Abstract

In the phenomenon called “chromatic polarization,” which is shown by a crystal plate placed between Nicol prisms, viewed with white light, it has long been known that there are sensitive colors in the case of parallel as well as crossed Nicols. However, it has not been noticed that the former has greater sensitivity than the latter. In this paper, we shall show, as the result of a colorimetric analysis, that the sensitivity of the former is more than twice as great as that of the latter in the case of first-order interference colors. It was also found, that, to get maximum sensitivity, the sensitive color plate must have a suitable retardation, dependent on the temperature of the light source, as given by Eq. (4) of this paper. Combining these facts, the authors have found a simple but very sensitive method of examining quarter-wavelength plates.

© 1951 Optical Society of America

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References

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  1. H. Kubota, J. Opt. Soc. Am. 40, 146 (1950).
    [CrossRef]
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  10. A. Köhler, Z. Wiss. Mikro. 38, 29 (1921); W. J. Schmidt, Chromasoma 1, 253 (1939); S. Inouye and K. Dan, J. Morphol. (to be published).
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  15. A. Marcelin, J. Chem. Phys. 28, 605 (1931).

1950 (2)

1949 (1)

1947 (1)

1946 (2)

1945 (1)

1943 (1)

1939 (1)

1935 (1)

1931 (1)

A. Marcelin, J. Chem. Phys. 28, 605 (1931).

1921 (1)

A. Köhler, Z. Wiss. Mikro. 38, 29 (1921); W. J. Schmidt, Chromasoma 1, 253 (1939); S. Inouye and K. Dan, J. Morphol. (to be published).
[CrossRef]

1917 (1)

A. Wenzel, Physik. Z. 18, 472 (1917).

1906 (1)

B. Trolle, Physik. Z. 7, 700 (1906).

1891 (1)

E. Lommel, Ann. Physik Chem. 43, 473 (1891).
[CrossRef]

Breckenridge, F. C.

Brown, W. R. J.

Judd,

Judd, D. B.

Köhler, A.

A. Köhler, Z. Wiss. Mikro. 38, 29 (1921); W. J. Schmidt, Chromasoma 1, 253 (1939); S. Inouye and K. Dan, J. Morphol. (to be published).
[CrossRef]

Kubota, H.

Lommel, E.

E. Lommel, Ann. Physik Chem. 43, 473 (1891).
[CrossRef]

MacAdam, D. L.

Marcelin, A.

A. Marcelin, J. Chem. Phys. 28, 605 (1931).

Milner, B. I.

Moon, P.

P. Moon and D. E. Spencer, J. Appl. Phys. 17, 506 (1946).
[CrossRef]

P. Moon and D. E. Spencer, J. Opt. Soc. Am. 35, 399 (1945).
[CrossRef]

Newhall,

Nickerson,

Osterberg, H.

Saunderson, J. L.

Schaub, W. R.

Spencer, D. E.

P. Moon and D. E. Spencer, J. Appl. Phys. 17, 506 (1946).
[CrossRef]

P. Moon and D. E. Spencer, J. Opt. Soc. Am. 35, 399 (1945).
[CrossRef]

Trolle, B.

B. Trolle, Physik. Z. 7, 700 (1906).

Wenzel, A.

A. Wenzel, Physik. Z. 18, 472 (1917).

Ann. Physik Chem. (1)

E. Lommel, Ann. Physik Chem. 43, 473 (1891).
[CrossRef]

J. Appl. Phys. (1)

P. Moon and D. E. Spencer, J. Appl. Phys. 17, 506 (1946).
[CrossRef]

J. Chem. Phys. (1)

A. Marcelin, J. Chem. Phys. 28, 605 (1931).

J. Opt. Soc. Am. (9)

Physik. Z. (2)

B. Trolle, Physik. Z. 7, 700 (1906).

A. Wenzel, Physik. Z. 18, 472 (1917).

Z. Wiss. Mikro. (1)

A. Köhler, Z. Wiss. Mikro. 38, 29 (1921); W. J. Schmidt, Chromasoma 1, 253 (1939); S. Inouye and K. Dan, J. Morphol. (to be published).
[CrossRef]

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Figures (15)

Fig. 1
Fig. 1

X, Y: Plane of polarization of light in crystal. P: Plane of polarization of polarizer. A: Plane of polarization of analyzer.

Fig. 2
Fig. 2

Color of chromatic polarization in I.C.I. diagram. (I): First-order color of symmetrical Nicols. (II): First-order color of crossed Nicols. (III): Second-order color of symmetrical Nicols.

Fig. 3
Fig. 3

Tristimulus values of the color symmetrical Nicols 3(a) and crossed Nicols 3(b). (Arrows and circles indicate the retardations of sensitive colors.)

Fig. 4
Fig. 4

Chromaticity sensitivity.

Fig. 5
Fig. 5

Comparison of chromaticity sensitivity of the cases of (I), (II), and (III).

Fig. 6
Fig. 6

Equi-chromaticity sensitivity curves of parallel Nicols.

Fig. 7
Fig. 7

Comparison of chromaticity sensitivity of different U.C.S. (1) by MacAdam’s U.C.S. (2) by Breckenridge and Schaub’s U.C.S. (3) by ζ-space. ΔS/Δ(μd) are multiplied by some factors so as to make the height of peaks equal.

Fig. 8
Fig. 8

Color of chromatic polarization in ζ-space (symmetrical Nicols).

Fig. 9
Fig. 9

Luminance sensitivity near (μd)=0 (crossed Nicols).

Fig. 10(a)
Fig. 10(a)

Luminance sensitivity (crossed Nicols).

Fig. 10(b)
Fig. 10(b)

Luminance sensitivity (symmetrical Nicols).

Fig. 11
Fig. 11

Color of chromatic polarization of the light source of various temperatures (symmetrical Nicols).

Fig. 12
Fig. 12

Chromaticity sensitivity of the light source of various temperature (by MacAdam’s U.C.S.).

Fig. 13
Fig. 13

μd〉 of the sensitive color.

Fig. 14
Fig. 14

Method of examining λ/4 plate.

Tables (4)

Tables Icon

Table I Maxima of chromaticity sensitivity.

Tables Icon

Table II Retardation of sensitive colors.

Tables Icon

Table III Combined sensitivity of luminance and chromaticity.

Tables Icon

Table IV Maxima of chromaticity sensitivity.

Equations (22)

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I = cos 2 ( ρ + θ ) + sin 2 ρ · sin 2 θ · cos 2 ( δ / 2 ) ~ + cos 2 ( δ / 2 ) ,
= cos 2 ( ρ + θ ) / sin 2 ρ · sin 2 θ ,             δ = 2 π ( μ d ) / λ .
X = E x ¯ I d λ ,             Y = E y ¯ I d λ ,             Z = E z ¯ I d λ ,
R 2 ~ + cos 2 ( δ / 2 ) ,             where             δ = 2 π ( 2 n d ) / λ .
I = cos 2 ( ρ + θ ) sin 2 ( δ / 2 ) + cos 2 ( ρ - θ ) · cos 2 ( δ / 2 ) .
ρ - θ = π / 2             or             ρ + θ = π / 2.
I = cos 2 ( δ / 2 ) .
1 / λ = ( 1 + α ) / λ 0 .
I = cos 2 [ m π ( 1 + α ) / 2 ] = sin 2 [ m π α / 2 ] m 2 π 2 α 2 / 4.
I = sin 2 ( δ / 2 ) ,
I = sin 2 [ m π ( 1 + α ) / 2 ] = sin 2 [ m π α / 2 ] m 2 π 2 α 2 / 4.
= cot 2 2 θ 0.03 ,             so             π / 4 - θ = δ θ 4 ° 5 0 .
{ ζ 1 = ( V x - V y ) ( 9.37 + 0.79 cos θ ) ζ 3 = ( V z - V y ) ( 9.33 + 0.87 sin θ ) ,
Y V = 1.2219 V - 0.23111 V 2 + 0.23951 V 3 - 0.021009 V 4 + 0.008404 V 5 .
I = α + sin 2 ( δ / 2 ) ,
x ¯ = A [ exp ( - q / λ ) ] / λ p ,             y ¯ = ,             z ¯ = .
E ( λ ) = C 1 n = 1 [ exp ( n C 2 / λ T ) ] / λ 5 ,
X = A C 1 Γ ( p + 4 ) n = 1 [ B n ± ( cos p + 4 u n ) · ( cos ( p + 4 ) u n ) ] ,
u n = tan - 1 [ 2 π ( μ d ) / ( q + n C 2 / T ) ] , B n = 1 / ( q + n C 2 / T ) p + 4 .
1 / T = 1 / T + 1 / γ , 1 / γ = λ 1 λ 2 C 2 ( λ 2 - λ 1 ) ln [ 1 - exp ( - C 2 / λ 1 T ) 1 - exp ( - C 2 / λ 2 T ) ] .
μ d = a + b T c ,
1000° T < 4000° , a = 0 , b = 512.40 , c = - 0.07605. 4000° < T , a = 251.2 , b = 101.478 , c = - 1.3020.