Abstract

In the polarizing microscope set for extinction, only that image whose polarization has been altered is available to form an image. The lenses themselves introduce such an alternation by rotation of the plane of polarization of rays having oblique incidence. This paper shows that the diffraction image of a pinhole has the form sin2θ·<i>J</i><sub>3</sub>(<i>r</i>)/<i>r</i>, where θ and <i>r</i> are polar coordinates in the image plane. The image has four bright zones separated by a dark cross and the central pattern becomes a four-leaf clover form. The diffraction image of a point source through a plate of uniaxial crystal cut perpendicular to its optic axis (z-cut) is also a four-leaf clover when the polarizers are crossed. When the polarizers are parallel, the diffraction image becomes similar to that of an astigmatic system.

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  1. B. R. A. Nijboer, Thesis, Groningen (1942).
  2. A. I. Mahan, J. Opt. Soc. Am. 40, 664 (1950), etc.; F. Zernike, J. Opt. Soc. Am. 47, 466 (1957). Dr. R. E. Hopkins kindly called our attention to this literature.
  3. H. Gamoh, Ôyö Butsuri 26, 102 (1957) (in Japanese); H. Slevogt, Optik 14, 383 (1957).
  4. F. Zernike, Physica 1, 689 (1934).
  5. C. J. Koester (private communication).
  6. E.g., M. Françon, Handbuch der Physik (Berlin, 1956), Vol. 24, p. 280.
  7. E.g., reference 6, p. 443.
  8. E.g., reference 1, p. 44.
  9. F. E. Wright, Am. J. Sci. 31, 157 (1911); J. Opt. Am. 7, 779 (1923); F. Rinne, Zentr. Mineral. Geol. 1, 88 (1900); S. Inoué, Exptl. Cell Research 3, 311 (1952); N. Rosenbusch and E. A. Würfing, Mikroskopischle Physiographie (Stuttgart, 1921/4), Vol. 1, p. 640.
  10. S. Inoué and W. L. Hyde, J. Biophys. Biochem. Cytol. 3, 391 (1957).
  11. H. H. Hopkins, Proc. Phys. Soc. (London) 55, 116 (1943); B. Richards and E. Wolf, Proc. Phys. Soc. B114, 854(L) (1956); R. Burtin, Optica Acta 3, 104 (1956).
  12. H. Wolter, Handbuclz der Pysik (Berlin, 1956), Vol. 24, p. 582.

Françon, M.

E.g., M. Françon, Handbuch der Physik (Berlin, 1956), Vol. 24, p. 280.

Gamoh, H.

H. Gamoh, Ôyö Butsuri 26, 102 (1957) (in Japanese); H. Slevogt, Optik 14, 383 (1957).

Hopkins, H. H.

H. H. Hopkins, Proc. Phys. Soc. (London) 55, 116 (1943); B. Richards and E. Wolf, Proc. Phys. Soc. B114, 854(L) (1956); R. Burtin, Optica Acta 3, 104 (1956).

Hyde, W. L.

S. Inoué and W. L. Hyde, J. Biophys. Biochem. Cytol. 3, 391 (1957).

Inoué, S.

S. Inoué and W. L. Hyde, J. Biophys. Biochem. Cytol. 3, 391 (1957).

Koester, C. J.

C. J. Koester (private communication).

Mahan, A. I.

A. I. Mahan, J. Opt. Soc. Am. 40, 664 (1950), etc.; F. Zernike, J. Opt. Soc. Am. 47, 466 (1957). Dr. R. E. Hopkins kindly called our attention to this literature.

Nijboer, B. R. A.

B. R. A. Nijboer, Thesis, Groningen (1942).

Wolter, H.

H. Wolter, Handbuclz der Pysik (Berlin, 1956), Vol. 24, p. 582.

Wright, F. E.

F. E. Wright, Am. J. Sci. 31, 157 (1911); J. Opt. Am. 7, 779 (1923); F. Rinne, Zentr. Mineral. Geol. 1, 88 (1900); S. Inoué, Exptl. Cell Research 3, 311 (1952); N. Rosenbusch and E. A. Würfing, Mikroskopischle Physiographie (Stuttgart, 1921/4), Vol. 1, p. 640.

Zernike, F.

F. Zernike, Physica 1, 689 (1934).

Other (12)

B. R. A. Nijboer, Thesis, Groningen (1942).

A. I. Mahan, J. Opt. Soc. Am. 40, 664 (1950), etc.; F. Zernike, J. Opt. Soc. Am. 47, 466 (1957). Dr. R. E. Hopkins kindly called our attention to this literature.

H. Gamoh, Ôyö Butsuri 26, 102 (1957) (in Japanese); H. Slevogt, Optik 14, 383 (1957).

F. Zernike, Physica 1, 689 (1934).

C. J. Koester (private communication).

E.g., M. Françon, Handbuch der Physik (Berlin, 1956), Vol. 24, p. 280.

E.g., reference 6, p. 443.

E.g., reference 1, p. 44.

F. E. Wright, Am. J. Sci. 31, 157 (1911); J. Opt. Am. 7, 779 (1923); F. Rinne, Zentr. Mineral. Geol. 1, 88 (1900); S. Inoué, Exptl. Cell Research 3, 311 (1952); N. Rosenbusch and E. A. Würfing, Mikroskopischle Physiographie (Stuttgart, 1921/4), Vol. 1, p. 640.

S. Inoué and W. L. Hyde, J. Biophys. Biochem. Cytol. 3, 391 (1957).

H. H. Hopkins, Proc. Phys. Soc. (London) 55, 116 (1943); B. Richards and E. Wolf, Proc. Phys. Soc. B114, 854(L) (1956); R. Burtin, Optica Acta 3, 104 (1956).

H. Wolter, Handbuclz der Pysik (Berlin, 1956), Vol. 24, p. 582.

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