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References

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  1. Y. Suzaki, A. Tachibarra, Appl. Opt. 16, 1481 (1977).
    [CrossRef] [PubMed]
  2. W. E. Webb, Appl. Opt. 17, 685 (1978).
    [CrossRef] [PubMed]
  3. I. M. Winer, Appl. Opt. 5, 1437 (1966).
    [CrossRef] [PubMed]
  4. Since dimensions z1, z2, and z12 are optical pathlengths, care must be taken to correct the physical distances by the optical thickness nt of beam attenuators, which may be used.
  5. This ambiguity could also be removed by determining the wavefront curvature as well as the Gaussian beam radius at a single station.

1978 (1)

1977 (1)

1966 (1)

Appl. Opt. (3)

Other (2)

Since dimensions z1, z2, and z12 are optical pathlengths, care must be taken to correct the physical distances by the optical thickness nt of beam attenuators, which may be used.

This ambiguity could also be removed by determining the wavefront curvature as well as the Gaussian beam radius at a single station.

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Figures (3)

Fig. 1
Fig. 1

Illustration of a typical laser setup for which beam parameters are to be determined. In the general case discussed in the text, beam radii are measured at planes z=z1 and z = z1 + z12. R1 and R2 are the curvature radii of the laser output coupler M2.

Fig. 2
Fig. 2

Plot of the square of the observed exposure radii vs attenuator thickness employed in the measurement of Gaussian beam radius. A true Gaussian distribution would give a straight line on this plot.

Fig. 3
Fig. 3

Comparison of beam profile measurements obtained with a linear pyroelectric array and with the method described. The inset shows typical raw array data, while the plot shows the results of a computer analysis of several array measurements in the vertical plane beam cross section. Similar results for the horizontal plane gave w ¯ hor = 0.475 cm with a 4% uncertainty, leading to a geometric mean radius w ¯ = [ ( w ¯ vert ) ( w ¯ hor ) ] 1 / 2 = 0.439 cm with a 3% uncertainty.

Tables (1)

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Table I Measured Exposure Radii ri and Attenuator Thicknesses ti

Equations (7)

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w ( z ) / w o = [ 1 + ( ψ z / w o ) 2 ] 1 / 2 ,
ψ = θ ( ) = λ / π w o
w o 2 = ( w 1 2 + w 2 2 2 ) + [ ( w 1 w 2 ) 2 ( λ z 12 π ) 2 ] 1 / 2 2 [ 1 + ( π 2 λ z 12 ) 2 ( w 2 2 w 1 2 ) 2 ] ,
z 1 = w 2 2 w 1 2 2 ψ 2 z 12 z 12 2 .
w o 2 = w 2 2 { 1 ± [ 1 ( 2 λ z / π w 2 ) 2 ] 1 / 2 } .
I ( r ) = I o exp ( 2 r 2 / w 2 α t ) .
w ( z ) = [ 2 ( r i 2 r j 2 ) α ( t j t i ) ] 1 / 2

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