Abstract

We present synthetic aperture ladar (SAL) imaging demonstrations where the return-signal level from the target is near the single-photon level per resolved pixel. Scenes consisting of both specular-point targets and diffuse-reflection, fully speckled targets are studied. Artificial retro-reflector-based phase references and/or phase-gradient-autofocus (PGA) algorithms were utilized for compensation of phase errors during the aperture motion. It was found that SAL images could reliably be formed with both methods even when the final max pixel intensity was at the few photon level, which means the SNR before azimuth compression is below unity. Mutual information-based comparison of SAL images show that average mutual information is reduced when the PGA is utilized for image-based phase compensation. The photon information efficiency of SAL and coherent imaging is discussed.

© 2014 Optical Society of America

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References

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2013 (2)

2012 (1)

2009 (2)

2007 (1)

K. W. Holman, D. G. Kocher, and S. Kaushik, “MIT/LL development of broadband linear frequency chirp for high resolution ladar,” Proc. SPIE 6572, 65720J (2007).
[CrossRef]

2005 (1)

1997 (1)

P. Viola and W. M. Wells, “Alignment by maximization of mutual information,” Int. J. Comput. Vis. 24, 137–154 (1997).
[CrossRef]

1989 (1)

Ashby, S.

B. W. Krause, J. Buck, C. Ryan, D. Hwang, P. Kondratko, A. Malm, A. Gleason, and S. Ashby, “Synthetic aperture ladar flight demonstration,” in Conference on Lasers and Electro-Optics (IEEE, 2011), pp. 1–2.

Babbitt, W. R.

Barber, Z. W.

Beck, S. M.

Berg, T.

Buck, J.

B. W. Krause, J. Buck, C. Ryan, D. Hwang, P. Kondratko, A. Malm, A. Gleason, and S. Ashby, “Synthetic aperture ladar flight demonstration,” in Conference on Lasers and Electro-Optics (IEEE, 2011), pp. 1–2.

Buck, J. R.

Buell, W. F.

Crouch, S.

Dahl, J. R.

Dickinson, R. P.

Eichel, P. H.

Erkmen, B. I.

Gleason, A.

B. W. Krause, J. Buck, C. Ryan, D. Hwang, P. Kondratko, A. Malm, A. Gleason, and S. Ashby, “Synthetic aperture ladar flight demonstration,” in Conference on Lasers and Electro-Optics (IEEE, 2011), pp. 1–2.

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley, 2000).

Holman, K. W.

K. W. Holman, D. G. Kocher, and S. Kaushik, “MIT/LL development of broadband linear frequency chirp for high resolution ladar,” Proc. SPIE 6572, 65720J (2007).
[CrossRef]

Hwang, D.

B. W. Krause, J. Buck, C. Ryan, D. Hwang, P. Kondratko, A. Malm, A. Gleason, and S. Ashby, “Synthetic aperture ladar flight demonstration,” in Conference on Lasers and Electro-Optics (IEEE, 2011), pp. 1–2.

Jakowatz, J.

Kaushik, S.

K. W. Holman, D. G. Kocher, and S. Kaushik, “MIT/LL development of broadband linear frequency chirp for high resolution ladar,” Proc. SPIE 6572, 65720J (2007).
[CrossRef]

Kaylor, B.

Kocher, D. G.

K. W. Holman, D. G. Kocher, and S. Kaushik, “MIT/LL development of broadband linear frequency chirp for high resolution ladar,” Proc. SPIE 6572, 65720J (2007).
[CrossRef]

Kondratko, P.

B. W. Krause, J. Buck, C. Ryan, D. Hwang, P. Kondratko, A. Malm, A. Gleason, and S. Ashby, “Synthetic aperture ladar flight demonstration,” in Conference on Lasers and Electro-Optics (IEEE, 2011), pp. 1–2.

Kozlowski, D. A.

Krause, B. W.

B. W. Krause, J. Buck, C. Ryan, D. Hwang, P. Kondratko, A. Malm, A. Gleason, and S. Ashby, “Synthetic aperture ladar flight demonstration,” in Conference on Lasers and Electro-Optics (IEEE, 2011), pp. 1–2.

Leyva, V.

Liu, L.

Malm, A.

B. W. Krause, J. Buck, C. Ryan, D. Hwang, P. Kondratko, A. Malm, A. Gleason, and S. Ashby, “Synthetic aperture ladar flight demonstration,” in Conference on Lasers and Electro-Optics (IEEE, 2011), pp. 1–2.

Marechal, N. J.

Maurer, C. R.

D. B. Russakoff, C. Tomasi, T. Rohlfing, and C. R. Maurer, “Image similarity using mutual information of regions,” in Computer Vision—ECCV, T. Pajdla and J. Matas, eds., Vol. 3023 of Lecture Notes in Computer Science (Springer, 2004), pp. 596–607.

Rakuljic, G.

Reibel, R. R.

Rohlfing, T.

D. B. Russakoff, C. Tomasi, T. Rohlfing, and C. R. Maurer, “Image similarity using mutual information of regions,” in Computer Vision—ECCV, T. Pajdla and J. Matas, eds., Vol. 3023 of Lecture Notes in Computer Science (Springer, 2004), pp. 596–607.

Roos, P. A.

Russakoff, D. B.

D. B. Russakoff, C. Tomasi, T. Rohlfing, and C. R. Maurer, “Image similarity using mutual information of regions,” in Computer Vision—ECCV, T. Pajdla and J. Matas, eds., Vol. 3023 of Lecture Notes in Computer Science (Springer, 2004), pp. 596–607.

Ryan, C.

B. W. Krause, J. Buck, C. Ryan, D. Hwang, P. Kondratko, A. Malm, A. Gleason, and S. Ashby, “Synthetic aperture ladar flight demonstration,” in Conference on Lasers and Electro-Optics (IEEE, 2011), pp. 1–2.

Satyan, N.

Sharpe, T. L.

Tomasi, C.

D. B. Russakoff, C. Tomasi, T. Rohlfing, and C. R. Maurer, “Image similarity using mutual information of regions,” in Computer Vision—ECCV, T. Pajdla and J. Matas, eds., Vol. 3023 of Lecture Notes in Computer Science (Springer, 2004), pp. 596–607.

Vasilyev, A.

Viola, P.

P. Viola and W. M. Wells, “Alignment by maximization of mutual information,” Int. J. Comput. Vis. 24, 137–154 (1997).
[CrossRef]

Wells, W. M.

P. Viola and W. M. Wells, “Alignment by maximization of mutual information,” Int. J. Comput. Vis. 24, 137–154 (1997).
[CrossRef]

Wright, T. J.

Yariv, A.

Zwillinger, D.

D. Zwillinger, and Chemical Rubber Company, CRC Standard Mathematical Tables and Formulae (Chapman & Hall/CRC, 2003).

Appl. Opt. (2)

Int. J. Comput. Vis. (1)

P. Viola and W. M. Wells, “Alignment by maximization of mutual information,” Int. J. Comput. Vis. 24, 137–154 (1997).
[CrossRef]

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

Opt. Express (2)

Opt. Lett. (2)

Proc. SPIE (1)

K. W. Holman, D. G. Kocher, and S. Kaushik, “MIT/LL development of broadband linear frequency chirp for high resolution ladar,” Proc. SPIE 6572, 65720J (2007).
[CrossRef]

Other (4)

J. W. Goodman, Statistical Optics (Wiley, 2000).

D. Zwillinger, and Chemical Rubber Company, CRC Standard Mathematical Tables and Formulae (Chapman & Hall/CRC, 2003).

D. B. Russakoff, C. Tomasi, T. Rohlfing, and C. R. Maurer, “Image similarity using mutual information of regions,” in Computer Vision—ECCV, T. Pajdla and J. Matas, eds., Vol. 3023 of Lecture Notes in Computer Science (Springer, 2004), pp. 596–607.

B. W. Krause, J. Buck, C. Ryan, D. Hwang, P. Kondratko, A. Malm, A. Gleason, and S. Ashby, “Synthetic aperture ladar flight demonstration,” in Conference on Lasers and Electro-Optics (IEEE, 2011), pp. 1–2.

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Figures (9)

Fig. 1.
Fig. 1.

(a) Probability of correctly locating a target among 100 resolvable range bins or pixels for shot-noise-limited coherent heterodyne detection for both specular (dotted line) and speckled (diffuse scattering) targets (solid line). (b) Resulting theoretical PIE based on (a).

Fig. 2.
Fig. 2.

Schematic of the experimental setup. All the fiber components are polarization maintaining. The transmit/receive optics consist of two bare fibers mounted in a single ferrule with a spacing of 250 μm. The amplifier was either a semiconductor optical amplifier that provided up to 80 mW of power or an erbium-doped fiber amplifier (EDFA), which could provide up to 1 W of power.

Fig. 3.
Fig. 3.

Example of a SAL image before PGA of two cat-eye retro targets with an image size of 138×125 pixels. The plots on the edges of the image are the mean (blue) and max (red) of the image along range (top) and cross-range (right). The correct ranges of the two targets can be seen in the plot of the mean on the right, but the targets are basically unobservable in the image. The image scale is scaled so that darker indicates higher intensity. The scales on the plots at top and to the right are scaled such that the shot-noise background is normalized, and the power reflects the measured return-signal level in photoelectrons.

Fig. 4.
Fig. 4.

Same SAL image as in Fig. 3 after PGA. The correct range and cross-ranges of the two targets are observed in both the image and the max plots (top-most and far right). The mean in the cross-range direction (first plot to the right) is identical to that of the pre-PGA image.

Fig. 5.
Fig. 5.

Mutual information of the two-target scene estimated from 100 independent images at different power levels.

Fig. 6.
Fig. 6.

Target as constructed and then projected into the range–cross-range plane as in the final SAL image. The inset is a photograph of the real target.

Fig. 7.
Fig. 7.

(a) Average of five independent 116×200 pixel SAL images with a mean of 1.1 photons per “on” pixel using a bright retro reflector for phase correction or (b) PGA image-based (no retro) phase-error correction are shown. The color bars are normalized to the shot-noise background. (c), (d) These SAL images have about 5 times higher transmit power and demonstrate marked improvement in the PGA-corrected images. No averaging was applied to provide direct comparison with (a), (b) at the same total image energy.

Fig. 8.
Fig. 8.

Estimated mutual information for the SAL imaging of the diffuse reference target. The red squares are data taken from a second run to fill in the high-intensity data.

Fig. 9.
Fig. 9.

Estimates of the measured PIE for SAL imaging to a diffuse target as a function of the average return power per “on” pixel in the image. The blue circles are the PIE estimates for the SAL images phased using a retro-reflecting point target in the scene. (The signal power in the bright-phase reference was removed from the images and the calculations.) The red circles and red squares are the PIE estimates for the PGA-corrected SAL images. The lines are the theoretical estimates of target location among M=22 and 12.5 bins for speckled targets.

Equations (7)

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p(z)dz=exp[(z+x)]I0(2zx)dz.
p(z)dz=11+λexp[z1+λ]dz.
Pcor=0(1ez)M111+λexp[z1+λ]dz.
Pcor=11+λΓ(11+λ)Γ(M)Γ(11+λ+M).
H(X|Y)=Plog2P(1P)log2(1PM1).
H=log2[(NM2)],
PRx=(PTxATx(R))(ρATarπ)(ARxR2),

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