Abstract

A detailed survey is given of the present-day knowledge of optical compensators. The compensators discussed are those of Babinet, Soleil, Rayleigh, De Forest Palmer, Brace, Szivessy, Senármont, and Richartz. Each instrument is described, the theory developed, the method of use for the measurement of small phase differences given, and reference made to the sensitivity and accuracy.

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  1. For a full account of the influence of reflections on a doubly refracting plate see F. Gabler and P. Sokob, Zeits. f. Physik 116, 47 (1940). The effect of absorption which is negligible is discussed by M. Berek, Ann. d. Physik 58, 165 (1919).
  2. G. Szivessy and W. Herzog, Zeits. f. Instrumentenk. 57, 53 (1937). For alternative forms see F. Gabler and P. Sokob, Zeits. f. Instrumentenk 58, 302 (1938). For a generalized intensity formula for a system of n plates see Hsien-Yü Hsü, M. Richartz, and Yüng-K'ang Liang, J. Opt. Soc. Am. 37, 99 (1947).
  3. G. Szivessy, Handbuch der Physik 19, 926 (1928).
  4. A. Bravais, Comptes rendus 32, 115 (1851) ; G. Szivessy, Zeits. f. Physik 29, 372 (1924).
  5. G. Szivessy, Handbuch der Physik 19, 941 (1928).
  6. Soleil, Comptes rendus, 21, 426 (1845).
  7. M. E. Mascart, Traité d'Optique (Gauthier-Villars, Paris, 1891), Vol. 2, p. 61.
  8. A composite plate consisting of two equally thick plates, usually of quartz cut at π/4 to the optical axis, lying on top of each other with their principal planes at right angles. See G. Szivessy, Handbuch der Physik 19, 942 (1928).
  9. Bravais, Zehnder, Biernacki, Zahrzewski, and Koenigsberger, Handbuch der Physik 19, 943 (1928).
  10. G. Szivessy, Zeits. f. Physik 29, 372 (1924).
  11. Lord Rayleigh, Phil Mag 4, 680 (1902); Sci. Pap. 5, 64 (1905).
  12. By using this compensator in conjunction with a Soleil, the fringe displacement of the former can be compensated whence the drum reading will give δ directly.
  13. P. Zeeman and C. M. Hoogenboom, Physik. Zeits. 13, 914 (1912).
  14. A. De Forest Palmer, Phys. Rev. 17, 409 (1921); H. A. Boorse, Phys. Rev. 46, 187 (1934).
  15. In the original the half-shade and compensator springs produced tensions of 0.285 g and 2.04 g per micrometer division, respectively. If PH and Pc are the tension expressed in micrometer divisions η=2.00PH × 10-6, K= 6.112Pc × 10-6; possible maxima being η= 3 × 54 × 10-4 ·2π and 1.77 × 10-4 ·2π whence the maximum value of the phase difference which can be measured is K0= 1.77 × 10-4 ·2π.
  16. D. B. Brace, Phil. Mag. 7, 320 (1904); Phys. Rev. 18, 70 (1904); ibid. 19, 218 (1904); G. Szivessy, Zeits. f. Instrumentenk. 57, 49 and 89 (1937).
  17. The effect of the sequence of the plates has been discussed in the introduction. The possible arrangements for the Brace compensator are shown in Fig. 10, where it can be seen that the essential difference between arrangements A and B is that in one case K never lies between H and D, in the other it always does.
  18. If Φ0is negative, 2Φ = ±2nπ-2Φ0 or ±(2n+1)π+2Φ0, (N=0,1,2…).
  19. For a detailed discussion see G. Szivessy, Zeits. f. Instrumentenk. 57, 92 (1937).
  20. To obtain a half-shadow plate of very small difference which can also be varied, a plate of phase difference η can be used in azimuth h(-π/2 ⋜ h ⋜ +π/2) differing from ±π/4 so that the effective phase difference in this azimuth is η = ±η sin2h, the positive value holding if 0 ⋜ h ⋜ +π/2, the negative if -π/2 ⋜ h ⋜ 0. Such a plate was devised by Wedeneewa (Zeits. f. Instrumentenk. 43, 17 (1923)), but its application is limited to cases where small phase differences are involved and, if arrangement A is used, the polarizer and analyzer must be crossed, thus precluding the use of the most favorable polarizer azimuth.
  21. G. Szivessy, Zeits. f. Physik 54, 594 (1929).
  22. G. Szivessy and A. Dierkesmann, Ann. d. Physik 11, 949 (1931).
  23. G. Szivessy and A. Dierkesmann, Ann. d. Physik 11, 956 (1931).
  24. G. Szivessy and W. Herzog, Zeits. f. Instrumentenk. 57, 305 (1937).
  25. Note that a value for η can be found without recourse to an independent measurement, for [equation] W. Herzog, Zeits. f. Physik 97, 225 (1935).
  26. If, in arrangement B, Eq. (82) is to be used for the calculation of δ, then it is immaterial whether OD and OH are parallel or perpendicular whatever the sign of sin2δ cosK tanη/2.
  27. H. de Sénarmont, Ann. Chim. Phys. 73, 337 (1840); F. Gabler and P. Sokob, Zeits. f. Instrumentenk. 58, 301 (1938); F. Gabler and P. Sokob, Zeits. f. Instrumentenk. 61, 298 (1941); F. Gabler and P. Sokob, Physik. Zeits. 42, 319 (1941).
  28. A symmetrical prism with right end faces, consisting of two Glan-Thomson prisms cemented together so that the vibration directions make a small angle 2ε with each other. O. Schönrock, Handbuch der Physik 19, 750 (1928).
  29. A polarizing prism combined with a λ/2 plate covering half the field of view. The vibration directions make an angle ε with each other; this angle can be varied. M. Chauvin, J. de Phys. 9, 21 (1890); Ann. de Toulouse 3(J) 28, (1889).
  30. For a full discussion see F. Gabler and P. Sokob, Zeits f. Instrumentenk. 58, 301 (1938) (see reference 27).
  31. F. Gabler and P. Sokob, Zeits. f. Instrumentenk. 58, 301 (1938).
  32. F. Gabler and P. Sokob, Zeits. f. Physik 116, 47 (1940).
  33. Reference 32, Eq. 22.
  34. Since s is dependent on the angle ε, which may be easily changed, this gives the Chauvin analyzer the decided advantage of variable sensitivity.
  35. M. Richartz, Zeits. f. Instrumentenk. 60, 357 (1940); J. Opt. Soc. Am. 31, 292 (1941).

Brace, D. B.

D. B. Brace, Phil. Mag. 7, 320 (1904); Phys. Rev. 18, 70 (1904); ibid. 19, 218 (1904); G. Szivessy, Zeits. f. Instrumentenk. 57, 49 and 89 (1937).

Bravais, A.

A. Bravais, Comptes rendus 32, 115 (1851) ; G. Szivessy, Zeits. f. Physik 29, 372 (1924).

De Forest Palmer, A.

A. De Forest Palmer, Phys. Rev. 17, 409 (1921); H. A. Boorse, Phys. Rev. 46, 187 (1934).

de Sénarmont, H.

H. de Sénarmont, Ann. Chim. Phys. 73, 337 (1840); F. Gabler and P. Sokob, Zeits. f. Instrumentenk. 58, 301 (1938); F. Gabler and P. Sokob, Zeits. f. Instrumentenk. 61, 298 (1941); F. Gabler and P. Sokob, Physik. Zeits. 42, 319 (1941).

Dierkesmann, A.

G. Szivessy and A. Dierkesmann, Ann. d. Physik 11, 949 (1931).

G. Szivessy and A. Dierkesmann, Ann. d. Physik 11, 956 (1931).

Gabler, F.

F. Gabler and P. Sokob, Zeits. f. Physik 116, 47 (1940).

For a full account of the influence of reflections on a doubly refracting plate see F. Gabler and P. Sokob, Zeits. f. Physik 116, 47 (1940). The effect of absorption which is negligible is discussed by M. Berek, Ann. d. Physik 58, 165 (1919).

F. Gabler and P. Sokob, Zeits. f. Instrumentenk. 58, 301 (1938).

For a full discussion see F. Gabler and P. Sokob, Zeits f. Instrumentenk. 58, 301 (1938) (see reference 27).

Herzog, W.

G. Szivessy and W. Herzog, Zeits. f. Instrumentenk. 57, 53 (1937). For alternative forms see F. Gabler and P. Sokob, Zeits. f. Instrumentenk 58, 302 (1938). For a generalized intensity formula for a system of n plates see Hsien-Yü Hsü, M. Richartz, and Yüng-K'ang Liang, J. Opt. Soc. Am. 37, 99 (1947).

G. Szivessy and W. Herzog, Zeits. f. Instrumentenk. 57, 305 (1937).

Note that a value for η can be found without recourse to an independent measurement, for [equation] W. Herzog, Zeits. f. Physik 97, 225 (1935).

Hoogenboom, C. M.

P. Zeeman and C. M. Hoogenboom, Physik. Zeits. 13, 914 (1912).

Mascart, M. E.

M. E. Mascart, Traité d'Optique (Gauthier-Villars, Paris, 1891), Vol. 2, p. 61.

Rayleigh, Lord

Lord Rayleigh, Phil Mag 4, 680 (1902); Sci. Pap. 5, 64 (1905).

Richartz, M.

M. Richartz, Zeits. f. Instrumentenk. 60, 357 (1940); J. Opt. Soc. Am. 31, 292 (1941).

Sokob, P.

For a full account of the influence of reflections on a doubly refracting plate see F. Gabler and P. Sokob, Zeits. f. Physik 116, 47 (1940). The effect of absorption which is negligible is discussed by M. Berek, Ann. d. Physik 58, 165 (1919).

For a full discussion see F. Gabler and P. Sokob, Zeits f. Instrumentenk. 58, 301 (1938) (see reference 27).

F. Gabler and P. Sokob, Zeits. f. Instrumentenk. 58, 301 (1938).

F. Gabler and P. Sokob, Zeits. f. Physik 116, 47 (1940).

Szivessy, G.

A composite plate consisting of two equally thick plates, usually of quartz cut at π/4 to the optical axis, lying on top of each other with their principal planes at right angles. See G. Szivessy, Handbuch der Physik 19, 942 (1928).

G. Szivessy and A. Dierkesmann, Ann. d. Physik 11, 956 (1931).

G. Szivessy, Zeits. f. Physik 54, 594 (1929).

G. Szivessy, Zeits. f. Physik 29, 372 (1924).

For a detailed discussion see G. Szivessy, Zeits. f. Instrumentenk. 57, 92 (1937).

G. Szivessy and W. Herzog, Zeits. f. Instrumentenk. 57, 53 (1937). For alternative forms see F. Gabler and P. Sokob, Zeits. f. Instrumentenk 58, 302 (1938). For a generalized intensity formula for a system of n plates see Hsien-Yü Hsü, M. Richartz, and Yüng-K'ang Liang, J. Opt. Soc. Am. 37, 99 (1947).

G. Szivessy, Handbuch der Physik 19, 926 (1928).

G. Szivessy, Handbuch der Physik 19, 941 (1928).

G. Szivessy and W. Herzog, Zeits. f. Instrumentenk. 57, 305 (1937).

G. Szivessy and A. Dierkesmann, Ann. d. Physik 11, 949 (1931).

Zeeman, P.

P. Zeeman and C. M. Hoogenboom, Physik. Zeits. 13, 914 (1912).

Other

For a full account of the influence of reflections on a doubly refracting plate see F. Gabler and P. Sokob, Zeits. f. Physik 116, 47 (1940). The effect of absorption which is negligible is discussed by M. Berek, Ann. d. Physik 58, 165 (1919).

G. Szivessy and W. Herzog, Zeits. f. Instrumentenk. 57, 53 (1937). For alternative forms see F. Gabler and P. Sokob, Zeits. f. Instrumentenk 58, 302 (1938). For a generalized intensity formula for a system of n plates see Hsien-Yü Hsü, M. Richartz, and Yüng-K'ang Liang, J. Opt. Soc. Am. 37, 99 (1947).

G. Szivessy, Handbuch der Physik 19, 926 (1928).

A. Bravais, Comptes rendus 32, 115 (1851) ; G. Szivessy, Zeits. f. Physik 29, 372 (1924).

G. Szivessy, Handbuch der Physik 19, 941 (1928).

Soleil, Comptes rendus, 21, 426 (1845).

M. E. Mascart, Traité d'Optique (Gauthier-Villars, Paris, 1891), Vol. 2, p. 61.

A composite plate consisting of two equally thick plates, usually of quartz cut at π/4 to the optical axis, lying on top of each other with their principal planes at right angles. See G. Szivessy, Handbuch der Physik 19, 942 (1928).

Bravais, Zehnder, Biernacki, Zahrzewski, and Koenigsberger, Handbuch der Physik 19, 943 (1928).

G. Szivessy, Zeits. f. Physik 29, 372 (1924).

Lord Rayleigh, Phil Mag 4, 680 (1902); Sci. Pap. 5, 64 (1905).

By using this compensator in conjunction with a Soleil, the fringe displacement of the former can be compensated whence the drum reading will give δ directly.

P. Zeeman and C. M. Hoogenboom, Physik. Zeits. 13, 914 (1912).

A. De Forest Palmer, Phys. Rev. 17, 409 (1921); H. A. Boorse, Phys. Rev. 46, 187 (1934).

In the original the half-shade and compensator springs produced tensions of 0.285 g and 2.04 g per micrometer division, respectively. If PH and Pc are the tension expressed in micrometer divisions η=2.00PH × 10-6, K= 6.112Pc × 10-6; possible maxima being η= 3 × 54 × 10-4 ·2π and 1.77 × 10-4 ·2π whence the maximum value of the phase difference which can be measured is K0= 1.77 × 10-4 ·2π.

D. B. Brace, Phil. Mag. 7, 320 (1904); Phys. Rev. 18, 70 (1904); ibid. 19, 218 (1904); G. Szivessy, Zeits. f. Instrumentenk. 57, 49 and 89 (1937).

The effect of the sequence of the plates has been discussed in the introduction. The possible arrangements for the Brace compensator are shown in Fig. 10, where it can be seen that the essential difference between arrangements A and B is that in one case K never lies between H and D, in the other it always does.

If Φ0is negative, 2Φ = ±2nπ-2Φ0 or ±(2n+1)π+2Φ0, (N=0,1,2…).

For a detailed discussion see G. Szivessy, Zeits. f. Instrumentenk. 57, 92 (1937).

To obtain a half-shadow plate of very small difference which can also be varied, a plate of phase difference η can be used in azimuth h(-π/2 ⋜ h ⋜ +π/2) differing from ±π/4 so that the effective phase difference in this azimuth is η = ±η sin2h, the positive value holding if 0 ⋜ h ⋜ +π/2, the negative if -π/2 ⋜ h ⋜ 0. Such a plate was devised by Wedeneewa (Zeits. f. Instrumentenk. 43, 17 (1923)), but its application is limited to cases where small phase differences are involved and, if arrangement A is used, the polarizer and analyzer must be crossed, thus precluding the use of the most favorable polarizer azimuth.

G. Szivessy, Zeits. f. Physik 54, 594 (1929).

G. Szivessy and A. Dierkesmann, Ann. d. Physik 11, 949 (1931).

G. Szivessy and A. Dierkesmann, Ann. d. Physik 11, 956 (1931).

G. Szivessy and W. Herzog, Zeits. f. Instrumentenk. 57, 305 (1937).

Note that a value for η can be found without recourse to an independent measurement, for [equation] W. Herzog, Zeits. f. Physik 97, 225 (1935).

If, in arrangement B, Eq. (82) is to be used for the calculation of δ, then it is immaterial whether OD and OH are parallel or perpendicular whatever the sign of sin2δ cosK tanη/2.

H. de Sénarmont, Ann. Chim. Phys. 73, 337 (1840); F. Gabler and P. Sokob, Zeits. f. Instrumentenk. 58, 301 (1938); F. Gabler and P. Sokob, Zeits. f. Instrumentenk. 61, 298 (1941); F. Gabler and P. Sokob, Physik. Zeits. 42, 319 (1941).

A symmetrical prism with right end faces, consisting of two Glan-Thomson prisms cemented together so that the vibration directions make a small angle 2ε with each other. O. Schönrock, Handbuch der Physik 19, 750 (1928).

A polarizing prism combined with a λ/2 plate covering half the field of view. The vibration directions make an angle ε with each other; this angle can be varied. M. Chauvin, J. de Phys. 9, 21 (1890); Ann. de Toulouse 3(J) 28, (1889).

For a full discussion see F. Gabler and P. Sokob, Zeits f. Instrumentenk. 58, 301 (1938) (see reference 27).

F. Gabler and P. Sokob, Zeits. f. Instrumentenk. 58, 301 (1938).

F. Gabler and P. Sokob, Zeits. f. Physik 116, 47 (1940).

Reference 32, Eq. 22.

Since s is dependent on the angle ε, which may be easily changed, this gives the Chauvin analyzer the decided advantage of variable sensitivity.

M. Richartz, Zeits. f. Instrumentenk. 60, 357 (1940); J. Opt. Soc. Am. 31, 292 (1941).

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