Abstract

We investigate the testing of collimation by Talbot interferometry with circular gratings. Circular gratings are immune to misalignment owing to rigid body rotations in a plane perpendicular to the optic axis. Experimental results of the investigation are presented, and they are in good agreement with the theoretical predictions. Experimental results verify that collimation testing with circular gratings can be superior to that with linear dual-field gratings.

© 2001 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. V. R. K. Murty, “The use of single parallel plate as a lateral shearing interferometer with a visible gas laser source,” Appl. Opt. 3, 531–534 (1964).
    [CrossRef]
  2. P. Langenback, “Improved collimation test,” Appl. Opt. 9, 2590–2593 (1970).
    [CrossRef]
  3. Y. W. Lee, H. M. Cho, I. W. Lee, “Half aperture shearing interferometry for collimation testing,” Opt. Eng. 32, 2837–2840 (1993).
    [CrossRef]
  4. J. S. Darlin, M. P. Kothiyal, R. S. Sirohi, “Wedge plate interferometer: a new dual field configuration for collimation testing,” Opt. Laser Technol. 30, 225–228 (1998).
    [CrossRef]
  5. U. Gouha, Z. Mingsham, Z. Jingbin, “Improved wedge plate shearing interferometeric technique for a collimation testing,” Appl. Opt. 31, 4363–4364 (1992).
    [CrossRef]
  6. D. E. Silva, “A simple interferometric method of beam collimation,” Appl. Opt. 10, 1980–1982 (1971).
  7. J. C. Fouere, D. Malacara, “Focusing errors in collimating lens or mirror: use of moiré technique,” Appl. Opt. 13, 1322–1326 (1974).
    [CrossRef]
  8. S. Yokozeki, K. Patorski, K. Ohnishi, “Collimation method using Fourier imaging and moiré techniques,” Opt. Commun. 14, 401–405 (1975).
    [CrossRef]
  9. D. W. Swift, “A simple moiré fringe technique for magnification checking,” J. Phys. E 7, 164–166 (1974).
    [CrossRef]
  10. M. P. Kothiyal, R. S. Sirohi, “Improved collimation testing using Talbot interferometry,” Appl. Opt. 26, 4056–4057 (1987).
    [CrossRef] [PubMed]
  11. C.-W. Chang, D.-C. Su, “Collimation method that uses spiral grating and Talbot interferometry,” Opt. Lett. 16, 1783–1784 (1991).
    [CrossRef] [PubMed]
  12. K. V. Sriram, M. P. Kothiyal, R. S. Sirohi, “Collimation testing with linear dual field, spiral and evolute grating: a comparative study,” Appl. Opt. 33, 7258–7260 (1994).
    [CrossRef] [PubMed]
  13. D. S. Mehta, H. C. Khandpal, “A simple method for testing laser beam collimation,” Opt. Laser Technol. 29, 469–474 (1998).
    [CrossRef]
  14. A. R. Ganesan, P. Venkateswarlu, “Laser beam collimation using Talbot interferometry,” Appl. Opt. 32, 2918–2920 (1993).
    [CrossRef] [PubMed]
  15. C. Shakher, A. J. Pramila Daniel, “Talbot interferometer with circular gratings for the measurement of temperature in axisymmetric gaseous flames,” Appl. Opt. 33, 6068–6072 (1994).
    [CrossRef] [PubMed]
  16. C. Shakher, A. J. Pramila Daniel, A. K. Nirala, “Temperature profile measurement of axisymmetric gaseous flames using speckle photography, speckle shearing interferometry and Talbot interferometry,” Opt. Eng. 33, 1983–1988 (1994).
    [CrossRef]
  17. D. E. Silva, “Talbot interferometer for lateral and radial derivatives,” Appl. Opt. 11, 2613–2624 (1972).
    [CrossRef] [PubMed]
  18. M. P. Kothiyal, K. V. Sriram, R. S. Sirohi, “Setting sensitivity in Talbot interferometry with modified gratings,” Opt. Laser Technol. 23, 361–365 (1991).
    [CrossRef]
  19. R. M. Springer, D. H. Harris, “The development of alignment techniques for the fabrication of microelectronic devices,” Hum. Factors 11, 189–196 (1969).

1998

J. S. Darlin, M. P. Kothiyal, R. S. Sirohi, “Wedge plate interferometer: a new dual field configuration for collimation testing,” Opt. Laser Technol. 30, 225–228 (1998).
[CrossRef]

D. S. Mehta, H. C. Khandpal, “A simple method for testing laser beam collimation,” Opt. Laser Technol. 29, 469–474 (1998).
[CrossRef]

1994

1993

A. R. Ganesan, P. Venkateswarlu, “Laser beam collimation using Talbot interferometry,” Appl. Opt. 32, 2918–2920 (1993).
[CrossRef] [PubMed]

Y. W. Lee, H. M. Cho, I. W. Lee, “Half aperture shearing interferometry for collimation testing,” Opt. Eng. 32, 2837–2840 (1993).
[CrossRef]

1992

1991

C.-W. Chang, D.-C. Su, “Collimation method that uses spiral grating and Talbot interferometry,” Opt. Lett. 16, 1783–1784 (1991).
[CrossRef] [PubMed]

M. P. Kothiyal, K. V. Sriram, R. S. Sirohi, “Setting sensitivity in Talbot interferometry with modified gratings,” Opt. Laser Technol. 23, 361–365 (1991).
[CrossRef]

1987

1975

S. Yokozeki, K. Patorski, K. Ohnishi, “Collimation method using Fourier imaging and moiré techniques,” Opt. Commun. 14, 401–405 (1975).
[CrossRef]

1974

D. W. Swift, “A simple moiré fringe technique for magnification checking,” J. Phys. E 7, 164–166 (1974).
[CrossRef]

J. C. Fouere, D. Malacara, “Focusing errors in collimating lens or mirror: use of moiré technique,” Appl. Opt. 13, 1322–1326 (1974).
[CrossRef]

1972

1971

1970

1969

R. M. Springer, D. H. Harris, “The development of alignment techniques for the fabrication of microelectronic devices,” Hum. Factors 11, 189–196 (1969).

1964

Chang, C.-W.

Cho, H. M.

Y. W. Lee, H. M. Cho, I. W. Lee, “Half aperture shearing interferometry for collimation testing,” Opt. Eng. 32, 2837–2840 (1993).
[CrossRef]

Darlin, J. S.

J. S. Darlin, M. P. Kothiyal, R. S. Sirohi, “Wedge plate interferometer: a new dual field configuration for collimation testing,” Opt. Laser Technol. 30, 225–228 (1998).
[CrossRef]

Fouere, J. C.

Ganesan, A. R.

Gouha, U.

Harris, D. H.

R. M. Springer, D. H. Harris, “The development of alignment techniques for the fabrication of microelectronic devices,” Hum. Factors 11, 189–196 (1969).

Jingbin, Z.

Khandpal, H. C.

D. S. Mehta, H. C. Khandpal, “A simple method for testing laser beam collimation,” Opt. Laser Technol. 29, 469–474 (1998).
[CrossRef]

Kothiyal, M. P.

J. S. Darlin, M. P. Kothiyal, R. S. Sirohi, “Wedge plate interferometer: a new dual field configuration for collimation testing,” Opt. Laser Technol. 30, 225–228 (1998).
[CrossRef]

K. V. Sriram, M. P. Kothiyal, R. S. Sirohi, “Collimation testing with linear dual field, spiral and evolute grating: a comparative study,” Appl. Opt. 33, 7258–7260 (1994).
[CrossRef] [PubMed]

M. P. Kothiyal, K. V. Sriram, R. S. Sirohi, “Setting sensitivity in Talbot interferometry with modified gratings,” Opt. Laser Technol. 23, 361–365 (1991).
[CrossRef]

M. P. Kothiyal, R. S. Sirohi, “Improved collimation testing using Talbot interferometry,” Appl. Opt. 26, 4056–4057 (1987).
[CrossRef] [PubMed]

Langenback, P.

Lee, I. W.

Y. W. Lee, H. M. Cho, I. W. Lee, “Half aperture shearing interferometry for collimation testing,” Opt. Eng. 32, 2837–2840 (1993).
[CrossRef]

Lee, Y. W.

Y. W. Lee, H. M. Cho, I. W. Lee, “Half aperture shearing interferometry for collimation testing,” Opt. Eng. 32, 2837–2840 (1993).
[CrossRef]

Malacara, D.

Mehta, D. S.

D. S. Mehta, H. C. Khandpal, “A simple method for testing laser beam collimation,” Opt. Laser Technol. 29, 469–474 (1998).
[CrossRef]

Mingsham, Z.

Murty, M. V. R. K.

Nirala, A. K.

C. Shakher, A. J. Pramila Daniel, A. K. Nirala, “Temperature profile measurement of axisymmetric gaseous flames using speckle photography, speckle shearing interferometry and Talbot interferometry,” Opt. Eng. 33, 1983–1988 (1994).
[CrossRef]

Ohnishi, K.

S. Yokozeki, K. Patorski, K. Ohnishi, “Collimation method using Fourier imaging and moiré techniques,” Opt. Commun. 14, 401–405 (1975).
[CrossRef]

Patorski, K.

S. Yokozeki, K. Patorski, K. Ohnishi, “Collimation method using Fourier imaging and moiré techniques,” Opt. Commun. 14, 401–405 (1975).
[CrossRef]

Pramila Daniel, A. J.

C. Shakher, A. J. Pramila Daniel, “Talbot interferometer with circular gratings for the measurement of temperature in axisymmetric gaseous flames,” Appl. Opt. 33, 6068–6072 (1994).
[CrossRef] [PubMed]

C. Shakher, A. J. Pramila Daniel, A. K. Nirala, “Temperature profile measurement of axisymmetric gaseous flames using speckle photography, speckle shearing interferometry and Talbot interferometry,” Opt. Eng. 33, 1983–1988 (1994).
[CrossRef]

Shakher, C.

C. Shakher, A. J. Pramila Daniel, A. K. Nirala, “Temperature profile measurement of axisymmetric gaseous flames using speckle photography, speckle shearing interferometry and Talbot interferometry,” Opt. Eng. 33, 1983–1988 (1994).
[CrossRef]

C. Shakher, A. J. Pramila Daniel, “Talbot interferometer with circular gratings for the measurement of temperature in axisymmetric gaseous flames,” Appl. Opt. 33, 6068–6072 (1994).
[CrossRef] [PubMed]

Silva, D. E.

Sirohi, R. S.

J. S. Darlin, M. P. Kothiyal, R. S. Sirohi, “Wedge plate interferometer: a new dual field configuration for collimation testing,” Opt. Laser Technol. 30, 225–228 (1998).
[CrossRef]

K. V. Sriram, M. P. Kothiyal, R. S. Sirohi, “Collimation testing with linear dual field, spiral and evolute grating: a comparative study,” Appl. Opt. 33, 7258–7260 (1994).
[CrossRef] [PubMed]

M. P. Kothiyal, K. V. Sriram, R. S. Sirohi, “Setting sensitivity in Talbot interferometry with modified gratings,” Opt. Laser Technol. 23, 361–365 (1991).
[CrossRef]

M. P. Kothiyal, R. S. Sirohi, “Improved collimation testing using Talbot interferometry,” Appl. Opt. 26, 4056–4057 (1987).
[CrossRef] [PubMed]

Springer, R. M.

R. M. Springer, D. H. Harris, “The development of alignment techniques for the fabrication of microelectronic devices,” Hum. Factors 11, 189–196 (1969).

Sriram, K. V.

K. V. Sriram, M. P. Kothiyal, R. S. Sirohi, “Collimation testing with linear dual field, spiral and evolute grating: a comparative study,” Appl. Opt. 33, 7258–7260 (1994).
[CrossRef] [PubMed]

M. P. Kothiyal, K. V. Sriram, R. S. Sirohi, “Setting sensitivity in Talbot interferometry with modified gratings,” Opt. Laser Technol. 23, 361–365 (1991).
[CrossRef]

Su, D.-C.

Swift, D. W.

D. W. Swift, “A simple moiré fringe technique for magnification checking,” J. Phys. E 7, 164–166 (1974).
[CrossRef]

Venkateswarlu, P.

Yokozeki, S.

S. Yokozeki, K. Patorski, K. Ohnishi, “Collimation method using Fourier imaging and moiré techniques,” Opt. Commun. 14, 401–405 (1975).
[CrossRef]

Appl. Opt.

M. V. R. K. Murty, “The use of single parallel plate as a lateral shearing interferometer with a visible gas laser source,” Appl. Opt. 3, 531–534 (1964).
[CrossRef]

P. Langenback, “Improved collimation test,” Appl. Opt. 9, 2590–2593 (1970).
[CrossRef]

U. Gouha, Z. Mingsham, Z. Jingbin, “Improved wedge plate shearing interferometeric technique for a collimation testing,” Appl. Opt. 31, 4363–4364 (1992).
[CrossRef]

D. E. Silva, “A simple interferometric method of beam collimation,” Appl. Opt. 10, 1980–1982 (1971).

J. C. Fouere, D. Malacara, “Focusing errors in collimating lens or mirror: use of moiré technique,” Appl. Opt. 13, 1322–1326 (1974).
[CrossRef]

M. P. Kothiyal, R. S. Sirohi, “Improved collimation testing using Talbot interferometry,” Appl. Opt. 26, 4056–4057 (1987).
[CrossRef] [PubMed]

K. V. Sriram, M. P. Kothiyal, R. S. Sirohi, “Collimation testing with linear dual field, spiral and evolute grating: a comparative study,” Appl. Opt. 33, 7258–7260 (1994).
[CrossRef] [PubMed]

A. R. Ganesan, P. Venkateswarlu, “Laser beam collimation using Talbot interferometry,” Appl. Opt. 32, 2918–2920 (1993).
[CrossRef] [PubMed]

C. Shakher, A. J. Pramila Daniel, “Talbot interferometer with circular gratings for the measurement of temperature in axisymmetric gaseous flames,” Appl. Opt. 33, 6068–6072 (1994).
[CrossRef] [PubMed]

D. E. Silva, “Talbot interferometer for lateral and radial derivatives,” Appl. Opt. 11, 2613–2624 (1972).
[CrossRef] [PubMed]

Hum. Factors

R. M. Springer, D. H. Harris, “The development of alignment techniques for the fabrication of microelectronic devices,” Hum. Factors 11, 189–196 (1969).

J. Phys. E

D. W. Swift, “A simple moiré fringe technique for magnification checking,” J. Phys. E 7, 164–166 (1974).
[CrossRef]

Opt. Commun.

S. Yokozeki, K. Patorski, K. Ohnishi, “Collimation method using Fourier imaging and moiré techniques,” Opt. Commun. 14, 401–405 (1975).
[CrossRef]

Opt. Eng.

Y. W. Lee, H. M. Cho, I. W. Lee, “Half aperture shearing interferometry for collimation testing,” Opt. Eng. 32, 2837–2840 (1993).
[CrossRef]

C. Shakher, A. J. Pramila Daniel, A. K. Nirala, “Temperature profile measurement of axisymmetric gaseous flames using speckle photography, speckle shearing interferometry and Talbot interferometry,” Opt. Eng. 33, 1983–1988 (1994).
[CrossRef]

Opt. Laser Technol.

M. P. Kothiyal, K. V. Sriram, R. S. Sirohi, “Setting sensitivity in Talbot interferometry with modified gratings,” Opt. Laser Technol. 23, 361–365 (1991).
[CrossRef]

D. S. Mehta, H. C. Khandpal, “A simple method for testing laser beam collimation,” Opt. Laser Technol. 29, 469–474 (1998).
[CrossRef]

J. S. Darlin, M. P. Kothiyal, R. S. Sirohi, “Wedge plate interferometer: a new dual field configuration for collimation testing,” Opt. Laser Technol. 30, 225–228 (1998).
[CrossRef]

Opt. Lett.

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 (4)

Fig. 1
Fig. 1

Schematic of the experimental setup for collimation setting with circular gratings.

Fig. 2
Fig. 2

Photographs of moiré patterns on an observation screen (a) at inside focus, (b) at focus (collimation), and (c) out of focus for a 500-mm grating separation G1G2 corresponding to a collimator 300-mm focal length.

Fig. 3
Fig. 3

Relationship between Δθ and Δf.

Fig. 4
Fig. 4

Graphic representation of variation of sensitivity (Δf) with focal length (f) for Talbot planes located at 500, 750, 1000, 1250, and 1500 mm.

Tables (1)

Tables Icon

Table 1 Variation of Sensitivity (Δf) with Grating Separation (G 1 G 2 ) for Lenses of Different Focal Lengths

Equations (19)

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

Zm=kd2/λ,
x2+y2=m2d2,
x2+y2=n2D2,
p=m-n  p an integer,p=x2+y2/d21/2-x2+y2/D21/2.
x2+y2=pdD/D-d2.
R=pDdΔd,Δd=D-d.
M=Dd,R=pd2MΔd, M=RΔdpd2.
MNN-1/21+12N,
MNN+1/21-12N.
Δd1+12Nd2R,Δθ=ΔdL.
Δθ1+12Nd2RL.
tan Δθ=hΔfff-Δf,
Δθ=hΔfff-Δf.
hΔff2-fΔf1+12Nd2RL.
1+12Nd2RL=c1,
Δfc1f2h+c1f.
Δf=c1f2h+c1f.
Δf=c2f2h+c2f,
c2=1-12Nd2RL.

Metrics