Abstract

A new type of wave-front analysis method for the collimation testing of laser beams is proposed. A concept of wave-front height is defined, and, on this basis, the wave-front analysis method of circular aperture sampling is introduced. The wave-front height of the tested noncollimated wave can be estimated from the distance between two identical fiducial diffraction planes of the sampled wave, and then the divergence is determined. The design is detailed, and the experiment is demonstrated. The principle and experiment results of the method are presented. Owing to the simplicity of the method and its low cost, it is a promising method for checking the collimation of a laser beam with a large divergence.

© 2005 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. E. Silva, “A simple interferometric method of beam collima-tion,” Appl. Opt. 10, 1980–1982 (1971).
    [CrossRef]
  2. S. Yokozeki, K. Patorski, K. Ohnishi, “Collimation method using Fourier imaging and moiré technique,” Opt. Commun. 14, 401–405 (1975).
    [CrossRef]
  3. K. V. Sriram, M. P. Kothiyal, R. S. Sirohi, “Collimation testing with linear dual-field, spiral, and evolute gratings: a comparative study,” Appl. Opt. 33, 7258–7260 (1994).
    [CrossRef] [PubMed]
  4. C. Shakher, S. Prakash, D. Nand, R. Kumar, “Collimation testing with circular gratings,” Appl. Opt. 40, 1175–1179 (2001).
    [CrossRef]
  5. M. V. R. K. Murty, “The use of a single parallel plate as a lateral shearing interferometer with a visible gas laser source,” Appl. Opt. 3, 531–534 (1964).
    [CrossRef]
  6. R. S. Sirohi, M. P. Kothiyal, “Double wedge plate shearing interferometer for collimation test,” Appl. Opt. 26, 4054–4056 (1987).
    [CrossRef] [PubMed]
  7. M. V. Mantravadi, “Lateral shearing interferometers,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1992), pp. 123–172.
  8. M. P. Kothiyal, R. S. Sirohi, “Improved collimation testing using Talbot interferometry,” Appl. Opt. 26, 4056–4057 (1987).
    [CrossRef] [PubMed]
  9. M. P. Kothiyal, R. S. Sirohi, K. J. Rosenburch, “Improved techniques of collimation testing,” Opt. Laser Technol. 10, 139–144 (1988).
    [CrossRef]
  10. 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]
  11. K. V. Sriram, M. P. Kothiyal, R. S. Sirohi, “Self-referencing collimation testing techniques,” Opt. Eng. 32, 94–100 (1993).
    [CrossRef]
  12. C. S. Narayanamurthy, “Collimation testing using temporal coherence,” Opt. Eng. 35, 1161–1164 (1996).
    [CrossRef]
  13. A. Anand, C. S. Narayanamurthy, “Collimation testing using photorefractive crystal and temporal coherence,” Opt. Eng. 42, 1108–1113 (2003).
    [CrossRef]

2003 (1)

A. Anand, C. S. Narayanamurthy, “Collimation testing using photorefractive crystal and temporal coherence,” Opt. Eng. 42, 1108–1113 (2003).
[CrossRef]

2001 (1)

1996 (1)

C. S. Narayanamurthy, “Collimation testing using temporal coherence,” Opt. Eng. 35, 1161–1164 (1996).
[CrossRef]

1994 (1)

1993 (1)

K. V. Sriram, M. P. Kothiyal, R. S. Sirohi, “Self-referencing collimation testing techniques,” Opt. Eng. 32, 94–100 (1993).
[CrossRef]

1991 (1)

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]

1988 (1)

M. P. Kothiyal, R. S. Sirohi, K. J. Rosenburch, “Improved techniques of collimation testing,” Opt. Laser Technol. 10, 139–144 (1988).
[CrossRef]

1987 (2)

1975 (1)

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

1971 (1)

1964 (1)

Anand, A.

A. Anand, C. S. Narayanamurthy, “Collimation testing using photorefractive crystal and temporal coherence,” Opt. Eng. 42, 1108–1113 (2003).
[CrossRef]

Kothiyal, M. P.

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

K. V. Sriram, M. P. Kothiyal, R. S. Sirohi, “Self-referencing collimation testing techniques,” Opt. Eng. 32, 94–100 (1993).
[CrossRef]

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, K. J. Rosenburch, “Improved techniques of collimation testing,” Opt. Laser Technol. 10, 139–144 (1988).
[CrossRef]

R. S. Sirohi, M. P. Kothiyal, “Double wedge plate shearing interferometer for collimation test,” Appl. Opt. 26, 4054–4056 (1987).
[CrossRef] [PubMed]

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

Kumar, R.

Mantravadi, M. V.

M. V. Mantravadi, “Lateral shearing interferometers,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1992), pp. 123–172.

Murty, M. V. R. K.

Nand, D.

Narayanamurthy, C. S.

A. Anand, C. S. Narayanamurthy, “Collimation testing using photorefractive crystal and temporal coherence,” Opt. Eng. 42, 1108–1113 (2003).
[CrossRef]

C. S. Narayanamurthy, “Collimation testing using temporal coherence,” Opt. Eng. 35, 1161–1164 (1996).
[CrossRef]

Ohnishi, K.

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

Patorski, K.

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

Prakash, S.

Rosenburch, K. J.

M. P. Kothiyal, R. S. Sirohi, K. J. Rosenburch, “Improved techniques of collimation testing,” Opt. Laser Technol. 10, 139–144 (1988).
[CrossRef]

Shakher, C.

Silva, D. E.

Sirohi, R. S.

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

K. V. Sriram, M. P. Kothiyal, R. S. Sirohi, “Self-referencing collimation testing techniques,” Opt. Eng. 32, 94–100 (1993).
[CrossRef]

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, K. J. Rosenburch, “Improved techniques of collimation testing,” Opt. Laser Technol. 10, 139–144 (1988).
[CrossRef]

R. S. Sirohi, M. P. Kothiyal, “Double wedge plate shearing interferometer for collimation test,” Appl. Opt. 26, 4054–4056 (1987).
[CrossRef] [PubMed]

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

Sriram, K. V.

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

K. V. Sriram, M. P. Kothiyal, R. S. Sirohi, “Self-referencing collimation testing techniques,” Opt. Eng. 32, 94–100 (1993).
[CrossRef]

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]

Yokozeki, S.

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

Appl. Opt. (6)

Opt. Commun. (1)

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

Opt. Eng. (3)

K. V. Sriram, M. P. Kothiyal, R. S. Sirohi, “Self-referencing collimation testing techniques,” Opt. Eng. 32, 94–100 (1993).
[CrossRef]

C. S. Narayanamurthy, “Collimation testing using temporal coherence,” Opt. Eng. 35, 1161–1164 (1996).
[CrossRef]

A. Anand, C. S. Narayanamurthy, “Collimation testing using photorefractive crystal and temporal coherence,” Opt. Eng. 42, 1108–1113 (2003).
[CrossRef]

Opt. Laser Technol. (2)

M. P. Kothiyal, R. S. Sirohi, K. J. Rosenburch, “Improved techniques of collimation testing,” Opt. Laser Technol. 10, 139–144 (1988).
[CrossRef]

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]

Other (1)

M. V. Mantravadi, “Lateral shearing interferometers,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1992), pp. 123–172.

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 (5)

Fig. 1
Fig. 1

(a) Wave-front height. (b) Calculation of the tested wave-front height.

Fig. 2
Fig. 2

Transverse intensity profiles behind the focusing lens for the collimated beam.

Fig. 3
Fig. 3

Computer-generated fiducial diffraction patterns for m = 1, 2, 3.

Fig. 4
Fig. 4

Experimental setup for collimation testing.

Fig. 5
Fig. 5

Experimental fiducial diffraction patterns for m = 1, 2, 3: (a) inside the focus and (b) outside the focus.

Tables (1)

Tables Icon

Table 1 Comparison of Calculated Versus Measured Wave-Front Heightsa

Equations (17)

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

W = a 2 / 2 R .
u ( r ) = exp ( j k a 2 W r 2 ) .
W 0 = ( a 0 2 / a 2 ) W .
ϕ = 4 W 0 / a 0 .
u z ( r z ) = 2 π j λ z exp ( jkz ) exp ( j k 2 z r z 2 ) × 0 exp ( j k W a 2 r 2 ) circ ( r a ) exp ( j k 2 f r 2 ) × exp ( j k 2 z r 2 ) J 0 ( 2 π ρ z r ) r d r ,
u z ( r z ) = 2 π j λ z 0 a exp { j k a 2 [ W a 2 ( z f ) 2 f z ] r 2 } × J 0 ( 2 π ρ z r ) r d r .
W = W a 2 ( z f ) 2 f z .
u z ( r z ) = 2 π j λ z 0 a exp ( j k a 2 W r 2 ) J 0 ( 2 π ρ z r ) r d r .
W = W a 2 ( z f ) 2 f z = ± m λ ,
u z ( r z ) = 2 π j λ z 0 a exp [ j k a 2 ( ± m λ ) r 2 ] J 0 ( 2 π ρ z r ) r d r .
u z ( 0 ) = 2 π j λ z 0 a exp [ j k a 2 ( ± m λ ) r 2 ] r d r = 0 .
I z ( 0 ) = | u z ( 0 ) | = 0 .
Z m = a 2 f a 2 2 f W + 2 f W m ,
Z m = a 2 f a 2 2 f W 2 f W m .
δ m = 4 a 2 f 2 W m ( a 2 2 f W ) 2 4 f 2 W m 2 .
W = a 2 δ m ( 4 f 2 W m 2 δ m 2 + 4 a 2 f 2 W m δ m ) 1 / 2 2 f δ m .
W = A 2 Δ f 8 f 2 ,

Metrics