Abstract

The spatial resolution of a conventional imaging laser radar system is constrained by the diffraction limit of the telescope’s aperture. We investigate a technique known as synthetic-aperture imaging laser radar (SAIL), which employs aperture synthesis with coherent laser radar to overcome the diffraction limit and achieve fine-resolution, long-range, two-dimensional imaging with modest aperture diameters. We detail our laboratory-scale SAIL testbed, digital signal-processing techniques, and image results. In particular, we report what we believe to be the first optical synthetic-aperture image of a fixed, diffusely scattering target with a moving aperture. A number of fine-resolution, well-focused SAIL images are shown, including both retroreflecting and diffuse scattering targets, with a comparison of resolution between real-aperture imaging and synthetic-aperture imaging. A general digital signal-processing solution to the laser waveform instability problem is described and demonstrated, involving both new algorithms and hardware elements. These algorithms are primarily data driven, without a priori knowledge of waveform and sensor position, representing a crucial step in developing a robust imaging system.

© 2005 Optical Society of America

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References

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  1. S. A. Hovenessian, An Introduction to Synthetic Aperture Array and Imaging Radars (Artech House, 1980).
  2. C. V. Jakowatz, D. E. Wahl, P. H. Eichel, D. C. Ghiglia, P. A. Thompson, Spotlight-Mode Synthetic Aperture Radar: A Signal Processing Approach (Kluwer Academic, 1996).
    [CrossRef]
  3. A. V. Jelalian, Laser Radar Systems (Artech House, 1992).
  4. T. S. Lewis, H. S. Hutchins, “A synthetic aperture at optical frequencies,” Proc. IEEE 58, 587–588 (1970).
    [CrossRef]
  5. T. S. Lewis, H. S. Hutchins, “A synthetic aperture at 10.6 microns,” Proc. IEEE 58, 1781–1782 (1970).
    [CrossRef]
  6. C. C. Aleksoff, J. S. Accetta, L. M. Peterson, A. M. Tai, A. Klossler, 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. SPIE783, 29–40 (1987).
    [CrossRef]
  7. D. Park, J. H. Shapiro, “Performance analysis of optical synthetic aperture radars,” in Laser Radar III, R. J. Becherer, ed., Proc. SPIE999, 100–116 (1988).
    [CrossRef]
  8. S. Yoshikado, T. Aruga, “Feasibility study of synthetic aperture infrared laser radar techniques for imaging of static and moving objects,” Appl. Opt. 37, 5631–5639 (1998).
    [CrossRef]
  9. T. G. Kyle, “High resolution laser imaging system,” Appl. Opt. 28, 2651–2656 (1989).
    [CrossRef] [PubMed]
  10. R. L. Lucke, L. J. Rickard, “Photon-limited synthetic-aperture imaging for planet surface studies,” Appl. Opt. 41, 5084–5095 (2002).
    [CrossRef] [PubMed]
  11. A. B. Gschwendtner, W. E. Keicher, “Development of coherent laser radar at Lincoln Laboratory,” Lincoln Lab. J. 12, 383–396 (2000).
  12. D. E. Mosley, C. L. Matson, S. R. Czyzak, “Active imaging of space objects using the HI-CLASS (high performance CO2 ladar surveillance sensor) laser system,” in Laser Radar Technology and Applications II, G. W. Kamerman, ed., Proc. SPIE3065, 52–60 (1997).
    [CrossRef]
  13. T. J. Green, S. Marcus, B. D. Colella, “Synthetic-aperture-radar imaging with a solid-state laser,” Appl. Opt. 34, 6941–6949 (1995).
    [CrossRef] [PubMed]
  14. S. Yoshikado, T. Aruga, “Short-range verification experiment of a trial one-dimensional synthetic aperture infrared laser radar operated in the 10 µm band,” Appl. Opt. 39, 1421–1425 (2000).
    [CrossRef]
  15. M. Bashkansky, R. L. Lucke, E. Funk, L. J. Rickard, J. Reintjes, “Two-dimensional synthetic aperture imaging in the optical domain,” Opt. Lett. 27, 1983–1985 (2002).
    [CrossRef]
  16. D. E. Wahl, P. H. Eichel, D. C. Ghiglia, C. V. Jakowatz, “Phase gradient autofocus—a robust tool for high resolution SAR phase correction,” IEEE Trans. Aerosp. Electron. Syst. 30, 827–835 (1994).
    [CrossRef]
  17. C. V. Jakowatz, D. E. Wahl, “Eigenvector method for maximum-likelihood estimation of phase errors in synthetic-aperture radar imagery,” J. Opt. Soc. Am. A 10, 2539–2546 (1993).
    [CrossRef]
  18. C. V. Jakowatz, P. A. Thompson, “A new look at spot-light mode synthetic aperture radar as tomography: imaging 3-D targets,” IEEE Trans. Image Process. 4, 699–703 (1995).
    [CrossRef]
  19. W. Buell, N. Marechal, J. Buck, R. Dickinson, D. Kozlowski, T. Wright, S. Beck, “Demonstrations of synthetic aperture imaging ladar,” in Defense and Security Symposium 2004, Proc. SPIE 5791, 152–166 (2005).
  20. R. A. Muller, A. Buffmgton, “Real-time correction of atmospherically degraded telescope image through image sharpening,” J. Opt. Soc. Am. 64, 1200–1210 (1974).
    [CrossRef]
  21. T. Karr, “Resolution of synthetic aperture imaging through turbulence,” J. Opt. Soc. Am. A. 20, 1067–1083 (2003).
    [CrossRef]

2005

W. Buell, N. Marechal, J. Buck, R. Dickinson, D. Kozlowski, T. Wright, S. Beck, “Demonstrations of synthetic aperture imaging ladar,” in Defense and Security Symposium 2004, Proc. SPIE 5791, 152–166 (2005).

2003

T. Karr, “Resolution of synthetic aperture imaging through turbulence,” J. Opt. Soc. Am. A. 20, 1067–1083 (2003).
[CrossRef]

2002

2000

S. Yoshikado, T. Aruga, “Short-range verification experiment of a trial one-dimensional synthetic aperture infrared laser radar operated in the 10 µm band,” Appl. Opt. 39, 1421–1425 (2000).
[CrossRef]

A. B. Gschwendtner, W. E. Keicher, “Development of coherent laser radar at Lincoln Laboratory,” Lincoln Lab. J. 12, 383–396 (2000).

1998

1995

C. V. Jakowatz, P. A. Thompson, “A new look at spot-light mode synthetic aperture radar as tomography: imaging 3-D targets,” IEEE Trans. Image Process. 4, 699–703 (1995).
[CrossRef]

T. J. Green, S. Marcus, B. D. Colella, “Synthetic-aperture-radar imaging with a solid-state laser,” Appl. Opt. 34, 6941–6949 (1995).
[CrossRef] [PubMed]

1994

D. E. Wahl, P. H. Eichel, D. C. Ghiglia, C. V. Jakowatz, “Phase gradient autofocus—a robust tool for high resolution SAR phase correction,” IEEE Trans. Aerosp. Electron. Syst. 30, 827–835 (1994).
[CrossRef]

1993

1989

1974

1970

T. S. Lewis, H. S. Hutchins, “A synthetic aperture at optical frequencies,” Proc. IEEE 58, 587–588 (1970).
[CrossRef]

T. S. Lewis, H. S. Hutchins, “A synthetic aperture at 10.6 microns,” Proc. IEEE 58, 1781–1782 (1970).
[CrossRef]

Abshier, J. O.

C. C. Aleksoff, J. S. Accetta, L. M. Peterson, A. M. Tai, A. Klossler, 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. SPIE783, 29–40 (1987).
[CrossRef]

Accetta, J. S.

C. C. Aleksoff, J. S. Accetta, L. M. Peterson, A. M. Tai, A. Klossler, 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. SPIE783, 29–40 (1987).
[CrossRef]

Aleksoff, C. C.

C. C. Aleksoff, J. S. Accetta, L. M. Peterson, A. M. Tai, A. Klossler, 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. SPIE783, 29–40 (1987).
[CrossRef]

Aruga, T.

Bashkansky, M.

Beck, S.

W. Buell, N. Marechal, J. Buck, R. Dickinson, D. Kozlowski, T. Wright, S. Beck, “Demonstrations of synthetic aperture imaging ladar,” in Defense and Security Symposium 2004, Proc. SPIE 5791, 152–166 (2005).

Buck, J.

W. Buell, N. Marechal, J. Buck, R. Dickinson, D. Kozlowski, T. Wright, S. Beck, “Demonstrations of synthetic aperture imaging ladar,” in Defense and Security Symposium 2004, Proc. SPIE 5791, 152–166 (2005).

Buell, W.

W. Buell, N. Marechal, J. Buck, R. Dickinson, D. Kozlowski, T. Wright, S. Beck, “Demonstrations of synthetic aperture imaging ladar,” in Defense and Security Symposium 2004, Proc. SPIE 5791, 152–166 (2005).

Buffmgton, A.

Colella, B. D.

Czyzak, S. R.

D. E. Mosley, C. L. Matson, S. R. Czyzak, “Active imaging of space objects using the HI-CLASS (high performance CO2 ladar surveillance sensor) laser system,” in Laser Radar Technology and Applications II, G. W. Kamerman, ed., Proc. SPIE3065, 52–60 (1997).
[CrossRef]

Dickinson, R.

W. Buell, N. Marechal, J. Buck, R. Dickinson, D. Kozlowski, T. Wright, S. Beck, “Demonstrations of synthetic aperture imaging ladar,” in Defense and Security Symposium 2004, Proc. SPIE 5791, 152–166 (2005).

Eichel, P. H.

D. E. Wahl, P. H. Eichel, D. C. Ghiglia, C. V. Jakowatz, “Phase gradient autofocus—a robust tool for high resolution SAR phase correction,” IEEE Trans. Aerosp. Electron. Syst. 30, 827–835 (1994).
[CrossRef]

C. V. Jakowatz, D. E. Wahl, P. H. Eichel, D. C. Ghiglia, P. A. Thompson, Spotlight-Mode Synthetic Aperture Radar: A Signal Processing Approach (Kluwer Academic, 1996).
[CrossRef]

Fee, M.

C. C. Aleksoff, J. S. Accetta, L. M. Peterson, A. M. Tai, A. Klossler, 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. SPIE783, 29–40 (1987).
[CrossRef]

Funk, E.

Ghiglia, D. C.

D. E. Wahl, P. H. Eichel, D. C. Ghiglia, C. V. Jakowatz, “Phase gradient autofocus—a robust tool for high resolution SAR phase correction,” IEEE Trans. Aerosp. Electron. Syst. 30, 827–835 (1994).
[CrossRef]

C. V. Jakowatz, D. E. Wahl, P. H. Eichel, D. C. Ghiglia, P. A. Thompson, Spotlight-Mode Synthetic Aperture Radar: A Signal Processing Approach (Kluwer Academic, 1996).
[CrossRef]

Green, T. J.

Gschwendtner, A. B.

A. B. Gschwendtner, W. E. Keicher, “Development of coherent laser radar at Lincoln Laboratory,” Lincoln Lab. J. 12, 383–396 (2000).

Hovenessian, S. A.

S. A. Hovenessian, An Introduction to Synthetic Aperture Array and Imaging Radars (Artech House, 1980).

Hutchins, H. S.

T. S. Lewis, H. S. Hutchins, “A synthetic aperture at optical frequencies,” Proc. IEEE 58, 587–588 (1970).
[CrossRef]

T. S. Lewis, H. S. Hutchins, “A synthetic aperture at 10.6 microns,” Proc. IEEE 58, 1781–1782 (1970).
[CrossRef]

Jakowatz, C. V.

C. V. Jakowatz, P. A. Thompson, “A new look at spot-light mode synthetic aperture radar as tomography: imaging 3-D targets,” IEEE Trans. Image Process. 4, 699–703 (1995).
[CrossRef]

D. E. Wahl, P. H. Eichel, D. C. Ghiglia, C. V. Jakowatz, “Phase gradient autofocus—a robust tool for high resolution SAR phase correction,” IEEE Trans. Aerosp. Electron. Syst. 30, 827–835 (1994).
[CrossRef]

C. V. Jakowatz, D. E. Wahl, “Eigenvector method for maximum-likelihood estimation of phase errors in synthetic-aperture radar imagery,” J. Opt. Soc. Am. A 10, 2539–2546 (1993).
[CrossRef]

C. V. Jakowatz, D. E. Wahl, P. H. Eichel, D. C. Ghiglia, P. A. Thompson, Spotlight-Mode Synthetic Aperture Radar: A Signal Processing Approach (Kluwer Academic, 1996).
[CrossRef]

Jelalian, A. V.

A. V. Jelalian, Laser Radar Systems (Artech House, 1992).

Karr, T.

T. Karr, “Resolution of synthetic aperture imaging through turbulence,” J. Opt. Soc. Am. A. 20, 1067–1083 (2003).
[CrossRef]

Keicher, W. E.

A. B. Gschwendtner, W. E. Keicher, “Development of coherent laser radar at Lincoln Laboratory,” Lincoln Lab. J. 12, 383–396 (2000).

Klossler, A.

C. C. Aleksoff, J. S. Accetta, L. M. Peterson, A. M. Tai, A. Klossler, 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. SPIE783, 29–40 (1987).
[CrossRef]

Kozlowski, D.

W. Buell, N. Marechal, J. Buck, R. Dickinson, D. Kozlowski, T. Wright, S. Beck, “Demonstrations of synthetic aperture imaging ladar,” in Defense and Security Symposium 2004, Proc. SPIE 5791, 152–166 (2005).

Kyle, T. G.

Lewis, T. S.

T. S. Lewis, H. S. Hutchins, “A synthetic aperture at 10.6 microns,” Proc. IEEE 58, 1781–1782 (1970).
[CrossRef]

T. S. Lewis, H. S. Hutchins, “A synthetic aperture at optical frequencies,” Proc. IEEE 58, 587–588 (1970).
[CrossRef]

Lucke, R. L.

Majewski, R. M.

C. C. Aleksoff, J. S. Accetta, L. M. Peterson, A. M. Tai, A. Klossler, 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. SPIE783, 29–40 (1987).
[CrossRef]

Marcus, S.

Marechal, N.

W. Buell, N. Marechal, J. Buck, R. Dickinson, D. Kozlowski, T. Wright, S. Beck, “Demonstrations of synthetic aperture imaging ladar,” in Defense and Security Symposium 2004, Proc. SPIE 5791, 152–166 (2005).

Matson, C. L.

D. E. Mosley, C. L. Matson, S. R. Czyzak, “Active imaging of space objects using the HI-CLASS (high performance CO2 ladar surveillance sensor) laser system,” in Laser Radar Technology and Applications II, G. W. Kamerman, ed., Proc. SPIE3065, 52–60 (1997).
[CrossRef]

Mosley, D. E.

D. E. Mosley, C. L. Matson, S. R. Czyzak, “Active imaging of space objects using the HI-CLASS (high performance CO2 ladar surveillance sensor) laser system,” in Laser Radar Technology and Applications II, G. W. Kamerman, ed., Proc. SPIE3065, 52–60 (1997).
[CrossRef]

Muller, R. A.

Park, D.

D. Park, J. H. Shapiro, “Performance analysis of optical synthetic aperture radars,” in Laser Radar III, R. J. Becherer, ed., Proc. SPIE999, 100–116 (1988).
[CrossRef]

Peterson, L. M.

C. C. Aleksoff, J. S. Accetta, L. M. Peterson, A. M. Tai, A. Klossler, 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. SPIE783, 29–40 (1987).
[CrossRef]

Reintjes, J.

Rickard, L. J.

Schroeder, K. S.

C. C. Aleksoff, J. S. Accetta, L. M. Peterson, A. M. Tai, A. Klossler, 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. SPIE783, 29–40 (1987).
[CrossRef]

Shapiro, J. H.

D. Park, J. H. Shapiro, “Performance analysis of optical synthetic aperture radars,” in Laser Radar III, R. J. Becherer, ed., Proc. SPIE999, 100–116 (1988).
[CrossRef]

Tai, A. M.

C. C. Aleksoff, J. S. Accetta, L. M. Peterson, A. M. Tai, A. Klossler, 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. SPIE783, 29–40 (1987).
[CrossRef]

Thompson, P. A.

C. V. Jakowatz, P. A. Thompson, “A new look at spot-light mode synthetic aperture radar as tomography: imaging 3-D targets,” IEEE Trans. Image Process. 4, 699–703 (1995).
[CrossRef]

C. V. Jakowatz, D. E. Wahl, P. H. Eichel, D. C. Ghiglia, P. A. Thompson, Spotlight-Mode Synthetic Aperture Radar: A Signal Processing Approach (Kluwer Academic, 1996).
[CrossRef]

Wahl, D. E.

D. E. Wahl, P. H. Eichel, D. C. Ghiglia, C. V. Jakowatz, “Phase gradient autofocus—a robust tool for high resolution SAR phase correction,” IEEE Trans. Aerosp. Electron. Syst. 30, 827–835 (1994).
[CrossRef]

C. V. Jakowatz, D. E. Wahl, “Eigenvector method for maximum-likelihood estimation of phase errors in synthetic-aperture radar imagery,” J. Opt. Soc. Am. A 10, 2539–2546 (1993).
[CrossRef]

C. V. Jakowatz, D. E. Wahl, P. H. Eichel, D. C. Ghiglia, P. A. Thompson, Spotlight-Mode Synthetic Aperture Radar: A Signal Processing Approach (Kluwer Academic, 1996).
[CrossRef]

Wright, T.

W. Buell, N. Marechal, J. Buck, R. Dickinson, D. Kozlowski, T. Wright, S. Beck, “Demonstrations of synthetic aperture imaging ladar,” in Defense and Security Symposium 2004, Proc. SPIE 5791, 152–166 (2005).

Yoshikado, S.

Appl. Opt.

Defense and Security Symposium 2004

W. Buell, N. Marechal, J. Buck, R. Dickinson, D. Kozlowski, T. Wright, S. Beck, “Demonstrations of synthetic aperture imaging ladar,” in Defense and Security Symposium 2004, Proc. SPIE 5791, 152–166 (2005).

IEEE Trans. Aerosp. Electron. Syst.

D. E. Wahl, P. H. Eichel, D. C. Ghiglia, C. V. Jakowatz, “Phase gradient autofocus—a robust tool for high resolution SAR phase correction,” IEEE Trans. Aerosp. Electron. Syst. 30, 827–835 (1994).
[CrossRef]

IEEE Trans. Image Process.

C. V. Jakowatz, P. A. Thompson, “A new look at spot-light mode synthetic aperture radar as tomography: imaging 3-D targets,” IEEE Trans. Image Process. 4, 699–703 (1995).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Opt. Soc. Am. A.

T. Karr, “Resolution of synthetic aperture imaging through turbulence,” J. Opt. Soc. Am. A. 20, 1067–1083 (2003).
[CrossRef]

Lincoln Lab. J.

A. B. Gschwendtner, W. E. Keicher, “Development of coherent laser radar at Lincoln Laboratory,” Lincoln Lab. J. 12, 383–396 (2000).

Opt. Lett.

Proc. IEEE

T. S. Lewis, H. S. Hutchins, “A synthetic aperture at optical frequencies,” Proc. IEEE 58, 587–588 (1970).
[CrossRef]

T. S. Lewis, H. S. Hutchins, “A synthetic aperture at 10.6 microns,” Proc. IEEE 58, 1781–1782 (1970).
[CrossRef]

Other

C. C. Aleksoff, J. S. Accetta, L. M. Peterson, A. M. Tai, A. Klossler, 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. SPIE783, 29–40 (1987).
[CrossRef]

D. Park, J. H. Shapiro, “Performance analysis of optical synthetic aperture radars,” in Laser Radar III, R. J. Becherer, ed., Proc. SPIE999, 100–116 (1988).
[CrossRef]

D. E. Mosley, C. L. Matson, S. R. Czyzak, “Active imaging of space objects using the HI-CLASS (high performance CO2 ladar surveillance sensor) laser system,” in Laser Radar Technology and Applications II, G. W. Kamerman, ed., Proc. SPIE3065, 52–60 (1997).
[CrossRef]

S. A. Hovenessian, An Introduction to Synthetic Aperture Array and Imaging Radars (Artech House, 1980).

C. V. Jakowatz, D. E. Wahl, P. H. Eichel, D. C. Ghiglia, P. A. Thompson, Spotlight-Mode Synthetic Aperture Radar: A Signal Processing Approach (Kluwer Academic, 1996).
[CrossRef]

A. V. Jelalian, Laser Radar Systems (Artech House, 1992).

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Figures (11)

Fig. 1
Fig. 1

Synthetic-aperture imaging ladar (SAIL). The illuminating spot size, Dspot, at the target is determined by the diffraction limit of the transceiver optic with diameter Dt, corresponding to the imaging resolution of a conventional imager with the same aperture. The resolution in the direction of travel (azimuthal, δx) is determined by the wavelength and spot size. The resolution in the orthogonal direction (range, δy) is determined by the transmitted waveform bandwidth, B.

Fig. 2
Fig. 2

Heterodyning the returned signal with the LO. The SAIL image formation relies on a measurement of the phase history of the returned ladar signal. Our system uses a series of pulses with a near-linear frequency modulation waveform. The returned signal is mixed with a delayed copy of the transmitted signal, so intermediate frequency νIF is a function of chirp bandwidth B, chirp time τC, and relative delay time τD.

Fig. 3
Fig. 3

Component layout for the fiber-based SAIL system. The components employed are all common, off-the-shelf, telecommunication fiber-based devices, allowing a compact system to be assembled that can easily be isolated from environmental effects: The source is split into five paths, for target illumination, target–LO, reference, reference–LO, and wavelength reference. A circulator is used to recover the return pulse, which is mixed with the target–LO in a balanced heterodyne detector. The reference channel is delayed by a fiber loop and then mixed with the reference–LO in a similar manner. The synthetic aperture is created by use of a translation stage to scan the aperture across the target.

Fig. 4
Fig. 4

Reference channel target range profile with associated phase error. (a) Ideal reference channel impulse response (IPR) and the actual IPR obtained from a signal with the intrapulse phase errors shown in (b). The IPR is obtained from the Fourier transform of the signal acquired by heterodyning of the reference and reference–LO channels. With no phase errors, the IPR would have a width determined by the sampling rate and the chirp time. Much of this error is due to nonlinearities in the transmitted laser waveform and is efficiently mitigated by the reference channel (see Fig. 6 below).

Fig. 5
Fig. 5

Sharpness curves computed for each pulse. The horizontal axis represents the rescaling of travel time along the reference path, as discussed in Section 3. The peak occurs for a scale factor of ∼1.005. This correction corresponds to 0.5%; however, as typically there is in excess of 104 degrees of intrapulse phase error, the scaling parameter needs to be determined to within 1 part in 100 to achieve sharply focused imagery. Ideally, the residual rms phase errors would be limited to approximately 10°. This demonstrates the need for processing techniques to deal with the common phase errors in real systems.

Fig. 6
Fig. 6

(a) Target range profile before and after removal of range phase error by use of the digital reference channel data as discussed in Section 3. The target in this case is the retroreflecting triangle target shown in Fig. 7. The intrapulse phase errors shown in Fig. 4 for the reference channel are applied as a correction to the target channel, producing a range compressed image. (b) Pulse-to-pulse phase errors for the sequence of pulses that constitute the synthetic aperture. These errors are estimated and removed by use of the phase-gradient techniques discussed in Section 3. The pulse-to-pulse errors result from uncompensated motion between pulses as well as from errors in synchronizing the starting frequency of each pulse. The range to target in this example was ∼2 m.

Fig. 7
Fig. 7

SAIL image of a 5 mm × 8 mm triangle cut from retroreflective material (lower center) together with a photograph of the target (lower left). A representation of the illuminating spot size is shown at the lower right, corresponding to the diffraction-limited resolution of the aperture. The image at the top is a beam-scan image that is obtained when the focusing algorithms are not employed. The SAIL image in the lower center is obtained through the signal-processing techniques described in Section 3. For our system parameters the range resolution is approximately 0.06 mm, corresponding to the c/(2B) resolution limit. The range to target in this example was ∼2 m, with range diversity achieved by placing the target at a 45° angle with respect to the incident light.

Fig. 8
Fig. 8

SAIL images derived from matched (upper) and mismatched (lower) target and reference channel delays. The range to target in both cases was approximately 2 m, and the target–reference mismatch was of the order of 1 m. The targets were placed at a 45° angle with respect to the incident light. By employing the digital compensation techniques outlined in Section 3, we were able to produce a well-focused image despite the significant mismatch between the target and reference channel delays. This is an important step for applications in which the range to target is either uncertain or variable.

Fig. 9
Fig. 9

Ghosting as a result of residual amplitude modulation of the carrier. (a) In this SAIL image, faint (35–40 dB down) ghost images above and below the main triangle are visible. These are the result of amplitude modulation of the laser intensity and should be easily removable through signal processing. (b) The amplitude modulation sidebands are clearly visible in the Fourier transformed return from a point target. The range to target in this example was ∼2 m, with range diversity achieved by placing the target at a 45° angle with respect to the incident light.

Fig. 10
Fig. 10

SAIL-boat target and mosaicked SAIL image results. The real-aperture diffraction-limited illuminating spot size is represented at the right. A picture of the target is shown at the left. This target consists of the same retroreflective material used for the triangle images, placed behind a transparency containing the negative of the sailboat image. We formed the image by scanning the target in overlapping strips and then pasting these images together to form a larger image. We see some degradation that is due to the phase-screening effects of the transparency film; however, the pattern of the retroreflective material is clearly visible. The range to target in this example was ∼2 m, with range diversity achieved by placing the target at a 45° angle with respect to the incident light.

Fig. 11
Fig. 11

SAIL image of a tie tack with a circle A design. The upper image is a close-range photo of a tie tack containing the Aerospace Corporation’s logo, with the scale at the right in millimeters. The lower figure is the focused SAIL image of this target, which contains both diffuse scattering and specular surfaces. This represents what is to our knowledge the first optical synthetic-aperture image of a fixed, diffusely scattering target with a moving aperture. The image is well focused, despite a relatively weak return from the diffuse surface. The range to target in this example was ∼2 m, with range diversity achieved by placing the target at a 45° angle with respect to the incident light.

Equations (5)

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φ k ( t n ) = m φ ̂ k exp ( i 2 π m t n / N ) ,
ξ ( t n ) = φ ( t n τ x ) φ ( t n τ x LO ) , ψ ( t n ) = φ ( t n τ r ) φ ( t n τ r LO ) ,
ξ ̂ m = exp [ i π m ( τ x LO + τ x ) ν s ̂ / N ] sin [ π m ( τ x LO τ x ) ν s ̂ / N ] exp [ i π m ( τ r LO + τ r ) ν s ̂ / N ] sin [ π m ( τ r LO τ r ) ν s ̂ / N ] × ψ ̂ m .
ξ ̂ m τ x LO τ x τ r LO τ r ψ ̂ m .
S ( p ) = x | σ ( x ; p ) | 4 | x | σ ( x ; p ) | 2 | 2 ,

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