Abstract

The properties of nontunable and tunable Lyot wide field elements are examined when the components of the elements deviate from their proper values. Special emphasis is put on determining what variations cause light to be transmitted at the transmission minima. The analysis shows that the nine- and ten-element plastic waveplates described in Paper 2 of this series can be used to make a Lyot filter that is tunable from 3500 Å to 10,000 Å.

© 1975 Optical Society of America

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References

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  1. J. Jefferies, R. Giovanelli, Aust. J. Phys. 1, 254 (1954).
  2. A. Title, Appl. Opt. 14, 00 (Jan.1975).
    [CrossRef]
  3. R. C. Jones, J. Opt. Soc. Am. 31, 488 (1941).
    [CrossRef]

1975

A. Title, Appl. Opt. 14, 00 (Jan.1975).
[CrossRef]

1954

J. Jefferies, R. Giovanelli, Aust. J. Phys. 1, 254 (1954).

1941

Giovanelli, R.

J. Jefferies, R. Giovanelli, Aust. J. Phys. 1, 254 (1954).

Jefferies, J.

J. Jefferies, R. Giovanelli, Aust. J. Phys. 1, 254 (1954).

Jones, R. C.

Title, A.

A. Title, Appl. Opt. 14, 00 (Jan.1975).
[CrossRef]

Appl. Opt.

A. Title, Appl. Opt. 14, 00 (Jan.1975).
[CrossRef]

Aust. J. Phys.

J. Jefferies, R. Giovanelli, Aust. J. Phys. 1, 254 (1954).

J. Opt. Soc. Am.

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Equations (54)

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M = R ( 45 ) G ( α ) R ( 45 ) R ( δ ) G ( γ ) R ( δ ) R ( 45 ) G ( β ) R ( 45 ) ,
R ( θ ) = ( cos θ sin θ sin θ cos θ ) ,
G ( γ ) = ( exp ( + i γ ) 0 0 exp ( i γ ) ) ,
α = 2 π Δ n d α / λ ,
β = 2 π Δ n d β / λ ,
γ = ( π / 2 ) + ,
R ( θ ) G ( γ ) R ( θ ) = cos γ 1 + i sin γ ER ( 2 θ ) ,
E = ( 1 0 0 1 ) .
E 2 = 1 ,
ER ( θ ) = R ( θ ) E .
M = [ cos α 1 + i sin α ER ( 90 ) ] [ cos γ 1 + i sinER ( 2 δ ) ] × [ cos β 1 + i sin β ER ( 90 ) ] .
M 11 = cos γ cos ξ + sin γ sin 2 δ sin ξ + i sin γ cos 2 δ cos η .
M 12 = sin η cos 2 δ sin γ + i [ cos ξ sin 2 δ sin γ + cos γ sin ξ ] .
T = M 11 M 11 # = cos 2 η cos 2 cos 2 2 δ + sin 2 cos 2 ξ + cos 2 sin 2 ξ si n 2 2 δ 1 2 sin 2 sin 2 ξ sin 2 δ
T = M 12 M 12 # = sin 2 η cos 2 cos 2 2 δ + sin 2 sin 2 ξ + cos 2 cos 2 ξ si n 2 2 δ 1 2 sin 2 sin 2 δ sin 2 ξ .
T = T 1 cos 2 η + sin 2 ( 1 sin 2 ξ ) ,
T = T 1 sin 2 η + sin 2 sin 2 ξ ,
T 1 = ( 1 sin 2 ) .
T = T 1 cos 2 η + sin 2 ξ si n 2 2 δ ,
T = T 1 sin 2 η + sin 2 2 δ ( 1 sin 2 ξ ) ,
T 1 = ( 1 cos 2 2 δ ) .
δ < ξ .
sin 2 si n 2 ξ 1 0 4 .
sin 2 1 0 3 , 1.8 ° .
Q = PR ( θ ) R ( l ) G ( ρ ) R ( l ) M ,
P = ( 1 0 0 0 ) ,
ρ = ( π / 4 ) + q ,
Q = ( 1 + i ) / 2 [ cos cos 2 δ sin ( ξ θ ) sin cos ( ξ θ ) + i cos cos 2 δ cos ( η + θ ) ] .
T = Q Q # ,
T = cos 2 ( η θ ) cos 2 cos 2 2 δ + cos 2 sin 2 2 δ sin 2 ( ξ + θ ) + sin 2 cos 2 ( ξ + θ ) 1 2 sin 2 sin 2 δ sin 2 ( ξ + θ ) .
( ξ + θ ) = n ( π / 2 ) , n odd ,
θ = n ( π / 2 ) ξ .
Q = 1 2 ( cos θ sin θ 0 0 ) [ cos q ( 1 + i 0 0 1 i ) + sin q ( 1 i 0 0 1 i ) + 2 i sin l ( sin q + cos q ) ( sin l cos l cos l sin l ) ] ( cos η i sin η + i sin η cos η ) .
2 Q 11 = ( 1 + i ) [ cos q cos ( η θ ) i sin q cos ( η + θ ) ] + 2 i sin l ( sin q + cos q ) [ cos η sin ( θ l ) + i sin η cos ( θ l ) ] .
2 Q 11 = ( 1 + i ) ( a + i e ) + i b ( c + i d ) .
2 Q Q # = 2 ( a 2 + e 2 ) + b 2 ( c 2 + d 2 ) + 2 a b ( c d ) + 2 b e ( c + d ) ,
a = cos q cos ( η θ ) ,
e = sin q cos ( η + θ ) ,
b = 2 sin l ( sin q + cos q ) ,
c = cos η sin ( θ l ) ,
d = sin η cos ( θ l ) .
T = a 2 + e 2 + b ( c d ) [ a + ( b / 2 ) ( c + d ) ] + b e ( c + d ) .
T = a 2 + e 2 = cos 2 q cos 2 ( η θ ) + sin 2 q cos 2 ( η + θ ) .
( η + θ ) = ( η θ + 2 θ ) ,
T = cos 2 ( η θ + sin 2 q [ cos 2 2 ( η θ ) sin 2 2 θ + sin 2 ( η θ ) sin 2 2 θ 1 2 sin 2 ( η θ ) sin 4 θ ] ,
T = T 1 cos 2 ( η θ ) + sin 2 q [ sin 2 2 θ 1 2 sin 2 ( η θ ) sin 4 θ ] ,
T 1 = ( 1 2 sin 2 q sin 2 2 θ ) .
T = a 2 + b ( c d ) [ a + ( b / 2 ) ( c + d ) ] .
T = T 1 cos 2 ( η θ ) sin l sin 2 ( η θ ) sin 2 l [ 2 cos 2 θ + sin 2 θ sin 2 ( η θ ) ] ,
T 1 = ( 1 4 sin 2 l sin 2 θ ) .
2 cos 2 ( η θ ) sin l sin q sin l sin q [ 2 cos 2 2 θ sin × 2 ( η θ ) sin 4 θ ]
T = T 1 cos ( η θ ) 1 2 sin 2 l sin 2 ( η θ ) × sin 2 l [ 2 cos 2 θ + sin 2 θ sin 2 ( η θ ) ] + sin 2 q [ sin 2 2 θ 1 2 sin 4 θ sin 2 ( η θ ) ] sin l sin q [ 2 cos 2 2 θ sin 2 ( η θ ) sin 4 θ ] ,
T = ( 1 2 sin 2 q sin 2 2 θ 4 sin 2 l sin 2 θ 2 sin l sin q sin 4 θ ) .
PR ( θ ) = i PR [ ( θ / 2 ) ] G ( π / 2 ) R ( θ / 2 ) .

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