Critical-point level-crossing geometry in random wave fields

Journal of the Optical Society of America A: Optics and Image Science, and Vision

Volumn 14, Issue 8, 1997, Pages 1911-1927

  Freund, Isaac ^a  

^a BAR ILAN UNIVERSITY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0242292294     PISSN: 10847529     EISSN: 15208532     Source Type: Journal    
DOI: 10.1364/JOSAA.14.001911     Document Type: Article

References (42)

1. J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London A 336, 165–190 (1974);
2. M. Berry, “Singularities in waves and rays,” in Physics of Defects, R. Balian, M. Kleman, and J.-P. Poirier, eds. (North-Holland, Amsterdam, 1981), pp. 453–549.
3. V. I. Arnold, Ordinary Differential Equations (MIT Press, Cambridge, Mass., 1973). Continuity is discussed in Secs. 12.2-12.9, pp. 81–92. The topological index is discussed in Sec. 36, pp. 254–268.
4. N. Shvartsman and I. Freund, “Vortices in random wave fields: nearest neighbor anticorrelations,” Phys. Rev. Lett. 72, 1008–1011 (1994);
5. I. Freund and N. Shvartsman, “Wave-field phase singularities: the sign principle,” Phys. Rev. A 50, 5164–5172 (1994);
6. N. Shvartsman and I. Freund, “Wave-field phase singularities: near-neighbor correlations and anticorrelations,” J. Opt. Soc. Am. A 11, 2710–2718 (1994);
7. I. Freund, “Amplitude topological singularities in random electromagnetic wavefields,” Phys. Lett. A 198, 139–144 (1995).
8. I. Freund, “Saddles, singularities, and extrema in random phase fields,” Phys. Rev. E 52, 2348–2360 (1995).
9. S. O. Rice, “Mathematical analysis of random noise,” in Selected Papers on Noise and Stochastic Processes, N. Wax, ed. (Dover, New York, 1954), pp. 133–294.
10. M. S. Longuet-Higgins, “On the statistical distribution of the heights of sea waves,” J. Mar. Res. 11, 245–266 (1952);
11. M. S. Longuet-Higgins, “The statistical analysis of a random moving surface,” Philos. Trans. R. Soc. London, Ser. A 249, 321–387 (1957);
12. M. S. Longuet-Higgins, “Re-flection and refraction at a random moving surface. I. Pattern and paths of specular points,” J. Opt. Soc. Am. 50, 838–844 (1960);
13. M. S. Longuet-Higgins, “II. Number of specular points in a Gaussian surface,” J. Opt. Soc. Am. 50, 845–850 (1960);
14. M. S. Longuet-Higgins, “III. Frequency of twinkling in a Gaussian surface,” J. Opt. Soc. Am. 50, 851–856 (1960);
15. M. S. Longuet-Higgins, D. E. Cartwright and M. S. Longuet-Higgins, “The statistical distribution of the maxima of a random function,” Proc. R. Soc. London Ser. A 237, 212–232 (1956).
16. R. J. Adler, The Geometry of Random Fields (Wiley, New York, 1981), Chap. 6, pp. 122–167.
17. R. Barakat, “Zero-crossing rate of differentiated speckle in-tensity,” J. Opt. Soc. Am. A 11, 671–673 (1994);
18. ‘R. Barakat, ‘Levelcrossing statistics of aperture integrated isotropic speckle,” J. Opt. Soc. Am. A 5, 1244–1247 (1988);
19. R. Barakat, “The level-crossing rate and above level duration time of the intensity of a Gaussian random process,” Inf. Sci. (New York) 20, 83–87 (1980).
20. K. Ebeling, “Statistical properties of spatial derivatives of the amplitude and intensity of monochromatic speckle patterns,” Opt. Acta 26, 1505–1527 (1979);
21. K. Ebeling, “Experimental investigation of some statistical properties of monochromatic speckle patterns,” Opt. Acta 26, 1345–1349 (1979);
22. K. Ebeling, “K-distributed spatial intensity derivatives in monochromatic speckle patterns,” Opt. Commun. 35, 323–326 (1980).
23. N. Takai, T. Iwai, and T. Asakura, “Real-time velocity measurement for a diffuse object using zero crossing of laser speckle,” J. Opt. Soc. Am. 70, 450–455 (1980);
24. N. Takai, T. Iwai, and T. Asakura, “Laser speckle velocimeters using a zero-crossing technique for spatially integrated intensity fluctuation,” Opt. Eng. 20, 324 (1981);
25. N. Takai and T. Asakura, “Displacement measurement of speckles using a 2-D level crossing technique,” Appl. Opt. 22, 3514–3519 (1983);
26. N. Takai, T. Iwai, T. Ushizaka, and T. Asakura, “Zero crossing study on dynamic properties of speckles,” J. Opt. (Paris) 11, 93–101 (1980).
27. R. D. Bahuguna, K. K. Gupta, and K. Singh, “Expected number of intensity level crossings in a normal speckle pattern,” J. Opt. Soc. Am. 70, 874–876 (1988).
28. N. Youssef, T. Munakata, and M. Takeda, “Rice probability functions for level-crossing intervals of speckle intensity fields,” Opt. Commun. 123, 55–62 (1996).
29. I. Freund, “Optical vortices in Gaussian random wave fields: statistical probability densities,” J. Opt. Soc. Am. A 11, 1644–1652 (1994);
30. I. Freund and D. A. Kessler, “Phase autocorrelation of random wave fields,” Opt. Commun. 124, 332 (1996);
31. I. Freund and N. Shvartsman, “Structural correlations in Gaussian random wave fields,” Phys. Rev. E 51, 3770–3773 (1995).
32. J. W. Goodman, Statistical Optics (Wiley, New York, 1985). The Van Cittert-Zernike theorem is discussed in Sec. 5.6, pp. 207–222. The random phasor model of Gaussian fields is discussed in Sec. 2.9, pp. 44–56.
33. N. Shvartsman and I. Freund, “Speckle spots ride phase saddles sidesaddle,” Opt. Commun. 17, 228–234 (1995).
34. A. L. Nelson, K. W. Foley, and W. B. Borgman, Calculus (Heath, Boston, Mass., 1946), Chap. 7, pp. 107–117.
35. I. Freund, “Intensity critical point correlation functions in random wave fields,” Opt. Commun. 128, 315–324 (1996).
36. D. Middleton, Introduction to Statistical Communication Theory (McGraw-Hill, New York, 1960), Chap. 7, pp. 335–368.
37. A. Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, New York, 1965), Sec. 9.6, pp. 312–323.
38. n are discussed in Chap. 9, pp. 358–389. Elliptic integrals E and F are discussed in Chap. 17, pp. 589–626.
39. M. Berry,“Disruption of wave-fronts: statistics of dislocations in incoherent Gaussian random waves,” J. Phys. A 11, 27–37 (1978).
40. A. Weinberg, “Percolation threshold of a two-dimensional continuum system,” Phys. Rev. B 26, 1352–1361 (1982).
41. A. Weinberg and B. I. Halperin, “Distribution of maxima, minima, and saddle points of the intensity of laser speckle patterns,” Phys. Rev. B 26, 1362–1368 (1982).
42. B. I. Halperin, “Statistical mechanics of topological defects,” in Physics of Defects, R. Balian, M. Kleman, and J.-P. Poirier, eds. (North-Holland, Amsterdam, 1981), pp. 814–857.