Abstract

We use cubic-phase plate imaging to demonstrate an order-of-magnitude improvement in the transverse resolution of three-dimensional objects reconstructed by extended depth-of-field tomography. Our algorithm compensates for the range shear of the cubic-phase approach and uses camera rotation to center the reconstructed volume on a target object point.

© 1999 Optical Society of America

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References

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1998

1997

1996

1995

E. Dowski and W. Cathey, Appl. Opt. 34, 1859 (1995).
[CrossRef] [PubMed]

J. van der Gracht, E. Dowski, and W. Cathey, Proc. SPIE 2537, 279 (1995).
[CrossRef]

1993

1990

Y. W. Chen, N. Miyanaga, and N. Yamanaka, J. Appl. Phys. 68, 1483 (1990).
[CrossRef]

1985

J. W. V. Gissen, M. A. Viergever, and C. Graaf, IEEE Trans. Med. Imaging MI-4, 91 (1985).
[CrossRef]

1979

Ardent, J. W.

Ashdown, I.

I. Ashdown, J. Illum. Eng. Soc. 22, 163 (1993).
[CrossRef]

Barrett, H. H.

Bradburn, S.

Brady, D.

Cathey, W.

Chen, Y. W.

Y. W. Chen, N. Miyanaga, and N. Yamanaka, J. Appl. Phys. 68, 1483 (1990).
[CrossRef]

Chiu, M. Y.

Chou, C.

Deaver, D. M.

Dowski, E.

Gindi, G. R.

Gissen, J. W. V.

J. W. V. Gissen, M. A. Viergever, and C. Graaf, IEEE Trans. Med. Imaging MI-4, 91 (1985).
[CrossRef]

Graaf, C.

J. W. V. Gissen, M. A. Viergever, and C. Graaf, IEEE Trans. Med. Imaging MI-4, 91 (1985).
[CrossRef]

Magnus, W. F.

W. F. Magnus, F. Oberhettinger, and R. Soni, Formulas and Theorems for the Special Functions of Mathe-matical Physics (Spinger-Verlag, New York, 1966), p. 76.

Marks, D.

Miyanaga, N.

Y. W. Chen, N. Miyanaga, and N. Yamanaka, J. Appl. Phys. 68, 1483 (1990).
[CrossRef]

Oberhettinger, F.

W. F. Magnus, F. Oberhettinger, and R. Soni, Formulas and Theorems for the Special Functions of Mathe-matical Physics (Spinger-Verlag, New York, 1966), p. 76.

Seltzer, S. M.

Simpson, R. G.

Soni, R.

W. F. Magnus, F. Oberhettinger, and R. Soni, Formulas and Theorems for the Special Functions of Mathe-matical Physics (Spinger-Verlag, New York, 1966), p. 76.

Taylor, M. G.

van der Gracht, J.

Viergever, M. A.

J. W. V. Gissen, M. A. Viergever, and C. Graaf, IEEE Trans. Med. Imaging MI-4, 91 (1985).
[CrossRef]

Yamanaka, N.

Y. W. Chen, N. Miyanaga, and N. Yamanaka, J. Appl. Phys. 68, 1483 (1990).
[CrossRef]

Yin, L. I.

Appl. Opt.

IEEE Trans. Med. Imaging

J. W. V. Gissen, M. A. Viergever, and C. Graaf, IEEE Trans. Med. Imaging MI-4, 91 (1985).
[CrossRef]

J. Appl. Phys.

Y. W. Chen, N. Miyanaga, and N. Yamanaka, J. Appl. Phys. 68, 1483 (1990).
[CrossRef]

J. Illum. Eng. Soc.

I. Ashdown, J. Illum. Eng. Soc. 22, 163 (1993).
[CrossRef]

J. Opt. Soc. Am.

Opt. Lett.

Proc. SPIE

J. van der Gracht, E. Dowski, and W. Cathey, Proc. SPIE 2537, 279 (1995).
[CrossRef]

Other

W. F. Magnus, F. Oberhettinger, and R. Soni, Formulas and Theorems for the Special Functions of Mathe-matical Physics (Spinger-Verlag, New York, 1966), p. 76.

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Figures (4)

Fig. 1
Fig. 1

System geometry.

Fig. 2
Fig. 2

Superimposed lateral cross sections of four digitally reconstructed 3D PSF's, labeled with their distances from the principal plane. The axes are angles labeled in milliradians.

Fig. 3
Fig. 3

Superimposed longitudinal cross sections of four digitally reconstructed 3D PSF's labeled with their distances from the principal plane. The horizontal axis is angle labeled in milliradians, and the vertical axis is projective depth labeled in centimeters. The vertical scale is plotted linearly in 1/z space but is marked in z space.

Fig. 4
Fig. 4

Three lateral slices through the reconstruction of a demonstration source. The axes correspond to angular position relative to the principal axis in milliradians.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

PSFx+zzx,y+zzy,z,z=1α4/3Ai2-α2/331/32πλzαx+zzx+π2γ23α2λ2×Ai2-α2/331/32πλzαy+zzy+π2γ23α2λ2,
xz=-xz-π6αλz02Δzz2,yz=-yz-π6αλz02Δzz2.
Iξ,η=Px,y,zδξz+x+x^z0z-x^z0+π6αλz021-z0z2δηz+yz+π6αλz021-z0z2dxdydz,
I˜kξ,kη,q=Pxp,yp,zpexpjkξxpexpjkηyp×expjqzpexp-jqz0pexpjkξπz6αλz02×1-z0zp2expjkηπz6αλz02×1-z0zp2dxpdypdzp.
xp+πz6αλz021-z0zp2,yp+πz6αλz021-z0zp2,zp-1z0,

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