Abstract

The plane of polarization of two or more wavelengths can be rotated by a predetermined amount through the use of two or more identical half-wave plates in series, the axes of which are oriented at predetermined angles with respect to the incident plane of polarization. For two wavelengths a rotation of 90° may be accomplished by the use of two plates with their slow axes at angles of 22.5°+δ and 67.5°-δ, respectively. For three wavelengths a 90° rotation is obtained by using three plates at angles of 11.25°+δ, 45°, and 78.75°-δ respectively. The quantity δ is a small angle usually less than 1° which determines the spectral range of achromatization. Identical half-wave plates are easily obtained by cutting a single splitting of mica or a plane parallel sheet of other birefringent material. The wavelength for which the plates have half-wave retardation is not critical. Rather than having a smaller angular aperture than the single half-wave plate, the three-element achromatic rotator has a larger angular aperture. The use of the stereographic projection of the Poincaré sphere for graphical solution of polarized light problems is discussed briefly.

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  1. See, for example, A. C. Hardy and F. H. Perrin, The Principles of Optics (McGraw-Hill Book Company, Inc., New York, 1932), p. 610.
  2. S. Inoué and W. L. Hyde, J. Biophys. Biochem. Cytol. 3, 831 (1957).
  3. A. A. Lebedeff, Rev, opt. 9, 385 (1930), and F. H. Smith, Research (London) 8, 385 (1955).
  4. M. Francon and B. Sergent, Compt. rend. 241, 27 (1955); M. Francon, Optica Acta (Paris) 2, 182 (1955).
  5. C. D. West and A. S. Makas [J. Opt. Soc. Am. 39, 791 (1949)], describe some achromatic plates and give references to earlier work.
  6. M. P. Lostis, J. phys. radium 18, 51S (1957).
  7. M. G. Destriau and J. Prouteau, J. phys. radium 10, 53 (1949).
  8. S. Pancharatnam, Proc. Indian Acad. Sci. A41, 130 (1955).
  9. S. Pancharatnam, Proc. Indian Acad. Sci. A41, 137 (1955).
  10. R. C. Jones, J. Opt. Soc. Am. 31, 488 (1941).
  11. H. Poincaré, Théorie mathématique de la lumière II (Paris, 1892), Chap. 12.
  12. A good discussion of the Poincaré sphere is given by H. G. Jerrard, J. Opt. Soc. Am. 44, 634 (1954).
  13. G. N. Ramachandran and V. Chandrasekharan, Proc. Indian Acad. Sci. A33, 199 (1951). See also G. N. Ramachandran and S. Ramaseshan, J. Opt. Soc. Am. 42, 49 (1952).
  14. More information on the stereographic projection is contained in the monograph: W. W. Flexner and G. L. Walker, Military and Naval Maps and Grids (Dryden Press, Inc., New York, 1942). A classical reference is S. L. Penfield, Am. J. Sci. 11, 1, 115 (1901).
  15. The Wulff net is described in N. H. Hartshorne and A. Stuart, Crystals and the Polarizing Microscope (Edward Arnold and Company, London, 1952), second edition, p. 35. Wulff net coordinate paper is currently available from the University of Toronto Press, and transparent plastic protractors can be obtained from Ward's Natural Science Establishment, Inc., Rochester 9, New York, and from N. P. Nies, 969 Skyline Drive, Laguna Beach, California.

Chandrasekharan, V.

G. N. Ramachandran and V. Chandrasekharan, Proc. Indian Acad. Sci. A33, 199 (1951). See also G. N. Ramachandran and S. Ramaseshan, J. Opt. Soc. Am. 42, 49 (1952).

Destriau, M. G.

M. G. Destriau and J. Prouteau, J. phys. radium 10, 53 (1949).

Flexner, W. W.

More information on the stereographic projection is contained in the monograph: W. W. Flexner and G. L. Walker, Military and Naval Maps and Grids (Dryden Press, Inc., New York, 1942). A classical reference is S. L. Penfield, Am. J. Sci. 11, 1, 115 (1901).

Francon, M.

M. Francon and B. Sergent, Compt. rend. 241, 27 (1955); M. Francon, Optica Acta (Paris) 2, 182 (1955).

Hardy, A. C.

See, for example, A. C. Hardy and F. H. Perrin, The Principles of Optics (McGraw-Hill Book Company, Inc., New York, 1932), p. 610.

Hartshorne, N. H.

The Wulff net is described in N. H. Hartshorne and A. Stuart, Crystals and the Polarizing Microscope (Edward Arnold and Company, London, 1952), second edition, p. 35. Wulff net coordinate paper is currently available from the University of Toronto Press, and transparent plastic protractors can be obtained from Ward's Natural Science Establishment, Inc., Rochester 9, New York, and from N. P. Nies, 969 Skyline Drive, Laguna Beach, California.

Hyde, W. L.

S. Inoué and W. L. Hyde, J. Biophys. Biochem. Cytol. 3, 831 (1957).

Inoué, S.

S. Inoué and W. L. Hyde, J. Biophys. Biochem. Cytol. 3, 831 (1957).

Jerrard, H. G.

A good discussion of the Poincaré sphere is given by H. G. Jerrard, J. Opt. Soc. Am. 44, 634 (1954).

Jones, R. C.

R. C. Jones, J. Opt. Soc. Am. 31, 488 (1941).

Lebedeff, A. A.

A. A. Lebedeff, Rev, opt. 9, 385 (1930), and F. H. Smith, Research (London) 8, 385 (1955).

Lostis, M. P.

M. P. Lostis, J. phys. radium 18, 51S (1957).

Makas, A. S.

C. D. West and A. S. Makas [J. Opt. Soc. Am. 39, 791 (1949)], describe some achromatic plates and give references to earlier work.

Pancharatnam, S.

S. Pancharatnam, Proc. Indian Acad. Sci. A41, 130 (1955).

S. Pancharatnam, Proc. Indian Acad. Sci. A41, 137 (1955).

Perrin, F. H.

See, for example, A. C. Hardy and F. H. Perrin, The Principles of Optics (McGraw-Hill Book Company, Inc., New York, 1932), p. 610.

Poincaré, H.

H. Poincaré, Théorie mathématique de la lumière II (Paris, 1892), Chap. 12.

Prouteau, J.

M. G. Destriau and J. Prouteau, J. phys. radium 10, 53 (1949).

Ramachandran, G. N.

G. N. Ramachandran and V. Chandrasekharan, Proc. Indian Acad. Sci. A33, 199 (1951). See also G. N. Ramachandran and S. Ramaseshan, J. Opt. Soc. Am. 42, 49 (1952).

Sergent, B.

M. Francon and B. Sergent, Compt. rend. 241, 27 (1955); M. Francon, Optica Acta (Paris) 2, 182 (1955).

Stuart, A.

The Wulff net is described in N. H. Hartshorne and A. Stuart, Crystals and the Polarizing Microscope (Edward Arnold and Company, London, 1952), second edition, p. 35. Wulff net coordinate paper is currently available from the University of Toronto Press, and transparent plastic protractors can be obtained from Ward's Natural Science Establishment, Inc., Rochester 9, New York, and from N. P. Nies, 969 Skyline Drive, Laguna Beach, California.

Walker, G. L.

More information on the stereographic projection is contained in the monograph: W. W. Flexner and G. L. Walker, Military and Naval Maps and Grids (Dryden Press, Inc., New York, 1942). A classical reference is S. L. Penfield, Am. J. Sci. 11, 1, 115 (1901).

West, C. D.

C. D. West and A. S. Makas [J. Opt. Soc. Am. 39, 791 (1949)], describe some achromatic plates and give references to earlier work.

Other (15)

See, for example, A. C. Hardy and F. H. Perrin, The Principles of Optics (McGraw-Hill Book Company, Inc., New York, 1932), p. 610.

S. Inoué and W. L. Hyde, J. Biophys. Biochem. Cytol. 3, 831 (1957).

A. A. Lebedeff, Rev, opt. 9, 385 (1930), and F. H. Smith, Research (London) 8, 385 (1955).

M. Francon and B. Sergent, Compt. rend. 241, 27 (1955); M. Francon, Optica Acta (Paris) 2, 182 (1955).

C. D. West and A. S. Makas [J. Opt. Soc. Am. 39, 791 (1949)], describe some achromatic plates and give references to earlier work.

M. P. Lostis, J. phys. radium 18, 51S (1957).

M. G. Destriau and J. Prouteau, J. phys. radium 10, 53 (1949).

S. Pancharatnam, Proc. Indian Acad. Sci. A41, 130 (1955).

S. Pancharatnam, Proc. Indian Acad. Sci. A41, 137 (1955).

R. C. Jones, J. Opt. Soc. Am. 31, 488 (1941).

H. Poincaré, Théorie mathématique de la lumière II (Paris, 1892), Chap. 12.

A good discussion of the Poincaré sphere is given by H. G. Jerrard, J. Opt. Soc. Am. 44, 634 (1954).

G. N. Ramachandran and V. Chandrasekharan, Proc. Indian Acad. Sci. A33, 199 (1951). See also G. N. Ramachandran and S. Ramaseshan, J. Opt. Soc. Am. 42, 49 (1952).

More information on the stereographic projection is contained in the monograph: W. W. Flexner and G. L. Walker, Military and Naval Maps and Grids (Dryden Press, Inc., New York, 1942). A classical reference is S. L. Penfield, Am. J. Sci. 11, 1, 115 (1901).

The Wulff net is described in N. H. Hartshorne and A. Stuart, Crystals and the Polarizing Microscope (Edward Arnold and Company, London, 1952), second edition, p. 35. Wulff net coordinate paper is currently available from the University of Toronto Press, and transparent plastic protractors can be obtained from Ward's Natural Science Establishment, Inc., Rochester 9, New York, and from N. P. Nies, 969 Skyline Drive, Laguna Beach, California.

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