## Linear algebraic theory of partial coherence: discrete fields and measures of partial coherence

JOSA A, Vol. 19, Issue 8, pp. 1563-1571 (2002)

http://dx.doi.org/10.1364/JOSAA.19.001563

Enhanced HTML Acrobat PDF (171 KB)

### Abstract

A linear algebraic theory of partial coherence is presented that allows precise mathematical definitions of concepts such as coherence and incoherence. This not only provides new perspectives and insights but also allows us to employ the conceptual and algebraic tools of linear algebra in applications. We define several scalar measures of the degree of partial coherence of an optical field that are zero for full incoherence and unity for full coherence. The mathematical definitions are related to our physical understanding of the corresponding concepts by considering them in the context of Young’s experiment.

© 2002 Optical Society of America

**OCIS Codes**

(000.5490) General : Probability theory, stochastic processes, and statistics

(030.0030) Coherence and statistical optics : Coherence and statistical optics

**History**

Original Manuscript: July 10, 2001

Revised Manuscript: January 11, 2002

Manuscript Accepted: February 20, 2002

Published: August 1, 2002

**Citation**

Haldun M. Ozaktas, Serdar Yüksel, and M. Alper Kutay, "Linear algebraic theory of partial coherence: discrete fields and measures of partial coherence," J. Opt. Soc. Am. A **19**, 1563-1571 (2002)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-19-8-1563

Sort: Year | Journal | Reset

### References

- L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, UK, 1995).
- M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, UK, 1980).
- J. W. Goodman, Statistical Optics (Wiley, New York, 1985).
- J. Perina, Coherence of Light (Van Nostrand Reinhold, London, 1971).
- G. Strang, Linear Algebra and Its Applications, 3rd ed. (Harcourt Brace Jovanovitch, San Diego, Calif., 1988).
- A. V. Oppenheim, R. W. Schafer, J. R. Buck, Discrete Time Signal Processing, 2nd ed. (Prentice-Hall, Englewood Cliffs, N.J., 1999).
- A. W. Lohmann, R. G. Dorsch, D. Mendlovic, Z. Zalevsky, C. Ferreira, “Space–bandwidth product of optical signals and systems,” J. Opt. Soc. Am. A 13, 470–473 (1996). [CrossRef]
- R. N. Bracewell, “Radio interferometry of discrete sources,” Proc. IRE 46, 97–105 (1958). [CrossRef]
- H. Gamo, “Matrix treatment of partial coherence,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1964), Vol. 3, pp. 187–332.
- H. M. Ozaktas, Z. Zalevsky, M. A. Kutay, “Sampling and the number of degrees of freedom,” in The Fractional Fourier Transform with Applications in Optics and Signal Processing (Wiley, New York, 2001), Sec. 3.3.
- A. Papoulis, Probability, Random Variables, and Stochastic Processes, 3rd ed. (McGraw-Hill, New York, 1991).
- T. Habashy, A. T. Friberg, E. Wolf, “Application of the coherent-mode representation to a class of inverse source problems,” Inverse Probl. 13, 47–61 (1997). [CrossRef]
- B. Zhang, B. Lu, “Transformation of Gaussian Schell-model beams and their coherent-mode representation,” J. Opt. 27, 99–103 (1996). [CrossRef]
- The formal analogy between the discrete and continuous cases is discussed in many texts; for instance, see C. Cohen-Tannoudji, B. Diu, F. Laloë, Quantum Mechanics (Wiley, New York, 1977), 2 vols.
- B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991).
- H. Gamo, “Intensity matrix and degree of coherence,” J. Opt. Soc. Am. 47, 976 (1957). [CrossRef]
- M. F. Erden, H. M. Ozaktas, D. Mendlovic, “Synthesis of mutual intensity distributions using the fractional Fourier transform,” Opt. Commun. 125, 288–301 (1996). [CrossRef]
- M. F. Erden, “Repeated filtering in consecutive fractional Fourier domains,” Ph.D. thesis (Bilkent University, Ankara, Turkey, 1997).
- M. A. Kutay, “Generalized filtering configurations with applications in digital and optical signal and image processing,” Ph.D. thesis (Bilkent University, Ankara, Turkey, 1999).
- M. A. Kutay, H. M. Ozaktas, M. F. Erden, S. Yüksel, “Discrete matrix model for synthesis of mutual intensity functions,” in Optical Processing and Computing: A Tribute to Adolf Lohmann, D. P. Casasent, H. J. Caulfield, W. J. Dallas, H. H. Szu, eds., Proc. SPIE4392, 87–98 (2001).
- T. D. Visser, A. T. Friberg, E. Wolf, “Phase-space inequality for partially coherent optical beams,” Opt. Commun. 187, 1–6 (2001). [CrossRef]

## 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.

« Previous Article | Next Article »

OSA is a member of CrossRef.