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  1. H. Kogelnick, T. Li, App. Opt. 5, 1550 (1966).
    [CrossRef]
  2. The ideal anti-Gaussian absorption filter was discussed in Optical Holography by R. J. Collier, C. B. Burckhardt, L. H. Lin (Academic, New York, 1971), pp. 166–167.

1966 (1)

H. Kogelnick, T. Li, App. Opt. 5, 1550 (1966).
[CrossRef]

Burckhardt, C. B.

The ideal anti-Gaussian absorption filter was discussed in Optical Holography by R. J. Collier, C. B. Burckhardt, L. H. Lin (Academic, New York, 1971), pp. 166–167.

Collier, R. J.

The ideal anti-Gaussian absorption filter was discussed in Optical Holography by R. J. Collier, C. B. Burckhardt, L. H. Lin (Academic, New York, 1971), pp. 166–167.

Kogelnick, H.

H. Kogelnick, T. Li, App. Opt. 5, 1550 (1966).
[CrossRef]

Li, T.

H. Kogelnick, T. Li, App. Opt. 5, 1550 (1966).
[CrossRef]

Lin, L. H.

The ideal anti-Gaussian absorption filter was discussed in Optical Holography by R. J. Collier, C. B. Burckhardt, L. H. Lin (Academic, New York, 1971), pp. 166–167.

App. Opt. (1)

H. Kogelnick, T. Li, App. Opt. 5, 1550 (1966).
[CrossRef]

Other (1)

The ideal anti-Gaussian absorption filter was discussed in Optical Holography by R. J. Collier, C. B. Burckhardt, L. H. Lin (Academic, New York, 1971), pp. 166–167.

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Figures (3)

Fig. 1
Fig. 1

Simple spherical lens.

Fig. 2
Fig. 2

Absorption lens for producing uniform laser beams.

Fig. 3
Fig. 3

Maximum deviation from uniformity.

Equations (15)

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t = [ F ( F 2 R 2 ) 1 2 ] [ F ( F 2 r 2 ) 1 2 ] = t 0 F [ 1 2 ( r / F ) 2 + 1 8 ( r / F ) 4 + ] for r R ,
T = exp ( α t ) ,
T = exp ( α t 0 ) exp [ α F ( 1 2 ( r / F ) 2 + 1 8 ( r / F ) 4 + ) ] for r R .
T = T 0 exp ( r 2 / β 2 ) for r R ,
β 2 = 2 F / α .
S = S 0 exp ( r 2 / σ 2 ) ,
I = S T = I 0 exp [ ( 1 / σ 2 1 / β 2 ) ] for r R ,
V = π S 0 σ 2 / e at r = σ .
η = utilization factor = 1 / e = 36.7 % .
T = T 0 exp ( r 2 / β 2 ) [ 1 + α F ( r / F ) 4 / 8 + ] .
T 0 = exp ( α t 0 ) = e 1
α t 0 = 1 = α F [ 1 cos ( tan 1 R / F ) ]
( 1 / 8 ) α F ( r / F ) 4 ( 1 / 8 ) α F ( R / F ) 4 = ( 1 / 8 ) [ 1 cos ( tan 1 R / F ) ] 1 ( R / F ) 4 .
( 1 / 8 ) α F ( R / F ) 4 ( 1 / 4 ) ( R / F ) 2 .
T = T e exp ( r 2 / β e 2 ) r R ,

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