Abstract

In the standard Turner Frustrated Total Reflection filter the pass bands occur in pairs which are oppositely polarized. The maximum theoretical transmission in any band is thus 50 percent. In this paper it is shown that if the high index layer of the filter is made of a birefringent material the oppositely polarized pass bands can be made to coincide so that the maximum theoretical transmission becomes 100 percent and the bands occur singly. Measurements are shown on a filter made with such a birefringent layer.

© 1950 Optical Society of America

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References

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  1. Walter Geffcken, German Patent No. 716153 (filed December8, 1939).
  2. H. D. Polster, J. Opt. Soc. Am. 39, 1054A (1949).
  3. C. DuFour, Le Vide 16, 3 (1948).
  4. B. Lyot, Comptes Rendus 197, 1593 (1933).
  5. J. Evans, Pubs. Astron. Soc. Pacific 52, 305 (1940).
    [CrossRef]
  6. B. Billings, J. Opt. Soc. Am. 37, 738 (1947).
    [CrossRef] [PubMed]
  7. P. Leurgans and A. F. Turner, J. Opt. Soc. Am. 37, 983 (1947).
  8. B. Billings and M. A. Pittman, J. Opt. Soc. Am. 39, 978 (1949).
    [CrossRef]
  9. E. E. Barr and C. D. West, U. S. Patent No. 2,447,790 (filed April11, 1945).
  10. E. R. Blout, U. S. Patent No. 2,447,792 (filed March24, 1945).
  11. M. Hyman, U. S. Patent No. 2,447,805 (filed April11, 1945).
  12. R. B. Woodward, U. S. Patent No. 2,447,831 (filed March3, 1945).
  13. O. Wiener, Sach. Akad. Leipzig Math. Phy. Kl. Berichte 53, 54, (1901–1902).

1949 (2)

H. D. Polster, J. Opt. Soc. Am. 39, 1054A (1949).

B. Billings and M. A. Pittman, J. Opt. Soc. Am. 39, 978 (1949).
[CrossRef]

1948 (1)

C. DuFour, Le Vide 16, 3 (1948).

1947 (2)

P. Leurgans and A. F. Turner, J. Opt. Soc. Am. 37, 983 (1947).

B. Billings, J. Opt. Soc. Am. 37, 738 (1947).
[CrossRef] [PubMed]

1940 (1)

J. Evans, Pubs. Astron. Soc. Pacific 52, 305 (1940).
[CrossRef]

1933 (1)

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

Barr, E. E.

E. E. Barr and C. D. West, U. S. Patent No. 2,447,790 (filed April11, 1945).

Billings, B.

Blout, E. R.

E. R. Blout, U. S. Patent No. 2,447,792 (filed March24, 1945).

DuFour, C.

C. DuFour, Le Vide 16, 3 (1948).

Evans, J.

J. Evans, Pubs. Astron. Soc. Pacific 52, 305 (1940).
[CrossRef]

Geffcken, Walter

Walter Geffcken, German Patent No. 716153 (filed December8, 1939).

Hyman, M.

M. Hyman, U. S. Patent No. 2,447,805 (filed April11, 1945).

Leurgans, P.

P. Leurgans and A. F. Turner, J. Opt. Soc. Am. 37, 983 (1947).

Lyot, B.

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

Pittman, M. A.

Polster, H. D.

H. D. Polster, J. Opt. Soc. Am. 39, 1054A (1949).

Turner, A. F.

P. Leurgans and A. F. Turner, J. Opt. Soc. Am. 37, 983 (1947).

West, C. D.

E. E. Barr and C. D. West, U. S. Patent No. 2,447,790 (filed April11, 1945).

Wiener, O.

O. Wiener, Sach. Akad. Leipzig Math. Phy. Kl. Berichte 53, 54, (1901–1902).

Woodward, R. B.

R. B. Woodward, U. S. Patent No. 2,447,831 (filed March3, 1945).

Comptes Rendus (1)

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

J. Opt. Soc. Am. (4)

H. D. Polster, J. Opt. Soc. Am. 39, 1054A (1949).

P. Leurgans and A. F. Turner, J. Opt. Soc. Am. 37, 983 (1947).

B. Billings and M. A. Pittman, J. Opt. Soc. Am. 39, 978 (1949).
[CrossRef]

B. Billings, J. Opt. Soc. Am. 37, 738 (1947).
[CrossRef] [PubMed]

Le Vide (1)

C. DuFour, Le Vide 16, 3 (1948).

Pubs. Astron. Soc. Pacific (1)

J. Evans, Pubs. Astron. Soc. Pacific 52, 305 (1940).
[CrossRef]

Sach. Akad. Leipzig Math. Phy. Kl. Berichte (1)

O. Wiener, Sach. Akad. Leipzig Math. Phy. Kl. Berichte 53, 54, (1901–1902).

Other (5)

Walter Geffcken, German Patent No. 716153 (filed December8, 1939).

E. E. Barr and C. D. West, U. S. Patent No. 2,447,790 (filed April11, 1945).

E. R. Blout, U. S. Patent No. 2,447,792 (filed March24, 1945).

M. Hyman, U. S. Patent No. 2,447,805 (filed April11, 1945).

R. B. Woodward, U. S. Patent No. 2,447,831 (filed March3, 1945).

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Figures (8)

Fig. 1
Fig. 1

Arrangement of the elements and path of the rays in the Turner Frustrated Total Reflection filter.

Fig. 2
Fig. 2

Transmission as a function of wave-length of a simple Frustrated Total Reflection filter. The filter is made with 67.5° glass prisms. The low index layer has n=1.38 and an optical thickness of 3 4 of a wave at 560 mμ. A high index layer has n=2.38 and an optical thickness of 6 waves at 600 mμ.

Fig. 3
Fig. 3

Variation of wave-length of peak transmission with angle of incidence for a Frustrated Total Reflection filter. λs is the wave-length for light polarized perpendicular to the plane of incidence; λp for light polarized parallel to the plane of incidence. d is the thickness of the high index layer. The indices are the same as in Fig. 2.

Fig. 4
Fig. 4

Formula for uric acid.

Fig. 5
Fig. 5

Variation of wave-length of peak transmission with angle of incidence for a Frustrated Total Reflection filter. In this filter the central layer is birefringent with ω 1.72, 1.55, and the low index layer 1.38.

Fig. 6
Fig. 6

Measured transmission of a birefringent Frustrated Total Reflection filter.

Fig. 7
Fig. 7

Measured transmission of the filter shown in Fig. 6 tilted to the angle at which the pass bands coincide.

Fig. 8
Fig. 8

Measured transmission of the birefringent filter of Figs. 6 and 7 tilted until the two bands have reversed their positions.

Tables (1)

Tables Icon

Table I Values of ωd/λ and θ at which coincidence is achieved between bands of a given order. This is calculated for a filter with n=1.38 for the low index layer and with ω=1.72 and =1.58 for the high index layer.

Equations (19)

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I I 0 = t 2 t 2 + 4 r sin 2 [ ( φ - 2 δ ) / 2 ] ,
r s = ( sinh 2 u ) ( n 1 2 - n 2 2 ) 2 D s ,
t s = 4 ( n 1 2 sin 2 θ - n 2 2 ) n 1 2 cos 2 θ D s ,
D s = sinh 2 u ( n 1 2 cos 2 θ - n 1 2 sin 2 θ + n 2 2 ) 2 + ( n 1 2 sin 2 θ - n 2 2 ) ( 2 n 1 cos θ ) 2 cosh 2 u ,
u = ( 2 π d ) / λ ( n 1 2 sin 2 θ - n 2 2 ) 1 2 .
tan δ s 2 = ( sin 2 θ - ( n 1 / n 0 ) 2 ) 1 2 cos θ ,
tan δ p 2 = ( sin 2 θ - ( n 1 / n 0 ) 2 ) 1 2 ( n 1 / n 0 ) 2 cos θ ,
φ = ( 4 π n d / λ ) cos θ ,
θ 0 = 67.5° n low = 1.38 n high = 2.38 n d low = 3.4 λ at 560 m μ n d high = 6 λ at 600 m μ .
4 π n d cos θ λ - 2 δ = 2 m π
λ = 2 π n d cos θ m π + 2 δ ,
Δ ν = δ s - δ p 2 π n d cos θ .
ω ( θ ) = ω ( θ ) = ω ( 2 cos 2 θ + ω 2 sin 2 θ ) 1 2 ,
4 π ( θ ) ω d cos θ ω λ - 2 δ s ( θ ) = 2 m π ,
4 π ω d cos θ λ 2 δ p ( θ ) = 2 m π .
( θ ) = ω m π + 2 δ s ( θ ) m π + 2 δ p ( θ ) .
θ 0 = 67.5° n low = 1.38 ω = 1.72 = 1.55.
θ 0 = 67° ( n d ) low = 3 / 4 λ at 520 m μ ( n d ) high = 9 / 4 λ at 600 m μ .
1 / λ = m π + δ ( θ ) 2 π n d cos θ ,