Abstract

This paper deals with the development of a computed optical tomography system designed and built to inspect glass lattices to locate various impurities inside the bulk. We focus on the investigation of the potential benefit in the usage of extended depth of focus optics for that application. The quality of 3D reconstruction for the application of glass lattice defect identification is tested numerically and experimentally against the corresponding result obtained with conventional optics.

© 2013 Optical Society of America

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References

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  1. S. R. Deans, The Radon Transform and Some of Its Applications (Wiley-Interscience, 1983), Chap. 1.
  2. C. M. Vest, “Formation of images from projections: Radon and Abel transforms,” J. Opt. Soc. Am. 64, 1215–1218 (1974).
    [CrossRef]
  3. H. P. Hiriyannaiah, “X-ray computer tomography for medical imaging,” IEEE Signal Process. Mag. 14(2), 42–59 (1997).
    [CrossRef]
  4. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).
  5. Z. Zalevsky, “Extended depth of focus imaging: a review,” SPIE Rev. 1, 018001 (2010).
    [CrossRef]
  6. Z. Zalevsky, A. Shemer, A. Zlotnik, E. Ben Eliezer, and E. Marom, “All-optical axial super resolving imaging using a low-frequency binary-phase mask,” Opt. Express 14, 2631–2643 (2006).
    [CrossRef]
  7. W. Choi, C. Fang-Yen, K. Badizadegan, and R. Dasari, “Extended depth of focus in tomographic phase microscopy using a propagation algorithm,” Opt. Lett. 33, 171–173 (2008).
    [CrossRef]
  8. L. Kye-Sung and J. P. Rolland, “Bessel beam spectral-domain high-resolution optical coherence tomography with micro-optic axicon providing extended focusing range,” Opt. Lett. 33, 1696–1698 (2008).
    [CrossRef]
  9. T. O’Haver, “Introduction to Signal Processing—Deconvolution,” http://terpconnect.umd.edu/~toh/spectrum/Deconvolution.html, University of Maryland at College Park, 2007.
  10. P. Boccacci and M. Bertero, Introduction to Inverse Problems in Imaging (Institute of Physics, 1998).
  11. N. Wiener, Extrapolation, Interpolation, and Smoothing of Stationary Time Series (MIT, 1964).
  12. A. P. Dhawan, R. M. Rangayyan, and R. Gordon, “Image restoration by Wiener deconvolution in limited-view computed tomography,” Appl. Opt. 24, 4013–4020 (1985).
    [CrossRef]
  13. E. Simonov, “Use of image reconstruction algorithms based on the integral Radon transform in small angle x-ray computer tomography,” Biomed. Eng. 38, 287–291 (2004).
    [CrossRef]
  14. A. Chesler and N. J. Pelc, “Utilization of cross-plane rays for 3D reconstruction by filtered backprojection,” J. Comput. Assist. Tomogr. 3, 385–395 (1979).
    [CrossRef]
  15. A. Iskender, P. J. Hurst, and W. K. Current, “VLSI Signal Processing IV,” in A Pipelined Architecture for Radon Transform Computation in a Multiprocessor Array (IEEE, 1990).
  16. R. N. Bracewell, Two-Dimensional Imaging (Prentice-Hall, 1995), pp. 505–537.
  17. J. S. Lim, Two-Dimensional Signal and Image Processing (Prentice-Hall, 1990), pp. 42–45.

2010

Z. Zalevsky, “Extended depth of focus imaging: a review,” SPIE Rev. 1, 018001 (2010).
[CrossRef]

2008

2006

2004

E. Simonov, “Use of image reconstruction algorithms based on the integral Radon transform in small angle x-ray computer tomography,” Biomed. Eng. 38, 287–291 (2004).
[CrossRef]

1997

H. P. Hiriyannaiah, “X-ray computer tomography for medical imaging,” IEEE Signal Process. Mag. 14(2), 42–59 (1997).
[CrossRef]

1985

1979

A. Chesler and N. J. Pelc, “Utilization of cross-plane rays for 3D reconstruction by filtered backprojection,” J. Comput. Assist. Tomogr. 3, 385–395 (1979).
[CrossRef]

1974

Badizadegan, K.

Ben Eliezer, E.

Bertero, M.

P. Boccacci and M. Bertero, Introduction to Inverse Problems in Imaging (Institute of Physics, 1998).

Boccacci, P.

P. Boccacci and M. Bertero, Introduction to Inverse Problems in Imaging (Institute of Physics, 1998).

Bracewell, R. N.

R. N. Bracewell, Two-Dimensional Imaging (Prentice-Hall, 1995), pp. 505–537.

Chesler, A.

A. Chesler and N. J. Pelc, “Utilization of cross-plane rays for 3D reconstruction by filtered backprojection,” J. Comput. Assist. Tomogr. 3, 385–395 (1979).
[CrossRef]

Choi, W.

Current, W. K.

A. Iskender, P. J. Hurst, and W. K. Current, “VLSI Signal Processing IV,” in A Pipelined Architecture for Radon Transform Computation in a Multiprocessor Array (IEEE, 1990).

Dasari, R.

Deans, S. R.

S. R. Deans, The Radon Transform and Some of Its Applications (Wiley-Interscience, 1983), Chap. 1.

Dhawan, A. P.

Fang-Yen, C.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

Gordon, R.

Hiriyannaiah, H. P.

H. P. Hiriyannaiah, “X-ray computer tomography for medical imaging,” IEEE Signal Process. Mag. 14(2), 42–59 (1997).
[CrossRef]

Hurst, P. J.

A. Iskender, P. J. Hurst, and W. K. Current, “VLSI Signal Processing IV,” in A Pipelined Architecture for Radon Transform Computation in a Multiprocessor Array (IEEE, 1990).

Iskender, A.

A. Iskender, P. J. Hurst, and W. K. Current, “VLSI Signal Processing IV,” in A Pipelined Architecture for Radon Transform Computation in a Multiprocessor Array (IEEE, 1990).

Kye-Sung, L.

Lim, J. S.

J. S. Lim, Two-Dimensional Signal and Image Processing (Prentice-Hall, 1990), pp. 42–45.

Marom, E.

O’Haver, T.

T. O’Haver, “Introduction to Signal Processing—Deconvolution,” http://terpconnect.umd.edu/~toh/spectrum/Deconvolution.html, University of Maryland at College Park, 2007.

Pelc, N. J.

A. Chesler and N. J. Pelc, “Utilization of cross-plane rays for 3D reconstruction by filtered backprojection,” J. Comput. Assist. Tomogr. 3, 385–395 (1979).
[CrossRef]

Rangayyan, R. M.

Rolland, J. P.

Shemer, A.

Simonov, E.

E. Simonov, “Use of image reconstruction algorithms based on the integral Radon transform in small angle x-ray computer tomography,” Biomed. Eng. 38, 287–291 (2004).
[CrossRef]

Vest, C. M.

Wiener, N.

N. Wiener, Extrapolation, Interpolation, and Smoothing of Stationary Time Series (MIT, 1964).

Zalevsky, Z.

Zlotnik, A.

Appl. Opt.

Biomed. Eng.

E. Simonov, “Use of image reconstruction algorithms based on the integral Radon transform in small angle x-ray computer tomography,” Biomed. Eng. 38, 287–291 (2004).
[CrossRef]

IEEE Signal Process. Mag.

H. P. Hiriyannaiah, “X-ray computer tomography for medical imaging,” IEEE Signal Process. Mag. 14(2), 42–59 (1997).
[CrossRef]

J. Comput. Assist. Tomogr.

A. Chesler and N. J. Pelc, “Utilization of cross-plane rays for 3D reconstruction by filtered backprojection,” J. Comput. Assist. Tomogr. 3, 385–395 (1979).
[CrossRef]

J. Opt. Soc. Am.

Opt. Express

Opt. Lett.

SPIE Rev.

Z. Zalevsky, “Extended depth of focus imaging: a review,” SPIE Rev. 1, 018001 (2010).
[CrossRef]

Other

A. Iskender, P. J. Hurst, and W. K. Current, “VLSI Signal Processing IV,” in A Pipelined Architecture for Radon Transform Computation in a Multiprocessor Array (IEEE, 1990).

R. N. Bracewell, Two-Dimensional Imaging (Prentice-Hall, 1995), pp. 505–537.

J. S. Lim, Two-Dimensional Signal and Image Processing (Prentice-Hall, 1990), pp. 42–45.

T. O’Haver, “Introduction to Signal Processing—Deconvolution,” http://terpconnect.umd.edu/~toh/spectrum/Deconvolution.html, University of Maryland at College Park, 2007.

P. Boccacci and M. Bertero, Introduction to Inverse Problems in Imaging (Institute of Physics, 1998).

N. Wiener, Extrapolation, Interpolation, and Smoothing of Stationary Time Series (MIT, 1964).

S. R. Deans, The Radon Transform and Some of Its Applications (Wiley-Interscience, 1983), Chap. 1.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

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Figures (12)

Fig. 1.
Fig. 1.

Illustration of all-optical approach for extending depth of focus.

Fig. 2.
Fig. 2.

Coordinate system for the RT.

Fig. 3.
Fig. 3.

System diagram.

Fig. 4.
Fig. 4.

Original system TMTF (through focus modulation transfer function) for frequencies of 40, 80, 90, and 100cycles/mm. OTF, optical transfer function.

Fig. 5.
Fig. 5.

TMTF of a system with the EDOF element.

Fig. 6.
Fig. 6.

TMTF of a system with the EDOF element and with a small illumination NA.

Fig. 7.
Fig. 7.

Preliminary simulation results of a reconstructed point (a) without the element, (b) with the element, and (c) with no optical PSF.

Fig. 8.
Fig. 8.

DOF measurements with the resolution target with the EDOF element at locations (a) 1mm, (b) 0 mm, and (c) 1 mm and without the EDOF element at locations (d) 1mm, (e) 0 mm, and (f) 1 mm.

Fig. 9.
Fig. 9.

DOF measurements with the resolution target (a) with the EDOF element (f-number 6) and (b) with the original optics (f-number/9.4).

Fig. 10.
Fig. 10.

TMTF with the decentered 0.2 mm EDOF plate.

Fig. 11.
Fig. 11.

Comparison between an inclusion inside a lattice (a) with the original system and (b) with the EDOF.

Fig. 12.
Fig. 12.

Impurities axially distributed inside the lattice.

Equations (4)

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

δxdiff=1.22λF\#=1.22λRD.
Δf=±2λF\#2.
P(r,ϑ)=f(x,y)·δ(x·cosθ+y·sinϑr)dxdy,
G(r,ϑ)=(f(x,y)PSF(x,y))·δ(x·cosθ+y·sinϑr)dxdy,

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