Abstract

Holographic aperture ladar is a variant of synthetic aperture ladar that seeks to increase cross-range scene resolution by synthesizing a large effective aperture through the motion of a smaller receiver and through the subsequent proper phasing and correlation of the detected signals in postprocessing. Unlike in conventional synthetic aperture ladar, however, holographic aperture ladar makes use of a two- dimensional translating sensor array, not simply a translating point detector. Also unlike in conventional synthetic aperture ladar, holographic aperture images will be formed in the two orthogonal cross-range dimensions parallel and perpendicular to the sensor platform’s direction of motion. The central focus is on the development of the stripmap and spotlight holographic aperture transformations. These transformations will allow sequentially collected pupil plane field segments to be coherently stitched together in order to synthesize complex pupil plane fields with larger spatial extent. The challenge in this process is in accounting for the practical fact that both the receiver aperture and the transmitter will be in motion in real-world airborne applications. However, we demonstrate that, owing to the synchronous motion of the transmitter and receiver, resolution enhancements of more than two (stripmap case) or three (spotlight case) times the ratio of the synthetic aperture to the real receiver aperture diameter can be realized. We also demonstrate that in practical applications the holographic aperture ladar image formation process is relatively insensitive to scene depth if a good estimate of nominal scene range is available.

© 2009 Optical Society of America

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Errata

Bradley D. Duncan and Matthew P. Dierking, "Holographic aperture ladar: erratum," Appl. Opt. 52, 706-708 (2013)
https://www.osapublishing.org/ao/abstract.cfm?uri=ao-52-4-706

References

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2007

J. C. Marron and R. L. Kendrick, “Distributed aperture active imaging,” Proc. SPIE 6550, 65500A (2007).
[CrossRef]

2005

2004

A. Stern and B. Javidi, “General sampling theorem and application in digital holography,” Proc. SPIE 5557, 110-123(2004).
[CrossRef]

2002

T. M. Kreis, M. Adams, and W. P.O. Jueptner, “Aperture synthesis in digital holography,” Proc. SPIE 4777, 69-76 (2002)
[CrossRef]

R. Binet, J. Colineau, and J.-C. Lehureau, “Short-range synthetic aperture imaging at 633 nm by digital holography,” Appl. Opt. 41, 4775-4782 (2002).
[CrossRef] [PubMed]

1995

1993

1989

1988

D. Park, “Performance analysis of optical synthetic aperture radars,” Proc. SPIE 999, 100-116 (1988).

1987

Adams, M.

T. M. Kreis, M. Adams, and W. P.O. Jueptner, “Aperture synthesis in digital holography,” Proc. SPIE 4777, 69-76 (2002)
[CrossRef]

Anderson, K. A.

J. E. Mason, K. A. Anderson, R. L. Kendrick, T. S. Kubo, J. C. Maron, and T. Zhao, “Experiments with multi-aperture three-dimensional coherent imaging,” presented at 14th Coherent Laser Radar Conference, Snowmass, Colo., 8-13 July 2007.

Beck, S. M.

Binet, R.

Buck, J. R.

Buell, W. F.

Colella, B. D.

Colineau, J.

Dickinson, R. P.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts, 2005), Chaps. 3 and 4.

Green, T. J.

Hoft, T. A.

J. C. Marron, R. L. Kendrick, T. A. Hoft, and N. Seldomridge, “Novel multi-aperture 3D imaging systems,” presented at 14th Coherent Laser Radar Conference, Snowmass, Colo., 8-13 July 2007.

Javidi, B.

A. Stern and B. Javidi, “General sampling theorem and application in digital holography,” Proc. SPIE 5557, 110-123(2004).
[CrossRef]

Jueptner, W. P.O.

T. M. Kreis, M. Adams, and W. P.O. Jueptner, “Aperture synthesis in digital holography,” Proc. SPIE 4777, 69-76 (2002)
[CrossRef]

Kendrick, R. L.

J. C. Marron and R. L. Kendrick, “Distributed aperture active imaging,” Proc. SPIE 6550, 65500A (2007).
[CrossRef]

J. E. Mason, K. A. Anderson, R. L. Kendrick, T. S. Kubo, J. C. Maron, and T. Zhao, “Experiments with multi-aperture three-dimensional coherent imaging,” presented at 14th Coherent Laser Radar Conference, Snowmass, Colo., 8-13 July 2007.

J. C. Marron, R. L. Kendrick, T. A. Hoft, and N. Seldomridge, “Novel multi-aperture 3D imaging systems,” presented at 14th Coherent Laser Radar Conference, Snowmass, Colo., 8-13 July 2007.

Kozlowski, D. A.

Kreis, T. M.

T. M. Kreis, M. Adams, and W. P.O. Jueptner, “Aperture synthesis in digital holography,” Proc. SPIE 4777, 69-76 (2002)
[CrossRef]

Kubo, T. S.

J. E. Mason, K. A. Anderson, R. L. Kendrick, T. S. Kubo, J. C. Maron, and T. Zhao, “Experiments with multi-aperture three-dimensional coherent imaging,” presented at 14th Coherent Laser Radar Conference, Snowmass, Colo., 8-13 July 2007.

Kyle, T. G.

Lehureau, J.-C.

Levanon, N.

N. Levanon and E. Mozeson, Radar Signals (Wiley, 2004).
[CrossRef]

Marcus, S.

Marechal, N. J.

Maron, J. C.

J. E. Mason, K. A. Anderson, R. L. Kendrick, T. S. Kubo, J. C. Maron, and T. Zhao, “Experiments with multi-aperture three-dimensional coherent imaging,” presented at 14th Coherent Laser Radar Conference, Snowmass, Colo., 8-13 July 2007.

Marron, J. C.

J. C. Marron and R. L. Kendrick, “Distributed aperture active imaging,” Proc. SPIE 6550, 65500A (2007).
[CrossRef]

J. C. Marron and K. S. Schroeder, “Holographic laser radar,” Opt. Lett. 18, 385-387 (1993).
[CrossRef] [PubMed]

J. C. Marron, R. L. Kendrick, T. A. Hoft, and N. Seldomridge, “Novel multi-aperture 3D imaging systems,” presented at 14th Coherent Laser Radar Conference, Snowmass, Colo., 8-13 July 2007.

Mason, J. E.

J. E. Mason, K. A. Anderson, R. L. Kendrick, T. S. Kubo, J. C. Maron, and T. Zhao, “Experiments with multi-aperture three-dimensional coherent imaging,” presented at 14th Coherent Laser Radar Conference, Snowmass, Colo., 8-13 July 2007.

Mozeson, E.

N. Levanon and E. Mozeson, Radar Signals (Wiley, 2004).
[CrossRef]

Park, D.

D. Park, “Performance analysis of optical synthetic aperture radars,” Proc. SPIE 999, 100-116 (1988).

Richards, M. A.

M. A. Richards, Fundamentals of Radar Signal Processing (McGraw-Hill, 2005), Chap. 8.

Schroeder, K. S.

Seldomridge, N.

J. C. Marron, R. L. Kendrick, T. A. Hoft, and N. Seldomridge, “Novel multi-aperture 3D imaging systems,” presented at 14th Coherent Laser Radar Conference, Snowmass, Colo., 8-13 July 2007.

Shapiro, J. H.

Siegman, A. E.

A. E. Siegman, Lasers (University Science Books, 1986), Chap. 17.

Soumekh, M.

M. Soumekh, Synthetic Aperture Radar Signal Processing (Wiley, 1999).

Stern, A.

A. Stern and B. Javidi, “General sampling theorem and application in digital holography,” Proc. SPIE 5557, 110-123(2004).
[CrossRef]

Wright, T. J.

Zhao, T.

J. E. Mason, K. A. Anderson, R. L. Kendrick, T. S. Kubo, J. C. Maron, and T. Zhao, “Experiments with multi-aperture three-dimensional coherent imaging,” presented at 14th Coherent Laser Radar Conference, Snowmass, Colo., 8-13 July 2007.

Appl. Opt.

Opt. Lett.

Proc. SPIE

D. Park, “Performance analysis of optical synthetic aperture radars,” Proc. SPIE 999, 100-116 (1988).

J. C. Marron and R. L. Kendrick, “Distributed aperture active imaging,” Proc. SPIE 6550, 65500A (2007).
[CrossRef]

J.-C. Lehureau and J. Colineau, “Optical synthetic aperture imagery,” Proc. SPIE 5816, 54-65 (2005).
[CrossRef]

T. M. Kreis, M. Adams, and W. P.O. Jueptner, “Aperture synthesis in digital holography,” Proc. SPIE 4777, 69-76 (2002)
[CrossRef]

A. Stern and B. Javidi, “General sampling theorem and application in digital holography,” Proc. SPIE 5557, 110-123(2004).
[CrossRef]

Other

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts, 2005), Chaps. 3 and 4.

A. E. Siegman, Lasers (University Science Books, 1986), Chap. 17.

M. A. Richards, Fundamentals of Radar Signal Processing (McGraw-Hill, 2005), Chap. 8.

M. Soumekh, Synthetic Aperture Radar Signal Processing (Wiley, 1999).

N. Levanon and E. Mozeson, Radar Signals (Wiley, 2004).
[CrossRef]

J. C. Marron, R. L. Kendrick, T. A. Hoft, and N. Seldomridge, “Novel multi-aperture 3D imaging systems,” presented at 14th Coherent Laser Radar Conference, Snowmass, Colo., 8-13 July 2007.

J. E. Mason, K. A. Anderson, R. L. Kendrick, T. S. Kubo, J. C. Maron, and T. Zhao, “Experiments with multi-aperture three-dimensional coherent imaging,” presented at 14th Coherent Laser Radar Conference, Snowmass, Colo., 8-13 July 2007.

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Figures (6)

Fig. 1
Fig. 1

Notional depiction of a HAL system. The imaging sensor is assumed to be moving in the direction of flight of an airborne platform. For clarity, the TX and the RX master oscillator (MO) are not shown.

Fig. 2
Fig. 2

HAL transformation geometry.

Fig. 3
Fig. 3

Uncorrected and corrected point object phase segments. Here the stripmap HAL transformation has been applied to a phase-only field segment resulting from an off-axis point target. Both the TX and the RX aperture are also off-axis in this bistatic TX–RX example.

Fig. 4
Fig. 4

Example of the stripmap HAL transformation applied to three sequentially collected phase-only field segments resulting from an off-axis point target. In this case the RX aperture is effectively tangent to itself during each subsequent TX–RX cycle. Monostatic conditions apply.

Fig. 5
Fig. 5

Example of the stripmap HAL transformation applied to five sequentially collected phase-only segments resulting from an off-axis point target. In this case the RX aperture effectively overlaps itself by half its diameter during each subsequent TX–RX cycle. Monostatic conditions apply.

Fig. 6
Fig. 6

Example of the spotlight HAL transformation applied to seven sequentially collected phase-only segments resulting from an off-axis point target. In this case the RX aperture effectively overlaps itself by two thirds of its diameter during each subsequent TX–RX cycle. Monostatic conditions apply.

Equations (29)

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g sm = C { f ( ξ , η ) exp ( j π λ R o [ ( ξ - x T ) 2 + ( η - y T ) 2 ] ) h R o ( ξ , η ) } ,
h R o = exp ( j π λ R o ( ξ 2 + η 2 ) ) ,
g sm ( x a ) = C f ( ξ ) exp ( j π λ R o ( ξ x T ) 2 ) exp ( j π λ R o ( x a ξ ) 2 ) d ξ = C exp ( j π λ R o x a 2 ) exp ( j π λ R o x T 2 ) f ( ξ ) exp ( j 2 π λ R o ξ 2 ) exp ( j p ξ ) d ξ
= C exp ( j π λ R o x a 2 ) exp ( j π λ R o x T 2 ) F ( x a + x T ) ,
p = 2 π λ R o ( x a + x T ) ( rad / m ) ,
g o ( x a ) = C exp ( j π λ R o x a 2 ) F ( x a ) .
g sm ( x a x T ) exp ( j π λ R o x T 2 ) = C exp ( j π λ R o ( x a x T ) 2 ) F ( x a ) .
g sm ( x a x T ) exp ( j 2 π λ R o x T ( x T x a ) ) = C exp ( j π λ R o x a 2 ) F ( x a ) = g o ( x a ) .
g o ( x a + x T , y a + y T ) = g sm ( x a , y a ) exp ( j 2 π λ R o [ x a x T + y a y T ] ) .
g p - sm ( x a ) = C exp ( j π λ R o ( x a 2 + x T 2 ) ) × δ ( ξ ξ p ) exp ( j 2 π λ R o ξ 2 ) exp ( j p ξ ) d ξ ,
g p - sm ( x a ) = C exp ( j 2 π λ R o ( x a 2 + x T 2 2 + ξ p 2 ( x a + x T ) ξ p ) ) .
g po ( x a ) = C exp ( j 2 π λ R o ( x a 2 2 + ξ p ( ξ p x a ) ) ) .
D eff -sm = 2 D SAR + D ap .
Δ C R VFP -sm = λ f V D eff-sm = λ f V 2 D SAR + D ap ,
Δ C R sm = λ R o 2 D SAR + D ap .
ISR sm = 2 D SAR + D ap D ap = 2 D SAR D ap + 1.
D SAR - max 1.2 ω o 1 + ( R o λ π ω o 2 ) 2 ,
g sp = C { f ( ξ , η ) exp ( j π λ R o [ ( ξ x T ) 2 + ( η y T ) 2 ] ) exp ( j 2 π λ R o [ ξ x T + η y T ] ) h R o ( ξ , η ) } ,
g sp ( x a ) = C - f ( ξ ) exp ( j π λ R o ( ξ - x T ) 2 ) × exp ( j 2 π λ R o ξ x T ) exp ( j π λ R o ( x a - ξ ) 2 ) d ξ = C exp ( j π λ R o x a 2 ) exp ( j π λ R o x T 2 ) × - f ( ξ ) exp ( j 2 π λ R o ( ξ 2 ξ x T ) ) exp ( - j p ξ ) d ξ
= C exp ( j π λ R o x a 2 ) exp ( j π λ R o x T 2 ) × [ F ( x a + x T ) δ ( x a + 2 x T ) ]
= C exp ( j π λ R o x a 2 ) exp ( j π λ R o x T 2 ) F ( x a + 2 x T ) ,
g o ( x a + 2 x T , y a + 2 y T ) = g sp ( x a , y a ) exp ( j π λ R o [ x T ( 4 x a + 3 x T ) + y T ( 4 y a + 3 y T ) ] ) ,
g p -sp ( x a ) = C exp ( j 2 π λ R o ( x a 2 + x T 2 2 + ξ p 2 ( x a + 2 x T ) ξ p ) ) .
D eff-sp = 3 D SAR + D ap .
Δ C R sp = λ R o D eff-sp = λ R o 3 D SAR + D ap ,
ISR sp = 3 D SAR + D ap D ap = 3 D SAR D ap + 1.
Δ ϕ sm = 2 π λ ( x a x T + y a y T ) ( 1 R o 1 R o + Δ R sm ) 2 π ( x a x T + y a y T ) ( Δ R sm λ R o 2 ) ,
Δ R sm 0.1 λ R o 2 ( x a x T + y a y T ) | max .
Δ R sp 0.1 λ R o 2 ( x T ( 2 x a + 1.5 x T ) + y T ( 2 y a + 1.5 y T ) ) | max .

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