Abstract

The use of an aperiodic ruling for the measurement of Gaussian laser beam diameters has been analyzed. We show that aperiodic rulings can provide spot-size measurements over a much broader range than available with Ronchi, triangular, or sinusoidal rulings used previously.

© 1989 Optical Society of America

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References

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1987 (1)

1985 (2)

M. A. Karim, Electron. Lett. 21, 427 (1985).
[CrossRef]

R. Csomor, Appl. Opt. 24, 2295 (1985).
[CrossRef] [PubMed]

1982 (1)

L. D. Dickson, G. T. Sincerbox, A. D. Wolfheimer, IBM J. Res. Dev. 26, 228 (1982).
[CrossRef]

1979 (1)

L. D. Dickson, Opt. Eng. 18, 70 (1979).

1971 (4)

1969 (1)

Anderson, R. J.

Arnaud, J. A.

Awwal, A. A. S.

Basit, A.

Csomor, R.

de la Claviero, D.

Dickson, L. D.

L. D. Dickson, G. T. Sincerbox, A. D. Wolfheimer, IBM J. Res. Dev. 26, 228 (1982).
[CrossRef]

L. D. Dickson, Opt. Eng. 18, 70 (1979).

Franke, E. A.

Franke, J. M.

Hubbard, W. M.

Karim, M. A.

Kurtin, S.

Larson, C.

Mandeville, G. D.

McGill, T. C.

Miller, G. D.

Nasiruddin, A. M.

Pearson, J. E.

Sincerbox, G. T.

L. D. Dickson, G. T. Sincerbox, A. D. Wolfheimer, IBM J. Res. Dev. 26, 228 (1982).
[CrossRef]

Smith, C. C.

Suzaki, Y.

Tachibana, A.

Vallese, L. M.

Vedak, D. S.

Wolfheimer, A. D.

L. D. Dickson, G. T. Sincerbox, A. D. Wolfheimer, IBM J. Res. Dev. 26, 228 (1982).
[CrossRef]

Yariv, A.

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Figures (6)

Fig. 1
Fig. 1

Transmission profile of an aperiodic ruling.

Fig. 2
Fig. 2

(a) Scan of output power Pt normalized to Pin/L versus the normalized ruling position x/L for the case L′ = L for the values of normalized r0/L indicated. (b) The ratio Pmin/Pmax versus normalized beam size r0/L.

Fig. 3
Fig. 3

Scan of output power Pt normalized to Pin/L versus normalized ruling position x/L for the case L′ = 5L for different values of normalized beam size r0/L.

Fig. 4
Fig. 4

Ratio Pmin/Pmax versus normalized beam size r0/L for the case L′ = 5L. Curves (a) and (b) correspond to the ratio obtained from periodic and aperiodic parts of the ruling, respectively.

Fig. 5
Fig. 5

Scan of output power Pt normalized to Pin/L versus the normalized ruling position x/L for the case L′ = 0.25L. Beam size r0/L is 0.1 and 0.2 for curves (a) and (b), respectively.

Fig. 6
Fig. 6

Ratio Pmin/Pmax versus normalized beam size r0/L for the case L′ = 0.25L. Curves (a) and (b) correspond to the ratio obtained from periodic and aperiodic parts of the ruling, respectively.

Equations (5)

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I ( x , y ) = I 0 exp [ 2 ( x 2 + y 2 ) / r 0 2 ] ,
P T = T ( x ) I ( x , y ) d x d y ,
P T = I 0 ( π / 2 ) 1 / 2 r 0 T ( x ) exp ( 2 x 2 r 0 2 ) d x .
P T = ( 2 / π ) 1 / 2 P in r 0 T ( x ) exp ( 2 x 2 r 0 2 ) d x ,
P in = I 0 2 π r 0 2 .

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