Abstract

Multi-transmitter aperture synthesis provides aperture gain and improves effective aperture fill factor by shifting the received speckle field through the use of multiple transmitter locations. It is proposed that by utilizing methods based on shearing interferometry some low-order aberrations, such as defocus, can be found directly rather than through iterative algorithms. The current work describes the theory behind multi-transmitter aberration correction and describes experiments used to validate this method. Experimental results are shown which demonstrate the ability of such a sensor to solve directly for defocus and toric curvature in the captured field values.

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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. D. J. Rabb, D. F. Jameson, A. J. Stokes, and J. W. Stafford, “Distributed aperture synthesis,” Opt. Express 18(10), 10334–10342 (2010).
    [CrossRef] [PubMed]
  3. 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]
  4. J. R. Fienup and J. J. Miller, “Aberration correction by maximizing generalized sharpness metrics,” J. Opt. Soc. Am. A 20(4), 609–620 (2003).
    [CrossRef] [PubMed]
  5. R. A. Hutchin, “Sheared coherent interferometric photography, a technique for lensless imaging,” in Digital Image Recover and Synthesis, P. S. Idell, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 2029, 161–168 (1993).
  6. T. Kreis, Handbook of Holographic Interferometry: Optical and Digital Methods (Wiley, 2005).
  7. M. Guizar-Sicairos, S. T. Thurman, and J. R. Fienup, “Efficient subpixel image registration algorithms,” Opt. Lett. 33(2), 156–158 (2008).
    [CrossRef] [PubMed]
  8. M. Guizar, “Efficient subpixel image registration by cross-correlation,” http://www.mathworks.com/matlabcentral/fileexchange/18401-efficient-subpixel-image-registration-by-cross-correlation

2010 (2)

2008 (1)

2007 (1)

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

2003 (1)

Fienup, J. R.

Guizar-Sicairos, M.

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, J. J.

Rabb, D. J.

Stafford, J. W.

Stokes, A. J.

Thurman, S. T.

J. Opt. Soc. Am. A (1)

Opt. Express (2)

Opt. Lett. (1)

Proc. SPIE (1)

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

Other (3)

M. Guizar, “Efficient subpixel image registration by cross-correlation,” http://www.mathworks.com/matlabcentral/fileexchange/18401-efficient-subpixel-image-registration-by-cross-correlation

R. A. Hutchin, “Sheared coherent interferometric photography, a technique for lensless imaging,” in Digital Image Recover and Synthesis, P. S. Idell, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 2029, 161–168 (1993).

T. Kreis, Handbook of Holographic Interferometry: Optical and Digital Methods (Wiley, 2005).

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Figures (7)

Fig. 1
Fig. 1

Illustration of a concept multi-transmitter system.

Fig. 2
Fig. 2

x and y shears for a three transmitter system.

Fig. 3
Fig. 3

The multi-transmitter experiment utilizes focal plane holography with a calibrated aberration source.

Fig. 4
Fig. 4

USAF symbol target composed of absorptive tape on brushed aluminum.

Fig. 5
Fig. 5

An illustration of the front of the multi-transmitter imaging system. The target is sequentially imaged using the Tx locations to capture target and aberration field values. The optical aberration is inserted in front of the 1” lens.

Fig. 6
Fig. 6

Initial incoherent average of four transmit realizations are in the left column, calculated aberrations for the transmit realizations are in the center column, and the coherently combined transmit realizations with aberrations corrected are in the right column. The first row was the best focus for the system, second row corresponds to the object being moved closer, the third and fourth rows are again at best focus with astigmatism added by rotating a pair of cylindrical lenses varying amounts.

Fig. 7
Fig. 7

Peak-to-valley aberrations found through the experiment and OSLO raytraces for (a) defocus as a function of target distance and (b) toric curvature as a function of rotation within a matched pair of cylindrical lenses.

Equations (18)

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U d ( x,y )=P( x,y )exp( j φ e ( x,y) ) ) U b ( x x T ,y y T ),
φ d ( x,y )=2π W e ( x,y )+2π W b ( x x T ,y y T ),
W d ( x+ x T ,y+ y T )= W e ( x+ x T ,y+ y T )+ W b ( x,y ),
ΔW( x,y )= W e ( x+ x T0 ,y+ y T0 )+ W b ( x,y ) ( W e ( x+ x T1 ,y+ y T1 )+ W b ( x,y ) ),
ΔW( x,y )= W e ( x+ x T0 ,y+ y T0 ) W e ( x+ x T1 ,y+ y T1 ).
W e ( x x T ,y y T )= i,j a ij ( x x T ) i ( y y T ) j .
ΔW( x,y )=x( a 11 Δy+2 a 20 Δx )+y( a 11 Δx+2 a 02 Δy ) + a 10 Δx+ a 01 Δy a 11 x T1 y T1 + a 11 x T0 y T0 + a 20 x T0 2 a 20 x T1 2 + a 02 y T0 2 a 02 y T1 2 ,
Δx= x T1 x T0 ,
Δy= y T1 y T0 ,
ΔW'( x,y )x( a 11 Δy+2 a 20 Δx )+y( a 11 Δx+2 a 02 Δy ).
Δ W 01 ( x,y )=2 a 20 x T1 x a 11 x T1 y
Δ W 02 ( x,y )= a 11 y T2 x2 a 02 y T2 y.
a 11 = γ 01y 2 x T1 γ 02x 2 y T2
a 02 = γ 02y 2 y T2
a 20 = γ 01x 2 x T1
a 11 = γ 01y + γ 02x + γ 23y + γ 13x 416mm
a 02 = γ 02y + γ 13y 416mm
a 20 = γ 01x + γ 23x 416mm

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