Abstract

An examination of the conditions under which the normalized coherence function γ(X<sub>1</sub>,X<sub>2</sub>,τ), at two points X<sub>1</sub> and X<sub>2</sub> in an optical field, is reducible to the product of a function of X<sub>1</sub>, X<sub>2</sub> and a function of τ leads to the concept of cross spectral purity. Spectrally pure beams of light are characterized by the property that their coherence function is so reducible and, operationally, by the fact that superposition does not affect the spectral distribution. Light beams that do not have this property are called spectrally impure, and it is shown to be characteristic of such beams that the interference fringes exhibit a detailed periodic coloring. A measure of the departure from cross-spectral purity is introduced and evaluated in some special cases. It is shown by an example that spectrally pure and spectrally impure beams of light may be derived from the same source with similar optical components. Moreover, these beams may be identical as regards their intensity, their spectral distribution, and their degree of coherence, and differ only as regards their state of spectral purity.

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  1. F. Zernike, Physica 1, 201 (1934).
  2. H. H. Hopkins, Proc. Roy. Soc. (London) A208, 263 (1951).
  3. E. Wolf, Proc. Roy. Soc. (London) A225, 96 (1954).
  4. E. Wolf, Proc. Roy. Soc. (London) A230, 246 (1955).
  5. H. H. Hopkins, J. Opt. Soc. Am. 47, 508 (1957).
  6. R. Hanbury Brown and R. Q. Twiss, Proc. Rov. Soc. (London) A243, 291 (1957).
  7. L. Mandel, Proc. Phys. Soc. (London) 71, 1037 (1958).
  8. D. Gabor, J. Inst. Electr. Engrs. (London) 93, Part III, 429 (1936).
  9. M. Born and E. Wolf, Principles of Optics (Pergamon Press, New York, 1959).
  10. In this representation a1, and a2 may be complex functions.
  11. W. P. Alford and A. Gold, Am. J. Phys. 56, 481 (1958).
  12. L. Mandel and E. Wolf, J. Opt. Soc. Am. 51, 815 (1961).
  13. G. B. Parrent, Jr., J. Opt. Soc. Am. 49, 787 (1959).

Alford, W. P.

W. P. Alford and A. Gold, Am. J. Phys. 56, 481 (1958).

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon Press, New York, 1959).

Brown, R. Hanbury

R. Hanbury Brown and R. Q. Twiss, Proc. Rov. Soc. (London) A243, 291 (1957).

Gabor, D.

D. Gabor, J. Inst. Electr. Engrs. (London) 93, Part III, 429 (1936).

Gold, A.

W. P. Alford and A. Gold, Am. J. Phys. 56, 481 (1958).

Hopkins, H. H.

H. H. Hopkins, J. Opt. Soc. Am. 47, 508 (1957).

H. H. Hopkins, Proc. Roy. Soc. (London) A208, 263 (1951).

Mandel, L.

L. Mandel and E. Wolf, J. Opt. Soc. Am. 51, 815 (1961).

L. Mandel, Proc. Phys. Soc. (London) 71, 1037 (1958).

Parrent, Jr., G. B.

G. B. Parrent, Jr., J. Opt. Soc. Am. 49, 787 (1959).

Twiss, R. Q.

R. Hanbury Brown and R. Q. Twiss, Proc. Rov. Soc. (London) A243, 291 (1957).

Wolf, E.

E. Wolf, Proc. Roy. Soc. (London) A225, 96 (1954).

L. Mandel and E. Wolf, J. Opt. Soc. Am. 51, 815 (1961).

M. Born and E. Wolf, Principles of Optics (Pergamon Press, New York, 1959).

E. Wolf, Proc. Roy. Soc. (London) A230, 246 (1955).

Zernike, F.

F. Zernike, Physica 1, 201 (1934).

Other (13)

F. Zernike, Physica 1, 201 (1934).

H. H. Hopkins, Proc. Roy. Soc. (London) A208, 263 (1951).

E. Wolf, Proc. Roy. Soc. (London) A225, 96 (1954).

E. Wolf, Proc. Roy. Soc. (London) A230, 246 (1955).

H. H. Hopkins, J. Opt. Soc. Am. 47, 508 (1957).

R. Hanbury Brown and R. Q. Twiss, Proc. Rov. Soc. (London) A243, 291 (1957).

L. Mandel, Proc. Phys. Soc. (London) 71, 1037 (1958).

D. Gabor, J. Inst. Electr. Engrs. (London) 93, Part III, 429 (1936).

M. Born and E. Wolf, Principles of Optics (Pergamon Press, New York, 1959).

In this representation a1, and a2 may be complex functions.

W. P. Alford and A. Gold, Am. J. Phys. 56, 481 (1958).

L. Mandel and E. Wolf, J. Opt. Soc. Am. 51, 815 (1961).

G. B. Parrent, Jr., J. Opt. Soc. Am. 49, 787 (1959).

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