Abstract

We present the design of a cemented doublet-lens axicon made from spherical surfaces only. Compared with diffractive axicons, refractive cone axicons, and earlier lens axicons with aspheric surfaces, this element is inexpensive and easy to manufacture even with large apertures. The lens axicon is based on the deliberate use of the spherical aberration of the surfaces. The design principles of the element and its characterization, numerically and experimentally, are presented in detail. Although performance was traded for simplicity and robustness, the results show that the lens axicon has the main axicon properties: a narrow, extended line focus of relatively constant width.

© 2004 Optical Society of America

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References

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  1. J. H. McLeod, “The axicon: a new type of optical element,” J. Opt. Soc. Am. 44, 592–597 (1954).
    [CrossRef]
  2. L. M. Soroko, Meso-Optics—Foundations and Applications (World Scientific, Singapore, 1996), Chap. 2 and references therein.
  3. Z. Jaroszewicz, Axicons: Design and Propagation Properties, Research and Development Treatises, Vol. 5 (SPIE Polish Chapter, Warsaw, 1997) and references therein.
  4. J. Sochacki, A. Kolodziejczyk, Z. Jaroszewicz, S. Bara, “Nonparaxial design of generalized axicons,” Appl. Opt. 31, 5326–5330 (1992).
    [CrossRef] [PubMed]
  5. J. A. Davis, E. Carcole, D. M. Cottrell, “Range-finding by triangulation with nondiffracting beams,” Appl. Opt. 35, 2159–2161 (1996).
    [CrossRef] [PubMed]
  6. G. Bickel, G. Haüsler, M. Haul, “Triangulation with extended range of depth,” Opt. Eng. 24, 975–977 (1985).
    [CrossRef]
  7. G. Haüsler, W. Heckel, “Light sectioning with large depth and high resolution,” Appl. Opt. 27, 5165–5169 (1988).
    [CrossRef] [PubMed]
  8. R. Arimoto, C. Saloma, T. Tanaka, S. Kawata, “Imaging properties of axicon in scanning optical system,” Appl. Opt. 31, 6653–6657 (1992).
    [CrossRef] [PubMed]
  9. R. Tremblay, Y. D’Astous, G. Roy, M. Blanchard, “Laser plasmas optically pumped by focusing with an axicon,” Opt. Commun. 28, 193–196 (1979).
    [CrossRef]
  10. K. Shinozaki, C. Xu, H. Sasaki, T. Kamijoh, “A comparison of optical second-harmonic generation efficiency using Bessel and Gaussian beams in bulk crystals,” Opt. Commun. 133, 300–304 (1997).
    [CrossRef]
  11. V. E. Peet, R. V. Tusbin, “Third-harmonic generation and multiphoton ionization in Bessel beams,” Phys. Rev. A 56, 1613–1620 (1997).
    [CrossRef]
  12. Y. Song, D. Milan, W. T. Hill, “Long, narrow all-light atom guide,” Opt. Lett. 24, 1805–1807 (1999).
    [CrossRef]
  13. J. Arlt, T. Hitomi, K. Dholakia, “Atom guiding along Laguerre–Gaussian and Bessel light beams,” Appl. Phys. B 71, 549–554 (2000).
    [CrossRef]
  14. Q.-S. Ru, N. Ohyama, T. Honda, “Fringe scanning radial shearing interferometer with circular gratings,” Opt. Commun. 69, 189–192 (1989).
    [CrossRef]
  15. R. Schreiner, M. Beyerlein, I. Harder, T. Dresel, N. Lindlein, J. Schwider, “Form assessment of hollow cylindrical specimens,” Appl. Opt. 41, 64–69 (2002).
    [CrossRef] [PubMed]
  16. A. Vasara, J. Turunen, A. T. Friberg, “Realization of general nondiffracting beams with computer-generated holograms,” J. Opt. Soc. Am. A 6, 1748–1754 (1989).
    [CrossRef] [PubMed]
  17. J. Arlt, K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177, 297–301 (2000).
    [CrossRef]
  18. R. M. Herman, T. A. Wiggins, “Production and uses of diffractionless beams,” J. Opt. Soc. Am. A 8, 932–942 (1991).
    [CrossRef]
  19. W. H. Steel, “Axicons with spherical surfaces,” in Colloquia of the International Commission for Optics: Optics in Metrology, P. Mollet, ed. (Pergamon, Oxford, 1960), pp. 181–192.
  20. Z. Jaroszewicz, J. Morales, “Lens axicons: systems composed of a diverging aberrated lens and a perfect converging lens,” J. Opt. Soc. Am. A 15, 2383–2390 (1998).
    [CrossRef]
  21. Z. Jaroszewicz, J. Morales, “Lens axicons: systems composed of a diverging aberrated lens and a converging aberrated lens,” J. Opt. Soc. Am. A 16, 191–197 (1999).
    [CrossRef]
  22. J. Pu, H. Zhang, S. Nemoto, “Lens axicons illuminated by Gaussian beams for generation of uniform-axial intensity bessel fields,” Opt. Eng. 39, 803–807 (2000).
    [CrossRef]
  23. M. Arif, M. M. Hossain, A. A. S. Awwal, M. N. Islam, “Refracting system for annular Gaussian-to-Bessel beam transformation,” Appl. Opt. 37, 649–652 (1998).
    [CrossRef]
  24. M. Arif, M. M. Hossain, A. A. S. Awwal, M. N. Islam, “Two-element refracting system for annular Gaussian-to-Bessel beam transformation,” Appl. Opt. 37, 4206–4209 (1998).
    [CrossRef]
  25. K. M. Iftekharuddin, A. A. S. Awwal, M. A. Karim, “Gaussian-to-Bessel beam transformation using a split refracting system,” Appl. Opt. 32, 2252–2256 (1993).
    [CrossRef]
  26. W. Chi, N. George, “Electronic imaging using a logarithmic asphere,” Opt. Lett. 26, 875–877 (2001).
    [CrossRef]
  27. R. M. Herman, T. A. Wiggins, “High-efficiency diffractionless beams of constant size and intensity,” Appl. Opt. 33, 7297–7306 (1994).
    [CrossRef] [PubMed]
  28. T. Aruga, “Generation of long-range nondiffracting narrow light beams,” Appl. Opt. 36, 3762–3768 (1997).
    [CrossRef] [PubMed]
  29. T. Aruga, S. W. Li, “Super high resolution for long-range imaging,” Appl. Opt. 38, 2795–2799 (1999).
    [CrossRef]
  30. Z. Ding, H. Ren, Y. Zhao, J. S. Nelson, Z. Chen, “High resolution optical coherence tomography over a large depth range with an axicon lens,” Opt. Lett. 27, 243–245 (2002).
    [CrossRef]
  31. We use the term doublet-lens axicon for a doublet lens with axicon properties. A similar term is the lens–axicon doublet, which refers to an axicon combined with a lens; see, e.g.,C. Parigger, Y. Tang, D. H. Plemmons, J. W. L. Lewis, “Spherical aberration effects in lens–axicon doublets: theoretical study,” Appl. Opt. 36, 8214–8221 (1997).
  32. We refer to positive spherical aberration when the wave-front aberration is positive, i.e., when the transverse and longitudinal aberrations are negative, and vice versa for negative spherical aberration; see, e.g., W. T. Welford, Aberrations of the Symmetrical Optical System (Academic, London, 1974).
  33. A. G. Sedukhin, “Beam-preshaping axicon focusing,” J. Opt. Soc. Am. A 15, 3057–3066 (1998).
    [CrossRef]
  34. J. Sochacki, Z. Jaroszewicz, L. R. Staronski, A. Kolodziejczyk, “Annular-aperture logarithmic axicon,” J. Opt. Soc. Am. A 10, 1765–1768 (1993).
    [CrossRef]
  35. G. E. Sommargren, H. J. Weaver, “Diffraction of light by an opaque sphere. 1: Description and properties of the diffraction pattern,” Appl. Opt. 29, 4646–4657 (1990).
    [CrossRef] [PubMed]
  36. A. G. Sedukhin, “Marginal phase correction of truncated Bessel beams,” J. Opt. Soc. Am. A 17, 1059–1066 (2000).
    [CrossRef]
  37. A. Thaning, Z. Jaroszewicz, A. T. Friberg, “Diffractive axicons in oblique illumination: analysis and experiments and comparison with elliptical axicons,” Appl. Opt. 42, 9–17 (2003).
    [CrossRef] [PubMed]

2003

2002

2001

2000

J. Arlt, K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177, 297–301 (2000).
[CrossRef]

J. Pu, H. Zhang, S. Nemoto, “Lens axicons illuminated by Gaussian beams for generation of uniform-axial intensity bessel fields,” Opt. Eng. 39, 803–807 (2000).
[CrossRef]

A. G. Sedukhin, “Marginal phase correction of truncated Bessel beams,” J. Opt. Soc. Am. A 17, 1059–1066 (2000).
[CrossRef]

J. Arlt, T. Hitomi, K. Dholakia, “Atom guiding along Laguerre–Gaussian and Bessel light beams,” Appl. Phys. B 71, 549–554 (2000).
[CrossRef]

1999

1998

1997

K. Shinozaki, C. Xu, H. Sasaki, T. Kamijoh, “A comparison of optical second-harmonic generation efficiency using Bessel and Gaussian beams in bulk crystals,” Opt. Commun. 133, 300–304 (1997).
[CrossRef]

V. E. Peet, R. V. Tusbin, “Third-harmonic generation and multiphoton ionization in Bessel beams,” Phys. Rev. A 56, 1613–1620 (1997).
[CrossRef]

T. Aruga, “Generation of long-range nondiffracting narrow light beams,” Appl. Opt. 36, 3762–3768 (1997).
[CrossRef] [PubMed]

We use the term doublet-lens axicon for a doublet lens with axicon properties. A similar term is the lens–axicon doublet, which refers to an axicon combined with a lens; see, e.g.,C. Parigger, Y. Tang, D. H. Plemmons, J. W. L. Lewis, “Spherical aberration effects in lens–axicon doublets: theoretical study,” Appl. Opt. 36, 8214–8221 (1997).

1996

1994

1993

1992

1991

1990

1989

Q.-S. Ru, N. Ohyama, T. Honda, “Fringe scanning radial shearing interferometer with circular gratings,” Opt. Commun. 69, 189–192 (1989).
[CrossRef]

A. Vasara, J. Turunen, A. T. Friberg, “Realization of general nondiffracting beams with computer-generated holograms,” J. Opt. Soc. Am. A 6, 1748–1754 (1989).
[CrossRef] [PubMed]

1988

1985

G. Bickel, G. Haüsler, M. Haul, “Triangulation with extended range of depth,” Opt. Eng. 24, 975–977 (1985).
[CrossRef]

1979

R. Tremblay, Y. D’Astous, G. Roy, M. Blanchard, “Laser plasmas optically pumped by focusing with an axicon,” Opt. Commun. 28, 193–196 (1979).
[CrossRef]

1954

Arif, M.

Arimoto, R.

Arlt, J.

J. Arlt, T. Hitomi, K. Dholakia, “Atom guiding along Laguerre–Gaussian and Bessel light beams,” Appl. Phys. B 71, 549–554 (2000).
[CrossRef]

J. Arlt, K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177, 297–301 (2000).
[CrossRef]

Aruga, T.

Awwal, A. A. S.

Bara, S.

Beyerlein, M.

Bickel, G.

G. Bickel, G. Haüsler, M. Haul, “Triangulation with extended range of depth,” Opt. Eng. 24, 975–977 (1985).
[CrossRef]

Blanchard, M.

R. Tremblay, Y. D’Astous, G. Roy, M. Blanchard, “Laser plasmas optically pumped by focusing with an axicon,” Opt. Commun. 28, 193–196 (1979).
[CrossRef]

Carcole, E.

Chen, Z.

Chi, W.

Cottrell, D. M.

D’Astous, Y.

R. Tremblay, Y. D’Astous, G. Roy, M. Blanchard, “Laser plasmas optically pumped by focusing with an axicon,” Opt. Commun. 28, 193–196 (1979).
[CrossRef]

Davis, J. A.

Dholakia, K.

J. Arlt, T. Hitomi, K. Dholakia, “Atom guiding along Laguerre–Gaussian and Bessel light beams,” Appl. Phys. B 71, 549–554 (2000).
[CrossRef]

J. Arlt, K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177, 297–301 (2000).
[CrossRef]

Ding, Z.

Dresel, T.

Friberg, A. T.

George, N.

Harder, I.

Haul, M.

G. Bickel, G. Haüsler, M. Haul, “Triangulation with extended range of depth,” Opt. Eng. 24, 975–977 (1985).
[CrossRef]

Haüsler, G.

G. Haüsler, W. Heckel, “Light sectioning with large depth and high resolution,” Appl. Opt. 27, 5165–5169 (1988).
[CrossRef] [PubMed]

G. Bickel, G. Haüsler, M. Haul, “Triangulation with extended range of depth,” Opt. Eng. 24, 975–977 (1985).
[CrossRef]

Heckel, W.

Herman, R. M.

Hill, W. T.

Hitomi, T.

J. Arlt, T. Hitomi, K. Dholakia, “Atom guiding along Laguerre–Gaussian and Bessel light beams,” Appl. Phys. B 71, 549–554 (2000).
[CrossRef]

Honda, T.

Q.-S. Ru, N. Ohyama, T. Honda, “Fringe scanning radial shearing interferometer with circular gratings,” Opt. Commun. 69, 189–192 (1989).
[CrossRef]

Hossain, M. M.

Iftekharuddin, K. M.

Islam, M. N.

Jaroszewicz, Z.

Kamijoh, T.

K. Shinozaki, C. Xu, H. Sasaki, T. Kamijoh, “A comparison of optical second-harmonic generation efficiency using Bessel and Gaussian beams in bulk crystals,” Opt. Commun. 133, 300–304 (1997).
[CrossRef]

Karim, M. A.

Kawata, S.

Kolodziejczyk, A.

Lewis, J. W. L.

Li, S. W.

Lindlein, N.

McLeod, J. H.

Milan, D.

Morales, J.

Nelson, J. S.

Nemoto, S.

J. Pu, H. Zhang, S. Nemoto, “Lens axicons illuminated by Gaussian beams for generation of uniform-axial intensity bessel fields,” Opt. Eng. 39, 803–807 (2000).
[CrossRef]

Ohyama, N.

Q.-S. Ru, N. Ohyama, T. Honda, “Fringe scanning radial shearing interferometer with circular gratings,” Opt. Commun. 69, 189–192 (1989).
[CrossRef]

Parigger, C.

Peet, V. E.

V. E. Peet, R. V. Tusbin, “Third-harmonic generation and multiphoton ionization in Bessel beams,” Phys. Rev. A 56, 1613–1620 (1997).
[CrossRef]

Plemmons, D. H.

Pu, J.

J. Pu, H. Zhang, S. Nemoto, “Lens axicons illuminated by Gaussian beams for generation of uniform-axial intensity bessel fields,” Opt. Eng. 39, 803–807 (2000).
[CrossRef]

Ren, H.

Roy, G.

R. Tremblay, Y. D’Astous, G. Roy, M. Blanchard, “Laser plasmas optically pumped by focusing with an axicon,” Opt. Commun. 28, 193–196 (1979).
[CrossRef]

Ru, Q.-S.

Q.-S. Ru, N. Ohyama, T. Honda, “Fringe scanning radial shearing interferometer with circular gratings,” Opt. Commun. 69, 189–192 (1989).
[CrossRef]

Saloma, C.

Sasaki, H.

K. Shinozaki, C. Xu, H. Sasaki, T. Kamijoh, “A comparison of optical second-harmonic generation efficiency using Bessel and Gaussian beams in bulk crystals,” Opt. Commun. 133, 300–304 (1997).
[CrossRef]

Schreiner, R.

Schwider, J.

Sedukhin, A. G.

Shinozaki, K.

K. Shinozaki, C. Xu, H. Sasaki, T. Kamijoh, “A comparison of optical second-harmonic generation efficiency using Bessel and Gaussian beams in bulk crystals,” Opt. Commun. 133, 300–304 (1997).
[CrossRef]

Sochacki, J.

Sommargren, G. E.

Song, Y.

Soroko, L. M.

L. M. Soroko, Meso-Optics—Foundations and Applications (World Scientific, Singapore, 1996), Chap. 2 and references therein.

Staronski, L. R.

Steel, W. H.

W. H. Steel, “Axicons with spherical surfaces,” in Colloquia of the International Commission for Optics: Optics in Metrology, P. Mollet, ed. (Pergamon, Oxford, 1960), pp. 181–192.

Tanaka, T.

Tang, Y.

Thaning, A.

Tremblay, R.

R. Tremblay, Y. D’Astous, G. Roy, M. Blanchard, “Laser plasmas optically pumped by focusing with an axicon,” Opt. Commun. 28, 193–196 (1979).
[CrossRef]

Turunen, J.

Tusbin, R. V.

V. E. Peet, R. V. Tusbin, “Third-harmonic generation and multiphoton ionization in Bessel beams,” Phys. Rev. A 56, 1613–1620 (1997).
[CrossRef]

Vasara, A.

Weaver, H. J.

Welford, W. T.

We refer to positive spherical aberration when the wave-front aberration is positive, i.e., when the transverse and longitudinal aberrations are negative, and vice versa for negative spherical aberration; see, e.g., W. T. Welford, Aberrations of the Symmetrical Optical System (Academic, London, 1974).

Wiggins, T. A.

Xu, C.

K. Shinozaki, C. Xu, H. Sasaki, T. Kamijoh, “A comparison of optical second-harmonic generation efficiency using Bessel and Gaussian beams in bulk crystals,” Opt. Commun. 133, 300–304 (1997).
[CrossRef]

Zhang, H.

J. Pu, H. Zhang, S. Nemoto, “Lens axicons illuminated by Gaussian beams for generation of uniform-axial intensity bessel fields,” Opt. Eng. 39, 803–807 (2000).
[CrossRef]

Zhao, Y.

Appl. Opt.

G. E. Sommargren, H. J. Weaver, “Diffraction of light by an opaque sphere. 1: Description and properties of the diffraction pattern,” Appl. Opt. 29, 4646–4657 (1990).
[CrossRef] [PubMed]

J. Sochacki, A. Kolodziejczyk, Z. Jaroszewicz, S. Bara, “Nonparaxial design of generalized axicons,” Appl. Opt. 31, 5326–5330 (1992).
[CrossRef] [PubMed]

R. Arimoto, C. Saloma, T. Tanaka, S. Kawata, “Imaging properties of axicon in scanning optical system,” Appl. Opt. 31, 6653–6657 (1992).
[CrossRef] [PubMed]

K. M. Iftekharuddin, A. A. S. Awwal, M. A. Karim, “Gaussian-to-Bessel beam transformation using a split refracting system,” Appl. Opt. 32, 2252–2256 (1993).
[CrossRef]

R. M. Herman, T. A. Wiggins, “High-efficiency diffractionless beams of constant size and intensity,” Appl. Opt. 33, 7297–7306 (1994).
[CrossRef] [PubMed]

T. Aruga, “Generation of long-range nondiffracting narrow light beams,” Appl. Opt. 36, 3762–3768 (1997).
[CrossRef] [PubMed]

We use the term doublet-lens axicon for a doublet lens with axicon properties. A similar term is the lens–axicon doublet, which refers to an axicon combined with a lens; see, e.g.,C. Parigger, Y. Tang, D. H. Plemmons, J. W. L. Lewis, “Spherical aberration effects in lens–axicon doublets: theoretical study,” Appl. Opt. 36, 8214–8221 (1997).

T. Aruga, S. W. Li, “Super high resolution for long-range imaging,” Appl. Opt. 38, 2795–2799 (1999).
[CrossRef]

J. A. Davis, E. Carcole, D. M. Cottrell, “Range-finding by triangulation with nondiffracting beams,” Appl. Opt. 35, 2159–2161 (1996).
[CrossRef] [PubMed]

M. Arif, M. M. Hossain, A. A. S. Awwal, M. N. Islam, “Refracting system for annular Gaussian-to-Bessel beam transformation,” Appl. Opt. 37, 649–652 (1998).
[CrossRef]

M. Arif, M. M. Hossain, A. A. S. Awwal, M. N. Islam, “Two-element refracting system for annular Gaussian-to-Bessel beam transformation,” Appl. Opt. 37, 4206–4209 (1998).
[CrossRef]

G. Haüsler, W. Heckel, “Light sectioning with large depth and high resolution,” Appl. Opt. 27, 5165–5169 (1988).
[CrossRef] [PubMed]

R. Schreiner, M. Beyerlein, I. Harder, T. Dresel, N. Lindlein, J. Schwider, “Form assessment of hollow cylindrical specimens,” Appl. Opt. 41, 64–69 (2002).
[CrossRef] [PubMed]

A. Thaning, Z. Jaroszewicz, A. T. Friberg, “Diffractive axicons in oblique illumination: analysis and experiments and comparison with elliptical axicons,” Appl. Opt. 42, 9–17 (2003).
[CrossRef] [PubMed]

Appl. Phys. B

J. Arlt, T. Hitomi, K. Dholakia, “Atom guiding along Laguerre–Gaussian and Bessel light beams,” Appl. Phys. B 71, 549–554 (2000).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Commun.

Q.-S. Ru, N. Ohyama, T. Honda, “Fringe scanning radial shearing interferometer with circular gratings,” Opt. Commun. 69, 189–192 (1989).
[CrossRef]

J. Arlt, K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177, 297–301 (2000).
[CrossRef]

R. Tremblay, Y. D’Astous, G. Roy, M. Blanchard, “Laser plasmas optically pumped by focusing with an axicon,” Opt. Commun. 28, 193–196 (1979).
[CrossRef]

K. Shinozaki, C. Xu, H. Sasaki, T. Kamijoh, “A comparison of optical second-harmonic generation efficiency using Bessel and Gaussian beams in bulk crystals,” Opt. Commun. 133, 300–304 (1997).
[CrossRef]

Opt. Eng.

G. Bickel, G. Haüsler, M. Haul, “Triangulation with extended range of depth,” Opt. Eng. 24, 975–977 (1985).
[CrossRef]

J. Pu, H. Zhang, S. Nemoto, “Lens axicons illuminated by Gaussian beams for generation of uniform-axial intensity bessel fields,” Opt. Eng. 39, 803–807 (2000).
[CrossRef]

Opt. Lett.

Phys. Rev. A

V. E. Peet, R. V. Tusbin, “Third-harmonic generation and multiphoton ionization in Bessel beams,” Phys. Rev. A 56, 1613–1620 (1997).
[CrossRef]

Other

L. M. Soroko, Meso-Optics—Foundations and Applications (World Scientific, Singapore, 1996), Chap. 2 and references therein.

Z. Jaroszewicz, Axicons: Design and Propagation Properties, Research and Development Treatises, Vol. 5 (SPIE Polish Chapter, Warsaw, 1997) and references therein.

W. H. Steel, “Axicons with spherical surfaces,” in Colloquia of the International Commission for Optics: Optics in Metrology, P. Mollet, ed. (Pergamon, Oxford, 1960), pp. 181–192.

We refer to positive spherical aberration when the wave-front aberration is positive, i.e., when the transverse and longitudinal aberrations are negative, and vice versa for negative spherical aberration; see, e.g., W. T. Welford, Aberrations of the Symmetrical Optical System (Academic, London, 1974).

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Figures (9)

Fig. 1
Fig. 1

Geometry of the annular-aperture axicon and illustration of the notations. The focal line segment indicated on the optical axis extends from z = d 1 to z = d 2, R 1 and R 2 are the inner and the outer radii of the annular aperture, and θ is the convergence angle.

Fig. 2
Fig. 2

Lenses with (a) a positive spherical aberration, and (b) a negative spherical aberration: θ, convergence angle; ρ, radial coordinate in the lens aperture.

Fig. 3
Fig. 3

Final design of the lens axicon adjusted to the radii of the available tools. The values of the parameters are in Table 2.

Fig. 4
Fig. 4

On-axis intensity for the lens axicon in Fig. 3 (see Table 2 for the parameters), calculated by using the Fresnel diffraction integral. The thick curve is the stationary-phase approximation in Eq. (4).

Fig. 5
Fig. 5

Solid curve, focal linewidth for the axicon in Fig. 3, calculated from Eq. (5); dotted lines, widths of the Arago spot before and after the focal segment, given by Eq. (6); solid squares, measured values of the focal linewidth.

Fig. 6
Fig. 6

Transverse intensity distribution produced by the lens axicon in Fig. 3: (a) z = 200 mm, (b) z = 300 mm, (c) z = 400 mm, (d) z = 800 mm, according to numerical evaluation of the Fresnel diffraction integral. The images are oversaturated in the middle to show the surrounding rings. The resolution is 0.7 μm/pixel.

Fig. 7
Fig. 7

Experimental layouts for measuring (a) the transverse intensity distributions and (b) the on-axis intensity profile.

Fig. 8
Fig. 8

Measured normalized on-axis intensity for the lens axicon in Fig. 3. Each point is an average of four measurements. Dotted curves, 95% confidence interval; solid curve, theoretical stationary-phase approximation in Eq. (4).

Fig. 9
Fig. 9

Measured transverse intensity distribution: (a) z = 180 mm, (b) z = 200 mm, (c) z = 250 mm, (d) z = 300 mm, (e) z = 400 mm, (f) z = 550 mm for the lens axicon in Fig. 3. The intensity of the incident laser beam has been adjusted to the sensitivity of the CCD camera before each image was taken, and so the intensity level is not the same in the six images. Each pixel is 1.33 μm.

Tables (2)

Tables Icon

Table 1 Desired and Actual Transverse Aberrations for 10 Rays

Tables Icon

Table 2 Parameters of the Final Design

Equations (6)

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

f=d1d2R22-R12d2R22-d1R12.
TAρ=-f Wρ,
φρ=ρ2/2f+Wρ.
Ispzλφ2ρ|1/z-φρ|
wz=2.4048λ2π1φρ.
wAz=2.40λ2πR z.

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