Coded-Aperture Imaging

  • R. G. Simpson
  • H. H. Barrett


In a photographic camera, the camera lens forms an image of the object and the image is detected by the photographic film. In the Anger camera described in Chapter 4, the pinhole aperture or the multihole collimator performs the imaging operation while a detector system consisting of a scintillation crystal and an arrangement of photomultiplier tubes detects the image. The detector system in the Anger camera is very efficient and records almost every X-ray or γ-ray photon that arrives with an energy within the preselected energy window. Unfortunately, the imaging system severely limits the number of photons that arrive. A collimator typically passes only 0.01% of the radiation emitted by the object. Since the statistical quality of the images formed in this way is dependent on the number of photons collected from a single element of the object, one needs to collect as many photons as possible. Patient-dose restrictions limit the number of photons available, while exposure time is limited by temporal-resolution requirements in a dynamic study, by image degradation due to patient motion, by patient fatigue, or by the expense involved in tying up a clinical instrument for extended periods.


Point Spread Function Object Plane Object Point Zone Plate Imaging Geometry 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Abels, J.G. (1968), Fourier transform photography: A new method for X-ray astronomy, Proc. Astron. Soc. Austr. 1: 1:72.Google Scholar
  2. Akcasu, A.Z., May, R.S., Knoll, G.F., Rogers, W.L., Koral, K.F., Jones, L.W. (1974), Coded aperture gamma ray imaging with stochastic apertures, Opt. Eng. 13: 117.CrossRefGoogle Scholar
  3. Barrett, H.H. (1972a), Pulse compression techniques in nuclear medicine, Proc. 60: 723.CrossRefGoogle Scholar
  4. Barrett, H.H. (1972b), Fresnel zone plate imaging in nuclear medicine, J. Nucl. Med. 13: 382.PubMedGoogle Scholar
  5. Barrett, H.H., DeMeester, G.D. (1974), Quantum noise in fresnel zone plate imaging, Appl. Opt. 13: 1100.PubMedCrossRefGoogle Scholar
  6. Barrett, H. H., Horrigan, F. A. (1973), Fresnel zone plate imaging of gamma rays; Theory, Appl. Opt. 12: 2686.PubMedCrossRefGoogle Scholar
  7. Barrett, H.H., Swindell, W. (1977), Analog reconstruction methods for transaxial tomography, Proc. IEEE 65: 89.CrossRefGoogle Scholar
  8. Barrett, H.H., Wilson, D.T., DeMeester, G.D. (1972), The use of half-tone screens in Fresnel zone plate imaging of incoherent sources, Opt. Commun. 5: 398.CrossRefGoogle Scholar
  9. Barrett, H.H., DeMeester, G.D.,Wilson, D.T., Farmelant, M.H. (1973a), Recent advances in Fresnel zone plate imaging, in Medical Radioisotope Scintigraphy 1972, Vol. I, International Atomic Energy Agency, Vienna.Google Scholar
  10. Barrett, H.H., Wilson, D.T., DeMeester, G.H., Sharfman, H. (1973b), Fresnel zone plate imaging in radiology and nuclear medicine, Opt. Eng. 12: 8.Google Scholar
  11. Barrett, H.H., Stoner, W.W., Wilson, D.T., DeMeester, G.D. (1974), Coded apertures derived from the Fresnel zone plate, Opt. Eng. 13: 539.CrossRefGoogle Scholar
  12. Born, M., Wolf, E. (1975), Principles of Optics, Pergamon Press, New York.Google Scholar
  13. Bracewell, R. (1965), The Fourier transform and its applications, McGraw-Hill, New York.Google Scholar
  14. Brown, C.M. (1972), Multiplex imaging and random arrays, Ph.D. dissertation, University of Chicago.Google Scholar
  15. Brown, C.M. (1974), Multiplex imaging with multiple-pinhole cameras, J. Appl. Phys. 45: 4.Google Scholar
  16. Budinger, T.F., Macdonald, B. (1975), Reconstruction of Fresnel coded gamma camera images by digital computer, J. Nucl. Med. 16: 309.PubMedGoogle Scholar
  17. Burckhardt, C.B., Doherty, E.T. (1968), Formation of carrier frequency holograms with an on-axis reference beam, Appl. Opt. 7: 1191.PubMedCrossRefGoogle Scholar
  18. Calabro, D., Wolf, J.K. (1968), On the synthesis of two-dimensional arrays with desirable correlation properties, Inf. Control 11: 537.CrossRefGoogle Scholar
  19. Chang, L.T. (1976), Radionuclide imaging with coded apertures and three-dimensional image reconstruction from focal-plane tomography, Ph.D. thesis, University of California Berkeley.Google Scholar
  20. Chang, L.T., Kaplan, S.N., Macdonald, B., Perez-Mendez, V., Shiraishi, L. (1974), A method of tomographic imaging using a multiple pinhole-coded aperture, J. Nucl. Med. 15: 1063.PubMedGoogle Scholar
  21. Dance, D.R., Wilson, B.C., Parker, R.P. (1975), Digital reconstruction of point sources imaged by a zone plate camera, Phys. Med. Biol. 20: 747.PubMedCrossRefGoogle Scholar
  22. Davenport, W.B., Jr., Root, W.L. (1958), An introduction to the theory of random signals and noise, McGraw-Hill, New York.Google Scholar
  23. Dicke, R.H. (1968), Scatter-hole cameras for X-rays and gamma rays, Astrophys. J. 153: L101.CrossRefGoogle Scholar
  24. Dowdy, J.E., Tipton, M.D., Murry, R.C., Stokely, E.M. (1977), Coded apertures for nuclear medicine imaging, Appl. Radiol. 6(4): 145 (July-Aug.)Google Scholar
  25. Farmelant, M.H., DeMeester, G.D., Wilson, D., Barrett, H. (1975), Initial clinical experiences with a Fresnel zone plate imager, J. Nucl. Med. 16: 183.PubMedGoogle Scholar
  26. Fenimore, E. E., Cannon, T. M. (1978), Coded aperture imaging with uniformly redundant arrays, Appl. Opt. 17: 337.PubMedCrossRefGoogle Scholar
  27. Gaskill, J.D. (1978), Linear Systems, Fourier Transforms, and Optics, Wiley, New York.Google Scholar
  28. Gaskill, J.D., Whitehead, F.R., Gray, J.E., O’Mara, R.E. (1972), Matched filter resto-ration of coded gamma and X-ray imagery, Proceedings of the SPIE, Vol. 35, November 29–30, Chicago,1972, SPIE, Redondo Beach, Cal., p. 193.Google Scholar
  29. Girard, A. (1963), Spectrometre a Grilles, Appl. Opt. 2: 79.CrossRefGoogle Scholar
  30. Golay, M.J.E. (1949), Multislit spectrometry, J. Opt. Soc. Am. 39: 437.PubMedCrossRefGoogle Scholar
  31. Golay, M.J.E. (1951), Static multislit spectrometry and its application to the panoramic display of infrared spectra, J. Opt. Soc. Am. 41: 468.PubMedCrossRefGoogle Scholar
  32. Golay, M.J.E. (1971), Point arrays having compact, nonredundant autocorrelations, J. Opt. Soc. Am. 61: 272.CrossRefGoogle Scholar
  33. Gottlieb, P. (1968), A television scanning scheme for a detector-noise-limited system, IEEE Trans. Inf. Theory IT 14: 428.CrossRefGoogle Scholar
  34. Groh, G., Hayat, G.S., Stroke, G.W. (1972), X-ray and gamma-ray imaging with multiple-pinhole cameras using a posteriori image synthesis, Appl. Opt. 11: 931.PubMedCrossRefGoogle Scholar
  35. Guha, D.K. (1976), Imaging by shadow casting, Ph.D. dissertation, University of Rhode Island.Google Scholar
  36. Harwitt, M. (1971), Spectrometric imager, Appl. Opt. 10: 1415.CrossRefGoogle Scholar
  37. Hayat, G.S. (1971), X-Ray and y-ray imaging with multiple-pinhole cameras, Ph.D. thesis, SUNY Stony Brook, New York.Google Scholar
  38. Jaszczak, R.J., Moore, F.E., Whitehead, F.R. (1974), Use of an array of three off-axis zone plates for large field of view gamma-ray imaging, in Proceedings of the SPIE Seminar on Application of Optical Instrumentation in Medicine II, Chicago, 1974.Google Scholar
  39. Klauder, J R., Price, A C., Darlingtin, D., Ablersheim, W.J. (1960), The theory and design of chirp radars, Bell Syst. Tech. J. 39: 745.Google Scholar
  40. Koral, K.F., Rogers, W.L., Knoll, G.F. (1975), Digital tomographic imaging with a time-modulated pseudorandom coded aperture and an Anger camera, J. Nucl. Med. 16: 402.PubMedGoogle Scholar
  41. Koral, K.F., Knoll, G.F., Rogers, W.L. (1977), Emission tomography with time-coded apertures, in A Review of Information Processing in Medical Imaging, Proceedings of the Fifth International Conference, Nashville, Tennessee, Vanderbilt University, 1977 (A.B. Brill, P.R. Price, W.J. McClain, M.W. Lindsay, eds.), pp. 252–265.Google Scholar
  42. Koral, K.F., Freitas, J.E., Rogers, W.L., Keyes, J. W.,Jr. (1979), Thyroid scintigraphy with time-coded aperture, J. Nucl. Med. 20: 345–349.PubMedGoogle Scholar
  43. Lindner, J. (1975), Binary sequences up to length 40 with best possible autocorrelation function, Electron. Lett. 11: 507.CrossRefGoogle Scholar
  44. Macdonald, B., Chang, L.T., Perez-Mendez, V., Shiraishi, L. (1974), Gamma-ray imaging using a Fresnel zone plate aperture, multiwire proportional chamber detector, and computer reconstruction, IEEE Trans. Nucl. Sci. 21: 672.CrossRefGoogle Scholar
  45. Macdonald, B.’ Chang, L.T., Perez-Mendez, V. (1975), Three dimensional image re-construction using pinhole arrays, in International Optical Computing Conference, Washington, D.C., April 23–25, 1975.Google Scholar
  46. Macovski, A. (1974), Gamma-ray imaging system using modulated apertures, Phys. Med. Biol. 19: 523.PubMedCrossRefGoogle Scholar
  47. MacWilliams, F.J., Sloane, N.J.A. (1976), Pseudo-random sequences and arrays, Proc. IEEE 64: 1715.CrossRefGoogle Scholar
  48. May, R.S. (1974), Stochastic aperture techniques in gamma-ray image formation, Ph.D. thesis, University of Michigan.Google Scholar
  49. May, R.S., Akcasu, Z., Knoll, G.F. (1974), Gamma ray imaging with stochastic apertures, Appl. Opt. 13: 2589.PubMedCrossRefGoogle Scholar
  50. Mertz, L. (1965), Transformations in Optics, Wiley, New York.Google Scholar
  51. Mertz, L., Young, N.O. (1961), Fresnel transformation of images, in Proceedings of the International Conference on Optical Instruments, Chapman and Hall, London, p. 305.Google Scholar
  52. Metz, C.E. (1969), A mathematical investigation of radioisotope scan image processing, Ph. D. dissertation, University of Pennsylvania.Google Scholar
  53. Metz, C.E., Beck, R.N, (1974), Quantitative effects of stationary linear image processing on noise and resolution of structure in radionuclide images, J. Nucl. Med. 15: 164.PubMedGoogle Scholar
  54. Miller, E. (1976), Aperture coding with a rotating slit, in Program of the Optical Society of America Annual Meeting, Tucson, Arizona, October 1976, American Institute of Physics, New York.Google Scholar
  55. Moffat, A.T. (1968), Minimum-redundancy linear arrays, IEEE Trans. Antennas Propag. AP-16: 172Google Scholar
  56. Papoulis, A. (1962), The Fourier integral and its applications, McGraw-Hill, New York.Google Scholar
  57. Pennington, K.S., Will, P.M., Shelton, G.L. (1970), Grid coding: A technique for extraction of differences from scenes, Opt. Commun. 2: 113.CrossRefGoogle Scholar
  58. Rogers, W. L.’ Han, K.S., Jones, L. W., Beierwaltes, W. H. (1972), Application of a Fresnel zone plate to gamma-ray imaging, J. Nucl. Med. 13: 612.PubMedGoogle Scholar
  59. Rogers, W.L., Jones, L. W., Beierwaltes, W.H. (1973), Imaging in nuclear medicine with incoherent holography, Opt. Eng. 12: 13.CrossRefGoogle Scholar
  60. Simpson, R.G. (1976), Decoding of annular coded aperture images, in Program of the Optical Society of America Annual Meeting, Tucson, Arizona, October 1976, American Institute of Physics, New York.Google Scholar
  61. Simpson, R.G., Barrett, H.H., Subach, J. A., Fisher, H.D. (1975), Digital processing of annular coded aperture imagery, Opt. Eng. 14: 490.CrossRefGoogle Scholar
  62. Simpson, R.G., Barrett, H.H., Fisher, H.D. (1976), Decoding techniques for use with annular coded apertures, in International Conference on Applications of Holography and Optical Data Processing, Jerusalem, Israel, Aug. 23–26, 1976.Google Scholar
  63. Simpson, R.G., Barrett, H.H., Kelly, J.G., Stalker, K.T. (1977), Some applications of one-dimensional coded apertures, in Proceedings of the SPIE, X-Ray Imaging. Vol. 106, p. 71.CrossRefGoogle Scholar
  64. Stroke, G. W., Hayat, G.S., Hoover, R.B., Underwood, J.H. (1969), X-ray imaging with multiple pinhole cameras using a posteriori holographic image synthesis, Opt. Commun. 1: 138.CrossRefGoogle Scholar
  65. Tamura, P. (1976), private communication.Google Scholar
  66. Tanaka, E., Iinuma, T.A. (1975), Image processing for coded aperture imaging and an attempt at rotating slit imaging, in Information Processing in Scintigraphy ( C. Raynaud and A. Todd-Pokropek, eds.), Commissariat a l’Energie Atomique, Orsay, France.Google Scholar
  67. Tipton, M.D., Dowdy, J.E., Caulfield, H.J. (1973), Coded aperture imaging with on- axis Fresnel zone plates, Opt. Eng. 12: 166.CrossRefGoogle Scholar
  68. Tipton, M.D., Dowdy, J.E., Bonte, F.J., Caulfield, H.J. (1974), Coded aperture imaging using on-axis Fresnel zone plates and extended gamma-ray sources, Radiology 112: 155.PubMedGoogle Scholar
  69. Tipton, M.D., Dowdy, J.D., Stokely, E.M. (1976), Background suppression of multiple pinhole-coded aperture scintigrams, in 4th International Conference on Medical Physics, Sponsored by AAPM, Ottawa, Canada, July 1976.Google Scholar
  70. Walton, P.W. (1973), An aperture imaging system with instant decoding and tomographic capabilities, J. Nucl. Med. 14: 861.PubMedGoogle Scholar
  71. Weiss, H. (1975), Nonredundant point distribution for coded aperture imaging with application to 3-dimensional online X-ray information retrieving, IEEE Trans. Comp. 24: 391–394.CrossRefGoogle Scholar
  72. Whitehead, F.R. (1976), A comparison of coded aperture imaging systems containing zone plate and random-phase code functions, Ph.D. dissertation, University of Arizona.Google Scholar
  73. Wilson, D.T., Barrett, H.H., DeMeester, G.D., Farmelant, M.H. (1973), Point source artifacts in Fresnel zone plate imaging, Opr. Eng. 12: 133.Google Scholar
  74. Wilson, B.C., Parker, R.P., Dance, D. R. (1975), Digital processing of images from a zone plate camera, Phys. Med. Biol. 20: 757.PubMedCrossRefGoogle Scholar
  75. Wouters, A., Simon, K.M., Hirschberg, J.G. (1973), Direct method of decoding multiple images, Appl. Opt. 12: 1871.PubMedCrossRefGoogle Scholar
  76. Young, N.O. (1963), Photography without lenses or mirrors, Sky Telescope 25: 8.Google Scholar

Copyright information

© Plenum Press, New York 1980

Authors and Affiliations

  • R. G. Simpson
    • 1
  • H. H. Barrett
    • 1
  1. 1.Optical Sciences CenterUniversity of ArizonaTucsonUSA

Personalised recommendations