Abstract

A diffractive optical element has been synthesized with laser phototechnology. It can transform a point source into a bright caustic (a light line) stretched along the optical axis. The element transforms a spherical wave into a conic and a point source in the object space to a ring structure in the image space. We investigated how the parameters of the light line (the length and the effective diameter) depend on the wavelength of the light source and the movement of the source along the optical axis. Also the interference field outside the caustic (Fresnel and Poisson fringes) was investigated. For an explanation of experimental data the geometrical theory of interferometers was used. The conditions for the appearance of fringes in white light are given. A device for rectilinear control of large tool beds and for centering machine components was manufactured. Experiments on determining the macroshape and the microshape of objects were performed.

© 1995 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. V. P. Korolkov, V. P. Koronkevich, I. A. Mikhaltsova, I. G. Palchikova, A. G. Poleshchuk, A. G. Sedukhin, A. P. Sokolov, E. G. Churin, Yu. I. Yurlov, “Kinoforms: technologies, new elements, and optical systems,” Autometria 4, 47–64 (1989) (in Russian).
  2. V. P. Koronkevich, V. P. Kiriyanov, F. I. Kokoulin, I. G. Palchikova, A. G. Poleshchuk, A. G. Sedukhin, E. G. Churin, A. M. Shcherbachenko, Yu. I. Yurlov, “Fabrication of kinoform optical elements” Optik (Stuttgart) 67, 257–266 (1984).
  3. Yu. I. Levashov, I. A. Mikhaltsova, Yu. A. Pupkov, M. G. Fedotov, “Device for measurement of nonrectilinearity—laser string,” Preprint 91-19, Institute of Nuclear Physics, Siberian Branch, USSR Academy of Science, Novosibirsk (1991) (in Russian).
  4. C. Chabrie, “Sur le diastoloscope, nouvel appareil d’optique destine a obtenur de tres forts grossements et a mesurer de tres petits deplacement d’objects lumineux,” Ann. Chim Phys. 2, 449–465 (1904).
  5. J. H. McLeod, “The axicon: a new type of optical element,” J. Opt. Soc. Am. 44, 592–597 (1954).
    [Crossref]
  6. J. H. McLeod, “The axicons and their uses,” J. Opt. Soc. Am. 50, 166–169 (1960).
    [Crossref]
  7. W. H. Steel, “Axicons with spherical surfaces,” in Optics in Metrology (Pergamon, London, 1960), pp. 181–192.
  8. B. M. Levin, Laser String DP-477 (State Optical Institute, Leningrad, 1966) (in Russian).
  9. B. M. Levin, V. T. Martynov, “Measurement of nonrectilinearity with the device Laser String DP-477,” Meas. Tech. USSR 5, 84–89 (1968) (in Russian).
  10. V. Ronchi, La Prova dei Sistemi Ottici (Zanichelli, Bologna, 1925).
  11. V. Ronchi, “Das Okularinterferometr und das Objektivinterferometr bei der Auflosung der Doppelsterne,” Z. Phys. 37, 732–757 (1926).
    [Crossref]
  12. J. Dyson, “Circular diffraction gratings,” Proc. R. Soc. London Ser. A 248, 93–106 (1958).
    [Crossref]
  13. J. Dyson, “Circular diffraction gratings as alignment devices,” in Optics in Metrology (Pergamon, London, 1960), pp. 169–171.
  14. A. N. Avdulov, A. N. Tabenkin, Modern Devices for the Industrial Control of Nonrectilinearity and Nonflatness (NIIT-Mash, Moscow, 1968) (in Russian).
  15. J. Leger, G. M. Morris, “Diffractive optics: new tools for optical engineering,” Opt. Photon. News54–55 (Mar.1992).
  16. V. P. Koronkevich, I. G. Palchikova, A. G. Poleshchuk, “Kinoforms optical elements with impulse ring response: technologies, new elements and optical systems,” Preprint 25, Institute of Autometry, Siberian Branch, USSR Academy of Science, Novosibirsk (1985) (in Russian).
  17. I. A. Mikhaltsova, V. I. Nalivaiko, I. S. Soldatenkov, “Kinoform axicons,” Optik (Stuttgart) 67, 267–278 (1984).
  18. J. Turunen, A. Vasara, A. T. Friberg, “Holographic generation of diffraction-free beams,” Appl. Opt. 27, 3959–3962 (1988).
    [Crossref] [PubMed]
  19. V. V. Kotlyar, V. A. Soifer, S. N. Khonina, “Phase optical elements for formation of free-space quasi-modes,” Kvantovaya Elektron. (Moscow) 18, 1391–1394 (1991) [Sov. J. Quantum Electron. 18, 1391–1394 (1991)].
  20. A. N. Zakharevsky, Interferometers (Defence Publishing, Moscow, 1968) (in Russian).
  21. P. Ditchburn, Physical Optics (Science, Moscow, 1965) (in Russian).
  22. V. P. Koronkevich, A. G. Poleshchuk, E. G. Churin, Yu. I. Yurlov, “The laser thermochemical technology for synthesis of diffraction optical elements on chromium films,” Kvantovaya Elektron. (Moscow) 12, 755–761 (1985) [Sov. J. Quantum Electron. 12, 255–761 (1985)].
  23. V. P. Koronkevich, V. S. Sobolev, Yu. N. Dubnischev, Laser Interferometry (Science, Novosibirsk, 1983) (in Russian).
  24. G. Häusler, W. Heckel “Light sectioning with large depth and high resolution,” Appl. Opt. 27, 5165–5169 (1988).
    [Crossref] [PubMed]
  25. M. Kato, S. Maeda, F. Yamagishi, H. Ikeda, T. Inagaki, “Wavelength independent grating lens system,” Appl. Opt. 28, 682–686 (1989).
    [Crossref] [PubMed]
  26. R. N. Smartt, “Zone plate interferometer,” Appl. Opt. 13, 1093–1099 (1974).
    [Crossref] [PubMed]

1992 (1)

J. Leger, G. M. Morris, “Diffractive optics: new tools for optical engineering,” Opt. Photon. News54–55 (Mar.1992).

1991 (1)

V. V. Kotlyar, V. A. Soifer, S. N. Khonina, “Phase optical elements for formation of free-space quasi-modes,” Kvantovaya Elektron. (Moscow) 18, 1391–1394 (1991) [Sov. J. Quantum Electron. 18, 1391–1394 (1991)].

1989 (2)

V. P. Korolkov, V. P. Koronkevich, I. A. Mikhaltsova, I. G. Palchikova, A. G. Poleshchuk, A. G. Sedukhin, A. P. Sokolov, E. G. Churin, Yu. I. Yurlov, “Kinoforms: technologies, new elements, and optical systems,” Autometria 4, 47–64 (1989) (in Russian).

M. Kato, S. Maeda, F. Yamagishi, H. Ikeda, T. Inagaki, “Wavelength independent grating lens system,” Appl. Opt. 28, 682–686 (1989).
[Crossref] [PubMed]

1988 (2)

1985 (1)

V. P. Koronkevich, A. G. Poleshchuk, E. G. Churin, Yu. I. Yurlov, “The laser thermochemical technology for synthesis of diffraction optical elements on chromium films,” Kvantovaya Elektron. (Moscow) 12, 755–761 (1985) [Sov. J. Quantum Electron. 12, 255–761 (1985)].

1984 (2)

I. A. Mikhaltsova, V. I. Nalivaiko, I. S. Soldatenkov, “Kinoform axicons,” Optik (Stuttgart) 67, 267–278 (1984).

V. P. Koronkevich, V. P. Kiriyanov, F. I. Kokoulin, I. G. Palchikova, A. G. Poleshchuk, A. G. Sedukhin, E. G. Churin, A. M. Shcherbachenko, Yu. I. Yurlov, “Fabrication of kinoform optical elements” Optik (Stuttgart) 67, 257–266 (1984).

1974 (1)

1968 (1)

B. M. Levin, V. T. Martynov, “Measurement of nonrectilinearity with the device Laser String DP-477,” Meas. Tech. USSR 5, 84–89 (1968) (in Russian).

1960 (1)

1958 (1)

J. Dyson, “Circular diffraction gratings,” Proc. R. Soc. London Ser. A 248, 93–106 (1958).
[Crossref]

1954 (1)

1926 (1)

V. Ronchi, “Das Okularinterferometr und das Objektivinterferometr bei der Auflosung der Doppelsterne,” Z. Phys. 37, 732–757 (1926).
[Crossref]

1904 (1)

C. Chabrie, “Sur le diastoloscope, nouvel appareil d’optique destine a obtenur de tres forts grossements et a mesurer de tres petits deplacement d’objects lumineux,” Ann. Chim Phys. 2, 449–465 (1904).

Avdulov, A. N.

A. N. Avdulov, A. N. Tabenkin, Modern Devices for the Industrial Control of Nonrectilinearity and Nonflatness (NIIT-Mash, Moscow, 1968) (in Russian).

Chabrie, C.

C. Chabrie, “Sur le diastoloscope, nouvel appareil d’optique destine a obtenur de tres forts grossements et a mesurer de tres petits deplacement d’objects lumineux,” Ann. Chim Phys. 2, 449–465 (1904).

Churin, E. G.

V. P. Korolkov, V. P. Koronkevich, I. A. Mikhaltsova, I. G. Palchikova, A. G. Poleshchuk, A. G. Sedukhin, A. P. Sokolov, E. G. Churin, Yu. I. Yurlov, “Kinoforms: technologies, new elements, and optical systems,” Autometria 4, 47–64 (1989) (in Russian).

V. P. Koronkevich, A. G. Poleshchuk, E. G. Churin, Yu. I. Yurlov, “The laser thermochemical technology for synthesis of diffraction optical elements on chromium films,” Kvantovaya Elektron. (Moscow) 12, 755–761 (1985) [Sov. J. Quantum Electron. 12, 255–761 (1985)].

V. P. Koronkevich, V. P. Kiriyanov, F. I. Kokoulin, I. G. Palchikova, A. G. Poleshchuk, A. G. Sedukhin, E. G. Churin, A. M. Shcherbachenko, Yu. I. Yurlov, “Fabrication of kinoform optical elements” Optik (Stuttgart) 67, 257–266 (1984).

Ditchburn, P.

P. Ditchburn, Physical Optics (Science, Moscow, 1965) (in Russian).

Dubnischev, Yu. N.

V. P. Koronkevich, V. S. Sobolev, Yu. N. Dubnischev, Laser Interferometry (Science, Novosibirsk, 1983) (in Russian).

Dyson, J.

J. Dyson, “Circular diffraction gratings,” Proc. R. Soc. London Ser. A 248, 93–106 (1958).
[Crossref]

J. Dyson, “Circular diffraction gratings as alignment devices,” in Optics in Metrology (Pergamon, London, 1960), pp. 169–171.

Fedotov, M. G.

Yu. I. Levashov, I. A. Mikhaltsova, Yu. A. Pupkov, M. G. Fedotov, “Device for measurement of nonrectilinearity—laser string,” Preprint 91-19, Institute of Nuclear Physics, Siberian Branch, USSR Academy of Science, Novosibirsk (1991) (in Russian).

Friberg, A. T.

Häusler, G.

Heckel, W.

Ikeda, H.

Inagaki, T.

Kato, M.

Khonina, S. N.

V. V. Kotlyar, V. A. Soifer, S. N. Khonina, “Phase optical elements for formation of free-space quasi-modes,” Kvantovaya Elektron. (Moscow) 18, 1391–1394 (1991) [Sov. J. Quantum Electron. 18, 1391–1394 (1991)].

Kiriyanov, V. P.

V. P. Koronkevich, V. P. Kiriyanov, F. I. Kokoulin, I. G. Palchikova, A. G. Poleshchuk, A. G. Sedukhin, E. G. Churin, A. M. Shcherbachenko, Yu. I. Yurlov, “Fabrication of kinoform optical elements” Optik (Stuttgart) 67, 257–266 (1984).

Kokoulin, F. I.

V. P. Koronkevich, V. P. Kiriyanov, F. I. Kokoulin, I. G. Palchikova, A. G. Poleshchuk, A. G. Sedukhin, E. G. Churin, A. M. Shcherbachenko, Yu. I. Yurlov, “Fabrication of kinoform optical elements” Optik (Stuttgart) 67, 257–266 (1984).

Korolkov, V. P.

V. P. Korolkov, V. P. Koronkevich, I. A. Mikhaltsova, I. G. Palchikova, A. G. Poleshchuk, A. G. Sedukhin, A. P. Sokolov, E. G. Churin, Yu. I. Yurlov, “Kinoforms: technologies, new elements, and optical systems,” Autometria 4, 47–64 (1989) (in Russian).

Koronkevich, V. P.

V. P. Korolkov, V. P. Koronkevich, I. A. Mikhaltsova, I. G. Palchikova, A. G. Poleshchuk, A. G. Sedukhin, A. P. Sokolov, E. G. Churin, Yu. I. Yurlov, “Kinoforms: technologies, new elements, and optical systems,” Autometria 4, 47–64 (1989) (in Russian).

V. P. Koronkevich, A. G. Poleshchuk, E. G. Churin, Yu. I. Yurlov, “The laser thermochemical technology for synthesis of diffraction optical elements on chromium films,” Kvantovaya Elektron. (Moscow) 12, 755–761 (1985) [Sov. J. Quantum Electron. 12, 255–761 (1985)].

V. P. Koronkevich, V. P. Kiriyanov, F. I. Kokoulin, I. G. Palchikova, A. G. Poleshchuk, A. G. Sedukhin, E. G. Churin, A. M. Shcherbachenko, Yu. I. Yurlov, “Fabrication of kinoform optical elements” Optik (Stuttgart) 67, 257–266 (1984).

V. P. Koronkevich, I. G. Palchikova, A. G. Poleshchuk, “Kinoforms optical elements with impulse ring response: technologies, new elements and optical systems,” Preprint 25, Institute of Autometry, Siberian Branch, USSR Academy of Science, Novosibirsk (1985) (in Russian).

V. P. Koronkevich, V. S. Sobolev, Yu. N. Dubnischev, Laser Interferometry (Science, Novosibirsk, 1983) (in Russian).

Kotlyar, V. V.

V. V. Kotlyar, V. A. Soifer, S. N. Khonina, “Phase optical elements for formation of free-space quasi-modes,” Kvantovaya Elektron. (Moscow) 18, 1391–1394 (1991) [Sov. J. Quantum Electron. 18, 1391–1394 (1991)].

Leger, J.

J. Leger, G. M. Morris, “Diffractive optics: new tools for optical engineering,” Opt. Photon. News54–55 (Mar.1992).

Levashov, Yu. I.

Yu. I. Levashov, I. A. Mikhaltsova, Yu. A. Pupkov, M. G. Fedotov, “Device for measurement of nonrectilinearity—laser string,” Preprint 91-19, Institute of Nuclear Physics, Siberian Branch, USSR Academy of Science, Novosibirsk (1991) (in Russian).

Levin, B. M.

B. M. Levin, V. T. Martynov, “Measurement of nonrectilinearity with the device Laser String DP-477,” Meas. Tech. USSR 5, 84–89 (1968) (in Russian).

B. M. Levin, Laser String DP-477 (State Optical Institute, Leningrad, 1966) (in Russian).

Maeda, S.

Martynov, V. T.

B. M. Levin, V. T. Martynov, “Measurement of nonrectilinearity with the device Laser String DP-477,” Meas. Tech. USSR 5, 84–89 (1968) (in Russian).

McLeod, J. H.

Mikhaltsova, I. A.

V. P. Korolkov, V. P. Koronkevich, I. A. Mikhaltsova, I. G. Palchikova, A. G. Poleshchuk, A. G. Sedukhin, A. P. Sokolov, E. G. Churin, Yu. I. Yurlov, “Kinoforms: technologies, new elements, and optical systems,” Autometria 4, 47–64 (1989) (in Russian).

I. A. Mikhaltsova, V. I. Nalivaiko, I. S. Soldatenkov, “Kinoform axicons,” Optik (Stuttgart) 67, 267–278 (1984).

Yu. I. Levashov, I. A. Mikhaltsova, Yu. A. Pupkov, M. G. Fedotov, “Device for measurement of nonrectilinearity—laser string,” Preprint 91-19, Institute of Nuclear Physics, Siberian Branch, USSR Academy of Science, Novosibirsk (1991) (in Russian).

Morris, G. M.

J. Leger, G. M. Morris, “Diffractive optics: new tools for optical engineering,” Opt. Photon. News54–55 (Mar.1992).

Nalivaiko, V. I.

I. A. Mikhaltsova, V. I. Nalivaiko, I. S. Soldatenkov, “Kinoform axicons,” Optik (Stuttgart) 67, 267–278 (1984).

Palchikova, I. G.

V. P. Korolkov, V. P. Koronkevich, I. A. Mikhaltsova, I. G. Palchikova, A. G. Poleshchuk, A. G. Sedukhin, A. P. Sokolov, E. G. Churin, Yu. I. Yurlov, “Kinoforms: technologies, new elements, and optical systems,” Autometria 4, 47–64 (1989) (in Russian).

V. P. Koronkevich, V. P. Kiriyanov, F. I. Kokoulin, I. G. Palchikova, A. G. Poleshchuk, A. G. Sedukhin, E. G. Churin, A. M. Shcherbachenko, Yu. I. Yurlov, “Fabrication of kinoform optical elements” Optik (Stuttgart) 67, 257–266 (1984).

V. P. Koronkevich, I. G. Palchikova, A. G. Poleshchuk, “Kinoforms optical elements with impulse ring response: technologies, new elements and optical systems,” Preprint 25, Institute of Autometry, Siberian Branch, USSR Academy of Science, Novosibirsk (1985) (in Russian).

Poleshchuk, A. G.

V. P. Korolkov, V. P. Koronkevich, I. A. Mikhaltsova, I. G. Palchikova, A. G. Poleshchuk, A. G. Sedukhin, A. P. Sokolov, E. G. Churin, Yu. I. Yurlov, “Kinoforms: technologies, new elements, and optical systems,” Autometria 4, 47–64 (1989) (in Russian).

V. P. Koronkevich, A. G. Poleshchuk, E. G. Churin, Yu. I. Yurlov, “The laser thermochemical technology for synthesis of diffraction optical elements on chromium films,” Kvantovaya Elektron. (Moscow) 12, 755–761 (1985) [Sov. J. Quantum Electron. 12, 255–761 (1985)].

V. P. Koronkevich, V. P. Kiriyanov, F. I. Kokoulin, I. G. Palchikova, A. G. Poleshchuk, A. G. Sedukhin, E. G. Churin, A. M. Shcherbachenko, Yu. I. Yurlov, “Fabrication of kinoform optical elements” Optik (Stuttgart) 67, 257–266 (1984).

V. P. Koronkevich, I. G. Palchikova, A. G. Poleshchuk, “Kinoforms optical elements with impulse ring response: technologies, new elements and optical systems,” Preprint 25, Institute of Autometry, Siberian Branch, USSR Academy of Science, Novosibirsk (1985) (in Russian).

Pupkov, Yu. A.

Yu. I. Levashov, I. A. Mikhaltsova, Yu. A. Pupkov, M. G. Fedotov, “Device for measurement of nonrectilinearity—laser string,” Preprint 91-19, Institute of Nuclear Physics, Siberian Branch, USSR Academy of Science, Novosibirsk (1991) (in Russian).

Ronchi, V.

V. Ronchi, “Das Okularinterferometr und das Objektivinterferometr bei der Auflosung der Doppelsterne,” Z. Phys. 37, 732–757 (1926).
[Crossref]

V. Ronchi, La Prova dei Sistemi Ottici (Zanichelli, Bologna, 1925).

Sedukhin, A. G.

V. P. Korolkov, V. P. Koronkevich, I. A. Mikhaltsova, I. G. Palchikova, A. G. Poleshchuk, A. G. Sedukhin, A. P. Sokolov, E. G. Churin, Yu. I. Yurlov, “Kinoforms: technologies, new elements, and optical systems,” Autometria 4, 47–64 (1989) (in Russian).

V. P. Koronkevich, V. P. Kiriyanov, F. I. Kokoulin, I. G. Palchikova, A. G. Poleshchuk, A. G. Sedukhin, E. G. Churin, A. M. Shcherbachenko, Yu. I. Yurlov, “Fabrication of kinoform optical elements” Optik (Stuttgart) 67, 257–266 (1984).

Shcherbachenko, A. M.

V. P. Koronkevich, V. P. Kiriyanov, F. I. Kokoulin, I. G. Palchikova, A. G. Poleshchuk, A. G. Sedukhin, E. G. Churin, A. M. Shcherbachenko, Yu. I. Yurlov, “Fabrication of kinoform optical elements” Optik (Stuttgart) 67, 257–266 (1984).

Smartt, R. N.

Sobolev, V. S.

V. P. Koronkevich, V. S. Sobolev, Yu. N. Dubnischev, Laser Interferometry (Science, Novosibirsk, 1983) (in Russian).

Soifer, V. A.

V. V. Kotlyar, V. A. Soifer, S. N. Khonina, “Phase optical elements for formation of free-space quasi-modes,” Kvantovaya Elektron. (Moscow) 18, 1391–1394 (1991) [Sov. J. Quantum Electron. 18, 1391–1394 (1991)].

Sokolov, A. P.

V. P. Korolkov, V. P. Koronkevich, I. A. Mikhaltsova, I. G. Palchikova, A. G. Poleshchuk, A. G. Sedukhin, A. P. Sokolov, E. G. Churin, Yu. I. Yurlov, “Kinoforms: technologies, new elements, and optical systems,” Autometria 4, 47–64 (1989) (in Russian).

Soldatenkov, I. S.

I. A. Mikhaltsova, V. I. Nalivaiko, I. S. Soldatenkov, “Kinoform axicons,” Optik (Stuttgart) 67, 267–278 (1984).

Steel, W. H.

W. H. Steel, “Axicons with spherical surfaces,” in Optics in Metrology (Pergamon, London, 1960), pp. 181–192.

Tabenkin, A. N.

A. N. Avdulov, A. N. Tabenkin, Modern Devices for the Industrial Control of Nonrectilinearity and Nonflatness (NIIT-Mash, Moscow, 1968) (in Russian).

Turunen, J.

Vasara, A.

Yamagishi, F.

Yurlov, Yu. I.

V. P. Korolkov, V. P. Koronkevich, I. A. Mikhaltsova, I. G. Palchikova, A. G. Poleshchuk, A. G. Sedukhin, A. P. Sokolov, E. G. Churin, Yu. I. Yurlov, “Kinoforms: technologies, new elements, and optical systems,” Autometria 4, 47–64 (1989) (in Russian).

V. P. Koronkevich, A. G. Poleshchuk, E. G. Churin, Yu. I. Yurlov, “The laser thermochemical technology for synthesis of diffraction optical elements on chromium films,” Kvantovaya Elektron. (Moscow) 12, 755–761 (1985) [Sov. J. Quantum Electron. 12, 255–761 (1985)].

V. P. Koronkevich, V. P. Kiriyanov, F. I. Kokoulin, I. G. Palchikova, A. G. Poleshchuk, A. G. Sedukhin, E. G. Churin, A. M. Shcherbachenko, Yu. I. Yurlov, “Fabrication of kinoform optical elements” Optik (Stuttgart) 67, 257–266 (1984).

Zakharevsky, A. N.

A. N. Zakharevsky, Interferometers (Defence Publishing, Moscow, 1968) (in Russian).

Ann. Chim Phys. (1)

C. Chabrie, “Sur le diastoloscope, nouvel appareil d’optique destine a obtenur de tres forts grossements et a mesurer de tres petits deplacement d’objects lumineux,” Ann. Chim Phys. 2, 449–465 (1904).

Appl. Opt. (4)

Autometria (1)

V. P. Korolkov, V. P. Koronkevich, I. A. Mikhaltsova, I. G. Palchikova, A. G. Poleshchuk, A. G. Sedukhin, A. P. Sokolov, E. G. Churin, Yu. I. Yurlov, “Kinoforms: technologies, new elements, and optical systems,” Autometria 4, 47–64 (1989) (in Russian).

J. Opt. Soc. Am. (2)

Kvantovaya Elektron. (Moscow) (2)

V. V. Kotlyar, V. A. Soifer, S. N. Khonina, “Phase optical elements for formation of free-space quasi-modes,” Kvantovaya Elektron. (Moscow) 18, 1391–1394 (1991) [Sov. J. Quantum Electron. 18, 1391–1394 (1991)].

V. P. Koronkevich, A. G. Poleshchuk, E. G. Churin, Yu. I. Yurlov, “The laser thermochemical technology for synthesis of diffraction optical elements on chromium films,” Kvantovaya Elektron. (Moscow) 12, 755–761 (1985) [Sov. J. Quantum Electron. 12, 255–761 (1985)].

Meas. Tech. USSR (1)

B. M. Levin, V. T. Martynov, “Measurement of nonrectilinearity with the device Laser String DP-477,” Meas. Tech. USSR 5, 84–89 (1968) (in Russian).

Opt. Photon. News (1)

J. Leger, G. M. Morris, “Diffractive optics: new tools for optical engineering,” Opt. Photon. News54–55 (Mar.1992).

Optik (Stuttgart) (2)

V. P. Koronkevich, V. P. Kiriyanov, F. I. Kokoulin, I. G. Palchikova, A. G. Poleshchuk, A. G. Sedukhin, E. G. Churin, A. M. Shcherbachenko, Yu. I. Yurlov, “Fabrication of kinoform optical elements” Optik (Stuttgart) 67, 257–266 (1984).

I. A. Mikhaltsova, V. I. Nalivaiko, I. S. Soldatenkov, “Kinoform axicons,” Optik (Stuttgart) 67, 267–278 (1984).

Proc. R. Soc. London Ser. A (1)

J. Dyson, “Circular diffraction gratings,” Proc. R. Soc. London Ser. A 248, 93–106 (1958).
[Crossref]

Z. Phys. (1)

V. Ronchi, “Das Okularinterferometr und das Objektivinterferometr bei der Auflosung der Doppelsterne,” Z. Phys. 37, 732–757 (1926).
[Crossref]

Other (10)

V. P. Koronkevich, V. S. Sobolev, Yu. N. Dubnischev, Laser Interferometry (Science, Novosibirsk, 1983) (in Russian).

J. Dyson, “Circular diffraction gratings as alignment devices,” in Optics in Metrology (Pergamon, London, 1960), pp. 169–171.

A. N. Avdulov, A. N. Tabenkin, Modern Devices for the Industrial Control of Nonrectilinearity and Nonflatness (NIIT-Mash, Moscow, 1968) (in Russian).

V. P. Koronkevich, I. G. Palchikova, A. G. Poleshchuk, “Kinoforms optical elements with impulse ring response: technologies, new elements and optical systems,” Preprint 25, Institute of Autometry, Siberian Branch, USSR Academy of Science, Novosibirsk (1985) (in Russian).

A. N. Zakharevsky, Interferometers (Defence Publishing, Moscow, 1968) (in Russian).

P. Ditchburn, Physical Optics (Science, Moscow, 1965) (in Russian).

Yu. I. Levashov, I. A. Mikhaltsova, Yu. A. Pupkov, M. G. Fedotov, “Device for measurement of nonrectilinearity—laser string,” Preprint 91-19, Institute of Nuclear Physics, Siberian Branch, USSR Academy of Science, Novosibirsk (1991) (in Russian).

V. Ronchi, La Prova dei Sistemi Ottici (Zanichelli, Bologna, 1925).

W. H. Steel, “Axicons with spherical surfaces,” in Optics in Metrology (Pergamon, London, 1960), pp. 181–192.

B. M. Levin, Laser String DP-477 (State Optical Institute, Leningrad, 1966) (in Russian).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (22)

Fig. 1
Fig. 1

Optical scheme of the lensacon. Beams emerging from the source at angle 2φ interfere at an arbitrary point of the field O”; l = f; l′ = ∞; b, element diameter.

Fig. 2
Fig. 2

Light-line section at a distance of 60 m from the lensacon. The circular fringes of equal width are obtained from the element whose parameters are given in Table 1, item 4.

Fig. 3
Fig. 3

Light-cord core on the background of fringes formed by the interference of 0 and −1st-order beams.

Fig. 4
Fig. 4

Distribution of the intensity of the light-line section: (a) lensacon with f = 300 mm and α = 10−2 illuminated by a He–Ne laser; (b) lensacon with f = 200 mm and α = 10−3 illuminated by a laser diode (λ = 0.67 μm). The rest of the element’s characteristics are indicated in Table 1.

Fig. 5
Fig. 5

Beam’s travel in the extrafocal localization of the source.

Fig. 6
Fig. 6

Light-line section every 20 m over a 100-m distance.

Fig. 7
Fig. 7

Dependence of the light-line diameter over the distance from the element and the source wavelength λ < λ0: 1, λ = 0.55 μm; 2, λ = 0.515 μm; 3, λ = 0.488 μm; 4, λ = 0.442 μm. (Curves 1′, 2′, 3′, and 4′ show a dependence between the distance L and the average radius of zones constructing the image at this distance for the same λ.)

Fig. 8
Fig. 8

Dependence of the light-line diameter on the distance from the element and on the source wavelength λ > λ0: 1, λ = 0.67 μm; 2, λ = 0.78 μm. (Curves 1′ and 2′ show the dependence between the distance L and the mean radius of zones constructing the image at this distance for the same λ.)

Fig. 9
Fig. 9

Specific regions behind the lensacon with the source position at 2f > l > f.

Fig. 10
Fig. 10

Interference field sections.

Fig. 11
Fig. 11

Appearance of interference in the near field. The formation of the light cord in beams of +3rd and +5th orders.

Fig. 12
Fig. 12

Interfering beams of the 0th, +1st, and −1st orders. The pupils and ports of the lensacon are shown.

Fig. 13
Fig. 13

Appearance of the interference field under lensacon illumination by a parallel beam. The distance from the screen, Lf. The element has phase structure. The element’s parameters are given in Table 1, item 4.

Fig. 14
Fig. 14

Two-beam fringes of [0, +1] and [+1, −1] types at distances from the screen of 5 and 30 m.

Fig. 15
Fig. 15

Intensity distribution in the source image (ring). In the center the Poisson’s fringes with a light center are visible.

Fig. 16
Fig. 16

Position of exit pupils S′ and S″, depending on the source S travel. (The source image is in the positive and the negative lenses.)

Fig. 17
Fig. 17

Interference field section for source positions from S1 to S4 (Fig. 16).

Fig. 18
Fig. 18

Field under lensacon illumination by a convergent beam (the source is in the image space): (a) fringes [+1, −1] in the center is a zero-order beam; (b) fringes behind the zero-order focus in the center are [0, +1] fringes; (c) origin of [−1, −1] fringes.

Fig. 19
Fig. 19

Laser String device schematic.

Fig. 20
Fig. 20

Object-shape control by the light-sectioning method.

Fig. 21
Fig. 21

Results of control and computer processing of an object shape (a saucer).

Fig. 22
Fig. 22

Interferometer for phase profile control.

Tables (1)

Tables Icon

Table 1 Lensacon Parameters

Equations (18)

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

( f 2 + r k 2 ) 1 / 2 - f + r k sin α = k λ 0 .
r k = ( 2 f k λ 0 + k 2 λ 0 2 + f 2 sin 2 α ) 1 / 2 - ( f + k λ 0 ) sin α cos 2 α .
N ( r ) sin φ ( r ) λ 0 + sin α λ 0 ,
I = c J 0 2 ( 2 π α ρ / λ 0 ) ,
d 0 = 2 ρ 1 = 0.766 λ 0 / α .
b = λ 0 / 2 φ λ 0 f / D .
d = [ 0.766 λ 0 L 0 ( 1 ± L x / f 2 ) ] / ( D / 2 ) = d 0 ( 1 ± L x / f 2 ) ,
Δ d / d 0 = ± L x / f 2 .
sin β ( r ) = ( λ / λ 0 ) sin α + ( λ / λ 0 - 1 ) sin φ ( r ) .
d = d 0 - d 0 ( λ / λ 0 - 1 ) L / f ,
d / d 0 = - Δ λ L / λ 0 f ,
Δ d / d 0 = - 1 / { [ λ 0 + Δ λ ) / Δ λ ] × ( sin α / sin φ ) + 1 } .
[ R k 2 / 2 ( L + l ) ] - [ R k 2 / 2 ( L + C ) ] = k λ [ 0 , - 1 ] , [ R k 2 / 2 ( L - l ) ] - [ R k 2 / 2 ( L + C ) ] = k λ [ 0 , + 1 ] , [ R k 2 / 2 ( L - l ) ] - [ R k 2 / 2 ( L + l ) ] = k λ [ + 1 , - 1 ] .
a R k 2 / 2 L 2 = k λ ,
R k = ( 2 k λ L 2 / a ) 1 / 2 .
f = k λ L 2 / R k 2 .
f = ( m - n ) λ L 2 / ( R m 2 - R n 2 ) .
R k 2 / 2 ( L - f ) = k λ ,

Metrics