Abstract

We describe a new one-dimensional synthetic aperture imaging laser radar (ladar) using the resonant sensitivity of a microchip laser to frequency-shifted optical feedback and galvanometric scanning of the target under investigation. In our experiment, the laser is both the source and the detector, providing optical amplification with self-aligned heterodyne detection. By using galvanometric scanning, we achieve an along-track spatial resolution better than the diffraction limit.

© 2006 Optical Society of America

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  1. R. O. Harger, Synthetic Aperture Radar Systems: Theory and Design (Academic, 1970), Chap. 2, pp. 18-58.
  2. J. C. Curlander and R. N. McDonough, Synthetic Aperture Radar: Systems and Signal Processing (Wiley, 1991), Chap. 1, pp. 1-66.
  3. T. S. Lewis and H. S. Hutchins, Proc. IEEE 58, 1781 (1970).
    [CrossRef]
  4. C. C. Aleksoff, J. S. Accetta, L. M. Peterson, A. M. Tai, A. Klossler, K. S. Schroeder, R. M. Majwski, J. O. Abshier, and M. Fee, in Proc. SPIE 783, 29 (1987).
  5. S. Markus, B. D. Colella, and T. J. Green, Jr., Appl. Opt. 33, 960 (1994).
  6. E. Lacot, R. Day, and F. Stoeckel, Opt. Lett. 24, 744 (1999).
    [CrossRef]
  7. K. Otsuka, Appl. Opt. 33, 1111 (1994).
    [PubMed]
  8. E. Lacot, R. Day, and F. Stoeckel, Phys. Rev. A 64, 043815 (2001).
    [CrossRef]
  9. M. Bashkansky, R. L. Lucke, E. Funk, L. J. Rickard, and J. Reintjes, Opt. Lett. 27, 1983 (2002).
    [CrossRef]
  10. S. M. Beck, J. R. Buck, W. F. Buell, R. P. Dickinson, D. A. Kozlowski, N. J. Marechal, and T. J. Wright, Appl. Opt. 44, 35 (2005).
    [CrossRef]
  11. D. Park and J. H. Shapiro, in Proc. SPIE 999, 100 (1988).

2005

S. M. Beck, J. R. Buck, W. F. Buell, R. P. Dickinson, D. A. Kozlowski, N. J. Marechal, and T. J. Wright, Appl. Opt. 44, 35 (2005).
[CrossRef]

2002

2001

E. Lacot, R. Day, and F. Stoeckel, Phys. Rev. A 64, 043815 (2001).
[CrossRef]

1999

1994

1988

D. Park and J. H. Shapiro, in Proc. SPIE 999, 100 (1988).

1987

C. C. Aleksoff, J. S. Accetta, L. M. Peterson, A. M. Tai, A. Klossler, K. S. Schroeder, R. M. Majwski, J. O. Abshier, and M. Fee, in Proc. SPIE 783, 29 (1987).

1970

T. S. Lewis and H. S. Hutchins, Proc. IEEE 58, 1781 (1970).
[CrossRef]

Abshier, J. O.

C. C. Aleksoff, J. S. Accetta, L. M. Peterson, A. M. Tai, A. Klossler, K. S. Schroeder, R. M. Majwski, J. O. Abshier, and M. Fee, in Proc. SPIE 783, 29 (1987).

Accetta, J. S.

C. C. Aleksoff, J. S. Accetta, L. M. Peterson, A. M. Tai, A. Klossler, K. S. Schroeder, R. M. Majwski, J. O. Abshier, and M. Fee, in Proc. SPIE 783, 29 (1987).

Aleksoff, C. C.

C. C. Aleksoff, J. S. Accetta, L. M. Peterson, A. M. Tai, A. Klossler, K. S. Schroeder, R. M. Majwski, J. O. Abshier, and M. Fee, in Proc. SPIE 783, 29 (1987).

Bashkansky, M.

Beck, S. M.

S. M. Beck, J. R. Buck, W. F. Buell, R. P. Dickinson, D. A. Kozlowski, N. J. Marechal, and T. J. Wright, Appl. Opt. 44, 35 (2005).
[CrossRef]

Buck, J. R.

S. M. Beck, J. R. Buck, W. F. Buell, R. P. Dickinson, D. A. Kozlowski, N. J. Marechal, and T. J. Wright, Appl. Opt. 44, 35 (2005).
[CrossRef]

Buell, W. F.

S. M. Beck, J. R. Buck, W. F. Buell, R. P. Dickinson, D. A. Kozlowski, N. J. Marechal, and T. J. Wright, Appl. Opt. 44, 35 (2005).
[CrossRef]

Colella, B. D.

Curlander, J. C.

J. C. Curlander and R. N. McDonough, Synthetic Aperture Radar: Systems and Signal Processing (Wiley, 1991), Chap. 1, pp. 1-66.

Day, R.

E. Lacot, R. Day, and F. Stoeckel, Phys. Rev. A 64, 043815 (2001).
[CrossRef]

E. Lacot, R. Day, and F. Stoeckel, Opt. Lett. 24, 744 (1999).
[CrossRef]

Dickinson, R. P.

S. M. Beck, J. R. Buck, W. F. Buell, R. P. Dickinson, D. A. Kozlowski, N. J. Marechal, and T. J. Wright, Appl. Opt. 44, 35 (2005).
[CrossRef]

Fee, M.

C. C. Aleksoff, J. S. Accetta, L. M. Peterson, A. M. Tai, A. Klossler, K. S. Schroeder, R. M. Majwski, J. O. Abshier, and M. Fee, in Proc. SPIE 783, 29 (1987).

Funk, E.

Green, T. J.

Harger, R. O.

R. O. Harger, Synthetic Aperture Radar Systems: Theory and Design (Academic, 1970), Chap. 2, pp. 18-58.

Hutchins, H. S.

T. S. Lewis and H. S. Hutchins, Proc. IEEE 58, 1781 (1970).
[CrossRef]

Klossler, A.

C. C. Aleksoff, J. S. Accetta, L. M. Peterson, A. M. Tai, A. Klossler, K. S. Schroeder, R. M. Majwski, J. O. Abshier, and M. Fee, in Proc. SPIE 783, 29 (1987).

Kozlowski, D. A.

S. M. Beck, J. R. Buck, W. F. Buell, R. P. Dickinson, D. A. Kozlowski, N. J. Marechal, and T. J. Wright, Appl. Opt. 44, 35 (2005).
[CrossRef]

Lacot, E.

E. Lacot, R. Day, and F. Stoeckel, Phys. Rev. A 64, 043815 (2001).
[CrossRef]

E. Lacot, R. Day, and F. Stoeckel, Opt. Lett. 24, 744 (1999).
[CrossRef]

Lewis, T. S.

T. S. Lewis and H. S. Hutchins, Proc. IEEE 58, 1781 (1970).
[CrossRef]

Lucke, R. L.

Majwski, R. M.

C. C. Aleksoff, J. S. Accetta, L. M. Peterson, A. M. Tai, A. Klossler, K. S. Schroeder, R. M. Majwski, J. O. Abshier, and M. Fee, in Proc. SPIE 783, 29 (1987).

Marechal, N. J.

S. M. Beck, J. R. Buck, W. F. Buell, R. P. Dickinson, D. A. Kozlowski, N. J. Marechal, and T. J. Wright, Appl. Opt. 44, 35 (2005).
[CrossRef]

Markus, S.

McDonough, R. N.

J. C. Curlander and R. N. McDonough, Synthetic Aperture Radar: Systems and Signal Processing (Wiley, 1991), Chap. 1, pp. 1-66.

Otsuka, K.

Park, D.

D. Park and J. H. Shapiro, in Proc. SPIE 999, 100 (1988).

Peterson, L. M.

C. C. Aleksoff, J. S. Accetta, L. M. Peterson, A. M. Tai, A. Klossler, K. S. Schroeder, R. M. Majwski, J. O. Abshier, and M. Fee, in Proc. SPIE 783, 29 (1987).

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. Majwski, J. O. Abshier, and M. Fee, in Proc. SPIE 783, 29 (1987).

Shapiro, J. H.

D. Park and J. H. Shapiro, in Proc. SPIE 999, 100 (1988).

Stoeckel, F.

E. Lacot, R. Day, and F. Stoeckel, Phys. Rev. A 64, 043815 (2001).
[CrossRef]

E. Lacot, R. Day, and F. Stoeckel, Opt. Lett. 24, 744 (1999).
[CrossRef]

Tai, A. M.

C. C. Aleksoff, J. S. Accetta, L. M. Peterson, A. M. Tai, A. Klossler, K. S. Schroeder, R. M. Majwski, J. O. Abshier, and M. Fee, in Proc. SPIE 783, 29 (1987).

Wright, T. J.

S. M. Beck, J. R. Buck, W. F. Buell, R. P. Dickinson, D. A. Kozlowski, N. J. Marechal, and T. J. Wright, Appl. Opt. 44, 35 (2005).
[CrossRef]

Appl. Opt.

S. M. Beck, J. R. Buck, W. F. Buell, R. P. Dickinson, D. A. Kozlowski, N. J. Marechal, and T. J. Wright, Appl. Opt. 44, 35 (2005).
[CrossRef]

K. Otsuka, Appl. Opt. 33, 1111 (1994).
[PubMed]

S. Markus, B. D. Colella, and T. J. Green, Jr., Appl. Opt. 33, 960 (1994).

Opt. Lett.

Phys. Rev. A

E. Lacot, R. Day, and F. Stoeckel, Phys. Rev. A 64, 043815 (2001).
[CrossRef]

Proc. IEEE

T. S. Lewis and H. S. Hutchins, Proc. IEEE 58, 1781 (1970).
[CrossRef]

Proc. SPIE

C. C. Aleksoff, J. S. Accetta, L. M. Peterson, A. M. Tai, A. Klossler, K. S. Schroeder, R. M. Majwski, J. O. Abshier, and M. Fee, in Proc. SPIE 783, 29 (1987).

D. Park and J. H. Shapiro, in Proc. SPIE 999, 100 (1988).

Other

R. O. Harger, Synthetic Aperture Radar Systems: Theory and Design (Academic, 1970), Chap. 2, pp. 18-58.

J. C. Curlander and R. N. McDonough, Synthetic Aperture Radar: Systems and Signal Processing (Wiley, 1991), Chap. 1, pp. 1-66.

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Figures (3)

Fig. 1
Fig. 1

Synthetic aperture LOFI experiment using a galvanometric scanning: BS, beam splitter; RF, radio-frequency generator; F, frequency shift; GM, galvanometric mirror. The dotted line shows the particular laser beam ray reaching a point target for a given position of the galvanometric mirror located at angle α.

Fig. 2
Fig. 2

(a) Relative phase Φ ̂ ( α ) of the LOFI signal numerically computed for a target located at x = 0 (solid curve), x = 0.5 mm (dashed curve), and second-order polynomial fit (dotted curve). (b) Phase error between the numerical computation and the analytical expression of Φ ̂ ( α ) for x = 0 . The curves are obtained with the following parameters: L = 180 cm , l = 20 cm , y s = 450 μ m .

Fig. 3
Fig. 3

Resolution beyond the diffraction limit after SA processing over the envelope of the Gaussian laser beam. Experimental parameters: L = 180 cm , l = 20 cm , y s = 450 μ m , ω 0 = 330 μ m , α ̇ = 8 deg s 1 , D 4 mm , (a) Δ x = 185 μ m , and (b) Δ x = 335 μ m .

Equations (10)

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Δ P out ( t , x , Ω ) P out = 2 R eff G ( Ω ) cos [ Ω t + Φ ( t , x ) + Φ R ] ,
G ( Ω ) = γ c [ ( η γ 1 ) 2 + Ω 2 ] 1 2 [ ( Ω R 2 Ω 2 ) 2 + ( η γ 1 Ω ) 2 ] 1 2 ,
A ( R eff ) = 2 R eff G ( Ω ) P out ,
Φ ( α ) = Φ 0 + 2 π [ K α α 2 2 + D α α + C ] = Φ 0 + 2 π [ 8 L l λ ( L + l ) α 2 2 + 4 y s l λ ( L + l ) α + y s 2 λ ( L + l ) ] ,
α in α α out ,
Φ 0 = 2 π λ 2 ( L + l ) .
α in = λ ( L + l ) π ω 0 y s 2 π ω 0 l ,
α out = λ ( L + l ) + π ω 0 y s 2 π ω 0 l .
B α = 1 8 2 [ d Φ ( α ) d α ] α out α in = K α π ( α in α out ) 4 2 .
x SAL = 1 2 B α = 2 ω 0 l L .

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