## Uncertainty principle for partially coherent light

JOSA, Vol. 73, Issue 3, pp. 251-255 (1983)

http://dx.doi.org/10.1364/JOSA.73.000251

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### Abstract

Two intensity functions are introduced for partially coherent light: one in a space domain and a second one in a spatial-frequency domain. Moreover, a quantity is defined that can be considered a measure of the overall degree of coherence of the partially coherent light. It is then shown that the following uncertainty principle can be formulated: the product of the effective widths of the two intensity functions has a lower bound, and this lower bound is inversely proportional to the overall degree of coherence.

© 1983 Optical Society of America

**Citation**

Martin J. Bastiaans, "Uncertainty principle for partially coherent light," J. Opt. Soc. Am. **73**, 251-255 (1983)

http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-73-3-251

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### References

- A. Papoulis, Signal Analysis (McGraw-Hill, New York, 1977).
- A. Papoulis, Systems and Transforms with Applications in Optics (McGraw-Hill, New York, 1968).
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- M. J. Bastiaans, "An uncertainty principle for spatially quasistationary, partially coherent light," J. Opt. Soc. Am. 72, 1441–1443 (1982).
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- The proof in Appendix A is due to M. L. J. Hautus, Technische Hogeschool Eindhoven, Eindhoven, The Netherlands (personal communication).
- From Ref. 4, Eq. (10), one might conclude that the minimum value 8/9 can be reached even without going into a limit. Indeed, if the Wigner distribution function had a form as described by Eq. (10) of Ref. 4, this would be the case. However, a function having such a form cannot be a proper Wigner distribution function, i.e., the power spectrum that would correspond to this function is not nonnegative definite hermitian. Therefore the equality signs in Eqs. (8) and (9) of Ref. 4 are somewhat misleading.
- M. Marcus and H. Minc, Introduction to Linear Algebra (Macmillan, New York, 1965), Sec. 3.5, Theorem 5.9.

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