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1980 (1)

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1967 (2)

1965 (1)

1945 (1)

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Figures (1)

Fig. 1
Fig. 1

Schematic of Czerny-Turner monochromator with off-axis correction.

Equations (15)

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F = r + r - w ( sin θ / 2 + sin θ / 2 ) + w 2 2 [ ( cos 2 θ / 2 r - cos θ / 2 R 1 ) + ( cos 2 θ / 2 r - cos θ / 2 R 1 ) ] + ½ w 3 [ sin θ / 2 r ( cos 2 θ / 2 r - cos θ / 2 R 1 ) + sin θ / 2 r ( cos 2 θ / 2 r - cos θ / 2 R 1 ) ] ,
( F w ) r = = - 1 cos θ / 2 ( sin θ / 2 + sin θ / 2 ) + w cos 2 θ / 2 ( cos 2 θ / 2 r - cos θ / 2 R 1 - cos θ / 2 R 1 ) + 3 w 2 2 cos 3 θ / 2 [ sin θ / 2 r ( cos 2 θ / 2 r - cos θ / 2 R 1 ) ] = 0.
( F w ) r = , w = W / 2 cos α g , θ / 2 = - θ / 2 = 3 W 2 cos 2 α g sin θ / 2 4 R 1 2 cos 2 θ / 2 .
n λ = d ( sin α g + sin β g ) .
θ = d ( cos α g δ α g + cos β g δ β g ) .
δ β g = - 3 W 2 4 R 1 2 sin θ / 2 cos 3 θ / 2 · cos 3 α g cos β g .
Δ 1 = ½ R 2 cos θ 2 δ β g = - 3 W 2 8 R 1 2 R 2 sin θ / 2 cos 3 θ / 2 · cos 3 α g cos θ / 2 cos β g ,
( F w ) r = , r = 1 / 2 R 2 cos θ / 2 = 3 W 2 sin θ / 2 cos 2 β g 4 R 2 2 cos 3 θ / 2 .
Δ 2 = ½ R 2 cos θ / 2 = 3 W 2 sin θ / 2 cos 2 β g 8 R 2 cos 2 θ / 2 .
Δ = Δ 1 + Δ 2 = 3 W 2 R 2 cos 2 α g cos θ / 2 8 cos 3 θ / 2 × [ sin θ / 2 × cos 2 β g cos 3 θ / 2 R 2 2 cos 2 α g cos 3 θ / 2 - sin θ / 2 cos α g R 1 2 cos β g ] .
sin θ / 2 sin θ / 2 = R 2 2 R 1 2 cos 3 θ / 2 cos 3 θ / 2 cos 3 α g cos 3 β g .
sin θ / 2 sin θ / 2 = cos 3 α g cos 3 β g
β g - α g = 28 ° .
n λ = 1.94 d [ sin ( β g - 14 ) ] .
1.0085 sin 2 β g - 0.0582 sin β g - 0.0324 = 0.

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