Skip to main content
Log in

Statistical properties of mutual intensity with finite measurement time

  • Contributed Papers
  • Published:
Applied physics Aims and scope Submit manuscript

Abstract

The accuracy with which the amplitude and phase of an interference fringe can be measured in quasi-thermal light is limited by the finite integration time used. The statistical errors expected in such a measurement are derived analytically, and their dependence on measurement time, the coherence time of the light, and the complex coherence factor are explored. An example illustrating the utility of the results is presented.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. The analytic signalu(P, t) has a real partu r (P, t) which is the actual real-valued wave disturbance, and an imaginary partu i (P, t) which is the Hilbert transform ofu r (P, t). For a discussion of analytic signals, see R.N. Bracewell:The Fourier Transform and its Applications (McGraw-Hill, New York 1965), pp. 267–272

    MATH  Google Scholar 

  2. E. Wolf: Proc. Roy. Society (A)225, 96 (1954);230, 226 (1955)

    ADS  Google Scholar 

  3. Throughout, a superbar over a symbol is used to indicate an infinite time average, or by ergodicity, an equivalent ensemble average

  4. See, for example, J.W. Goodman: Synthetic Aperture Optics, inProgress in Optics, Vol. VII, ed. by E. Wolf (North-Holland Pub. Co., Amsterdam 1970), pp. 4–9

    Google Scholar 

  5. M. Born, E. Wolf:Principles of Optics, 2nd rev. Ed. (Pergamon Press, Oxoford 1964) Section 10.4.1

    Google Scholar 

  6. L. Mandel: J. Opt. Soc. Am.51, 1342 (1961)

    Google Scholar 

  7. S. Lowenthal, D. Joyeaux: J. Opt. Soc. Am.61, 847 (1971)

    Google Scholar 

  8. L. Mandel: Proc. Phys. Soc.72, 1037 (1958)

    Article  Google Scholar 

  9. D. Middleton:An Introduction to Statistical Communication Theory (McGraw-Hill New York 1960) Section 7.7

    Google Scholar 

  10. P. Beckmann:Probability in Communication Engineering (Harcourt, Brace & World, Inc., New York 1967) Section 4.4

    Google Scholar 

  11. See Ref.—:Probability in Communication Engineering (Harcourt, Brace & World, Inc., New York 1967), Section 4.6

    Google Scholar 

  12. J.B. Thomas:An Introduction to Statistical Communication Theory (John Wiley & Sons New York 1969) Section 4.8

    MATH  Google Scholar 

  13. See Ref.—:An Introduction to Statistical Communication Theory (John Wiley & Sons New York 1969), Fig. 4.8

    MATH  Google Scholar 

  14. The symbolE[·] is used to represent a statistical expectation operator

  15. See Ref.—:An Introduction to Statistical Communication Theory (John Wiley & Sons New York 1969), p. 168

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Work supported by the Office of Naval Research

Rights and permissions

Reprints and permissions

About this article

Cite this article

Goodman, J.W. Statistical properties of mutual intensity with finite measurement time. Appl. Phys. 2, 95–101 (1973). https://doi.org/10.1007/BF00934178

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00934178

Index Headings

Navigation