Abstract

As a result of interest in imaging strongly scattering targets, the Air Force Research Laboratory is making available to the community sets of data from various targets. We describe a nonlinear filtering technique, namely, homomorphic filtering, which we have applied to recover an image of the target from the backpropagated field calculated from the scattering data. We show new results for targets that other methods, especially linearized methods, are unable to image. While we obtain good images with real data, convolutional effects arising from limited data can sometimes degrade performance.

© 1999 Optical Society of America

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  1. M. Slaney, A. C. Kak, L. E. Larsen, “Limitations of imaging with first-order diffraction tomography,” IEEE Trans. Microwave Theory Tech. MTT-32, 860–874 (1984).
    [CrossRef]
  2. F. C. Lin, M. A. Fiddy, “Image estimation from scattered field data,” Int. J. Imaging Syst. Technol. 2, 76–95 (1990).
    [CrossRef]
  3. E. Wolf, “Three-dimensional structure determination of semi-transparent objects from holographic data,” Opt. Commun. 1, 153–156 (1969).
    [CrossRef]
  4. N. Joachimowicz, Ch. Pichot, J. P. Hugonin, “Inverse scattering: an iterative numerical method for electromagnetic imaging,” IEEE Trans. Antennas Propag. 29, 1742–1752 (1991).
    [CrossRef]
  5. R. E. Kleinman, P. M. Van den Berg, “An extended range modified gradient technique for profile inversion,” Radio Sci. 28, 877–884 (1993).
    [CrossRef]
  6. G. P. Otto, W. Chew, “Microwave scattering—local shape function imaging for improved resolution of strong scatterers,” IEEE Trans. Microwave Theory Tech. 42, 137–141 (1994).
    [CrossRef]
  7. R. V. McGahan, R. E. Kleinman, eds., “Special session on image reconstruction using real data,” IEEE Antennas Propag. Mag.38, 39–59 (1996).
    [CrossRef]
  8. R. V. McGahan, R. E. Kleinman, eds., “Second annual special session on image reconstruction using real data,” IEEE Antennas Propag. Mag.39, 7–32 (1997).
    [CrossRef]
  9. R. V. McGahan, “Scattering experiments at the Ipswich electromagnetic measurements facility: swept bistatic angle measurement system,” (Rome Laboratory, Hanscom Air Force Base, Mass., 1991).
  10. M. G. Cote, “Automated swept-angle bistatic scattering measurements using continuous wave radar,” IEEE Trans. Instrum. Meas. 41, 185–192 (1992).
    [CrossRef]
  11. D. Dudgeon, R. M. Mersereau, Multidimensional Digital Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1984).
  12. J. B. Morris, M. A. Fiddy, D. A. Pommet, “Nonlinear filtering applied to single-view backpropagated images of strong scatterers,” J. Opt. Soc. Am. A 13, 1506–1515 (1996).
    [CrossRef]
  13. J. B. Morris, R. V. McGahan, J. L. Schmitz, R. M. Wing, D. A. Pommet, M. A. Fiddy, “Imaging of strongly scattering targets from real data,” IEEE Antennas Propag. Mag. 39, 22–26 (1997).
    [CrossRef]
  14. J. B. Morris, D. A. Pommet, R. V. McGahan, M. A. Fiddy, “Imaging of unknown targets from measured scattering data,” IEEE Antennas Propag. Mag. 38, 53–56 (1996).
    [CrossRef]
  15. D. A. Pommet, R. A. Marr, U. H. W. Lammers, R. V. McGahan, J. B. Morris, M. A. Fiddy, “Imaging using limited-angle backscattered data from real targets,” IEEE Antennas Propag. Mag. 39, 19–22 (1997).
    [CrossRef]

1997 (2)

J. B. Morris, R. V. McGahan, J. L. Schmitz, R. M. Wing, D. A. Pommet, M. A. Fiddy, “Imaging of strongly scattering targets from real data,” IEEE Antennas Propag. Mag. 39, 22–26 (1997).
[CrossRef]

D. A. Pommet, R. A. Marr, U. H. W. Lammers, R. V. McGahan, J. B. Morris, M. A. Fiddy, “Imaging using limited-angle backscattered data from real targets,” IEEE Antennas Propag. Mag. 39, 19–22 (1997).
[CrossRef]

1996 (2)

J. B. Morris, M. A. Fiddy, D. A. Pommet, “Nonlinear filtering applied to single-view backpropagated images of strong scatterers,” J. Opt. Soc. Am. A 13, 1506–1515 (1996).
[CrossRef]

J. B. Morris, D. A. Pommet, R. V. McGahan, M. A. Fiddy, “Imaging of unknown targets from measured scattering data,” IEEE Antennas Propag. Mag. 38, 53–56 (1996).
[CrossRef]

1994 (1)

G. P. Otto, W. Chew, “Microwave scattering—local shape function imaging for improved resolution of strong scatterers,” IEEE Trans. Microwave Theory Tech. 42, 137–141 (1994).
[CrossRef]

1993 (1)

R. E. Kleinman, P. M. Van den Berg, “An extended range modified gradient technique for profile inversion,” Radio Sci. 28, 877–884 (1993).
[CrossRef]

1992 (1)

M. G. Cote, “Automated swept-angle bistatic scattering measurements using continuous wave radar,” IEEE Trans. Instrum. Meas. 41, 185–192 (1992).
[CrossRef]

1991 (1)

N. Joachimowicz, Ch. Pichot, J. P. Hugonin, “Inverse scattering: an iterative numerical method for electromagnetic imaging,” IEEE Trans. Antennas Propag. 29, 1742–1752 (1991).
[CrossRef]

1990 (1)

F. C. Lin, M. A. Fiddy, “Image estimation from scattered field data,” Int. J. Imaging Syst. Technol. 2, 76–95 (1990).
[CrossRef]

1984 (1)

M. Slaney, A. C. Kak, L. E. Larsen, “Limitations of imaging with first-order diffraction tomography,” IEEE Trans. Microwave Theory Tech. MTT-32, 860–874 (1984).
[CrossRef]

1969 (1)

E. Wolf, “Three-dimensional structure determination of semi-transparent objects from holographic data,” Opt. Commun. 1, 153–156 (1969).
[CrossRef]

Chew, W.

G. P. Otto, W. Chew, “Microwave scattering—local shape function imaging for improved resolution of strong scatterers,” IEEE Trans. Microwave Theory Tech. 42, 137–141 (1994).
[CrossRef]

Cote, M. G.

M. G. Cote, “Automated swept-angle bistatic scattering measurements using continuous wave radar,” IEEE Trans. Instrum. Meas. 41, 185–192 (1992).
[CrossRef]

Dudgeon, D.

D. Dudgeon, R. M. Mersereau, Multidimensional Digital Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1984).

Fiddy, M. A.

J. B. Morris, R. V. McGahan, J. L. Schmitz, R. M. Wing, D. A. Pommet, M. A. Fiddy, “Imaging of strongly scattering targets from real data,” IEEE Antennas Propag. Mag. 39, 22–26 (1997).
[CrossRef]

D. A. Pommet, R. A. Marr, U. H. W. Lammers, R. V. McGahan, J. B. Morris, M. A. Fiddy, “Imaging using limited-angle backscattered data from real targets,” IEEE Antennas Propag. Mag. 39, 19–22 (1997).
[CrossRef]

J. B. Morris, M. A. Fiddy, D. A. Pommet, “Nonlinear filtering applied to single-view backpropagated images of strong scatterers,” J. Opt. Soc. Am. A 13, 1506–1515 (1996).
[CrossRef]

J. B. Morris, D. A. Pommet, R. V. McGahan, M. A. Fiddy, “Imaging of unknown targets from measured scattering data,” IEEE Antennas Propag. Mag. 38, 53–56 (1996).
[CrossRef]

F. C. Lin, M. A. Fiddy, “Image estimation from scattered field data,” Int. J. Imaging Syst. Technol. 2, 76–95 (1990).
[CrossRef]

Hugonin, J. P.

N. Joachimowicz, Ch. Pichot, J. P. Hugonin, “Inverse scattering: an iterative numerical method for electromagnetic imaging,” IEEE Trans. Antennas Propag. 29, 1742–1752 (1991).
[CrossRef]

Joachimowicz, N.

N. Joachimowicz, Ch. Pichot, J. P. Hugonin, “Inverse scattering: an iterative numerical method for electromagnetic imaging,” IEEE Trans. Antennas Propag. 29, 1742–1752 (1991).
[CrossRef]

Kak, A. C.

M. Slaney, A. C. Kak, L. E. Larsen, “Limitations of imaging with first-order diffraction tomography,” IEEE Trans. Microwave Theory Tech. MTT-32, 860–874 (1984).
[CrossRef]

Kleinman, R. E.

R. E. Kleinman, P. M. Van den Berg, “An extended range modified gradient technique for profile inversion,” Radio Sci. 28, 877–884 (1993).
[CrossRef]

Lammers, U. H. W.

D. A. Pommet, R. A. Marr, U. H. W. Lammers, R. V. McGahan, J. B. Morris, M. A. Fiddy, “Imaging using limited-angle backscattered data from real targets,” IEEE Antennas Propag. Mag. 39, 19–22 (1997).
[CrossRef]

Larsen, L. E.

M. Slaney, A. C. Kak, L. E. Larsen, “Limitations of imaging with first-order diffraction tomography,” IEEE Trans. Microwave Theory Tech. MTT-32, 860–874 (1984).
[CrossRef]

Lin, F. C.

F. C. Lin, M. A. Fiddy, “Image estimation from scattered field data,” Int. J. Imaging Syst. Technol. 2, 76–95 (1990).
[CrossRef]

Marr, R. A.

D. A. Pommet, R. A. Marr, U. H. W. Lammers, R. V. McGahan, J. B. Morris, M. A. Fiddy, “Imaging using limited-angle backscattered data from real targets,” IEEE Antennas Propag. Mag. 39, 19–22 (1997).
[CrossRef]

McGahan, R. V.

D. A. Pommet, R. A. Marr, U. H. W. Lammers, R. V. McGahan, J. B. Morris, M. A. Fiddy, “Imaging using limited-angle backscattered data from real targets,” IEEE Antennas Propag. Mag. 39, 19–22 (1997).
[CrossRef]

J. B. Morris, R. V. McGahan, J. L. Schmitz, R. M. Wing, D. A. Pommet, M. A. Fiddy, “Imaging of strongly scattering targets from real data,” IEEE Antennas Propag. Mag. 39, 22–26 (1997).
[CrossRef]

J. B. Morris, D. A. Pommet, R. V. McGahan, M. A. Fiddy, “Imaging of unknown targets from measured scattering data,” IEEE Antennas Propag. Mag. 38, 53–56 (1996).
[CrossRef]

R. V. McGahan, “Scattering experiments at the Ipswich electromagnetic measurements facility: swept bistatic angle measurement system,” (Rome Laboratory, Hanscom Air Force Base, Mass., 1991).

Mersereau, R. M.

D. Dudgeon, R. M. Mersereau, Multidimensional Digital Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1984).

Morris, J. B.

J. B. Morris, R. V. McGahan, J. L. Schmitz, R. M. Wing, D. A. Pommet, M. A. Fiddy, “Imaging of strongly scattering targets from real data,” IEEE Antennas Propag. Mag. 39, 22–26 (1997).
[CrossRef]

D. A. Pommet, R. A. Marr, U. H. W. Lammers, R. V. McGahan, J. B. Morris, M. A. Fiddy, “Imaging using limited-angle backscattered data from real targets,” IEEE Antennas Propag. Mag. 39, 19–22 (1997).
[CrossRef]

J. B. Morris, M. A. Fiddy, D. A. Pommet, “Nonlinear filtering applied to single-view backpropagated images of strong scatterers,” J. Opt. Soc. Am. A 13, 1506–1515 (1996).
[CrossRef]

J. B. Morris, D. A. Pommet, R. V. McGahan, M. A. Fiddy, “Imaging of unknown targets from measured scattering data,” IEEE Antennas Propag. Mag. 38, 53–56 (1996).
[CrossRef]

Otto, G. P.

G. P. Otto, W. Chew, “Microwave scattering—local shape function imaging for improved resolution of strong scatterers,” IEEE Trans. Microwave Theory Tech. 42, 137–141 (1994).
[CrossRef]

Pichot, Ch.

N. Joachimowicz, Ch. Pichot, J. P. Hugonin, “Inverse scattering: an iterative numerical method for electromagnetic imaging,” IEEE Trans. Antennas Propag. 29, 1742–1752 (1991).
[CrossRef]

Pommet, D. A.

J. B. Morris, R. V. McGahan, J. L. Schmitz, R. M. Wing, D. A. Pommet, M. A. Fiddy, “Imaging of strongly scattering targets from real data,” IEEE Antennas Propag. Mag. 39, 22–26 (1997).
[CrossRef]

D. A. Pommet, R. A. Marr, U. H. W. Lammers, R. V. McGahan, J. B. Morris, M. A. Fiddy, “Imaging using limited-angle backscattered data from real targets,” IEEE Antennas Propag. Mag. 39, 19–22 (1997).
[CrossRef]

J. B. Morris, D. A. Pommet, R. V. McGahan, M. A. Fiddy, “Imaging of unknown targets from measured scattering data,” IEEE Antennas Propag. Mag. 38, 53–56 (1996).
[CrossRef]

J. B. Morris, M. A. Fiddy, D. A. Pommet, “Nonlinear filtering applied to single-view backpropagated images of strong scatterers,” J. Opt. Soc. Am. A 13, 1506–1515 (1996).
[CrossRef]

Schmitz, J. L.

J. B. Morris, R. V. McGahan, J. L. Schmitz, R. M. Wing, D. A. Pommet, M. A. Fiddy, “Imaging of strongly scattering targets from real data,” IEEE Antennas Propag. Mag. 39, 22–26 (1997).
[CrossRef]

Slaney, M.

M. Slaney, A. C. Kak, L. E. Larsen, “Limitations of imaging with first-order diffraction tomography,” IEEE Trans. Microwave Theory Tech. MTT-32, 860–874 (1984).
[CrossRef]

Van den Berg, P. M.

R. E. Kleinman, P. M. Van den Berg, “An extended range modified gradient technique for profile inversion,” Radio Sci. 28, 877–884 (1993).
[CrossRef]

Wing, R. M.

J. B. Morris, R. V. McGahan, J. L. Schmitz, R. M. Wing, D. A. Pommet, M. A. Fiddy, “Imaging of strongly scattering targets from real data,” IEEE Antennas Propag. Mag. 39, 22–26 (1997).
[CrossRef]

Wolf, E.

E. Wolf, “Three-dimensional structure determination of semi-transparent objects from holographic data,” Opt. Commun. 1, 153–156 (1969).
[CrossRef]

IEEE Antennas Propag. Mag. (3)

J. B. Morris, R. V. McGahan, J. L. Schmitz, R. M. Wing, D. A. Pommet, M. A. Fiddy, “Imaging of strongly scattering targets from real data,” IEEE Antennas Propag. Mag. 39, 22–26 (1997).
[CrossRef]

J. B. Morris, D. A. Pommet, R. V. McGahan, M. A. Fiddy, “Imaging of unknown targets from measured scattering data,” IEEE Antennas Propag. Mag. 38, 53–56 (1996).
[CrossRef]

D. A. Pommet, R. A. Marr, U. H. W. Lammers, R. V. McGahan, J. B. Morris, M. A. Fiddy, “Imaging using limited-angle backscattered data from real targets,” IEEE Antennas Propag. Mag. 39, 19–22 (1997).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

N. Joachimowicz, Ch. Pichot, J. P. Hugonin, “Inverse scattering: an iterative numerical method for electromagnetic imaging,” IEEE Trans. Antennas Propag. 29, 1742–1752 (1991).
[CrossRef]

IEEE Trans. Instrum. Meas. (1)

M. G. Cote, “Automated swept-angle bistatic scattering measurements using continuous wave radar,” IEEE Trans. Instrum. Meas. 41, 185–192 (1992).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (2)

M. Slaney, A. C. Kak, L. E. Larsen, “Limitations of imaging with first-order diffraction tomography,” IEEE Trans. Microwave Theory Tech. MTT-32, 860–874 (1984).
[CrossRef]

G. P. Otto, W. Chew, “Microwave scattering—local shape function imaging for improved resolution of strong scatterers,” IEEE Trans. Microwave Theory Tech. 42, 137–141 (1994).
[CrossRef]

Int. J. Imaging Syst. Technol. (1)

F. C. Lin, M. A. Fiddy, “Image estimation from scattered field data,” Int. J. Imaging Syst. Technol. 2, 76–95 (1990).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Commun. (1)

E. Wolf, “Three-dimensional structure determination of semi-transparent objects from holographic data,” Opt. Commun. 1, 153–156 (1969).
[CrossRef]

Radio Sci. (1)

R. E. Kleinman, P. M. Van den Berg, “An extended range modified gradient technique for profile inversion,” Radio Sci. 28, 877–884 (1993).
[CrossRef]

Other (4)

R. V. McGahan, R. E. Kleinman, eds., “Special session on image reconstruction using real data,” IEEE Antennas Propag. Mag.38, 39–59 (1996).
[CrossRef]

R. V. McGahan, R. E. Kleinman, eds., “Second annual special session on image reconstruction using real data,” IEEE Antennas Propag. Mag.39, 7–32 (1997).
[CrossRef]

R. V. McGahan, “Scattering experiments at the Ipswich electromagnetic measurements facility: swept bistatic angle measurement system,” (Rome Laboratory, Hanscom Air Force Base, Mass., 1991).

D. Dudgeon, R. M. Mersereau, Multidimensional Digital Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1984).

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Figures (13)

Fig. 1
Fig. 1

Image ips008, which consists of two cardboard cylin- ders—the smaller one filled with salt; the outer one, with sand. The permittivities of these media are assumed to be 2.4 and 2.6, respectively.

Fig. 2
Fig. 2

Image ips012 (see Section 5 for description).

Fig. 3
Fig. 3

Reconstruction of ips008, assuming the first Born approximation.

Fig. 4
Fig. 4

Born reconstruction of ips007, which consists of empty cylinders.

Fig. 5
Fig. 5

Born reconstruction of ips012.

Fig. 6
Fig. 6

log(VΨ) reconstruction of ips008.

Fig. 7
Fig. 7

log(C+real{VΨ}) reconstruction of ips008.

Fig. 8
Fig. 8

log(1+|VΨ|) reconstruction of ips008.

Fig. 9
Fig. 9

log(VΨ) reconstruction of ips008 with background support imposed.

Fig. 10
Fig. 10

Difference between fields ips008 and ips007.

Fig. 11
Fig. 11

log(VΨ) reconstruction of ips012.

Fig. 12
Fig. 12

log(1+|VΨ|) reconstruction of ips012.

Fig. 13
Fig. 13

Difference between fields ips012 and ips011 (the latter consists of an empty open metal cylinder).

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

Ψ(r, kr^0)=Ψ0(r, kr^0)-k2DdrG0(r, r)V(r)Ψ(r, kr^0),
Ψ(r, kr^0)=Ψ0(r, kr^0)-k2DdrG0(r, r)×V(r)Ψ(r, kr^0)Ψ0(r, kr^0)Ψ0(r, kr^0).
f(kβˆ, kαˆ)=Ddr^ exp[-ik(βˆ-αˆ)r]×V(r)Ψ(r, kαˆ)Ψ0(r, kαˆ),
V(r)Ψ(r, kr^0)/Ψ0(r, kr^0).
i[VΨ(θi)/Ψ0(θi)]*h(θi)
=i[V+VΨs(θi)/Ψ0(θi)]*h(θi)
=i[V+N(θi)]*h(θi),

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