Abstract

Distributed aperture synthesis is an exciting technique for recovering high-resolution images from an array of small telescopes. Such a system requires optical field values measured at individual apertures to be phased together so that a single, high-resolution image can be synthesized. This paper describes the application of sharpness metrics to the process of phasing multiple coherent imaging systems into a single high-resolution system. Furthermore, this paper will discuss hardware and present the results of simulations and experiments which will illustrate how aperture synthesis is performed.

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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]
  4. R. L. Kendrick and J. C. Marron, “Analytic Versus Adaptive Image Formation Using Optical Phased Arrays,” Proc. SPIE 7468, 75680N (2009).
  5. N. J. Miller, M. P. Dierking, and B. D. Duncan, “Optical sparse aperture imaging,” Appl. Opt. 46(23), 5933–5943 (2007).
    [CrossRef] [PubMed]
  6. Q. Wu, L. Qian, and W. Shen, “Image Recovering for Sparse-aperture Systems,” Proc. SPIE 5642, 478–486 (2005).
    [CrossRef]
  7. R. G. Paxman and J. C. Marron, “Aberration Correction of Speckled Imagery with an Image Sharpness Criterion,” Statistical Optics,” Proc. SPIE 976, 37–47 (1988).
  8. S. T. Thurman and J. R. Fienup, “Phase-error correction in digital holography,” J. Opt. Soc. Am. A 25(4), 983–994 (2008).
    [CrossRef]
  9. J. C. Marron, R. L. Kendrick, N. Seldomridge, T. D. Grow, and T. A. Höft, “Atmospheric turbulence correction using digital holographic detection: experimental results,” Opt. Express 17(14), 11638–11651 (2009).
    [CrossRef] [PubMed]

2009 (2)

2008 (1)

2007 (2)

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

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

2005 (1)

Q. Wu, L. Qian, and W. Shen, “Image Recovering for Sparse-aperture Systems,” Proc. SPIE 5642, 478–486 (2005).
[CrossRef]

2003 (1)

1988 (1)

R. G. Paxman and J. C. Marron, “Aberration Correction of Speckled Imagery with an Image Sharpness Criterion,” Statistical Optics,” Proc. SPIE 976, 37–47 (1988).

1974 (1)

Buffington, A.

Dierking, M. P.

Duncan, B. D.

Fienup, J. R.

Grow, T. D.

Höft, T. A.

Kendrick, R. L.

J. C. Marron, R. L. Kendrick, N. Seldomridge, T. D. Grow, and T. A. Höft, “Atmospheric turbulence correction using digital holographic detection: experimental results,” Opt. Express 17(14), 11638–11651 (2009).
[CrossRef] [PubMed]

R. L. Kendrick and J. C. Marron, “Analytic Versus Adaptive Image Formation Using Optical Phased Arrays,” Proc. SPIE 7468, 75680N (2009).

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

Marron, J. C.

R. L. Kendrick and J. C. Marron, “Analytic Versus Adaptive Image Formation Using Optical Phased Arrays,” Proc. SPIE 7468, 75680N (2009).

J. C. Marron, R. L. Kendrick, N. Seldomridge, T. D. Grow, and T. A. Höft, “Atmospheric turbulence correction using digital holographic detection: experimental results,” Opt. Express 17(14), 11638–11651 (2009).
[CrossRef] [PubMed]

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

R. G. Paxman and J. C. Marron, “Aberration Correction of Speckled Imagery with an Image Sharpness Criterion,” Statistical Optics,” Proc. SPIE 976, 37–47 (1988).

Miller, J. J.

Miller, N. J.

Muller, R. A.

Paxman, R. G.

R. G. Paxman and J. C. Marron, “Aberration Correction of Speckled Imagery with an Image Sharpness Criterion,” Statistical Optics,” Proc. SPIE 976, 37–47 (1988).

Qian, L.

Q. Wu, L. Qian, and W. Shen, “Image Recovering for Sparse-aperture Systems,” Proc. SPIE 5642, 478–486 (2005).
[CrossRef]

Seldomridge, N.

Shen, W.

Q. Wu, L. Qian, and W. Shen, “Image Recovering for Sparse-aperture Systems,” Proc. SPIE 5642, 478–486 (2005).
[CrossRef]

Thurman, S. T.

Wu, Q.

Q. Wu, L. Qian, and W. Shen, “Image Recovering for Sparse-aperture Systems,” Proc. SPIE 5642, 478–486 (2005).
[CrossRef]

Appl. Opt. (1)

J. Opt. Soc. Am. (1)

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

Opt. Express (1)

Proc. SPIE (4)

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

R. L. Kendrick and J. C. Marron, “Analytic Versus Adaptive Image Formation Using Optical Phased Arrays,” Proc. SPIE 7468, 75680N (2009).

Q. Wu, L. Qian, and W. Shen, “Image Recovering for Sparse-aperture Systems,” Proc. SPIE 5642, 478–486 (2005).
[CrossRef]

R. G. Paxman and J. C. Marron, “Aberration Correction of Speckled Imagery with an Image Sharpness Criterion,” Statistical Optics,” Proc. SPIE 976, 37–47 (1988).

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Figures (8)

Fig. 1
Fig. 1

Aperture synthesis initially allows large monolithic apertures, (a), to be replaced with dense-packed distributed arrays, (b). Over time, the array patterns will become sparser and system depth can be minimized by utilizing pupil-plane imaging techniques, (c).

Fig. 2
Fig. 2

Illustration of coherent aperture synthesis architecture. The hardware consists of a transmitter Tx, coherent receivers Rx1-Rx3 which capture holographic fringes across a camera array, and a computer which forms images in software.

Fig. 3
Fig. 3

Digital holography using spatial heterodyne technique. The pupil field, Ut(x,y), is imaged onto the CMOS array using the afocal telescope formed by lenses L1 and L2. A non-polarizing beam splitter is used to insert a tilted LO reference, ULO(x,y), which is interfered with pupil field. The resulting fringes are then captured across the CMOS array.

Fig. 4
Fig. 4

The first stage of the image sharpening algorithm relies on sharpening the data taken across a single sub-aperture. This algorithm corrects the phase across a single pupil realization such that the speckle-averaged image is sharpened.

Fig. 5
Fig. 5

The second step of the image sharpening algorithm combines the pupils into a single digital pupil plane based on speckle realization. The individual pupil functions are then corrected so that the synthesized and speckle-averaged imagery is appropriately sharpened.

Fig. 6
Fig. 6

A portion of the ISO 12233 Target.

Fig. 7
Fig. 7

The average RMS piston error for values of 0.025 ≤ γ ≤ 2 from simulated results are shown as dots and the solid line represents a fourth degree polynomial fit.

Fig. 8
Fig. 8

Imagery from (a) a simulated single aperture with 360 speckle realizations and (b) lab data from a single, corrected aperture and 360 speckle realizations. Also shown are results for (c) 120 speckle realizations of a simulated aperture coherently synthesized from three horizontally arrayed sub-apertures and (d) lab results for an equivalent synthesized aperture.

Tables (1)

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Table 1 Predicted resolution for a single aperture and a sparse array.

Equations (6)

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I(x,y)=|ULO(x,y)|2+|Ut(x,y)|2+ULO(x,y)Ut*(x,y)+ULO*(x,y)Ut(x,y),
F{I(x,y)}=F{|ULO(x,y)|2}+F{|Ut(x,y)|2}+F{ULO(x,y)Ut*(x,y)}+F{ULO*(x,y)Ut(x,y)}.
F{I(x,y)}=ALO2δ(fx,fy)+F{   |Ut(x,y)|2}+F{ALOexp(jk(θxx+θyy))Ut*(x,y)}+F{ALOexp(jk(θxx+θyy))Ut(x,y)},
F{I(x,y)}=ALO2δ(fx,fy)+F{   |Ut(x,y)|2}+ALOF{Ut*(x,y)}δ(fxfx0,fyfy0)+ALOF{Ut(x,y)}δ(fx+fx0,fy+fy0),
S=Iγ(x,y)dxdy,
SA=dxdy|1Nn=1NIn(x,y)|γ,

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