Abstract

Experimental results are shown for an integrated computational imaging system with a phase-coded aperture. A spatial light modulator works as a phase screen that diffracts light from a point object into a uniformly redundant array (URA). Excellent imaging results are achieved after correlation processing. The system has the same depth of field as a diffraction-limited lens. Potential applications are discussed.

© 2011 OSA

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References

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  1. W. Chi and N. George, “Phase-coded aperture for optical imaging,” Opt. Commun. 282, 2110–2117 (2009).
    [CrossRef]
  2. R. H. Dicke, “Scatter-hole cameras for X-rays and Gamma rays,” Astrophys. J. 153, L101 (1968).
    [CrossRef]
  3. E. E. Fenimore and T. M. Cannon, “Coded aperture imaging with uniformly redundant array,” Appl. Opt. 17, 337–347 (1978).
    [CrossRef] [PubMed]
  4. R. G. Simpson and H. H. Barrett, “Coded aperture imaging,” in Imaging in Diagnositc Medicine, S. Nudel-man, (Ed.) (Plenum, 1980).
  5. F. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21, 2758–2769 (1982).
    [CrossRef] [PubMed]
  6. J. C. Dainty and F. R. Fienup, “Phase retrieval and image reconstruction for astronomy,” in Image Recovery: Theory and Application, H. Stark, (Ed.) (Academic, 1987).
  7. D. P. Casasent and T. Clark (Ed.), “Adaptive Coded Aperture Imaging and Non-imaging Sensors,” Proc. SPIE 6714 (2007).
  8. D. P. Casasent and S. Rogers (Ed.), “Adaptive Coded Aperture Imaging and Non-imaging Sensors II,” Proc. SPIE 7096 (2008).

2009 (1)

W. Chi and N. George, “Phase-coded aperture for optical imaging,” Opt. Commun. 282, 2110–2117 (2009).
[CrossRef]

2008 (1)

D. P. Casasent and S. Rogers (Ed.), “Adaptive Coded Aperture Imaging and Non-imaging Sensors II,” Proc. SPIE 7096 (2008).

2007 (1)

D. P. Casasent and T. Clark (Ed.), “Adaptive Coded Aperture Imaging and Non-imaging Sensors,” Proc. SPIE 6714 (2007).

1982 (1)

1978 (1)

1968 (1)

R. H. Dicke, “Scatter-hole cameras for X-rays and Gamma rays,” Astrophys. J. 153, L101 (1968).
[CrossRef]

Barrett, H. H.

R. G. Simpson and H. H. Barrett, “Coded aperture imaging,” in Imaging in Diagnositc Medicine, S. Nudel-man, (Ed.) (Plenum, 1980).

Cannon, T. M.

Chi, W.

W. Chi and N. George, “Phase-coded aperture for optical imaging,” Opt. Commun. 282, 2110–2117 (2009).
[CrossRef]

Dainty, J. C.

J. C. Dainty and F. R. Fienup, “Phase retrieval and image reconstruction for astronomy,” in Image Recovery: Theory and Application, H. Stark, (Ed.) (Academic, 1987).

Dicke, R. H.

R. H. Dicke, “Scatter-hole cameras for X-rays and Gamma rays,” Astrophys. J. 153, L101 (1968).
[CrossRef]

Fenimore, E. E.

Fienup, F. R.

F. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21, 2758–2769 (1982).
[CrossRef] [PubMed]

J. C. Dainty and F. R. Fienup, “Phase retrieval and image reconstruction for astronomy,” in Image Recovery: Theory and Application, H. Stark, (Ed.) (Academic, 1987).

George, N.

W. Chi and N. George, “Phase-coded aperture for optical imaging,” Opt. Commun. 282, 2110–2117 (2009).
[CrossRef]

Simpson, R. G.

R. G. Simpson and H. H. Barrett, “Coded aperture imaging,” in Imaging in Diagnositc Medicine, S. Nudel-man, (Ed.) (Plenum, 1980).

Appl. Opt. (2)

Astrophys. J. (1)

R. H. Dicke, “Scatter-hole cameras for X-rays and Gamma rays,” Astrophys. J. 153, L101 (1968).
[CrossRef]

Opt. Commun. (1)

W. Chi and N. George, “Phase-coded aperture for optical imaging,” Opt. Commun. 282, 2110–2117 (2009).
[CrossRef]

Proc. SPIE (2)

D. P. Casasent and T. Clark (Ed.), “Adaptive Coded Aperture Imaging and Non-imaging Sensors,” Proc. SPIE 6714 (2007).

D. P. Casasent and S. Rogers (Ed.), “Adaptive Coded Aperture Imaging and Non-imaging Sensors II,” Proc. SPIE 7096 (2008).

Other (2)

J. C. Dainty and F. R. Fienup, “Phase retrieval and image reconstruction for astronomy,” in Image Recovery: Theory and Application, H. Stark, (Ed.) (Academic, 1987).

R. G. Simpson and H. H. Barrett, “Coded aperture imaging,” in Imaging in Diagnositc Medicine, S. Nudel-man, (Ed.) (Plenum, 1980).

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Figures (7)

Fig. 1
Fig. 1

The experimental setup for the coded aperture imaging system: O, Object; BS, Beam Splitter; A, Aperture; SLM, Spatial light modulator; D, Detector array; BP, Blackened metal plate.

Fig. 2
Fig. 2

Illustration of the correlation image processing using a point object located at a distance of 1275mm. (a) the intermediate image or bl-URA at the detector, D in Fig. 1, (also refer to Fig. 6a for a better view); (b) the repeated URA pattern; (c) the result of image cross-correlation between (a) and (b); (d) the center section of (c) or a point object recovery (also refer to Fig. 3a).

Fig. 3
Fig. 3

Image recovery result with a point source located at a distance of 1275mm using URAs of different sizes in correlation processing. URA size is (a) 6.3mm; (b) 6.2mm and (c) 6mm.

Fig. 4
Fig. 4

Experimental result with a letter object located at a distance of 1275mm. (a) intermediate image (the arrows indicate regions where CCD pixel response is low. All of these are not labeled); (b) image recovery result by correlation processing. The linear size of recovery is about half the size of the intermediate image.

Fig. 5
Fig. 5

Image recovery result for the object located at different distances. The same URA pattern as shown in Fig. 2 is used for correlation processing. The object is located at a distance of (a) 1275mm; (b) 1225mm; (c) 1175mm; (d) 1100mm; (e) 1050mm; (f) 1000mm. The corresponding defocus amounts are 0, λ/4, λ/2, λ, 1.3λ and 1.6λ, respectively.

Fig. 6
Fig. 6

The intermediate images for a point object located at (a) 1275mm and (b) 1100mm.

Fig. 7
Fig. 7

Image recovery result for object located at 1100mm using repeated URA pattern of different scales. The size of URA array is (a) 6.3mm, (b) 6.42mm.

Equations (8)

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i ( x , y ) = o ( ξ , η ) h ( x ξ , y η ) d ξ d η .
L { h ( x , y ) } = f δ ( x , y ) + g ( x , y ) ,
L { i ( x , y ) } = o ( ξ , η ) f δ ( x ξ , y η ) d ξ d η + o ( ξ , η ) g ( x ξ , y η ) d ξ d η .
h ( x , y ) = t ( x , y ) * b ( x , y ) ,
L { h ( x , y ) } = h ( x , y ) t R ( x , y ) ,
t R ( x , y ) = [ t ( x ξ , y η ) t ] comb ( ξ / D x , η / D y ) d ξ d η ,
L { h ( x , y ) } = C comb ( x / D x , y / D y ) * Λ ( x / Δ x , y / Δ y ) * b ( x , y ) ,
f δ ( x , y ) = Λ ( x / Δ x , y / Δ y ) * b ( x , y ) ,

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