Abstract

We demonstrate a new optical imaging technique based on a directional detector that measures the intensity of light waves that propagate only in a narrow angular window around a specific direction. Light waves that propagate in other directions do not significantly affect the detector output. The directional detector is obtained by illuminating the interrogated object with a high-coherence light source and measuring the interference between the light wave reflected from the object and a reference wave. By measuring the intensity of the interference pattern with an optical detector that has a finite width and moving the object by use of a rotation stage, one can obtain the angular directionality of the filter. The use of coherent detection in the directional detector makes it possible to increase the sensitivity of the system. The directional detector was analyzed theoretically and demonstrated experimentally for a Gaussian beam scattered from a conducting cylinder. The interference enabled us to theoretically increase the angular resolution by a factor of ∼10 and experimentally by a factor of 8.5. A configuration for using a directional detector array to reconstruct a two-dimensional object is suggested. Since the directional detector makes it possible to reduce the effect of diffraction and scattering, reconstruction techniques based on nondiffracting sources, as implemented in x-ray tomography, may be used.

© 2004 Optical Society of America

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References

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  1. T. Wilson, C. J. R. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, New York, 1984).
  2. L. C. Ingesson, V. V. Pickalov, A. J. H. Donne, D. C. Schram, “First tomographic reconstruction and a study of interference filters for visible-light tomography on RTP,” Rev. Sci. Instrum. 66, 622–624 (1995).
    [CrossRef]
  3. F. C. Chang, G. S. Kino, “325-nm interference microscope,” Appl. Opt. 37, 3471–3479 (1998).
    [CrossRef]
  4. G. N. Vishnyakov, G. G. Levin, “Optical microtomography of phase objects,” Opt. Spectrosc. (USSR) 85, 73–77 (1998).
  5. H. Suhara, “Interferometric measurement of the refractive-index distribution in plastic lenses by use of computed tomography,” Appl. Opt. 41, 5317–5325 (2002).
    [CrossRef] [PubMed]
  6. G. Wiegand, K. R. Neumaier, E. Sackmann, “Microinterferometry: three-dimensional reconstruction of surface microtopography for thin-film and wetting studies by reflection interference contrast microscopy (RICM),” Appl. Opt. 37, 6892–6905 (1998).
    [CrossRef]
  7. D. Fischer, B. Ovryn, “Interfacial shape and contrast-angle measurement of transparent samples with confocal interference microscopy,” Opt. Lett. 25, 478–480 (2000).
    [CrossRef]
  8. G. Li, P.-C. Sun, P. C. Lin, Y. Fainman, “Interference microscopy for three-dimensional imaging with wavelength-to-depth encoding,” Opt. Lett. 25, 1505–1507 (2000).
    [CrossRef]
  9. J. M. Schmitt, “Optical coherence tomography (OCT): a review,” IEEE J. Sel. Top. Quantum Electron. 5, 1205–1215 (1999).
    [CrossRef]
  10. A. C. Kak, M. Slaney, Principles of Computerized Tomographic Imaging (Society for Industrial and Applied Mathematics, New York, 1988).
  11. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
    [CrossRef]
  12. M. Born, E. Wolf, Principle of Optics (Cambridge U. Press, New York, 1999).
  13. J. A. Kong, Electromagnetic Wave Theory, 1st ed. (Wiley, New York, 1986), Chap. 6.
  14. P. Gunter, J. P. Huingard, eds., Photorefractive Materials and Their Applications I (Springer-Verlag, Berlin, 1988).

2002 (1)

2000 (2)

1999 (1)

J. M. Schmitt, “Optical coherence tomography (OCT): a review,” IEEE J. Sel. Top. Quantum Electron. 5, 1205–1215 (1999).
[CrossRef]

1998 (3)

1995 (1)

L. C. Ingesson, V. V. Pickalov, A. J. H. Donne, D. C. Schram, “First tomographic reconstruction and a study of interference filters for visible-light tomography on RTP,” Rev. Sci. Instrum. 66, 622–624 (1995).
[CrossRef]

1969 (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principle of Optics (Cambridge U. Press, New York, 1999).

Chang, F. C.

Donne, A. J. H.

L. C. Ingesson, V. V. Pickalov, A. J. H. Donne, D. C. Schram, “First tomographic reconstruction and a study of interference filters for visible-light tomography on RTP,” Rev. Sci. Instrum. 66, 622–624 (1995).
[CrossRef]

Fainman, Y.

Fischer, D.

Ingesson, L. C.

L. C. Ingesson, V. V. Pickalov, A. J. H. Donne, D. C. Schram, “First tomographic reconstruction and a study of interference filters for visible-light tomography on RTP,” Rev. Sci. Instrum. 66, 622–624 (1995).
[CrossRef]

Kak, A. C.

A. C. Kak, M. Slaney, Principles of Computerized Tomographic Imaging (Society for Industrial and Applied Mathematics, New York, 1988).

Kino, G. S.

Kogelnik, H.

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
[CrossRef]

Kong, J. A.

J. A. Kong, Electromagnetic Wave Theory, 1st ed. (Wiley, New York, 1986), Chap. 6.

Levin, G. G.

G. N. Vishnyakov, G. G. Levin, “Optical microtomography of phase objects,” Opt. Spectrosc. (USSR) 85, 73–77 (1998).

Li, G.

Lin, P. C.

Neumaier, K. R.

Ovryn, B.

Pickalov, V. V.

L. C. Ingesson, V. V. Pickalov, A. J. H. Donne, D. C. Schram, “First tomographic reconstruction and a study of interference filters for visible-light tomography on RTP,” Rev. Sci. Instrum. 66, 622–624 (1995).
[CrossRef]

Sackmann, E.

Schmitt, J. M.

J. M. Schmitt, “Optical coherence tomography (OCT): a review,” IEEE J. Sel. Top. Quantum Electron. 5, 1205–1215 (1999).
[CrossRef]

Schram, D. C.

L. C. Ingesson, V. V. Pickalov, A. J. H. Donne, D. C. Schram, “First tomographic reconstruction and a study of interference filters for visible-light tomography on RTP,” Rev. Sci. Instrum. 66, 622–624 (1995).
[CrossRef]

Sheppard, C. J. R.

T. Wilson, C. J. R. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, New York, 1984).

Slaney, M.

A. C. Kak, M. Slaney, Principles of Computerized Tomographic Imaging (Society for Industrial and Applied Mathematics, New York, 1988).

Suhara, H.

Sun, P.-C.

Vishnyakov, G. N.

G. N. Vishnyakov, G. G. Levin, “Optical microtomography of phase objects,” Opt. Spectrosc. (USSR) 85, 73–77 (1998).

Wiegand, G.

Wilson, T.

T. Wilson, C. J. R. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, New York, 1984).

Wolf, E.

M. Born, E. Wolf, Principle of Optics (Cambridge U. Press, New York, 1999).

Appl. Opt. (3)

Bell Syst. Tech. J. (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

J. M. Schmitt, “Optical coherence tomography (OCT): a review,” IEEE J. Sel. Top. Quantum Electron. 5, 1205–1215 (1999).
[CrossRef]

Opt. Lett. (2)

Opt. Spectrosc. (USSR) (1)

G. N. Vishnyakov, G. G. Levin, “Optical microtomography of phase objects,” Opt. Spectrosc. (USSR) 85, 73–77 (1998).

Rev. Sci. Instrum. (1)

L. C. Ingesson, V. V. Pickalov, A. J. H. Donne, D. C. Schram, “First tomographic reconstruction and a study of interference filters for visible-light tomography on RTP,” Rev. Sci. Instrum. 66, 622–624 (1995).
[CrossRef]

Other (5)

T. Wilson, C. J. R. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, New York, 1984).

A. C. Kak, M. Slaney, Principles of Computerized Tomographic Imaging (Society for Industrial and Applied Mathematics, New York, 1988).

M. Born, E. Wolf, Principle of Optics (Cambridge U. Press, New York, 1999).

J. A. Kong, Electromagnetic Wave Theory, 1st ed. (Wiley, New York, 1986), Chap. 6.

P. Gunter, J. P. Huingard, eds., Photorefractive Materials and Their Applications I (Springer-Verlag, Berlin, 1988).

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Figures (6)

Fig. 1
Fig. 1

Schematic description of (a) a directional detector and (b) the experimental setup used to demonstrate the device. The directional filter measures the intensity of light waves that propagate only in a narrow angular window around a specific direction. D.F., a directional filter; BS, a beam splitter; C, a perfectly conducting cylinder with a diameter 2 a . An iris, S, was added to the experimental setup to limit the size of the region where interference is obtained. ρ and ϕ are the length and the angle of the optical path between the center of the cylinder and a point ( x ,   y ) on the detector. θ is the rotation angle of the stage.

Fig. 2
Fig. 2

Calculated detector intensity versus the angle of the rotation stage for a scattering cylinder, with a diameter 2 a = 1   mm , rotated on a circumference of a circle, with a radius R = 1.1   cm , at an angular velocity Ω = 20 ° / s . The laser beam waist was equal to 6 mm, the detector width was equal to 2 D = 0.8   mm , and the length of the optical path between the middle of the detector and the rotation axis was equal to L = 0.5   m . The inset of the figure zooms in the interference structure.

Fig. 3
Fig. 3

Comparison between the calculated envelope of the interference pattern (solid curve), shown in Fig. 2, and the intensity on the detector when the reference beam is blocked (dashed curve) as a function of the rotation angle of the stage. The figure shows that the interference increases the angular resolution of the system by a factor of ∼8.45.

Fig. 4
Fig. 4

Measured detector voltage versus the angle of the rotation stage for a cylinder, with a diameter 2 a = 1   mm , rotated on a circumference of a circle, with a radius R = 1.1   cm , at an angular velocity Ω = 20 ° / s . The laser beam waist was equal to 4 mm, the detector width was equal to 2 D = 0.8   mm , and the optical path between the middle of the detector and the rotation axis was equal to L = 0.51   m . An iris with a diameter of ∼0.3 mm was used to limit the region where a uniformly distributed interference pattern is obtained.

Fig. 5
Fig. 5

Comparison of the measured envelope of the interference pattern shown in Fig. 4 (solid curve) and the detector voltage, measured when the reference beam was blocked (dashed curve) as a function of the angle of the rotation stage. The figure shows that the interference increases the resolution of the system by a factor of ∼8.5.

Fig. 6
Fig. 6

Schematic description of a system that can be used to reconstruct a 2-D object. The system is based on a directional detector array with a narrow angular window that makes it possible to reduce the diffraction effect and to obtain the projection of the object along a specific direction. By measuring the projections at different angles of the rotation stage, it may be possible to reconstruct the image with simple methods as used in x-ray computerized tomography for a nondiffracting source.

Equations (6)

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A r ( x ,   y ,   θ ) = A i ( θ ) a   cos ( ϕ / 2 ) 2 ρ 1 / 2 × exp { ik [ ρ - 2 a   cos ( ϕ / 2 ) ] } ,
i inc ( x 0 ,   y ,   θ ) = | A r ( x 0 ,   y ,   θ ) | 2 + | A ref ( x 0 ,   y ) | 2 + [ 2 a   cos ( ϕ / 2 ) / ρ ] 1 / 2 | A i ( θ ) | × | A ref ( x 0 ,   y ) | cos k ρ - 2 a   cos ϕ 2 ,
i ( x 0 ,   θ ) = η - D D i inc ( x 0 ,   y ,   θ ) d y ,
I int = 2 D a sinc kR θ D L .
2 Δ θ = 3.792 L kDR .
i ( y ) η I in object t ( x ,   y ) d x ,

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