either on an illumination system or on post-detection processing of the data collected by the system. An extreme example of this is a system with no receiver optics whatsoever. By illuminating an object or scene with coherent light having a shaped illumination pattern, the receiver can be a simple detector array with no imaging optics, detecting the speckle intensity pattern reflected from the object; an image of the object can be reconstructed by a phase retrieval algorithm.

© 2006 Optical Society of America

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References

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  1. E.N. Leith and J. Upatnieks, "Reconstructed Wavefronts and Communication Theory," J. Opt. Soc. Am. 52, 1123-1130 (l962).
    [CrossRef]
  2. J.W. Goodman, Introduction to Fourier Optics, 2nd Ed. (McGraw-Hill, San Francisco, l996).
  3. P.S. Idell, J.R. Fienup and R.S. Goodman, "Image Synthesis from Nonimaged Laser Speckle Patterns," Opt. Lett. 12, 858-860 (1987).
    [CrossRef] [PubMed]
  4. J.R. Fienup and P.S. Idell, "Imaging Correlography with Sparse Arrays of Detectors," Opt. Engr. 27, 778-784 (1988).
  5. R.G. Paxman, J.R. Fienup, M.F. Reiley, and B.J. Thelen, "Phase Retrieval with an Opacity Constraint in LAser IMaging (PROCLAIM)," in Technical Digest on Signal Recovery and Synthesis 6 (Optical Society of America, Washington, D.C., 1998), pp. 34-36.
  6. 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).
    [CrossRef]
  7. J.N. Cederquist, J.R. Fienup, J.C. Marron and R.G. Paxman, "Phase Retrieval from Experimental Far-Field Data," Opt. Lett. 13, 619-621 (1988).
    [CrossRef] [PubMed]
  8. T.R. Crimmins, J.R. Fienup and B.J. Thelen, "Improved Bounds on Object Support from Autocorrelation Support and Application to Phase Retrieval," J. Opt. Soc. Am. A 7, 3-13 (1990).
    [CrossRef]
  9. J.R. Fienup and A.M. Kowalczyk, "Phase Retrieval for a Complex-Valued Object by Using a Low-Resolution Image," J. Opt. Soc. Am. A 7, 450-458 (1990).
    [CrossRef]
  10. R.G. Paxman, J.R. Fienup and J.T. Clinthorne, "Effect of Tapered Illumination and Fourier Intensity Errors on Phase Retrieval," in Digital Image Recovery and Synthesis, Proc. SPIE 828-28 (1987), pp. 184-189.
  11. J.R. Fienup and C.C. Wackerman, "Phase Retrieval Stagnation Problems and Solutions," J. Opt. Soc. Am. A 3, 1897-1907 (1986).
    [CrossRef]
  12. J.R. Fienup, "Reconstruction of Objects Having Latent Reference Points," J. Opt. Soc. Am. 73, 1421-1426 (l983).
    [CrossRef]
  13. T.R. Crimmins, "Phase Retrieval for Discrete Functions with Support Constraints," J. Opt. Soc. Am. A 4, 124-34 (1987).
    [CrossRef]
  14. Yu.M. Bruck and L.G. Sodin, "On the Ambiguity of the Image Reconstruction Problem," Opt. Commun. 30, 304-308 (l979)
    [CrossRef]
  15. T.R. Crimmins and J.R. Fienup, "Uniqueness of Phase Retrieval for Functions with Sufficiently Disconnected Support," J. Opt. Soc. Am. 73, 218-221 (l983) .
    [CrossRef]
  16. J.R. Fienup, "Phase Retrieval Algorithms: A Comparison," Appl. Opt. 21, 2758-2769 (1982).
    [CrossRef] [PubMed]
  17. J.R. Fienup, "Phase-Retrieval Algorithms for a Complicated Optical System," Appl. Opt. 32, 1737-1746 (1993).
    [CrossRef] [PubMed]
  18. A. Tippie and J.R. Fienup, "X-Ray Diffraction Imaging Methods using Phase Retrieval Methods," REU Presentation, University of Rochester, August 6, 2004
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  20. J.R. Fienup, "Lensless Coherent Imaging with Shaped Illumination and Phase-Retrieval Image Reconstruction," in Computational Optical Sensing and Imaging, Topical Meeting of the Optical Society of America (June 2005), paper JMA1.

Appl. Opt.

J.R. Fienup, "Phase Retrieval Algorithms: A Comparison," Appl. Opt. 21, 2758-2769 (1982).
[CrossRef] [PubMed]

J.R. Fienup, "Phase-Retrieval Algorithms for a Complicated Optical System," Appl. Opt. 32, 1737-1746 (1993).
[CrossRef] [PubMed]

Comp. Optical Sensing and Imaging

J.R. Fienup, "Lensless Coherent Imaging with Shaped Illumination and Phase-Retrieval Image Reconstruction," in Computational Optical Sensing and Imaging, Topical Meeting of the Optical Society of America (June 2005), paper JMA1.

Frontiers in Optics

J.R. Fienup, "Coherent Imaging with Illumination Optics Designed for the Reconstruction Algorithm," Proceedings of the Frontiers in Optics 2004 (Annual Meeting of the Optical Society of America), October 2004, paper FTuO4.

J. Opt. Soc. Am.

T.R. Crimmins and J.R. Fienup, "Uniqueness of Phase Retrieval for Functions with Sufficiently Disconnected Support," J. Opt. Soc. Am. 73, 218-221 (l983) .
[CrossRef]

J.R. Fienup, "Reconstruction of Objects Having Latent Reference Points," J. Opt. Soc. Am. 73, 1421-1426 (l983).
[CrossRef]

E.N. Leith and J. Upatnieks, "Reconstructed Wavefronts and Communication Theory," J. Opt. Soc. Am. 52, 1123-1130 (l962).
[CrossRef]

J. Opt. Soc. Am. A

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).
[CrossRef]

T.R. Crimmins, J.R. Fienup and B.J. Thelen, "Improved Bounds on Object Support from Autocorrelation Support and Application to Phase Retrieval," J. Opt. Soc. Am. A 7, 3-13 (1990).
[CrossRef]

J.R. Fienup and A.M. Kowalczyk, "Phase Retrieval for a Complex-Valued Object by Using a Low-Resolution Image," J. Opt. Soc. Am. A 7, 450-458 (1990).
[CrossRef]

T.R. Crimmins, "Phase Retrieval for Discrete Functions with Support Constraints," J. Opt. Soc. Am. A 4, 124-34 (1987).
[CrossRef]

J.R. Fienup and C.C. Wackerman, "Phase Retrieval Stagnation Problems and Solutions," J. Opt. Soc. Am. A 3, 1897-1907 (1986).
[CrossRef]

Opt. Commun.

Yu.M. Bruck and L.G. Sodin, "On the Ambiguity of the Image Reconstruction Problem," Opt. Commun. 30, 304-308 (l979)
[CrossRef]

Opt. Engr.

J.R. Fienup and P.S. Idell, "Imaging Correlography with Sparse Arrays of Detectors," Opt. Engr. 27, 778-784 (1988).

Opt. Lett.

J.N. Cederquist, J.R. Fienup, J.C. Marron and R.G. Paxman, "Phase Retrieval from Experimental Far-Field Data," Opt. Lett. 13, 619-621 (1988).
[CrossRef] [PubMed]

P.S. Idell, J.R. Fienup and R.S. Goodman, "Image Synthesis from Nonimaged Laser Speckle Patterns," Opt. Lett. 12, 858-860 (1987).
[CrossRef] [PubMed]

Proc. SPIE

R.G. Paxman, J.R. Fienup and J.T. Clinthorne, "Effect of Tapered Illumination and Fourier Intensity Errors on Phase Retrieval," in Digital Image Recovery and Synthesis, Proc. SPIE 828-28 (1987), pp. 184-189.

Signal Recovery and Synthesis

R.G. Paxman, J.R. Fienup, M.F. Reiley, and B.J. Thelen, "Phase Retrieval with an Opacity Constraint in LAser IMaging (PROCLAIM)," in Technical Digest on Signal Recovery and Synthesis 6 (Optical Society of America, Washington, D.C., 1998), pp. 34-36.

Other

J.W. Goodman, Introduction to Fourier Optics, 2nd Ed. (McGraw-Hill, San Francisco, l996).

A. Tippie and J.R. Fienup, "X-Ray Diffraction Imaging Methods using Phase Retrieval Methods," REU Presentation, University of Rochester, August 6, 2004

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Figures (9)

Fig. 1.
Fig. 1.

Lensless imaging with a detector array, sensing the intensity of a laser speckle pattern backscattered from the object. [Figure modified from a figure from Brad Tousley (DARPA/TTO)]

Fig. 2.
Fig. 2.

Radial cut through expanding weighting function on the Fourier magnitude. Lower curves are used for earlier iterations and upper curves for later iterations. The diffraction cutoff frequency is at pixel 192.

Fig. 3.
Fig. 3.

Simulated data. (a) Magnitude of SAR complex-valued SAR image, (b) illumination pattern, (c) illuminated image.

Fig. 4.
Fig. 4.

Cut through illumination pattern amplitude (lower curve). Upper (dashed) curve is 50x.

Fig. 5.
Fig. 5.

Simulated speckle pattern collected at sensor.

Fig. 6.
Fig. 6.

Partially reconstructed images with increasing iterations and increasing resolution owing to the use of the expanding Fourier magnitude. (a) through (f) are for the first six weighting functions shown in Fig. 2.

Fig. 7.
Fig. 7.

Illustration of extended patching method. (a)–(c) Three partially reconstructed images from different starting guesses; (d)–(f) same, but overexposed by a factor of 20; (g)–(i) same, but with region of object support masked out; (j)–(l), the magnitudes of the Fourier transforms of (g)–(i) respectively, showing the regions in which the Fourier transforms of the images in (a)–(c) are in error.

Fig. 8.
Fig. 8.

Imaging example with triangular illumination pattern. (a) Illuminated object, (b) example partially reconstructed image, (c) result of patching algorithm.

Fig. 9.
Fig. 9.

Images reconstructed with different SNRs. (a) Illuminated object (for comparison); reconstructed images with SNR of (b) 32, (c) 10, (d) 6.3, (e) 3.2.

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