Abstract

A circular Dammann grating in the front focal plane of a lens is used to generate an annular beam in the back focal plane to code an object by two-dimensional scanning. The coded image of the object is decoded digitally by convolving it with the same annular beam used to code the object. Simple inverse filtering is subsequently used to improve the contrast of the decoded image.

© 2008 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]

2007

2003

2001

2000

1990

M. Toda, “Single mode behavior of a circular grating for potential disk-shaped DFB lasers,” IEEE J. Quantum Electron. 26, 473-481 (1990).
[CrossRef]

1986

G. Indebetouw, “Scanning heterodyne reconstruction of coded aperture images,” Opt. Laser Technol. 18, 268-272 (1986).
[CrossRef]

1984

1981

1980

1979

W. T. Dallas, “Prefolded Fourier filter reconstruction of coded aperture images,” Opt. Acta 26, 1359-1365 (1979).
[CrossRef]

1978

1977

N. M. Ceglio, D. T. Attwood, and E. V. George, “Zone-plate coded imaging of laser-produced plasma,” J. Appl. Phys. 48, 1566-1669 (1977).
[CrossRef]

1974

E. Klotz, R. Linde, and H. Weiss,” A new method for deconvoluting coded aperture images of 3-D x-rays objects,” Opt. Commun. 12, 183-187 (1974).
[CrossRef]

1973

Andres, P.

Attwood, D. T.

N. M. Ceglio, D. T. Attwood, and E. V. George, “Zone-plate coded imaging of laser-produced plasma,” J. Appl. Phys. 48, 1566-1669 (1977).
[CrossRef]

Barrett, H. H.

Ceglio, N. M.

N. M. Ceglio, D. T. Attwood, and E. V. George, “Zone-plate coded imaging of laser-produced plasma,” J. Appl. Phys. 48, 1566-1669 (1977).
[CrossRef]

Chiou, A.

Chung, P. S.

Dallas, W. T.

W. T. Dallas, “Prefolded Fourier filter reconstruction of coded aperture images,” Opt. Acta 26, 1359-1365 (1979).
[CrossRef]

Doh, K.

Fu, Y.

H. M. Shang, S. L. Toh, Y. Fu, C. Quan, and C. J. Tay, “The use of circular optical grating for measuring angular rotation of mirrors,” Opt. Lasers Eng. 36, 487-500 (2001).
[CrossRef]

George, E. V.

N. M. Ceglio, D. T. Attwood, and E. V. George, “Zone-plate coded imaging of laser-produced plasma,” J. Appl. Phys. 48, 1566-1669 (1977).
[CrossRef]

Gindi, G. R.

Gluckstad, J.

Gonzalez, R. C.

R. C. Gonzalez and P. Wintz, Digital Image Processing (Addison-Wesley, 1977).

Indebetouw, G.

G. Indebetouw, “Scanning heterodyne reconstruction of coded aperture images,” Opt. Laser Technol. 18, 268-272 (1986).
[CrossRef]

G. Indebetouw and W. P. Sing, “Optical scanning reconstruction of Fresnel zone plate coded images,” Appl. Opt. 20, 3996-3998 (1981).
[CrossRef] [PubMed]

Javidi, B.

Jia, J.

Kim, T.

Klotz, E.

E. Klotz, U. Tiemens, and H. Weiss,” X-ray tomography by grid coding,” Appl. Opt. 19, 474-476 (1980).
[CrossRef] [PubMed]

E. Klotz, R. Linde, and H. Weiss,” A new method for deconvoluting coded aperture images of 3-D x-rays objects,” Opt. Commun. 12, 183-187 (1974).
[CrossRef]

Lai, S.

S. Lai and M. A. Neifeld, “Digital wavefront reconstruction and its applications to image encryption,” Opt. Commun. 178, 283-289 (2000).
[CrossRef]

Lancis, J.

Linde, R.

E. Klotz, R. Linde, and H. Weiss,” A new method for deconvoluting coded aperture images of 3-D x-rays objects,” Opt. Commun. 12, 183-187 (1974).
[CrossRef]

Liu, L.

Liu, S.

Magensen, P. C.

Morrigan, F. A.

Neifeld, M. A.

S. Lai and M. A. Neifeld, “Digital wavefront reconstruction and its applications to image encryption,” Opt. Commun. 178, 283-289 (2000).
[CrossRef]

Paxman, R. G.

Poon, T. -C.

Quan, C.

H. M. Shang, S. L. Toh, Y. Fu, C. Quan, and C. J. Tay, “The use of circular optical grating for measuring angular rotation of mirrors,” Opt. Lasers Eng. 36, 487-500 (2001).
[CrossRef]

Ran, Q.

Shang, H. M.

H. M. Shang, S. L. Toh, Y. Fu, C. Quan, and C. J. Tay, “The use of circular optical grating for measuring angular rotation of mirrors,” Opt. Lasers Eng. 36, 487-500 (2001).
[CrossRef]

Sing, W. P.

Su, W.-C.

Sun, C.-C.

Tajahuerce, E.

Tay, C. J.

H. M. Shang, S. L. Toh, Y. Fu, C. Quan, and C. J. Tay, “The use of circular optical grating for measuring angular rotation of mirrors,” Opt. Lasers Eng. 36, 487-500 (2001).
[CrossRef]

Tiemens, U.

Toda, M.

M. Toda, “Single mode behavior of a circular grating for potential disk-shaped DFB lasers,” IEEE J. Quantum Electron. 26, 473-481 (1990).
[CrossRef]

Toh, S. L.

H. M. Shang, S. L. Toh, Y. Fu, C. Quan, and C. J. Tay, “The use of circular optical grating for measuring angular rotation of mirrors,” Opt. Lasers Eng. 36, 487-500 (2001).
[CrossRef]

Tyler, G. A.

Wang, B.

Weiss, H.

E. Klotz, U. Tiemens, and H. Weiss,” X-ray tomography by grid coding,” Appl. Opt. 19, 474-476 (1980).
[CrossRef] [PubMed]

E. Klotz, R. Linde, and H. Weiss,” A new method for deconvoluting coded aperture images of 3-D x-rays objects,” Opt. Commun. 12, 183-187 (1974).
[CrossRef]

Wen, J. F.

Wintz, P.

R. C. Gonzalez and P. Wintz, Digital Image Processing (Addison-Wesley, 1977).

Zhao, S.

Zhou, C.

Zhu, B.

Appl. Opt.

IEEE J. Quantum Electron.

M. Toda, “Single mode behavior of a circular grating for potential disk-shaped DFB lasers,” IEEE J. Quantum Electron. 26, 473-481 (1990).
[CrossRef]

J. Appl. Phys.

N. M. Ceglio, D. T. Attwood, and E. V. George, “Zone-plate coded imaging of laser-produced plasma,” J. Appl. Phys. 48, 1566-1669 (1977).
[CrossRef]

Opt. Acta

W. T. Dallas, “Prefolded Fourier filter reconstruction of coded aperture images,” Opt. Acta 26, 1359-1365 (1979).
[CrossRef]

Opt. Commun.

E. Klotz, R. Linde, and H. Weiss,” A new method for deconvoluting coded aperture images of 3-D x-rays objects,” Opt. Commun. 12, 183-187 (1974).
[CrossRef]

S. Lai and M. A. Neifeld, “Digital wavefront reconstruction and its applications to image encryption,” Opt. Commun. 178, 283-289 (2000).
[CrossRef]

Opt. Laser Technol.

G. Indebetouw, “Scanning heterodyne reconstruction of coded aperture images,” Opt. Laser Technol. 18, 268-272 (1986).
[CrossRef]

Opt. Lasers Eng.

H. M. Shang, S. L. Toh, Y. Fu, C. Quan, and C. J. Tay, “The use of circular optical grating for measuring angular rotation of mirrors,” Opt. Lasers Eng. 36, 487-500 (2001).
[CrossRef]

Opt. Lett.

Other

T. -C. Poon, Optical Scanning Holography with MATLAB (Springer, 2007).
[CrossRef]

R. C. Gonzalez and P. Wintz, Digital Image Processing (Addison-Wesley, 1977).

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Figures (9)

Fig. 1
Fig. 1

(a) Impulse ring, (b) autoconvolution of the impulse ring, (c) cross section of (b) through the peak.

Fig. 2
Fig. 2

(a) Original “VT” image, (b) impulse ring as a coding function, (c) coded image, (d) decoded image.

Fig. 3
Fig. 3

(a) Original “VT” image, (b) impulse ring as a coding function, (c) coded image, (d) decoded image.

Fig. 4
Fig. 4

Conventional laser-scanning image processor. PD, photodetector.

Fig. 5
Fig. 5

(a) Cross section of a first-order Dammann grating and (b) an annular beam (focal plane intensity distribution due to the first-order CDG).

Fig. 6
Fig. 6

(a) Original “VT” image, (b) optically coded image, (c) self-convolution of the annular scanning beam, (d) cross section of (c) through the peak, (e) digitally decoded image.

Fig. 7
Fig. 7

(a) Original image, (b) coded image, (c) decoded image, (d) inverse filter of the coded image shown in (c).

Fig. 8
Fig. 8

(a) Original image, (b) coded image, (c) decoded image, (d) inverse filter of the coded image shown in (a).

Fig. 9
Fig. 9

Inverse filter of Fig. 6e.

Equations (11)

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i c ( x , y ) = o ( x , y ) * c ( x , y ) ,
f ( x , y ) * g ( x , y ) = - - f ( x , y ) g ( x x , y - y ) d x d y .
i d ( x , y ) = i c ( x , y ) * d ( x , y ) .
i d ( x , y ) = i c ( x , y ) * d ( x , y ) = o ( x , y ) * c ( x , y ) * d ( x , y ) .
c ( x , y ) * d ( x , y ) = δ ( x , y ) ,
i d ( x , y ) = o ( x , y ) * δ ( x , y ) = o ( x , y ) ,
I i ( x , y ) = ipsf ( x , y ) I 0 ( x + x , y + y ) d x d y = ipsf ( x , y ) I 0 ( x , y ) ,
ipsf ( x , y ) = | F { p ( x , y ) } | 2 = | P ( x λ f , y λ f ) | 2 ,
I i ( x , y ) = ipsf ( x , y ) * I 0 ( x , y ) ,
H ( ρ ) = F { δ ( r - r 0 ) } F { δ ( r - r 0 ) } = [ 2 π r 0 J 0 ( 2 π r 0 ρ ) ] 2 .
inverse   filtered   decoded   image = F - 1 { F { i d } / [ H ( ρ ) + ε ] } ,

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