Abstract

We demonstrate experimentally an optical imaging method that makes use of a slit to collect tomographic projection data of arbitrarily shaped light beams; a tomographic backprojection algorithm is then used to reconstruct the intensity profiles of these beams. Two different implementations of the method are presented. In one, a single slit is scanned and rotated in front of the laser beam. In the other, the sides of a polygonal slit, which is linearly displaced in a x-y plane perpendicular to the beam, are used to collect the data. This latter version is more suitable than the other for adaptation at micrometer-size scale. A mathematical justification is given here for the superior performance against laser-power fluctuations of the tomographic slit technique compared with the better-known tomographic knife-edge technique.

© 1997 Optical Society of America

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References

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  1. J. Soto, “Arbitrary-intensity-profiles measurement of laser beams by a scanning and rotating slit,” Appl. Opt. 32, 7272–7276 (1993).
    [Crossref] [PubMed]
  2. A. Kak, M. Slaney, Principles of Computed Tomographic Imaging (Institute of Electrical and Electronic Engineers, New York, 1988), Chap. 3.
  3. H. M. Hertz, G. W. Faris, “Emission tomography of flame radicals,” Opt. Lett. 13, 351–353 (1988).
    [Crossref] [PubMed]
  4. H. M. Hertz, “Experimental determination of 2-D flame temperature fields by interferometric tomography,” Opt. Commun. 54, 131 (1985).
    [Crossref]
  5. H. M. Hertz, “Kerr effect tomography for noninstrusive spatially resolved measurements of asymmetric electric field distributions,” Appl. Phys. 25, 914–921 (1986).
  6. H. M. Hertz, R. L. Byer, “Tomographic imaging of micrometer-sized optical and soft-x-ray beams,” Opt. Lett. 15, 396–398 (1990).
    [Crossref] [PubMed]
  7. S. Samson, A. Korpel, “Two-dimensional operation of a scanning optical microscope by vibrating knife-edge tomography,” Appl. Opt. 34, 285–289 (1995).
    [Crossref] [PubMed]
  8. Ref. 2, Chap. 5.
  9. R. L. McCally, “Measurement of Gaussian beam parameters,” Appl. Opt. 23, 2227 (1984).
    [Crossref] [PubMed]
  10. See, for example, Newport Catalog 94/95, for positioning equipment (Newport Corporation, Irvine, Calif., 1994), Sec. 4.
  11. Lasers and Instruments Guide (Melles Griot Electro-Optics, Boulder, Colo. 80301, 1994).

1995 (1)

1993 (1)

1990 (1)

1988 (1)

1986 (1)

H. M. Hertz, “Kerr effect tomography for noninstrusive spatially resolved measurements of asymmetric electric field distributions,” Appl. Phys. 25, 914–921 (1986).

1985 (1)

H. M. Hertz, “Experimental determination of 2-D flame temperature fields by interferometric tomography,” Opt. Commun. 54, 131 (1985).
[Crossref]

1984 (1)

Byer, R. L.

Faris, G. W.

Hertz, H. M.

H. M. Hertz, R. L. Byer, “Tomographic imaging of micrometer-sized optical and soft-x-ray beams,” Opt. Lett. 15, 396–398 (1990).
[Crossref] [PubMed]

H. M. Hertz, G. W. Faris, “Emission tomography of flame radicals,” Opt. Lett. 13, 351–353 (1988).
[Crossref] [PubMed]

H. M. Hertz, “Kerr effect tomography for noninstrusive spatially resolved measurements of asymmetric electric field distributions,” Appl. Phys. 25, 914–921 (1986).

H. M. Hertz, “Experimental determination of 2-D flame temperature fields by interferometric tomography,” Opt. Commun. 54, 131 (1985).
[Crossref]

Kak, A.

A. Kak, M. Slaney, Principles of Computed Tomographic Imaging (Institute of Electrical and Electronic Engineers, New York, 1988), Chap. 3.

Korpel, A.

McCally, R. L.

Samson, S.

Slaney, M.

A. Kak, M. Slaney, Principles of Computed Tomographic Imaging (Institute of Electrical and Electronic Engineers, New York, 1988), Chap. 3.

Soto, J.

Appl. Opt. (3)

Appl. Phys. (1)

H. M. Hertz, “Kerr effect tomography for noninstrusive spatially resolved measurements of asymmetric electric field distributions,” Appl. Phys. 25, 914–921 (1986).

Opt. Commun. (1)

H. M. Hertz, “Experimental determination of 2-D flame temperature fields by interferometric tomography,” Opt. Commun. 54, 131 (1985).
[Crossref]

Opt. Lett. (2)

Other (4)

Ref. 2, Chap. 5.

A. Kak, M. Slaney, Principles of Computed Tomographic Imaging (Institute of Electrical and Electronic Engineers, New York, 1988), Chap. 3.

See, for example, Newport Catalog 94/95, for positioning equipment (Newport Corporation, Irvine, Calif., 1994), Sec. 4.

Lasers and Instruments Guide (Melles Griot Electro-Optics, Boulder, Colo. 80301, 1994).

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Figures (5)

Fig. 1
Fig. 1

Schematic diagram of the scanned-and-rotated slit; the slit is perpendicular to the motion produced by stepper motor 1. This is used for obtaining a tomographic projection of the intensity distribution by rotating the disk plate with motor 2.

Fig. 2
Fig. 2

Reconstructed image, by means of the backprojection method, from the projection measurements obtained with the system of Fig. 1.

Fig. 3
Fig. 3

Three concentric polygonal slits; in the slits 45 different orientations are obtained with 8° angular increments. The final dimension, from the center of one side to the opposite vertex, of the largest polygon is approximately 8.1 mm, and the width of each slit is close to 20 µm.

Fig. 4
Fig. 4

Reconstructed images obtained with the polygonal-slit technique: (a) for a 0.5-mm-diameter round hole, (b) for a semi-circle of the same diameter.

Fig. 5
Fig. 5

Schematic diagram of the knife-edge technique. Here the line integrals P θ (t) are obtained from the difference of consecutive edge-response measurements.

Equations (7)

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Fθt= uncovered areaθ,tIx, ydA,
Pθt=dFθtdt.
Nkeθ, t = NLP¯θtΔt/F¯θt.
Nkeθ, t  NL.
σslθ, t = σ0P¯θtΔw/P¯,
Nslθ, t=P¯θtΔw/σslθ, t=NL.
Nkeθ, tNslθ, t.

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