Abstract

Multi-transmitter aperture synthesis is a method in which multiple transmitters can be used to improve resolution and contrast of distributed aperture systems. Such a system utilizes multiple transmitter locations to interrogate a target from multiple look angles thus increasing the angular spectrum content captured by the receiver aperture array. Furthermore, such a system can improve the contrast of sparsely populated receiver arrays by capturing field data in the region between sub-apertures by utilizing multiple transmitter locations. This paper discusses the theory behind multi-transmitter aperture synthesis and provides experimental verification that imagery captured using multiple transmitters will provide increased resolution.

© 2010 OSA

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References

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  1. J. C. Marron and R. L. Kendrick, “Distributed Aperture Active Imaging,” Proc. SPIE 6550, 65500A (2007).
    [CrossRef]
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    [CrossRef]
  3. J. C. Marron, and R. L. Kendrick, “Multi-Aperture 3D Imaging Systems,” Aerospace Conference, 2008 IEEE (2008).
  4. N. J. Miller, M. P. Dierking, and B. D. Duncan, “Optical sparse aperture imaging,” Appl. Opt. 46(23), 5933–5943 (2007).
    [CrossRef] [PubMed]
  5. A. J. Stokes, B. D. Duncan, and M. P. Dierking, “Improving mid-frequency contrast in sparse aperture optical imaging systems based upon the Golay-9 array,” Opt. Express 18(5), 4417–4427 (2010).
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    [CrossRef] [PubMed]
  7. J. W. Stafford, B. D. Duncan, and M. P. Dierking, “Experimental demonstration of a stripmap holographic aperture ladar system,” Appl. Opt. 49(12), 2262-2270 (2010).
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    [CrossRef]
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2010 (3)

2009 (1)

2008 (1)

2007 (2)

J. C. Marron and R. L. Kendrick, “Distributed Aperture Active Imaging,” Proc. SPIE 6550, 65500A (2007).
[CrossRef]

N. J. Miller, M. P. Dierking, and B. D. Duncan, “Optical sparse aperture imaging,” Appl. Opt. 46(23), 5933–5943 (2007).
[CrossRef] [PubMed]

Dierking, M. P.

Duncan, B. D.

Fienup, J. R.

Jameson, D. F.

Kendrick, R. L.

J. C. Marron and R. L. Kendrick, “Distributed Aperture Active Imaging,” Proc. SPIE 6550, 65500A (2007).
[CrossRef]

Marron, J. C.

J. C. Marron and R. L. Kendrick, “Distributed Aperture Active Imaging,” Proc. SPIE 6550, 65500A (2007).
[CrossRef]

Miller, N. J.

Rabb, D. J.

Stafford, J. W.

Stokes, A. J.

Thurman, S. T.

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Figures (7)

Fig. 1
Fig. 1

The HAL concept combines synthetic aperture ladar with digital holography. Translation of a linear array through positions 1 to 4 allows a very large synthetic aperture to be formed. A single transmitter is shown as a white circle which translates along with the receiver array shown by the grey circles.

Fig. 2
Fig. 2

A multi-transmitter, multi-aperture imaging system will (a) illuminate the target with a pulse from a single transmitter element and capture the backscatter. The subsequent transmitter pulse will (b) illuminate the target from a different location and the receiver array will capture a shifted version of the reflected wavefront.

Fig. 3
Fig. 3

Theoretical layout of an imaging system which utilizes multiple transmitters with a active distributed aperture system.

Fig. 4
Fig. 4

A diagram of the digital holography receiver setup used to capture the incident wavefront Ut(x,y).

Fig. 5
Fig. 5

A diagram of the optical apertures and transmitter locations in the pupil plane.

Fig. 6
Fig. 6

Registered pupil-field amplitudes (a) have increased amplitude where the registered field values overlap and have been added. An amplitude correction is applied to remove the aperture-registration artifacts resulting in a corrected field amplitude (b).

Fig. 7
Fig. 7

An image formed from (a) 36 averages of an unsharpened, single-aperture image of the quarter and (b) 36 averages of a sharpened single aperture. The application of image sharpening algorithms on the field captured at a single aperture allows for aberrations to be corrected. An image formed from (c) 12 averages of a synthesized aperture from the three physical apertures and a single transmitter, and lastly an image (d) is shown which is created from the set of 36 field values synthesized into a single, large field.

Tables (1)

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Table 1 Relative transmitter locations.

Equations (9)

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U T ( x T , y T ) = e j k z e j k 2 z ( x T 2 + y T 2 ) j λ z F { U ( x x n , y y n ) } ,
U T ( x T , y T ) = g ˜ ( x T , y T ) F { U ( x , y ) δ ( x x n , y y n ) } ,
U T ( x T , y T ) = e j 2 π λ z ( x T x n + y T y n ) U T ' ( x T , y T ) ,
U T ' ( x T , y T ) = g ˜ ( x T , y T ) F { U ( x , y ) ​ ​ } ​ ​ ​ .
U r e f l ( x T , y T ) = e j 2 π λ z ( x T x n + y T y n ) U T ' ( x T , y T ) r ( x T , y T ) ,
U R ( x , y ) = P ( x , y ) e j k z e j k 2 z ( x 2 + y 2 ) j λ z F { e j 2 π λ z ( x T x n + y T y n ) U T ' ( x T , y T ) r ( x T , y T ) } ,
U R ( x , y ) = P ( x , y ) e j k z e j k 2 z ( x 2 + y 2 ) j λ z U r ( x x n , y y n ) ,
U r ( x , y ) = F { U T ' ( x T , y T ) r ( x T , y T ) } .
S A = d x d y | 1 N n = 1 N I n ( x , y ) | γ ,

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