OSA's Digital Library

Optics Letters

Optics Letters


  • Vol. 14, Iss. 4 — Feb. 15, 1989
  • pp: 199–201

Fisher information as the basis for diffraction optics

B. Roy Frieden  »View Author Affiliations

Optics Letters, Vol. 14, Issue 4, pp. 199-201 (1989)

View Full Text Article

Enhanced HTML    Acrobat PDF (399 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



It is shown that the Helmholtz wave equation follows from a new uncertainty principle: Given, as data, the position of a photon in an unknown diffraction pattern, the estimated position of the centroid of the pattern will suffer minimum precision. This implies a maximally spread out diffraction pattern, obeying a principle of minimum Fisher information. The minimum is constrained by knowledge of the refractive-index function n(x, y, z) of the medium through a requirement that the mean-square spatial phase gradient across the medium should be generally nonzero. Operationally the principle works directly with intensities and not complex amplitudes. As a practical matter the numerical use of the intensity-based principle might permit a widening of the known scope of solutions to diffraction problems.

© 1989 Optical Society of America

Original Manuscript: February 8, 1988
Manuscript Accepted: December 9, 1988
Published: February 15, 1989

B. Roy Frieden, "Fisher information as the basis for diffraction optics," Opt. Lett. 14, 199-201 (1989)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. P. J. Huber, Ann. Math. Stat. 35, 73 (1964). [CrossRef]
  2. P. J. Huber, Ann. Math. Stat. 43, 1041 (1972). [CrossRef]
  3. P. J. Huber, Ann. Stat. 2, 1029 (1974). [CrossRef]
  4. B. R. Frieden, J. Mod. Opt. 35, 1297 (1988). [CrossRef]
  5. H. L. van Trees, Detection, Estimation, and Modulation Theory (Wiley, New York, 1968), Part I, p. 66.
  6. B. R. Frieden, J. Opt. Soc. Am. 62, 511 (1972). [CrossRef] [PubMed]
  7. See, e.g., J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 34.
  8. G. A. Korn, T. M. Korn, Mathematical Handbook for Scientists and Engineers (McGraw-Hill, New York, 1968), p. 633.
  9. Ref. 5, pp. 79–81.
  10. P. M. Morse, H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), Part I, pp. 306–307.
  11. Ref. 8, p. 355.
  12. Ref. 8, p. 356.
  13. R. Eisberg, R. Resnick, Quantum Physics (Wiley, New York, 1974), p. 167.
  14. More discussion of these points is given in A. S. Marathay, Elements of Optical Coherence Theory (Wiley, New York, 1982), pp. 7–8.
  15. B. R. Frieden, “Fisher information as the basis for the Schrödinger wave equation,” Am. J. Phys. (to be published).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


Fig. 1

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited