Shannon and Weaver, Ref. 4, p. 19.
J. C. Dainty, Proceedings of the SPSE International Conference on Image Analysis and Evaluation, July 19-23, 1976, Toronto, Canada; "The Statistics of Speckle Patterns" in Progress in Optics, edited by E. Wolf (North-Holland, Amsterdam, 1976), Vol. XIV.
The exponential distribution is sometimes referred to as the geometrical or the "pure Bose" distribution in the literature.
See, for example, the extensive bibliography in Refs. 1 and 2.
F. T. S. Yu, Optics and Information Theory (Wiley, New York, 1976); M. Ross, Laser Receivers (Wiley, New York, 1966); T. E. Stern, "Some Quantum Effects in Information Channels," IRE Trans. Information Theory IT-6, 435–440 (1960); T. E. Stern, "Information Rates in Photon Channels and Photon Amplifiers," IRE Int. Convention Record, Part 4, 182–188 (1960); J. P. Gordon, "Quantum Effects in Communication Systems," Proc. IRE 50, 1898–1908 (1962); B. M. Oliver, "Thermal and Quantum Noise," Proc. IEEE 53, 436–454 (1965).
Calculated from data given in J. Kraus, Radio Astronomy (McGraw-Hill, New York, 1966).
R. von Mises, Mathematical Theory of Probability and Statistics (Academic, New York, 1964), Chap. IV, Sec. 3.2.
The negative binomial distribution was first introduced by F. Eggenberger and G. Pólya, Zeits. Ang. Math. Mech. 3, 276 (1923). According to Mandel, it was first applied to this problem by R. Fürth, Z. Phys. 48, 323 (1928); 50, 310 (1928).
A. Zardecki, C. Delisle and J. Bures, Coherence and Quantum Optics, edited by L. Mandel and E. Wolf, Proc. 3rd Rochester Conf., June 1972 (Plenum, New York, 1973).
R. W. Ditchburn, Light, 3rd ed. (Interscience, New York, 1976), p. 697; or G. R. Fowles, Introduction to Modern Optics (Holt Rinehart & Winston, New York, 1968), p. 211.
Ludwig Boltzmann, Vorlesunger über Gastheorie (J. A. Barth, Leipzig-Part T, 1896; Part II, 1898), translated by Stephen G. Brush as Lectures in Gas Theory (University of California, Berkeley, 1969). See pp. 56ff, 74ff, and 371, where Boltzmann refers to the proportionality between entropy and the logarithm of the probability of a state.
M. Planck, Theory of Heat Radiation, translated by M. Masius (Blakiston's, Philadelphia, 1914), Part III, Chap. I. The equation S = k logW, which is now referred to as Boltzmann's Principle, first appears in this work.
See, for example, L. Mandel, in Progress in Optics, edited by E. Wolf (North-Holland, Amsterdam, 1963), Vol. II; L. Mandel and E. Wolf, "Coherence Properties of Optical Fields, " Rev. Mod. Phys. 37, 231–287 (1965). The quantity n/z is often referred to in these references and elsewhere in the literature as the degeneracy parameter of the radiation. We deliberately avoid this usage to prevent a later semantic confusion.
J. Klauder and E. C. G. Sudarshan, Fundamentals of Quantum Optics (Benjamin, New York, 1968), p. 138.
B. R. Frieden and D. C. Wells, "Restoring with Maximum Entropy III: Poisson Sources and Backgrounds," J. Opt. Soc. Am. (to be published).
M. Scully, in Quantum Optics Course XLII, edited by R. J. Glauber (Academic, New York, 1969), p. 620ff. A succinct statement of the problem in terms of the coherent state representation. See also Ref. 14.
J. Perina, in Quantum Optics, edited by S. M. Kay and A. Maitland (Academic, New York, 1970).
B. R. Frieden, in Picture Processing and Digital Filtering, edited by T. S. Huang (Springer-Verlag, New York, 1975).
S. J. Wernecke and L. R. D'Addario, "Maximum Entropy Image Reconstruction, " IEEE Trans. Computers C-26, 351 (1977); S. J. Wernecke, "Two-Dimensional Maximum Entropy Reconstruction of Radio Brightness, " Radio Sci. (to be published).
J. P. Burg, project scientist, "Analytical Studies of Techniques for the Computation of High-Resolution Wavenumber Spectra," prepared by T. E. Barnard, Texas Instruments., Advanced Array Research Special Report No. 9, Contract No. F33657-68-C-0867, May 14, 1969.
C. E. Shannon and W. Weaver, The Mathematical Theory of Communication (University of Illinois, Urbana, 1949).