Abstract

The maximum resolution of a multiple-input multiple-output (MIMO) imaging system is determined by the size of the synthetic aperture. The synthetic aperture is determined by a coordinate shift using the relative positions of the illuminators and receive apertures. Previous methods have shown non-iterative phasing for multiple illuminators with a single receive aperture for intra-aperture synthesis. This work shows non-iterative phasing with both multiple illuminators and multiple receive apertures for inter-aperture synthesis. Simulated results show that piston, tip, and tilt can be calculated using inter-aperture phasing after intra-aperture phasing has been performed. Use of a fourth illuminator for increased resolution is shown. The modulation transfer function (MTF) is used to quantitatively judge increased resolution.

© 2016 Optical Society of America

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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]
  2. N. J. Miller, M. P. Dierking, and B. D. Duncan, “Optical sparse aperture imaging,” Appl. Opt. 46(23), 5933–5943 (2007).
    [Crossref] [PubMed]
  3. D. Rabb, D. Jameson, A. Stokes, and J. Stafford, “Distributed aperture synthesis,” Opt. Express 18(10), 10334–10342 (2010).
    [Crossref] [PubMed]
  4. D. J. Rabb, D. F. Jameson, J. W. Stafford, and A. J. Stokes, “Multi-transmitter aperture synthesis,” Opt. Express 18(24), 24937–24945 (2010).
    [Crossref] [PubMed]
  5. A. E. Tippie, A. Kumar, and J. R. Fienup, “High-resolution synthetic-aperture digital holography with digital phase and pupil correction,” Opt. Express 19(13), 12027–12038 (2011).
    [Crossref] [PubMed]
  6. S. M. Venable, B. D. Duncan, M. P. Dierking, and D. J. Rabb, “Demonstrated resolution enhancement capability of a stripmap holographic aperture ladar system,” Appl. Opt. 51(22), 5531–5542 (2012).
    [Crossref] [PubMed]
  7. D. J. Rabb, J. W. Stafford, and D. F. Jameson, “Non-iterative aberration correction of a multiple transmitter system,” Opt. Express 19(25), 25048–25056 (2011).
    [Crossref] [PubMed]
  8. B. K. Gunturk, D. J. Rabb, and D. F. Jameson, “Multi-transmitter aperture synthesis with Zernike based aberration correction,” Opt. Express 20(24), 26448–26457 (2012).
    [Crossref] [PubMed]
  9. S. E. Reichenbach, S. K. Park, and R. Narayanswamy, “Characterizing digital image acquisition devices,” Opt. Eng. 30(2), 170–177 (1991).
    [Crossref]
  10. J. D. Schmidt, Numerical Simulation for Optical Wave Propagation (SPIE, 2010).
  11. J. W. Goodman, Introduction to Fourier Optics (Roberts and Company Publishers, 2005).
  12. P. D. Burns, “sfrmat3: SFR evaluation for digital cameras and scanners.” http://losburns.com/imaging/software/SFRedge/sfrmat3_post/index.html

2012 (2)

2011 (2)

2010 (2)

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]

1991 (1)

S. E. Reichenbach, S. K. Park, and R. Narayanswamy, “Characterizing digital image acquisition devices,” Opt. Eng. 30(2), 170–177 (1991).
[Crossref]

Dierking, M. P.

Duncan, B. D.

Fienup, J. R.

Gunturk, B. K.

Jameson, D.

Jameson, D. F.

Kendrick, R. L.

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

Kumar, A.

Marron, J. C.

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

Miller, N. J.

Narayanswamy, R.

S. E. Reichenbach, S. K. Park, and R. Narayanswamy, “Characterizing digital image acquisition devices,” Opt. Eng. 30(2), 170–177 (1991).
[Crossref]

Park, S. K.

S. E. Reichenbach, S. K. Park, and R. Narayanswamy, “Characterizing digital image acquisition devices,” Opt. Eng. 30(2), 170–177 (1991).
[Crossref]

Rabb, D.

Rabb, D. J.

Reichenbach, S. E.

S. E. Reichenbach, S. K. Park, and R. Narayanswamy, “Characterizing digital image acquisition devices,” Opt. Eng. 30(2), 170–177 (1991).
[Crossref]

Stafford, J.

Stafford, J. W.

Stokes, A.

Stokes, A. J.

Tippie, A. E.

Venable, S. M.

Appl. Opt. (2)

Opt. Eng. (1)

S. E. Reichenbach, S. K. Park, and R. Narayanswamy, “Characterizing digital image acquisition devices,” Opt. Eng. 30(2), 170–177 (1991).
[Crossref]

Opt. Express (5)

Proc. SPIE (1)

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

Other (3)

J. D. Schmidt, Numerical Simulation for Optical Wave Propagation (SPIE, 2010).

J. W. Goodman, Introduction to Fourier Optics (Roberts and Company Publishers, 2005).

P. D. Burns, “sfrmat3: SFR evaluation for digital cameras and scanners.” http://losburns.com/imaging/software/SFRedge/sfrmat3_post/index.html

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Figures (12)

Fig. 1
Fig. 1 (a) Single receive aperture, light green, with three illuminator apertures, magenta. (b) Field overlap due to a single receiver aperture and three illuminator cluster.
Fig. 2
Fig. 2 Difference between the wavefronts of two overlapped pupil fields. The fringed section in the middle is where the two fields overlap.
Fig. 3
Fig. 3 (a) Example of a three illuminator and five aperture array. The light green circles are filled receive apertures and the magenta circles are illuminators. (b) Example of the field overlaps from the three illuminator and five aperture array shown on top. The light blue areas are where only one field is present, the yellow are areas of two fields overlapping, and the red is where three fields overlap.
Fig. 4
Fig. 4 Wavefront difference between two pupils coming from two different apertures. (a) Piston, tip, and tilt error remains. (b) Piston error remains.
Fig. 5
Fig. 5 (a) Example of a four illuminator and five aperture array. The light green circles are filled receive apertures and the magenta circles are illuminators. (b) Example of the field overlaps from the four illuminator and five aperture array shown on top.
Fig. 6
Fig. 6 MTF plots for the arrays shown in Fig. 3 and Fig. 5. The x-axis is in cycles per mm. (a) Horizontal MTF for array shown in Fig. 3. (b) Horizontal MTF for array shown in Fig. 5.
Fig. 7
Fig. 7 Target used in simulation.
Fig. 8
Fig. 8 200 speckle realization averaged images formed from non aberrated pupil fields. (a) Single aperture with one illuminator. (b) Four illuminator and five aperture array.
Fig. 9
Fig. 9 200 speckle realization averaged images formed from aberrated pupil fields. (a) Single aperture with one illuminator. (b) Four illuminator and five aperture array.
Fig. 10
Fig. 10 Aberration corrected image from four illuminator and five aperture array.
Fig. 11
Fig. 11 Comparison between a portion of the non aberrated image and the aberration corrected image. The images have been rotated. (a)Non aberrated. (b)Aberration corrected.
Fig. 12
Fig. 12 Comparisons of analytic and experimental MTF curves. (a) MTFs for the three illuminator five receive aperture system. (b) MTFs for the four illuminator five receive aperture system.

Equations (4)

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U i ( x,y )=P( x,y )exp( j2π W e ( x,y ) ) U b ( x x i ,y y i ), i=1,2,
W i ( x,y )= W e ( x,y )+ W b ( x x i ,y y i ), i=1,2.
ΔW( x,y )= W 1 ( x x 1 ,y y 1 ) W 2 ( x x 2 ,y y 2 ) =( W e ( x+ x 1 ,y+ y 1 )+ W b ( x,y ) )( W e ( x+ x 2 ,y+ y 2 )+ W b ( x,y ) ) = W e ( x+ x 1 ,y+ y 1 ) W e ( x+ x 2 ,y+ y 2 ).
ΔW( x,y )= W e,i1,j1 ( x,y ) W e,i2,j2 ( x,y ) i1i2,j1j2

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