Abstract

A physical account of the Solc birefringent filter is given. The theory of both the Solc and Lyot filters is then developed, assuming imperfections in the polarizers and ignoring birefringence. An anticipated advantage of the Solc filter under these conditions is not confirmed. Formulas for the transmittances of the two filters are derived in a form suitable for tabulation by digital computer.

© 1967 Optical Society of America

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References

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  1. I. Solc, J. Opt. Soc. Am. 55, 21 (1965).
    [CrossRef]
  2. I. Solc, Jemna Mechanika a Optika 5, 137 (1957).
  3. Hsien-Yü Hsü, M. Richartz, and Yüng-K’ang. Liang, J. Opt. Soc. Am. 37, 99 (1947).
    [CrossRef]
  4. J. W. Evans, J. Opt. Soc. Am. 48, 142 (1958).
    [CrossRef]
  5. R. Clark Jones, J. Opt. Soc. Am. 31, 488, 493, 500 (1941).
    [CrossRef]
  6. The use of primes is that of optics, not matrix algebra; the transpose is not used implicitly.
  7. I am indebted to Dr. J. W. Evans for Eq. (2b), which is simpler than the form I originally used.
  8. John W. Evans, J. Opt. Soc. Am. 39, 229 (1949).
    [CrossRef]

1965 (1)

1958 (1)

1957 (1)

I. Solc, Jemna Mechanika a Optika 5, 137 (1957).

1949 (1)

1947 (1)

1941 (1)

J. Opt. Soc. Am. (5)

Jemna Mechanika a Optika (1)

I. Solc, Jemna Mechanika a Optika 5, 137 (1957).

Other (2)

The use of primes is that of optics, not matrix algebra; the transpose is not used implicitly.

I am indebted to Dr. J. W. Evans for Eq. (2b), which is simpler than the form I originally used.

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Equations (36)

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= ( E x E y )
P x = ( 10 00 ) .
E x = p 1 E x             p 1 < 1
E y = p 2 E y             p 2 small .
P 1 = ( p 1 0 0 p 2 ) .
P 2 = ( p 2 0 0 p 1 ) .
G = ( e i γ 0 0 e - i γ ) = cos γ I + i sin γ J ,
2 γ = phase difference due to the plate , I = the idempotent matrix ,
J = ( 1 0 0 - 1 ) ( called B by Hsien-Y ü Hs ü ) ;
S ( α ) = ( cos α - sin α sin α cos α ) ;
A n = q A + r I ,
q = ( d 2 n - d 1 n ) / ( d 2 - d 1 )
r = ( d 1 d 2 n - d 2 d 1 n ) / ( d 2 - d 1 ) .
ω j = 1 2 α + ( j - 1 ) α             ( j = 1 , 2 n )
= P 1 S ( α / 2 ) S ( π / 2 ) [ S ( - α ) G ] n S ( - α / 2 ) P 1 ,
= P 2 S ( α / 2 ) [ S ( - α ) G ] n S ( - α / 2 ) P 1 .
t s i = t s p 1 4 - p 1 3 p 2 ( sin 2 n χ ) / ( sin χ ) cos χ tan α ,
t s = 1 2 [ ( sin n χ / sin χ ) cos χ tan α ] 2 .
= P 1 S ( - π / 4 ) G 2 N - 1 S ( π / 4 ) P 1 S ( - π / 4 ) P 1 S ( - π / 4 ) G 2 S ( π / 4 ) P 1 S ( - π / 4 ) G S ( π / 4 ) P 1 .
= S ( - π / 4 ) A s = 1 N [ ( cos 2 s - 1 γ I + i sin 2 s - 1 γ J ) A ] S ( π / 4 ) .
A N + 1 = 1 2 p 1 N + 1 ( 1 1 1 1 )
i A r J A N - r + 1
- A r J A s J A N - s - r + 1 ,
1 2 p 1 N p 2 ( 1 1 1 1 ) .
E x = p 1 N ( p 1 r = 1 N cos 2 r - 1 γ - p 2 r = 1 N - 1 sin 2 r γ sin 2 r - 1 γ × s = 1 r = 1 ( s r ) N cos 2 s - 1 γ ) .
t L i = t L p 1 2 N + 1 [ p 1 - 2 p 2 r = 1 N - 1 ( 1 cos 2 r γ - 1 ) ] ,
t L = 1 2 ( sin 2 N γ / 2 N sin γ ) 2 .
t = t g ( p 1 - 2 p 2 l )
t s i = p 1 3 ( p 1 A n - 2 p 2 B n ) / 2 ,
t s = A n / 2 ,
t L i = p 1 2 N + 1 C N ( p 1 - 2 p 2 D N ) / 2 ,
t L = C N / 2 ,
A n = [ ( sin n χ / sin χ ) cos χ tan χ ] 2 ,
B n = ( sin 2 n χ / sin χ ) cos χ tan χ
C N = ( sin 2 N χ / 2 N sin γ ) ,
D N = r = 1 N - 1 ( 1 cos 2 r γ - 1 ) .