Abstract

Polarization interference filters are described which can have a pass band ranging from a fraction of an angstrom to several hundred angstroms in width. The pass band can be shifted to any desired region of the spectrum. These tunable filters are based on the fixed filters discussed by Lyot and Evans. The transmission band is formed by the superposition of the polarized channel spectra, produced by x-cut plates of quartz or other birefringent media placed between parallel polarizers. The birefringent plates have thicknesses in the ratio 1:2:4 etc. The tuning is accomplished by changing the retardation of successive elements so that transmission maxima in the various channel spectra coincide at the desired wave-length. The retardation change can be made mechanically, for example, by stretching supplemental plastic sheets in series with the filter elements, or can be made electrically by using Kerr cells or crystals with high electro-optic coefficients, such as ammonium dihydrogen phosphate. The additional retardation never has to exceed a full wave at the wave-length of peak transmission. The measured transmission of an experimental filter is shown. The electrical tuning method is particularly adapted to cathode-ray oscillograph presentation of spectra. The filter also has possible application in color reproduction and colorimetry. With a pass band of a half-angstrom line of sight motion of solar prominences could be determined by the use of the Doppler shift of the prominence radiation.

© 1947 Optical Society of America

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References

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  1. B. Lyot, Comptes rendus 197, 1593 (1933).
  2. Y. Ohman, Nature 141, 291 (1938);J. Evans, Pub. Astro. Soc. Pacific 52, 305 (1940).
    [Crossref]
  3. B. Lyot, Ann. Astrophys. 7, No. 1–2, (1944).
  4. J. Evans, Cientia e Investigacione, to be published.
  5. This material is made by the Resinous Products Company in Philadelphia, Pennsylvania.
  6. This crystal is grown by the Brush Development Company in Cleveland, Ohio.

1944 (1)

B. Lyot, Ann. Astrophys. 7, No. 1–2, (1944).

1938 (1)

Y. Ohman, Nature 141, 291 (1938);J. Evans, Pub. Astro. Soc. Pacific 52, 305 (1940).
[Crossref]

1933 (1)

B. Lyot, Comptes rendus 197, 1593 (1933).

Evans, J.

J. Evans, Cientia e Investigacione, to be published.

Lyot, B.

B. Lyot, Ann. Astrophys. 7, No. 1–2, (1944).

B. Lyot, Comptes rendus 197, 1593 (1933).

Ohman, Y.

Y. Ohman, Nature 141, 291 (1938);J. Evans, Pub. Astro. Soc. Pacific 52, 305 (1940).
[Crossref]

Ann. Astrophys. (1)

B. Lyot, Ann. Astrophys. 7, No. 1–2, (1944).

Comptes rendus (1)

B. Lyot, Comptes rendus 197, 1593 (1933).

Nature (1)

Y. Ohman, Nature 141, 291 (1938);J. Evans, Pub. Astro. Soc. Pacific 52, 305 (1940).
[Crossref]

Other (3)

J. Evans, Cientia e Investigacione, to be published.

This material is made by the Resinous Products Company in Philadelphia, Pennsylvania.

This crystal is grown by the Brush Development Company in Cleveland, Ohio.

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Figures (13)

F. 1
F. 1

Transmission between parallel polarizers of the individual retardation plates of a four-element filter and the transmission of the assembled filter.

F. 2
F. 2

Four-element plastic tunable filter. The circular filter elements are laminated to polarizers. The tuning elements are mounted with screw clamps. Examination of the behavior of the filter is made with the prism.

F. 3
F. 3

Carbon disulfide prism spectrum of the light transmitted by an untuned four-element filter and spectrum of the light transmitted by the same filter tuned to a different wave-length region. The source is a tungsten lamp. A mercury arc spectrum is shown for comparison.

F. 4
F. 4

Calculated transmission of a five-element filter with two waves retardation for the thinnest element.

F. 5
F. 5

Calculated transmission of a five-element filter tuned to transmit a wave-length at which the angular retardation of the thinnest plate is 17π/4.

F. 6
F. 6

Calculated transmission of a five-element filter tuned to transmit a wave-length at which the angular retardation of the thinnest plate is 35π/8.

F. 7
F. 7

Calculated transmission of a five-element filter tuned to transmit a wave-length at which the angular retardation of the thinnest plate is shifted to 9π/2.

F. 8
F. 8

Calculated transmission of a five-element filter tuned to transmit a wave-length at which the angular retardation of the thinnest plate is 11π/2. In the calculation retardation was subtracted from each plate.

F. 9
F. 9

Calculated transmission of a five-element filter tuned to transmit a wave-length at which the angular retardation of the thinnest plate is 11π/2. In this calculation retardation was added to each plate.

F. 10
F. 10

Angular retardation in fractions of waves at λ0 which must be added to the plates of a three-element filter to shift its pass band continuously from 0.8 λ0 to 1.33 λ0.

F. 11
F. 11

Schematic diagram of a four-element tunable filter with an associated electrical network used to set the pass band to four discrete wave-lengths.

F. 12
F. 12

Green transmission of a three-element tunable filter to be used for transmitting red, green, and blue for color television.

F. 13
F. 13

Color of three possible positions for the pass band of a three-element tunable filter which might be used in color television. The Wratten A, B, and C are shown for comparison.

Tables (1)

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Table I

Equations (34)

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T = ( A cos θ cos 2 θ cos 4 θ cos 2 N 1 θ ) 2 ,
cos n θ = ( e n i θ + e n i θ ) / 2 .
cos n θ = ( e n i θ / 2 ) ( 1 + e 2 n i θ ) .
T 1 2 = A e i θ 2 ( 1 + e 2 i θ ) e 2 i θ 2 ( 1 + e 4 i θ ) e 4 i θ 2 ( 1 + e 8 i θ ) × exp [ 2 N 1 i θ ] 2 ( 1 + exp [ 2 N i θ ] ) .
T 1 2 = ( A / 2 N ) e i θ N = 1 N 2 N 1 × [ 1 + e 2 i θ + e 4 i θ + e 6 i θ + e i θ N = 1 N 2 N ] .
N = 1 N 2 N 1 = 2 N 1 ; N = 1 N 2 N = 2 N + 1 2 ,
T 1 2 = A 2 N ( exp [ i θ ( 2 N 1 ) ] ) 1 exp [ 2 i θ ( 2 N ) ] 1 exp [ 2 i θ ] ;
T 1 2 = A 2 N exp [ 2 N i θ ] exp [ 2 N i θ ] 2 i 2 i e i θ e i θ ,
T = [ A sin 2 N θ / 2 N sin θ ] 2 .
T = A ( sin 2 α / α 2 ) ( sin 2 n φ / sin 2 φ ) ,
α = ( π / λ ) d sin θ , φ = ( π / λ ) ( d + b ) sin θ .
θ N x = 2 N 1 θ 1 x = x π + 2 N 1 p π .
θ N n = ( n N + 2 N 1 p ) π ,
θ N x = a θ N x .
a = ( 2 N 1 p + n N ) / ( 2 N 1 p + x ) .
a = [ 2 N 1 p + ( 2 N K ) n K ] / [ 2 N 1 p + x ] ,
a i = a K = a K + 1 = a i .
T = A 2 [ cos a 1 θ cos 2 a 2 θ cos 4 a 3 θ ] 2 .
T = i = 1 p ( sin 2 n i a i θ / 2 n i sin a i θ ) 2 ,
n i = N .
x = 1.
p = 2 , n K = 0 , a 1 = 32 / 33 .
T 1 = [ cos a θ cos 2 a θ cos 4 a θ cos 8 a θ cos 16 θ ] 2 .
T 3 = [ cos a 1 θ cos 2 a 1 θ cos 4 a 1 θ cos 8 a 2 θ cos 16 θ ] 2 .
T 12 = [ cos ( 8 / 11 ) θ cos ( 20 / 11 ) θ cos 4 θ cos 8 θ cos 16 θ ] 2 .
T 12 = [ cos ( 12 / 11 ) θ ( cos 24 / 11 ) θ cos 4 θ cos 8 θ cos 16 θ ] 2 .
T = A cos 2 a θ .
T = A cos 2 ( a θ + δ ) ,
Δ δ K = 2 ( θ K 0 θ K 0 ) ,
Δ δ K = 2 K ( a K 1 ) θ 1 , 0 .
Δ δ K = ( 2 N n K 2 K x / 2 N 1 p + x ) θ 1 , 0 .
x = 2 N 1 p ( λ 0 λ ) / λ ,
Δ δ K = λ ( n K + 2 K 1 p ) 2 K 1 p λ 0 p λ 0 2 π ,
( 2 K p λ 0 / 2 n K + 1 + 2 K p ) < λ < ( 2 K p λ 0 / 2 n K 1 + 2 K p ) .