Abstract

Transmittance (or reflectance) characteristics of generalized gratings are described for Gaussian-laser-beam-diameter measurements. The generalized gratings provide for accurate measurement of both small and large Gaussian beam diameters and are superior to the Ronchi, the triangular, and the sinusoidal rulings. Also the proposed generalized gratings account for all width variations of the opaque, transparent, and transitional regions within a selected ruling.

© 1993 Optical Society of America

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References

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  1. R. J. Anderson, C. Larson, “Reflective relay optics for use in laser deflection systems,” Appl. Opt. 10, 1605–1608 (1971).
    [CrossRef] [PubMed]
  2. L. M. Vallese, “Measurement of the beam parameters of a laser,” Appl. Opt. 10, 959–960 (1971).
    [CrossRef] [PubMed]
  3. L. D. Dickson, “Ronchi ruling method for measuring Gaussian beam diameter,” Opt. Eng. 18, 70–75 (1979).
  4. B. Cannon, T. S. Gardner, D. K. Cohen, “Measurement of 1-μm diam beams,” Appl. Opt. 25, 2981–2983 (1986).
    [CrossRef] [PubMed]
  5. M. A. Karim, “Measurement of Gaussian beam diameter using Ronchi rulings,” Electron. Lett. 21, 427–429 (1985).
    [CrossRef]
  6. Y. Suzaki, A. Tachibana, “Measurement of the μm sized radius of Gaussian laser beam using the scanning knife-edge,” Appl. Opt. 14, 2809–2810 (1975).
    [CrossRef] [PubMed]
  7. J. A. Arnaud, W. M. Hubbard, G. D. Mandeville, D. de la Claviero, E. A. Franke, J. M. Franke, “Technique for fast measurement of Gaussian laser beam parameters,” Appl. Opt. 10, 2775–2776 (1971).
    [CrossRef] [PubMed]
  8. J. E. Pearson, T. C. McGill, S. Kurtin, A. Yariv, “The fraction of Gaussian laser beam by a semi-infinite plane,” J. Opt. Soc. Am. 59, 1440–1445 (1969).
    [CrossRef]
  9. M. A. Karim, A. A. S. Awwal, A. M. Nasiruddin, A. Basit, D. S. Vedak, C. C. Smith, G. D. Miller, “Gaussian laser-beam-diameter measurement using sinusoidal and triangular rulings,” Opt. Lett. 12, 93–95 (1987).
    [CrossRef] [PubMed]
  10. J. S. Uppal, P. K. Gupta, R. G. Harrison, “Aperiodic ruling for the measurement of Gaussian beam diameters,” Opt. Lett. 14, 683–685 (1989).
    [CrossRef] [PubMed]
  11. E. C. Brookman, L. D. Dickson, R. C. Fortenberry, “Generalization of the Ronchi ruling method for measuring Gaussian beam diameter,” Opt. Eng. 22, 643–647 (1983).
  12. J. T. Verdeyen, Laser Electronics (Prentice-Hall, Englewood Cliffs, N.J., 1989), Chap. 3, p. 70.
  13. M. A. Karim, H. K. Liu, “Linear versus logarithmic spatial filtering in the removal of multiplicative noises,” Opt. Lett. 6, 207–209 (1981).
    [CrossRef] [PubMed]
  14. M. A. Karim, “Fabrication of precompensated contact screens for finite-gamma recording media,” J. Appl. Photogr. Eng. 9, 100–104 (1983).
  15. M. A. Karim, “Realization of precompensated monotonic contact screens,” Opt. Lett. 9, 527–529 (1984).
    [CrossRef] [PubMed]

1989

1987

1986

1985

M. A. Karim, “Measurement of Gaussian beam diameter using Ronchi rulings,” Electron. Lett. 21, 427–429 (1985).
[CrossRef]

1984

1983

E. C. Brookman, L. D. Dickson, R. C. Fortenberry, “Generalization of the Ronchi ruling method for measuring Gaussian beam diameter,” Opt. Eng. 22, 643–647 (1983).

M. A. Karim, “Fabrication of precompensated contact screens for finite-gamma recording media,” J. Appl. Photogr. Eng. 9, 100–104 (1983).

1981

1979

L. D. Dickson, “Ronchi ruling method for measuring Gaussian beam diameter,” Opt. Eng. 18, 70–75 (1979).

1975

1971

1969

Anderson, R. J.

Arnaud, J. A.

Awwal, A. A. S.

Basit, A.

Brookman, E. C.

E. C. Brookman, L. D. Dickson, R. C. Fortenberry, “Generalization of the Ronchi ruling method for measuring Gaussian beam diameter,” Opt. Eng. 22, 643–647 (1983).

Cannon, B.

Cohen, D. K.

de la Claviero, D.

Dickson, L. D.

E. C. Brookman, L. D. Dickson, R. C. Fortenberry, “Generalization of the Ronchi ruling method for measuring Gaussian beam diameter,” Opt. Eng. 22, 643–647 (1983).

L. D. Dickson, “Ronchi ruling method for measuring Gaussian beam diameter,” Opt. Eng. 18, 70–75 (1979).

Fortenberry, R. C.

E. C. Brookman, L. D. Dickson, R. C. Fortenberry, “Generalization of the Ronchi ruling method for measuring Gaussian beam diameter,” Opt. Eng. 22, 643–647 (1983).

Franke, E. A.

Franke, J. M.

Gardner, T. S.

Gupta, P. K.

Harrison, R. G.

Hubbard, W. M.

Karim, M. A.

Kurtin, S.

Larson, C.

Liu, H. K.

Mandeville, G. D.

McGill, T. C.

Miller, G. D.

Nasiruddin, A. M.

Pearson, J. E.

Smith, C. C.

Suzaki, Y.

Tachibana, A.

Uppal, J. S.

Vallese, L. M.

Vedak, D. S.

Verdeyen, J. T.

J. T. Verdeyen, Laser Electronics (Prentice-Hall, Englewood Cliffs, N.J., 1989), Chap. 3, p. 70.

Yariv, A.

Appl. Opt.

Electron. Lett.

M. A. Karim, “Measurement of Gaussian beam diameter using Ronchi rulings,” Electron. Lett. 21, 427–429 (1985).
[CrossRef]

J. Appl. Photogr. Eng.

M. A. Karim, “Fabrication of precompensated contact screens for finite-gamma recording media,” J. Appl. Photogr. Eng. 9, 100–104 (1983).

J. Opt. Soc. Am.

Opt. Eng.

E. C. Brookman, L. D. Dickson, R. C. Fortenberry, “Generalization of the Ronchi ruling method for measuring Gaussian beam diameter,” Opt. Eng. 22, 643–647 (1983).

L. D. Dickson, “Ronchi ruling method for measuring Gaussian beam diameter,” Opt. Eng. 18, 70–75 (1979).

Opt. Lett.

Other

J. T. Verdeyen, Laser Electronics (Prentice-Hall, Englewood Cliffs, N.J., 1989), Chap. 3, p. 70.

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Figures (11)

Fig. 1
Fig. 1

Setup for measuring the Gaussian laser beam radius.

Fig. 2
Fig. 2

(a) Laser beam completely blocked by the ruling, (b) laser beam covering several opaque and transparent regions, (c) a large opaque section within a ruling obstructing a large-diameter beam.

Fig. 3
Fig. 3

Transmittance profiles of (a) the generalized RS ruling, (b) the generalized RS ruling reduced to Ronchi and sinusoidal rulings, and (c) the special case of the generalized RS ruling.

Fig. 4
Fig. 4

Transmittance profiles of (a) the generalized RT ruling, (b) the generalized RT ruling reduced to Ronchi and triangular rulings, and (c) the special case of the generalized RT ruling.

Fig. 5
Fig. 5

Power ratio versus r0/L curves for the generalized RS ruling (a) for equal space/bar and variable transitional width regions and (b) for a fixed transitional and variable space/bar width regions.

Fig. 6
Fig. 6

K versus r0/L curves for the generalized RS ruling for variable contrast ratio ΔT.

Fig. 7
Fig. 7

K versus r0/L curves for the special case of the generalized RS ruling (a) for an ideal contrast ratio ΔT = 1 and (b) for a typical grating of ΔT = 0.6.

Fig. 8
Fig. 8

Power ratio versus r0/L curves for the generalized RT ruling (a) for equal space/bar and variable transitional width regions and (b) for fixed transitional and variable space/bar region widths.

Fig. 9
Fig. 9

K versus r0/L curves for the generalized RT ruling for variable contrast ratio ΔT.

Fig. 10
Fig. 10

K versus r0/L curves for the special case of the generalized RT ruling for an ideal contrast ratio ΔT = 1.

Fig. 11
Fig. 11

Discrete step-size approximation of the generalized RT characteristics for one period.

Equations (19)

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k = P min / P max ,
I ( x , y ) = I 0 exp [ 2 ( x 2 + y 2 ) / r 0 2 ] ,
P = T ( x ) I ( x , y ) d x d y ,
T ( x ) = { ( 1 + Δ T ) / 2 | x | < a b 1 Δ T sin [ π ( x a ) / ( 2 b ) ] 2 | x a | < b ( 1 Δ T ) / 2 a + b < | x | < L / 2 ,
T M ( x ) = 2 [ a Δ T + ( 1 Δ T ) L / 4 ] / L + n = 1 2 Δ T [ sin ( 2 π n a / L ) cos ( 2 π n b / L ) ] / { π n [ 1 ( 4 n b / L ) 2 ] } cos ( 2 π n x / L ) ,
T m ( x ) = 2 [ a Δ T + ( 1 Δ T ) L / 4 ] / L n = 1 2 Δ T [ sin ( 2 π n a / L ) cos ( 2 π n b / L ) ] / { π n [ 1 ( 4 n b / L ) 2 ] } cos ( 2 π n x / L ) .
P max = P T { 2 [ a Δ T + ( 1 Δ T ) L / 4 ] / L + n = 1 2 Δ T [ sin ( 2 π n a / L ) cos ( 2 π n b / L ) ] / { π n [ 1 ( 4 n b / L ) 2 ] } exp [ 0.5 ( n π r 0 / L ) 2 ] } ,
P min = P T { 2 [ a Δ T + ( 1 Δ T ) L / 4 ] / L n = 1 2 Δ T [ sin ( 2 π n a / L ) cos ( 2 π n b / L ) ] / { π n [ 1 ( 4 n b / L ) 2 ] } exp [ 0.5 ( n π r 0 / L ) 2 ] } ,
k = [ a Δ T + ( 1 Δ T ) L / 4 ] / L n = 1 Δ T [ sin ( 2 π n a / L ) cos ( 2 π n b / L ) ] / { π n [ 1 ( 4 n b / L ) 2 ] } exp [ 0.5 ( n π r 0 / L ) 2 ] [ a Δ T + ( 1 Δ T ) L / 4 ] / L + n = 1 Δ T [ sin ( 2 π n a / L ) cos ( 2 π n b / L ) ] / { π n [ 1 ( 4 n b / L ) 2 ] } exp [ 0.5 ( n π r 0 / L ) 2 ] .
T ( x ) = { ( 1 + Δ T ) / 2 | x | < a b { 1 Δ T sin [ π ( x a ) / ( 2 b ) ] } / 2 a b < | x | < a + b = L / 2 '
k = [ 2 b + ( 1 + Δ T ) ( a b ) ] / L n = 1 Δ T { sin [ 2 π n ( a b ) / L ] } / { π n [ 1 ( 4 n b / L ) 2 ] } exp [ 0.5 ( n π r 0 / L ) 2 ] [ 2 b + ( 1 + Δ T ) ( a b ) ] / L + n = 1 Δ T { sin [ 2 π n ( a b ) / L ] } / { π n [ 1 ( 4 n b / L ) 2 ] } exp [ 0.5 ( n π r 0 / L ) 2 ] .
T ( x ) = { ( 1 + Δ T ) / 2 | x | < a b Δ T x / ( 2 b ) + 1 / 2 + Δ T a / ( 2 b ) | x a | < b ( 1 Δ T ) / 2 a + b < | x | < L / 2
T M ( x ) = [ 2 a Δ T + ( 1 Δ T ) L / 2 ] / L + n = 1 Δ T L [ sin ( 2 π n a / L ) sin ( 2 π n b / L ) / b ] / ( π n ) 2 cos ( 2 π n x / L ) ,
T m ( x ) = [ 2 a Δ T + ( 1 Δ T ) L / 2 ] / L n = 1 Δ T L [ sin ( 2 π n a / L ) sin ( 2 π n b / L ) / b ] / ( π n ) 2 cos ( 2 π n x / L ) ,
P max = P T { [ 2 a Δ T + ( 1 Δ T ) L / 2 ] / L + n = 1 Δ T L [ sin ( 2 π n a / L ) sin ( 2 π n b / L ) / b ] / ( π n ) 2 exp [ 0.5 ( n π r 0 / L ) 2 ] } ,
P min = P T { [ 2 a Δ T + ( 1 Δ T ) L / 2 ] / L n = 1 Δ T L [ sin ( 2 π n a / L ) sin ( 2 π n b / L ) / b ] / ( π n ) 2 exp [ 0.5 ( n π r 0 / L ) 2 ] } ,
k = [ 2 a Δ T + ( 1 Δ T ) L / 2 ] / L n = 1 Δ T L [ sin ( 2 π n a / L ) sin ( 2 π n b / L ) / b ] / ( π n ) 2 exp [ 0.5 ( n π r 0 / L ) 2 ] [ 2 a Δ T + ( 1 Δ T ) L / 2 ] / L + n = 1 Δ T L [ sin ( 2 π n a / L ) sin ( 2 π n b / L ) / b ] / ( π n ) 2 exp [ 0.5 ( n π r 0 / L ) 2 ] .
T ( x ) = { ( 1 + Δ T ) / 2 | x | < a b Δ T x / ( 2 b ) + 1 / 2 + Δ T a / ( 2 b ) a b < | x | < a + b = L / 2 .
k = 0.5 + ( a b ) Δ T / L n = 1 Δ T L [ sin ( 2 π n a / L ) sin ( 2 π n b / L ) / b ] / ( π n ) 2 exp [ 0.5 ( n π r 0 / L ) 2 ] 0.5 + ( a b ) Δ T / L + n = 1 Δ T L [ sin ( 2 π n a / L ) sin ( 2 π n b / L ) / b ] / ( π n ) 2 exp [ 0.5 ( n π r 0 / L ) 2 ] .

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