Abstract

A design for a birefringent filter is proposed in which alternate polarizers are partial polarizers. Calculated performance characteristics of alternate partial polarizer filters (APP) are compared with those of Lyot and contrast element Lyot filters. These calculations show that the APP design has significant advantages in both transmission and profile shape. Using pulse techniques, partial polarizer systems are shown to be a natural evolution from the standard Lyot and contrast element Lyot systems. The APP filter using achromatic waveplates discussed in earlier papers of this series has been used to construct a universal alternate partial polarizer filter. This filter has a measured full width at half-maximum (FWHM) of 0.09 Å at 5500 Å and a transmission in polarized light of 38%. It is tunable from 4500 Å to 8500 Å. The measured characteristics of the filter agree well with theoretical predictions.

© 1976 Optical Society of America

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References

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  1. A. M. Title, Solar Phys. 33, 521 (1973).
  2. A. M. Title, Appl. Opt. 14, 229 (1975).
  3. A. M. Title, Appl. Opt. 14, 445 (1975).
  4. S. E. Harris, E. O. Ammann, I. C. Chang, J. Opt. Soc. Am. 54, 1267 (1964).
  5. E. O. Ammann, I. C. Chang, J. Opt. Soc. Am. 55, 835 (1965).
  6. E. O. Ammann, J. Opt. Soc. Am. 56, 943 (1966).
  7. J. W. Evans, J. Opt. Soc. Am. 39, 229 (1949).
  8. J. W. Evans, J. Opt. Soc. Am. 48, 142 (1958).
  9. L. Mertz, J. Opt. Soc. Am. Adv. 49 (Dec.1959).
  10. L. Mertz, J. Opt. Soc. Am. Adv. 50 (June1960).
  11. R. G. Giovanelli, J. T. Jefferies, Astron. J. Phys. 7, 254 (1954).
  12. J. M. Beckers, R. B. Dunn, AFCRL-65-605 (Aug.1965).
  13. A. M. Title, Solar Phys. 38, 523 (1974).
  14. B. Lyot, Ann. Astron. 7, 31 (1944).
  15. S. A. Schoolman, Solar Phys. 30, 255 (1973).

1975 (2)

1974 (1)

A. M. Title, Solar Phys. 38, 523 (1974).

1973 (2)

A. M. Title, Solar Phys. 33, 521 (1973).

S. A. Schoolman, Solar Phys. 30, 255 (1973).

1966 (1)

1965 (1)

1964 (1)

1960 (1)

L. Mertz, J. Opt. Soc. Am. Adv. 50 (June1960).

1959 (1)

L. Mertz, J. Opt. Soc. Am. Adv. 49 (Dec.1959).

1958 (1)

1954 (1)

R. G. Giovanelli, J. T. Jefferies, Astron. J. Phys. 7, 254 (1954).

1949 (1)

1944 (1)

B. Lyot, Ann. Astron. 7, 31 (1944).

Ammann, E. O.

Beckers, J. M.

J. M. Beckers, R. B. Dunn, AFCRL-65-605 (Aug.1965).

Chang, I. C.

Dunn, R. B.

J. M. Beckers, R. B. Dunn, AFCRL-65-605 (Aug.1965).

Evans, J. W.

Giovanelli, R. G.

R. G. Giovanelli, J. T. Jefferies, Astron. J. Phys. 7, 254 (1954).

Harris, S. E.

Jefferies, J. T.

R. G. Giovanelli, J. T. Jefferies, Astron. J. Phys. 7, 254 (1954).

Lyot, B.

B. Lyot, Ann. Astron. 7, 31 (1944).

Mertz, L.

L. Mertz, J. Opt. Soc. Am. Adv. 50 (June1960).

L. Mertz, J. Opt. Soc. Am. Adv. 49 (Dec.1959).

Schoolman, S. A.

S. A. Schoolman, Solar Phys. 30, 255 (1973).

Title, A. M.

A. M. Title, Appl. Opt. 14, 229 (1975).

A. M. Title, Appl. Opt. 14, 445 (1975).

A. M. Title, Solar Phys. 38, 523 (1974).

A. M. Title, Solar Phys. 33, 521 (1973).

Ann. Astron. (1)

B. Lyot, Ann. Astron. 7, 31 (1944).

Appl. Opt. (2)

Astron. J. Phys. (1)

R. G. Giovanelli, J. T. Jefferies, Astron. J. Phys. 7, 254 (1954).

J. Opt. Soc. Am. (5)

J. Opt. Soc. Am. Adv. (2)

L. Mertz, J. Opt. Soc. Am. Adv. 49 (Dec.1959).

L. Mertz, J. Opt. Soc. Am. Adv. 50 (June1960).

Solar Phys. (3)

S. A. Schoolman, Solar Phys. 30, 255 (1973).

A. M. Title, Solar Phys. 33, 521 (1973).

A. M. Title, Solar Phys. 38, 523 (1974).

Other (1)

J. M. Beckers, R. B. Dunn, AFCRL-65-605 (Aug.1965).

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Figures (22)

Fig. 1
Fig. 1

Pulse diagram of two Lyot modules with length ratios of 1:1/2.

Fig. 2
Fig. 2

Pulse diagram for a contrast element Lyot module. Note that the second and third Lyot modules have equal lengths, and that pulse overlap occurs at the output of L3.

Fig. 3
Fig. 3

Transmission vs wavelength (solid) and contribution function (dotted) from a transmission peak for a pure Lyot filter. The graph is plotted to halt to the FSR.

Fig. 4
Fig. 4

Transmission (solid) and contribution function (dotted) vs wavelength for a contrast element Lyot.

Fig. 5
Fig. 5

Optical schematic of an alternate partial polarizer module.

Fig. 6
Fig. 6

Pulse diagram of an APP module illustrating the perfect polarizer and neutral density concept.

Fig. 7
Fig. 7

Pulse diagram for an APP module followed by two Lyot modules with length ratios of 1:1/2:1/4:1/8.

Fig. 8
Fig. 8

Transmission (solid) and contribution function (dotted) vs wavelength for APP-Lyot system.

Fig. 9
Fig. 9

Pulse diagram for a pair of APP modules with Lyot filter length ratios.

Fig. 10
Fig. 10

Pulse diagram for a pair of APP modules with length ratios 1:1/2:1/3:1/6.

Fig. 11
Fig. 11

Transmission (solid) and contribution function (dotted) for a four module APP filter. Half of the FSR occurs at 6 wavelength units.

Fig. 12
Fig. 12

Optical schematic of double partial polarizer module.

Fig. 13
Fig. 13

Transmission (solid) and contribution function (dotted) for a DPP plus two APP module filters. The half FSR occurs at 6 wavelength units.

Fig. 14
Fig. 14

Segment of a pulse diagram illustrating end and taper effects introduced by pulse interleaving.

Fig. 15
Fig. 15

Transmission (solid) and contribution function (dotted) vs wavelength for a seven element Lyot filter in which the last element is three times normal length. The length ratios are 1:1/2:1/4:1/8:1/16:1/32:3/64.

Fig. 16
Fig. 16

Transmission (solid) and contribution function (dotted) vs wavelength for three module APP plus two Lyot modules, the last of which is three times normal length. The length ratios are 1:1/2:1/3:1/6:1/9:1/18:1/32:3/64.

Fig. 17
Fig. 17

Measured filter transmission in the neighborhood of λ5324. The FWHM is 0.11 Å. The spectrograph instrumental profile is 0.02 Å wide, so that the measurement agrees with the theoretical FWHM.

Fig. 18
Fig. 18

Photograph of LAPPU filter before installation of outer corner.

Fig. 19
Fig. 19

Photograph of complete LAPPU filter.

Fig. 20
Fig. 20

Explode view of an APP module that is both wide field and tunable.

Fig. 21
Fig. 21

Transmission vs finesse for APP, Lyot, and contrast element Lyot filters.

Fig. 22
Fig. 22

Number of crystals vs finesse for APP, Lyot, and contrast element Lyot filters.

Equations (31)

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A f = A i cos θ A s = A i sin θ ,
A o f = A i cos θ cos θ , A o s = A i sin θ sin θ ,
t = μ d / c ,
A ( ν ) = cos ( 2 π μ d ν ) .
P ( t ) = R L ( t ) ¯ ( t t N ) ,
R L ( t ) = 1 t L 2 = 0 t > L 2
L = k = 1 N d 1 2 k - 1 2 d 1 ,
t N = ( μ d 1 ) / ( c 2 N - 1 ) ,
A ( ν ) = sinc ( L ν ) ¯ ( ν ν N ) .
P ( t ) = [ R L 1 ( t ) + R L 2 ( t ) ] ¯ ( t t N ) ,
L 2 = 3 5 L 1
L 1 = k = 1 N d 1 2 k - 1 + d 1 2 = 5 2 = d 1 .
A ( ν ) = [ sinc ( L 1 ν ) + sinc L 2 ( ν ) ] ¯ ( ν ν N ) .
c ( λ ) = λ FSR / 2 T ( λ ) d λ / 0 FSR / 2 T ( λ ) d λ .
PP = ( ρ x 0 0 ρ y ) ,
T x = ρ x 2 , T y = ρ y 2 ,
PP = ( ρ x - ρ y ) [ ( 00 10 ) + ρ y / ( ρ x - ρ y ) ( 01 10 ) ] .
A ( ν ) = [ PM ( α 1 , 45 ) PPM ( α 2 , - 45 ) P ] 11 ,
A ( ν ) = ( ρ x - ρ y ) [ PM ( α 1 , 45 ) PM ( α 2 , - 45 ) P + PM ( α 1 , 45 ) M ( α 2 , - 45 ) P ] 11 ,
= ρ y / ( ρ x - ρ y ) , M ( α , ± 45 ) = cos α I + i sin α ER ( ± 90 ) , α i = 2 π μ d i ν , E = ( 0 - 1 10 ) ,
A ( ν ) = ( ρ x - ρ y ) [ cos α 1 cos α 2 + cos ( α 1 - α 2 ) ] ,
A ( ν ) = ( ρ x - ρ y ) [ cos ( α 1 + α 2 ) + ( 1 + 2 ) cos ( α 1 - α 2 ) ] .
A ( ν ) = ( 2 3 ) N / 2 k - 1 N / 2 [ cos ( π μ d 1 ν 3 k - 2 ) + 2 cos ( π μ d 1 ν 3 k - 1 ) ] 2 ,
d oddk = ( d 1 2 ) / 3 k - 1 2
d evenk = ( 3 2 d 1 ) / 3 k / 2 ,
A ( ν ) = [ ( ρ x - ρ y ) ( ρ x - ρ y ) [ P M ( α 1 , 45 ) PPM ( ρ 2 , - 45 ) PPM ( α 3 , 45 ) P ] 11 ,
α i = 2 π μ d i ν
A ( ν ) = c [ PM ( α 1 , 45 ) PM ( α 2 , - 45 ) P M ( α 3 , 45 ) P + PM ( α 1 , 45 ) M ( α 2 , - 45 ) P M ( α 3 , 45 ) P + P M ( α 1 , 45 ) PM ( α 2 , - 45 ) M ( α 3 , 45 ) P + PM ( α 1 , 45 ) M ( α 2 , - 45 ) M ) α 3 , 45 ) P ] 11 ,
c = ( ρ x - ρ y ) ( ρ x - ρ y ) , = ρ y / ρ y - ρ x , = ρ y / ρ y - ρ x .
A ( ν ) = c [ cos α 1 cos α 2 cos α 3 + cos ( α 1 - α 2 ) cos α 3 + cos α 1 cos ( α 2 - α 3 ) + cos ( α 1 - α 2 + α 3 ) ] .
A ( ν ) = c 4 [ cos ( α 1 + α 2 + α 3 ) + ( 1 + 2 ) cos ( α 1 + α 2 - α 3 ) + ( 1 + 2 ) cos ( α 1 - α 2 - α 3 ) + [ 1 + 2 ( + ) + 4 ] cos ( α 1 - α 2 + α 3 ) ] .

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