Abstract

A laser radar system for three-dimensional (3-D) lensless imaging is analyzed in theory and experiment. 3-D imaging is accomplished by making use of the relationship between the angular and wavelength dependence of the scattered light and an object’s 3-D Fourier transform. The concept is demonstrated by obtaining a 3-D image of an extended object by using a charge-coupled device detector array and an argon-ion laser with a tunable intracavity étalon.

© 1992 Optical Society of America

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References

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  1. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, Calif., 1968).
  2. D. R. Wehner, High Resolution Radar (Artech House, Norwood, Mass., 1987).
  3. J. W. Walker, “Range-Doppler imaging of rotating objects,” IEEE Trans. Aerosp. Electron. Syst. AES-16, 23–52 (1980).
    [CrossRef]
  4. D. A. Ausherman, A. Kozma, J. L. Walker, H. M. Jones, E. C. Poggio, “Developments in radar imaging,” IEEE Trans. Aerosp. Electron. Syst. AES-20, 363–400 (1984).
    [CrossRef]
  5. F. K. Knight, D. I. Klick, D. P. Ryan-Howard, J. R. Theriault, B. K. Tussey, A. M. Beckman, “Three-dimensional imaging using a single laser pulse,” in Laser Radar IV, R. J. Becherer, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1103, 174–189 (1989).
  6. C. C. Aleksoff, “Interferometric two-dimensional imaging of rotating objects,” Opt. Lett. 1, 54–55 (1977).
    [CrossRef] [PubMed]
  7. C. C. Aleksoff, J. S. Accetta, L. M. Peterson, A. M. Tai, A. Klooster, K. S. Schroeder, R. M. Majewski, J. O. Abshier, M. Fee, “Synthetic aperture imaging with a pulsed CO2 TEA laser,” in Laser Radar II, R. J. Becherer, R. C. Harney, eds. Proc. Soc. Photo-Opt. Instrum. Eng.783, 29–41 (1987).
  8. M. Bair, R. Sampson, D. Zuk, “Three-dimensional imaging and applications,” in Intelligent Robots and Computer Vision, D. P. Casasent, ed., Proc. Soc. Photo-Opt. Instrum. Eng.726, 263–274 (1986).
  9. N. H. Farhat, “Holography, wavelength diversity and inverse scattering,” in Optics in Four Dimensions—1980, M. A. Machado, L. M. Narducci, eds. (American Institute of Physics, New York, 1981).
  10. R. M. Lewis, “Physical optics inverse diffraction,” IEEE Trans. Antennas Propag. AP-17, 308–314 (1969).
    [CrossRef]
  11. C. K. Chan, N. H. Farhat, “Frequency swept tomographic imaging of three-dimensional perfectly conducting objects,” IEEE Trans. Antennas Propag. AP-29, 312–319 (1981).
    [CrossRef]
  12. J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21, 2758–2709 (1982).
    [CrossRef] [PubMed]
  13. R. G. Paxman, “Superresolution with an opacity constraint,” in Digest of Topical Meeting on Signal Recovery and Synthesis III, Vol. 15 of OSA 1989 Technical Digest Series (Optical Society of America, Washington, D.C., 1989), pp. 181–184.
  14. O. Svelto, Principles of Lasers (Plenum, New York, 1976).

1984 (1)

D. A. Ausherman, A. Kozma, J. L. Walker, H. M. Jones, E. C. Poggio, “Developments in radar imaging,” IEEE Trans. Aerosp. Electron. Syst. AES-20, 363–400 (1984).
[CrossRef]

1982 (1)

1981 (1)

C. K. Chan, N. H. Farhat, “Frequency swept tomographic imaging of three-dimensional perfectly conducting objects,” IEEE Trans. Antennas Propag. AP-29, 312–319 (1981).
[CrossRef]

1980 (1)

J. W. Walker, “Range-Doppler imaging of rotating objects,” IEEE Trans. Aerosp. Electron. Syst. AES-16, 23–52 (1980).
[CrossRef]

1977 (1)

1969 (1)

R. M. Lewis, “Physical optics inverse diffraction,” IEEE Trans. Antennas Propag. AP-17, 308–314 (1969).
[CrossRef]

Abshier, J. O.

C. C. Aleksoff, J. S. Accetta, L. M. Peterson, A. M. Tai, A. Klooster, K. S. Schroeder, R. M. Majewski, J. O. Abshier, M. Fee, “Synthetic aperture imaging with a pulsed CO2 TEA laser,” in Laser Radar II, R. J. Becherer, R. C. Harney, eds. Proc. Soc. Photo-Opt. Instrum. Eng.783, 29–41 (1987).

Accetta, J. S.

C. C. Aleksoff, J. S. Accetta, L. M. Peterson, A. M. Tai, A. Klooster, K. S. Schroeder, R. M. Majewski, J. O. Abshier, M. Fee, “Synthetic aperture imaging with a pulsed CO2 TEA laser,” in Laser Radar II, R. J. Becherer, R. C. Harney, eds. Proc. Soc. Photo-Opt. Instrum. Eng.783, 29–41 (1987).

Aleksoff, C. C.

C. C. Aleksoff, “Interferometric two-dimensional imaging of rotating objects,” Opt. Lett. 1, 54–55 (1977).
[CrossRef] [PubMed]

C. C. Aleksoff, J. S. Accetta, L. M. Peterson, A. M. Tai, A. Klooster, K. S. Schroeder, R. M. Majewski, J. O. Abshier, M. Fee, “Synthetic aperture imaging with a pulsed CO2 TEA laser,” in Laser Radar II, R. J. Becherer, R. C. Harney, eds. Proc. Soc. Photo-Opt. Instrum. Eng.783, 29–41 (1987).

Ausherman, D. A.

D. A. Ausherman, A. Kozma, J. L. Walker, H. M. Jones, E. C. Poggio, “Developments in radar imaging,” IEEE Trans. Aerosp. Electron. Syst. AES-20, 363–400 (1984).
[CrossRef]

Bair, M.

M. Bair, R. Sampson, D. Zuk, “Three-dimensional imaging and applications,” in Intelligent Robots and Computer Vision, D. P. Casasent, ed., Proc. Soc. Photo-Opt. Instrum. Eng.726, 263–274 (1986).

Beckman, A. M.

F. K. Knight, D. I. Klick, D. P. Ryan-Howard, J. R. Theriault, B. K. Tussey, A. M. Beckman, “Three-dimensional imaging using a single laser pulse,” in Laser Radar IV, R. J. Becherer, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1103, 174–189 (1989).

Chan, C. K.

C. K. Chan, N. H. Farhat, “Frequency swept tomographic imaging of three-dimensional perfectly conducting objects,” IEEE Trans. Antennas Propag. AP-29, 312–319 (1981).
[CrossRef]

Farhat, N. H.

C. K. Chan, N. H. Farhat, “Frequency swept tomographic imaging of three-dimensional perfectly conducting objects,” IEEE Trans. Antennas Propag. AP-29, 312–319 (1981).
[CrossRef]

N. H. Farhat, “Holography, wavelength diversity and inverse scattering,” in Optics in Four Dimensions—1980, M. A. Machado, L. M. Narducci, eds. (American Institute of Physics, New York, 1981).

Fee, M.

C. C. Aleksoff, J. S. Accetta, L. M. Peterson, A. M. Tai, A. Klooster, K. S. Schroeder, R. M. Majewski, J. O. Abshier, M. Fee, “Synthetic aperture imaging with a pulsed CO2 TEA laser,” in Laser Radar II, R. J. Becherer, R. C. Harney, eds. Proc. Soc. Photo-Opt. Instrum. Eng.783, 29–41 (1987).

Fienup, J. R.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, Calif., 1968).

Jones, H. M.

D. A. Ausherman, A. Kozma, J. L. Walker, H. M. Jones, E. C. Poggio, “Developments in radar imaging,” IEEE Trans. Aerosp. Electron. Syst. AES-20, 363–400 (1984).
[CrossRef]

Klick, D. I.

F. K. Knight, D. I. Klick, D. P. Ryan-Howard, J. R. Theriault, B. K. Tussey, A. M. Beckman, “Three-dimensional imaging using a single laser pulse,” in Laser Radar IV, R. J. Becherer, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1103, 174–189 (1989).

Klooster, A.

C. C. Aleksoff, J. S. Accetta, L. M. Peterson, A. M. Tai, A. Klooster, K. S. Schroeder, R. M. Majewski, J. O. Abshier, M. Fee, “Synthetic aperture imaging with a pulsed CO2 TEA laser,” in Laser Radar II, R. J. Becherer, R. C. Harney, eds. Proc. Soc. Photo-Opt. Instrum. Eng.783, 29–41 (1987).

Knight, F. K.

F. K. Knight, D. I. Klick, D. P. Ryan-Howard, J. R. Theriault, B. K. Tussey, A. M. Beckman, “Three-dimensional imaging using a single laser pulse,” in Laser Radar IV, R. J. Becherer, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1103, 174–189 (1989).

Kozma, A.

D. A. Ausherman, A. Kozma, J. L. Walker, H. M. Jones, E. C. Poggio, “Developments in radar imaging,” IEEE Trans. Aerosp. Electron. Syst. AES-20, 363–400 (1984).
[CrossRef]

Lewis, R. M.

R. M. Lewis, “Physical optics inverse diffraction,” IEEE Trans. Antennas Propag. AP-17, 308–314 (1969).
[CrossRef]

Majewski, R. M.

C. C. Aleksoff, J. S. Accetta, L. M. Peterson, A. M. Tai, A. Klooster, K. S. Schroeder, R. M. Majewski, J. O. Abshier, M. Fee, “Synthetic aperture imaging with a pulsed CO2 TEA laser,” in Laser Radar II, R. J. Becherer, R. C. Harney, eds. Proc. Soc. Photo-Opt. Instrum. Eng.783, 29–41 (1987).

Paxman, R. G.

R. G. Paxman, “Superresolution with an opacity constraint,” in Digest of Topical Meeting on Signal Recovery and Synthesis III, Vol. 15 of OSA 1989 Technical Digest Series (Optical Society of America, Washington, D.C., 1989), pp. 181–184.

Peterson, L. M.

C. C. Aleksoff, J. S. Accetta, L. M. Peterson, A. M. Tai, A. Klooster, K. S. Schroeder, R. M. Majewski, J. O. Abshier, M. Fee, “Synthetic aperture imaging with a pulsed CO2 TEA laser,” in Laser Radar II, R. J. Becherer, R. C. Harney, eds. Proc. Soc. Photo-Opt. Instrum. Eng.783, 29–41 (1987).

Poggio, E. C.

D. A. Ausherman, A. Kozma, J. L. Walker, H. M. Jones, E. C. Poggio, “Developments in radar imaging,” IEEE Trans. Aerosp. Electron. Syst. AES-20, 363–400 (1984).
[CrossRef]

Ryan-Howard, D. P.

F. K. Knight, D. I. Klick, D. P. Ryan-Howard, J. R. Theriault, B. K. Tussey, A. M. Beckman, “Three-dimensional imaging using a single laser pulse,” in Laser Radar IV, R. J. Becherer, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1103, 174–189 (1989).

Sampson, R.

M. Bair, R. Sampson, D. Zuk, “Three-dimensional imaging and applications,” in Intelligent Robots and Computer Vision, D. P. Casasent, ed., Proc. Soc. Photo-Opt. Instrum. Eng.726, 263–274 (1986).

Schroeder, K. S.

C. C. Aleksoff, J. S. Accetta, L. M. Peterson, A. M. Tai, A. Klooster, K. S. Schroeder, R. M. Majewski, J. O. Abshier, M. Fee, “Synthetic aperture imaging with a pulsed CO2 TEA laser,” in Laser Radar II, R. J. Becherer, R. C. Harney, eds. Proc. Soc. Photo-Opt. Instrum. Eng.783, 29–41 (1987).

Svelto, O.

O. Svelto, Principles of Lasers (Plenum, New York, 1976).

Tai, A. M.

C. C. Aleksoff, J. S. Accetta, L. M. Peterson, A. M. Tai, A. Klooster, K. S. Schroeder, R. M. Majewski, J. O. Abshier, M. Fee, “Synthetic aperture imaging with a pulsed CO2 TEA laser,” in Laser Radar II, R. J. Becherer, R. C. Harney, eds. Proc. Soc. Photo-Opt. Instrum. Eng.783, 29–41 (1987).

Theriault, J. R.

F. K. Knight, D. I. Klick, D. P. Ryan-Howard, J. R. Theriault, B. K. Tussey, A. M. Beckman, “Three-dimensional imaging using a single laser pulse,” in Laser Radar IV, R. J. Becherer, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1103, 174–189 (1989).

Tussey, B. K.

F. K. Knight, D. I. Klick, D. P. Ryan-Howard, J. R. Theriault, B. K. Tussey, A. M. Beckman, “Three-dimensional imaging using a single laser pulse,” in Laser Radar IV, R. J. Becherer, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1103, 174–189 (1989).

Walker, J. L.

D. A. Ausherman, A. Kozma, J. L. Walker, H. M. Jones, E. C. Poggio, “Developments in radar imaging,” IEEE Trans. Aerosp. Electron. Syst. AES-20, 363–400 (1984).
[CrossRef]

Walker, J. W.

J. W. Walker, “Range-Doppler imaging of rotating objects,” IEEE Trans. Aerosp. Electron. Syst. AES-16, 23–52 (1980).
[CrossRef]

Wehner, D. R.

D. R. Wehner, High Resolution Radar (Artech House, Norwood, Mass., 1987).

Zuk, D.

M. Bair, R. Sampson, D. Zuk, “Three-dimensional imaging and applications,” in Intelligent Robots and Computer Vision, D. P. Casasent, ed., Proc. Soc. Photo-Opt. Instrum. Eng.726, 263–274 (1986).

Appl. Opt. (1)

IEEE Trans. Aerosp. Electron. Syst. (2)

J. W. Walker, “Range-Doppler imaging of rotating objects,” IEEE Trans. Aerosp. Electron. Syst. AES-16, 23–52 (1980).
[CrossRef]

D. A. Ausherman, A. Kozma, J. L. Walker, H. M. Jones, E. C. Poggio, “Developments in radar imaging,” IEEE Trans. Aerosp. Electron. Syst. AES-20, 363–400 (1984).
[CrossRef]

IEEE Trans. Antennas Propag. (2)

R. M. Lewis, “Physical optics inverse diffraction,” IEEE Trans. Antennas Propag. AP-17, 308–314 (1969).
[CrossRef]

C. K. Chan, N. H. Farhat, “Frequency swept tomographic imaging of three-dimensional perfectly conducting objects,” IEEE Trans. Antennas Propag. AP-29, 312–319 (1981).
[CrossRef]

Opt. Lett. (1)

Other (8)

C. C. Aleksoff, J. S. Accetta, L. M. Peterson, A. M. Tai, A. Klooster, K. S. Schroeder, R. M. Majewski, J. O. Abshier, M. Fee, “Synthetic aperture imaging with a pulsed CO2 TEA laser,” in Laser Radar II, R. J. Becherer, R. C. Harney, eds. Proc. Soc. Photo-Opt. Instrum. Eng.783, 29–41 (1987).

M. Bair, R. Sampson, D. Zuk, “Three-dimensional imaging and applications,” in Intelligent Robots and Computer Vision, D. P. Casasent, ed., Proc. Soc. Photo-Opt. Instrum. Eng.726, 263–274 (1986).

N. H. Farhat, “Holography, wavelength diversity and inverse scattering,” in Optics in Four Dimensions—1980, M. A. Machado, L. M. Narducci, eds. (American Institute of Physics, New York, 1981).

F. K. Knight, D. I. Klick, D. P. Ryan-Howard, J. R. Theriault, B. K. Tussey, A. M. Beckman, “Three-dimensional imaging using a single laser pulse,” in Laser Radar IV, R. J. Becherer, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1103, 174–189 (1989).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, Calif., 1968).

D. R. Wehner, High Resolution Radar (Artech House, Norwood, Mass., 1987).

R. G. Paxman, “Superresolution with an opacity constraint,” in Digest of Topical Meeting on Signal Recovery and Synthesis III, Vol. 15 of OSA 1989 Technical Digest Series (Optical Society of America, Washington, D.C., 1989), pp. 181–184.

O. Svelto, Principles of Lasers (Plenum, New York, 1976).

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Figures (10)

Fig. 1
Fig. 1

Relationship between the Fourier domain and the 3-D image domain.

Fig. 2
Fig. 2

Definition of location vectors used to derive the Fourier transform relationship.

Fig. 3
Fig. 3

Schematic of the system used for data collection.

Fig. 4
Fig. 4

Photograph of the source and detection equipment.

Fig. 5
Fig. 5

Object configuration.

Fig. 6
Fig. 6

Photograph of the object.

Fig. 7
Fig. 7

Example of a 128 × 128 recorded speckle pattern.

Fig. 8
Fig. 8

Azimuth-elevation image of the object: (a) illustration of the image orientation with respect to the object, (b) azimuth-elevation image.

Fig. 9
Fig. 9

Range-azimuth image of the object: (a) illustration of the image orientation with respect to the object, (b) range-azimuth image.

Fig. 10
Fig. 10

Range-elevation image of the object: (a) illustration of the image orientation with respect to the object, (b) range-elevation image.

Equations (14)

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| r 1 | | r s | r · r ˆ s ,
| r 2 | | r d | r · r ˆ d ,
U ( ρ ) = κ | r 1 | | r 2 | exp [ i k ( | r s | + | r d | ) ] σ ( r ) exp ( i 2 π ρ · r ) d 3 r ,
ρ = r ˆ s + r ˆ d λ .
Δ R res = λ 2 / 2 Δ λ .
Δ R res = c / 2 Δ ν ,
I ( ρ ) = | κ | r 1 | | r 2 | σ ( r ) exp ( i 2 π ρ · r ) d 3 r | 2 .
I ( ρ ) = | κ | r 1 | | r 2 | × [ σ ( r ) + K exp ( i ϕ ) δ ( r ) ] exp ( i 2 π ρ · r ) d 3 r | 2 ,
I ( ρ ) = | [ κ | r 1 | | r 2 | σ ( r ) exp ( i 2 π ρ · r ) dr + κ | r 1 | | r 2 | K exp ( i ϕ ) ] | 2 ,
I ( ρ ) = | [ O + exp ( i ϕ ) R ] | 2 ,
I ( ρ ) = | O | 2 + | R | 2 + exp ( i ϕ ) R O * + exp ( i ϕ ) O R * .
Δ ν inst c 2 Δ R .
Δ ν inc = c 2 Δ R .
Δ R res = c 2 Δ ν tot .

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