Abstract

By synthesizing large effective apertures through the translation of a smaller imaging sensor and the subsequent proper phasing and correlation of detected signals in postprocessing, holographic aperture ladar (HAL) systems seek to increase the resolution of remotely imaged targets. The stripmap HAL process was demonstrated in the laboratory, for the first time to our knowledge. Our results show that the stripmap HAL transformation can precisely account for off-axis transmitter induced phase migrations. This in turn allows multiple pupil plane field segments, sequentially collected across a synthetic aperture, to be coherently mosaiced together. As a direct consequence, we have been able to confirm the capability of the HAL method to potentially provide substantial increases in longitudinal cross-range resolution. The measurement and sampling of complex pupil plane field segments, as well as target related issues arising from short laboratory ranges, have also been addressed.

© 2010 Optical Society of America

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References

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  1. S. Beck, J. R. Buck, W. F. Buell, R. P. Dickinson, D. A. Kozlowski, N. J. Marechal, and T. J. Wright, “Synthetic-aperture imaging laser radar: laboratory demonstration and signal processing,” Appl. Opt.  44, 7621–7629 (2005).
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  7. B. D. Duncan and M. P. Dierking, “Holographic aperture ladar,” Appl. Opt.  48, 1168–1177 (2009).
    [CrossRef]
  8. J. W. Stafford, B. D. Duncan, and M. P. Dierking, “Holographic aperture ladar laboratory demonstration,” paper presented at the 15th Coherent Laser Radar Conference, Toulouse, France, 22–26 June 2009.
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2009 (1)

2005 (1)

2002 (1)

2000 (1)

1999 (1)

1997 (1)

1995 (1)

1994 (1)

1947 (1)

A. Maréchal, “Étude des effets combinés de la diffraction et des aberration géométriques sur l’image d’un point lumineux,” Rev. Opt. Theor. Instrum.  26, 257–277 (1947).

Beck, S.

Binet, R.

Buck, J. R.

Buell, W. F.

Colella, B. D.

Colineau, J.

Collot, L.

Davis, C. D.

C. D. Davis, Lasers and Electro-Optics (Cambridge Univ. Press, 2002).

Dickinson, R. P.

Dierking, M. P.

B. D. Duncan and M. P. Dierking, “Holographic aperture ladar,” Appl. Opt.  48, 1168–1177 (2009).
[CrossRef]

J. W. Stafford, B. D. Duncan, and M. P. Dierking, “Holographic aperture ladar laboratory demonstration,” paper presented at the 15th Coherent Laser Radar Conference, Toulouse, France, 22–26 June 2009.

Duncan, B. D.

B. D. Duncan and M. P. Dierking, “Holographic aperture ladar,” Appl. Opt.  48, 1168–1177 (2009).
[CrossRef]

J. W. Stafford, B. D. Duncan, and M. P. Dierking, “Holographic aperture ladar laboratory demonstration,” paper presented at the 15th Coherent Laser Radar Conference, Toulouse, France, 22–26 June 2009.

Green, T. J.

Gross, M.

Kozlowski, D. A.

Le Clerc, F.

Lehureau, J.-C.

Marcus, S.

Marechal, N. J.

Maréchal, A.

A. Maréchal, “Étude des effets combinés de la diffraction et des aberration géométriques sur l’image d’un point lumineux,” Rev. Opt. Theor. Instrum.  26, 257–277 (1947).

Pedrotti, F. L.

F. L. Pedrotti and L. S. Pedrotti, Introduction to Optics(Prentice-Hall, 1993).

Pedrotti, L. S.

F. L. Pedrotti and L. S. Pedrotti, Introduction to Optics(Prentice-Hall, 1993).

Richards, M. A.

M. A. Richards, Fundamentals of Radar Signal Processing (McGraw-Hill, 2005).

Saleh, B. E. A.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley-Interscience, 2007).

Schnars, U.

Smith, W. J.

W. J. Smith, Modern Optical Engineering (McGraw-Hill, 2000).

Stafford, J. W.

J. W. Stafford, B. D. Duncan, and M. P. Dierking, “Holographic aperture ladar laboratory demonstration,” paper presented at the 15th Coherent Laser Radar Conference, Toulouse, France, 22–26 June 2009.

Teich, M. C.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley-Interscience, 2007).

van den Bos, A.

Wright, T. J.

Yamaguchi, I.

Zhang, T.

Appl. Opt. (4)

J. Opt. Soc. Am. A (2)

Opt. Lett. (2)

Rev. Opt. Theor. Instrum. (1)

A. Maréchal, “Étude des effets combinés de la diffraction et des aberration géométriques sur l’image d’un point lumineux,” Rev. Opt. Theor. Instrum.  26, 257–277 (1947).

Other (6)

M. A. Richards, Fundamentals of Radar Signal Processing (McGraw-Hill, 2005).

C. D. Davis, Lasers and Electro-Optics (Cambridge Univ. Press, 2002).

W. J. Smith, Modern Optical Engineering (McGraw-Hill, 2000).

F. L. Pedrotti and L. S. Pedrotti, Introduction to Optics(Prentice-Hall, 1993).

J. W. Stafford, B. D. Duncan, and M. P. Dierking, “Holographic aperture ladar laboratory demonstration,” paper presented at the 15th Coherent Laser Radar Conference, Toulouse, France, 22–26 June 2009.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley-Interscience, 2007).

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Figures (8)

Fig. 1
Fig. 1

Phase accumulation due to a nonparaxial spherical reflector. The transmitter is assumed to be aimed at the center of the target and parallel to the z axis. Δ R 1 and Δ R 1 are the propagation distances whose cumulative length is responsible for the reflected phase accumulation, while C denotes the center of the sphere.

Fig. 2
Fig. 2

Nonparaxial reflection phase accumulation. The horizontal dashed line corresponds to the Marechal limit, leading to a ξ 0 value (vertical dashed line) in our experiment of 185 μm .

Fig. 3
Fig. 3

Diagram of our ball bearing target illustrating effective focal point rotation along the circle whose diameter is D / 2 .

Fig. 4
Fig. 4

Diagram of our experimental setup.

Fig. 5
Fig. 5

Sequence of steps employed to acquire and process complex pupil plane target field information.

Fig. 6
Fig. 6

One-dimensional slice ( y a = 0 ) through a measured phase segment arising from an off-axis point target located at cross-range position ξ c = 1 cm and range R 0 = 1.95 m . Since the center of RX aperture is located at x a = 0 for this shot, the center of HAL transformed phase segment is relocated directly above the TX.

Fig. 7
Fig. 7

Same data of Fig. 6 zoomed in around the region of the HAL transformed phase segment. Due to residual tilt phase errors, this fully processed phase segment had an RMS wavefront error of 0.44 wave.

Fig. 8
Fig. 8

Result of applying the stripmap HAL transformation to three sequentially collected phase-only field segments. In this case the TX/RX combination are effectively shifted by D ap / 2 between each data collection cycle.

Equations (18)

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g 0 ( x a + x T , y a + y T ) = g sm ( x a , y a ) exp ( j 2 π λ R 0 [ x a x T + y a y T ] ) ,
D eff = 2 D SAR + D ap .
ISR = D eff D ap = 2 D SAR D ap + 1.
ϕ = k { ( D 2 D 2 4 ξ 2 ) cos ( 2 sin ( 2 ξ D ) ) + ( D 2 D 2 4 ξ 2 ) } ,
ϕ i = k ξ 2 ( D / 2 ) .
θ 1 = tan 1 ( x T ξ c R 0 + D / 4 ) ,
Δ ϕ piston = 2 2 π λ Δ z = π D λ ( 1 cos θ 1 ) ,
Δ ξ = D 4 sin θ 1 D 4 R 0 ( x T ξ c ) D 4 ,
D SAR - max 1.22 ω 0 1 + ( R 0 λ π ω 0 2 ) 2 ,
θ afocal = 2 tan 1 ( D L N P x 2 ( f 1 + f 2 ) ) ,
Λ = M λ R 0 d ,
d 0 = M λ R 0 4 P x .
D SAR - CCD = 2 d 0 = M λ R 0 2 P x .
| g i ( x , y ) + f LO ( x , y ) | 2 = | g i | 2 + | f LO | 2 + g i f LO * + g i * f LO ,
| g i ( x , y ) + f L O ( x , y ) | 2 exp ( j ϕ R 0 ) ,
ϕ R 0 = π λ R 0 1 M 2 ( x 2 + y 2 ) .
g i exp ( j ϕ R 0 ) f LO * = [ g i exp ( j ϕ R 0 ) ] exp [ j ( ϕ AF + ϕ Tilt ) ] = g i ( x , y ) exp ( j ϕ Tilt ) ,
g 0 ( x a ) = C exp ( j 2 π λ R 0 ( x a 2 2 + ξ c ( ξ c x a ) ) ) ,

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