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References

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  1. D. K. Cohen, B. Little, F. S. Luecke, “Techniques for Measuring 1-μm diam Gaussian Beams,” Appl. Opt. 23, 637 (1984).
    [CrossRef] [PubMed]
  2. E C. Broockman, L. D. Dickson, R. S. Fortenberry, “Generalization of the Ronchi Ruling Method for Measuring Gaussian Beam Diameter,” Opt. Eng. 22, 643 (1983).
    [CrossRef]
  3. Gy. Ákos, R. Csomor, “Fókuszált lézernyaláb átméröjének közvetett meghatározása” (“An Indirect Method for Measuring the Diameter of a Focused Laser Beam,”)MIKI Közleményei 23, 49 (1984).

1984 (2)

D. K. Cohen, B. Little, F. S. Luecke, “Techniques for Measuring 1-μm diam Gaussian Beams,” Appl. Opt. 23, 637 (1984).
[CrossRef] [PubMed]

Gy. Ákos, R. Csomor, “Fókuszált lézernyaláb átméröjének közvetett meghatározása” (“An Indirect Method for Measuring the Diameter of a Focused Laser Beam,”)MIKI Közleményei 23, 49 (1984).

1983 (1)

E C. Broockman, L. D. Dickson, R. S. Fortenberry, “Generalization of the Ronchi Ruling Method for Measuring Gaussian Beam Diameter,” Opt. Eng. 22, 643 (1983).
[CrossRef]

Ákos, Gy.

Gy. Ákos, R. Csomor, “Fókuszált lézernyaláb átméröjének közvetett meghatározása” (“An Indirect Method for Measuring the Diameter of a Focused Laser Beam,”)MIKI Közleményei 23, 49 (1984).

Broockman, E C.

E C. Broockman, L. D. Dickson, R. S. Fortenberry, “Generalization of the Ronchi Ruling Method for Measuring Gaussian Beam Diameter,” Opt. Eng. 22, 643 (1983).
[CrossRef]

Cohen, D. K.

Csomor, R.

Gy. Ákos, R. Csomor, “Fókuszált lézernyaláb átméröjének közvetett meghatározása” (“An Indirect Method for Measuring the Diameter of a Focused Laser Beam,”)MIKI Közleményei 23, 49 (1984).

Dickson, L. D.

E C. Broockman, L. D. Dickson, R. S. Fortenberry, “Generalization of the Ronchi Ruling Method for Measuring Gaussian Beam Diameter,” Opt. Eng. 22, 643 (1983).
[CrossRef]

Fortenberry, R. S.

E C. Broockman, L. D. Dickson, R. S. Fortenberry, “Generalization of the Ronchi Ruling Method for Measuring Gaussian Beam Diameter,” Opt. Eng. 22, 643 (1983).
[CrossRef]

Little, B.

Luecke, F. S.

Appl. Opt. (1)

MIKI Közleményei (1)

Gy. Ákos, R. Csomor, “Fókuszált lézernyaláb átméröjének közvetett meghatározása” (“An Indirect Method for Measuring the Diameter of a Focused Laser Beam,”)MIKI Közleményei 23, 49 (1984).

Opt. Eng. (1)

E C. Broockman, L. D. Dickson, R. S. Fortenberry, “Generalization of the Ronchi Ruling Method for Measuring Gaussian Beam Diameter,” Opt. Eng. 22, 643 (1983).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Relative position of a Gaussian beam and a nonideal ruling. R(x) = reflectivity of the ruling; I(x) = intensity distribution of the beam.

Fig. 2
Fig. 2

Nonideal ruling as the superposition of two rulings having maximum contrast.

Fig. 3
Fig. 3

d/W ratio as a function of modulation η0 and intensity ratio K0 in case of a symmetrical ruling having ideal reflectivity.

Equations (28)

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I ( x ) = I T 8 d π exp ( 8 x 2 d 2 )
R ( x ) = n = { R E · rect [ x + 2 n W W ( 1 ) ] + R S · rect [ x + ( 2 n + 1 ) W W ( 1 + ) ] } ,
I D ( ξ ) = R ( x ) I ( ξ x ) d x .
I D ( ξ ) = F 1 { F { R ( x ) } · F { I ( x ) } } ,
R ( f ) = F { R ( x ) } = R ( x ) exp ( 2 π i ƒ x ) d x = R E n = F { rect [ x + 2 n W W ( 1 ) ] } + R S n = F { rect [ x + ( 2 n + 1 ) W W ( 1 + ) ] } .
F { rect [ x + x 0 a ] } = exp ( 2 π i ƒ x 0 ) F { rect [ x a ] } = exp ( 2 π i ƒ x 0 ) sin π a ƒ π ƒ ,
R ( f ) = n = e xp ( 2 π i · n · 2 f W ) × [ R E · sin π f W ( 1 ) π f + R S · sin π f W ( 1 + ) π f · exp ( 2 π i f W ) ] .
n = exp ( 2 π i n x ) = l = δ ( l x ) ,
R ( f ) = l = δ ( f l 2 W ) 2 W [ R E · sin π f W ( 1 ) π f + R S · sin π f W ( 1 + ) π f · exp ( 2 π i f W ) ] = R E ( f ) + R S ( f ) .
F { I ( x ) } = I ( f ) = I T exp ( π 2 f 2 d 2 8 ) .
I D ( ξ ) = I D E ( ξ ) + I D S ( ξ ) ,
I D E ( ξ ) = I T R E ( 1 ) 2 l = sin l π 2 ( 1 ) l π 2 ( 1 ) exp [ π 2 l 2 32 ( d W ) 2 ] exp ( i l π ξ W ) = I T R E ( 1 ) 2 { 1 + k = 1 sin k π 2 ( 1 ) k π 2 ( 1 ) exp [ π 2 k 2 32 ( d W ) 2 ] [ exp ( i k π ξ W ) + exp ( i k π ξ W ) ] } = I T 2 { R E ( 1 ) + 4 R E π k = 1 sin k π 2 ( 1 ) k exp [ π 2 k 2 32 ( d W ) 2 ] cos k π ξ W } .
I D S ( ξ ) = I T 2 { R S ( 1 + ) + 4 R S π k = 1 [ ( 1 ) k sin k π 2 ( 1 + ) k × exp [ π 2 k 2 32 ( d W ) 2 ] cos k π ξ W ] }
sin k π 2 ( 1 ) = sin k π 2 ( 1 + ) = sin k π 2 cos k π 2 ,
sin k π 2 k = { 0 if k = 2 l ( k 0 ) , ( 1 ) l 2 l + 1 if k = 2 l + 1 ( l 0 ) ,
I D ( ξ ) = I T 2 { R E ( 1 ) + R S ( 1 + ) + 4 π ( R E R S ) k = 0 [ ( 1 ) k cos [ ( 2 k + 1 ) π 2 ] 2 k + 1 × exp [ π 2 d 2 ( 2 k + 1 ) 2 32 W 2 ] cos [ ( 2 k + 1 ) π ξ W ] } .
η = I m a x I min I m a x + I m in = I D ( 0 ) I D ( W ) I D ( 0 ) + I D ( W ) .
I m ax = I T 2 [ R E ( 1 ) + R S ( 1 + ) + η 0 ( ; d W ) · ( R E R S ) ] ,
I min = I T 2 [ R E ( 1 ) + R S ( 1 + ) η 0 ( ; d W ) · ( R E R S ) ] ,
η 0 ( ; d W ) = 4 π k = 0 ( 1 ) k 2 k + 1 cos [ ( 2 k + 1 ) π 2 ] exp [ π 2 ( 2 k + 1 ) 2 32 ( d W ) 2 ] .
η ( ; d / W ) = η gr η 0 ( ; d / W ) 1 · η gr ,
η gr = R E R S R E + R S .
η sym = η gr · η 0 ( d / W ) ,
K L = K 0 + K gr 1 + K gr K 0 ,
K 0 = K L K gr 1 K L K gr ,
I max = R S · I min 0 + R E · I max 0 ,
I min = R S · I max 0 + R E · I min 0 ,
d W = 2 . 2 K 0 + 1

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