Abstract

The imaging properties of a scanning optical system that incorporates an axicon are presented. Beam-shape characteristics including the axial distribution of the J0 beam and its control and aberration effects arising from off-axis illumination are experimentally studied. These parameters are relevant when the axiconis used in an imaging system operating in the beam-scanning mode. The J0 pattern produced by a blazed axicon transmittance grating is also presented.

© 1992 Optical Society of America

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References

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    [CrossRef]
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  14. N. G. Van Kampen, “The method of stationary phase and the method of Fresnel zones,” Physica 24, 437–444 (1958).
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  15. J. H. MacLeod, “Axicon and their uses,” J. Opt. Soc. Am. 50, 166–169 (1960).
    [CrossRef]
  16. M. V. Perez, C. Gomez-Reino, J. Cuadrado, “Diffraction patterns and zone plates produced by linear thin axicons,” Opt. Acta 33, 1161–1176 (1986).
    [CrossRef]

1991

1990

R. Arimoto, S. Kawata, “Laser-scan fluorescence microscope with annular excitation,” Optik (Stuttgart) 86, 651–654 (1990).

Q. Ren, R. Birngruber, “Axicon: a new laser beam delivery system for corneal surgery,” IEEE J. Quantum Electron. 26, 2305–2308 (1990).
[CrossRef]

1987

J. Durnin, “Exact solutions for non-diffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A 4, 651–654 (1987).
[CrossRef]

J. Durnin, J. Miceli, J. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

1986

M. V. Perez, C. Gomez-Reino, J. Cuadrado, “Diffraction patterns and zone plates produced by linear thin axicons,” Opt. Acta 33, 1161–1176 (1986).
[CrossRef]

1985

1978

1962

1960

1958

N. G. Van Kampen, “The method of stationary phase and the method of Fresnel zones,” Physica 24, 437–444 (1958).
[CrossRef]

1954

Arimoto, R.

S. Kawata, R. Arimoto, O. Nakamura, “Three-dimensional optical-transfer-function analysis for a laser-scan fluorescence microscopy,” J. Opt. Soc. Am. A 8, 171–175 (1991).
[CrossRef]

R. Arimoto, S. Kawata, “Laser-scan fluorescence microscope with annular excitation,” Optik (Stuttgart) 86, 651–654 (1990).

Balykin, V. I.

Belanguer, P. A.

Birngruber, R.

Q. Ren, R. Birngruber, “Axicon: a new laser beam delivery system for corneal surgery,” IEEE J. Quantum Electron. 26, 2305–2308 (1990).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1989), pp. 416–417.

Chikuma, K.

S. Okamoto, K. Chikuma, T. Tohma, S. Umegaki, “Focussing system of optical second harmonic wave from crystal cored fiber,” in Proceedings of the Semiannual Meeting of the Japanese Society of Applied Physics (Fukuoka, Japan, 1989), p.923.

Cuadrado, J.

M. V. Perez, C. Gomez-Reino, J. Cuadrado, “Diffraction patterns and zone plates produced by linear thin axicons,” Opt. Acta 33, 1161–1176 (1986).
[CrossRef]

Durnin, J.

J. Durnin, “Exact solutions for non-diffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A 4, 651–654 (1987).
[CrossRef]

J. Durnin, J. Miceli, J. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

Eberly, J.

J. Durnin, J. Miceli, J. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

Fujiwara, S.

Gomez-Reino, C.

M. V. Perez, C. Gomez-Reino, J. Cuadrado, “Diffraction patterns and zone plates produced by linear thin axicons,” Opt. Acta 33, 1161–1176 (1986).
[CrossRef]

Herman, R.

Kawata, S.

S. Kawata, R. Arimoto, O. Nakamura, “Three-dimensional optical-transfer-function analysis for a laser-scan fluorescence microscopy,” J. Opt. Soc. Am. A 8, 171–175 (1991).
[CrossRef]

R. Arimoto, S. Kawata, “Laser-scan fluorescence microscope with annular excitation,” Optik (Stuttgart) 86, 651–654 (1990).

Letokhov, V. S.

MacLeod, J. H.

McLeod, J. H.

Miceli, J.

J. Durnin, J. Miceli, J. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

Minogin, V. G.

Nakamura, O.

Okamoto, S.

S. Okamoto, K. Chikuma, T. Tohma, S. Umegaki, “Focussing system of optical second harmonic wave from crystal cored fiber,” in Proceedings of the Semiannual Meeting of the Japanese Society of Applied Physics (Fukuoka, Japan, 1989), p.923.

Perez, M. V.

M. V. Perez, C. Gomez-Reino, J. Cuadrado, “Diffraction patterns and zone plates produced by linear thin axicons,” Opt. Acta 33, 1161–1176 (1986).
[CrossRef]

Ren, Q.

Q. Ren, R. Birngruber, “Axicon: a new laser beam delivery system for corneal surgery,” IEEE J. Quantum Electron. 26, 2305–2308 (1990).
[CrossRef]

Rioux, M.

Rozbdestvenskyt, Yu. V.

Sidorov, A. L.

Tohma, T.

S. Okamoto, K. Chikuma, T. Tohma, S. Umegaki, “Focussing system of optical second harmonic wave from crystal cored fiber,” in Proceedings of the Semiannual Meeting of the Japanese Society of Applied Physics (Fukuoka, Japan, 1989), p.923.

Tremblay, R.

Umegaki, S.

S. Okamoto, K. Chikuma, T. Tohma, S. Umegaki, “Focussing system of optical second harmonic wave from crystal cored fiber,” in Proceedings of the Semiannual Meeting of the Japanese Society of Applied Physics (Fukuoka, Japan, 1989), p.923.

Van Kampen, N. G.

N. G. Van Kampen, “The method of stationary phase and the method of Fresnel zones,” Physica 24, 437–444 (1958).
[CrossRef]

Wiggins, T.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1989), pp. 416–417.

Appl. Opt.

IEEE J. Quantum Electron.

Q. Ren, R. Birngruber, “Axicon: a new laser beam delivery system for corneal surgery,” IEEE J. Quantum Electron. 26, 2305–2308 (1990).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Opt. Acta

M. V. Perez, C. Gomez-Reino, J. Cuadrado, “Diffraction patterns and zone plates produced by linear thin axicons,” Opt. Acta 33, 1161–1176 (1986).
[CrossRef]

Optik (Stuttgart)

R. Arimoto, S. Kawata, “Laser-scan fluorescence microscope with annular excitation,” Optik (Stuttgart) 86, 651–654 (1990).

Phys. Rev. Lett.

J. Durnin, J. Miceli, J. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

Physica

N. G. Van Kampen, “The method of stationary phase and the method of Fresnel zones,” Physica 24, 437–444 (1958).
[CrossRef]

Other

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1989), pp. 416–417.

S. Okamoto, K. Chikuma, T. Tohma, S. Umegaki, “Focussing system of optical second harmonic wave from crystal cored fiber,” in Proceedings of the Semiannual Meeting of the Japanese Society of Applied Physics (Fukuoka, Japan, 1989), p.923.

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Figures (8)

Fig. 1
Fig. 1

Geometry of an axicon during the J0 beam production and the equivalent optics of an annular pupil with a lens to the axicon.

Fig. 2
Fig. 2

Far-field pattern produced by an axicon at z = 32.1 mm: (a) θ = 0 deg, (b) θ = 1 deg, (c) θ = 1.5 deg, and (d) θ = 2.0 deg. (The peak of the spot on the photograph is saturated to make the first ring appear.)

Fig. 3
Fig. 3

Peak intensity distribution of the J0 beam central spot inside the depth of focus.

Fig. 4
Fig. 4

Beam-scanning imaging using an axicon as a generator of the primary light source.

Fig. 5
Fig. 5

Evolution of the J0 beam in the secondary source plane resulting from the mirror scan: θ = 0; B, θ = 1.0 deg; C, θ = 2.0 deg; D, θ = 3.0 deg. The intensity of each pattern is normalized by its maximum intensity.

Fig. 6
Fig. 6

Same result as shown in Fig. 6 but with an aberration-corrected lens for L2.

Fig. 7
Fig. 7

Geometry of a blazed axicon grating (transmittance type: line spacing, 4.79 μm; diameter, 4 mm; blazed angle, 7.30 angle).

Fig. 8
Fig. 8

Intensity distribution of a J0 beam produced by a blazed axicon grating: (a) normal incidence; (b) off-axis illumination.

Equations (4)

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I ( r , z ) = 4 π 2 E 2 ( R ) λ R sin β cos 2 β J 0 2 ( 2 π r sin β λ ) ,             z z D and R R 0 ,
n sin α = sin ( α + β ) ,
z D = R ( cot β - tan α ) ,
z D = R 0 ( n - 1 ) α .

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