Expected number of intensity level crossings in a normal speckle pattern

Bahuguna, R. D.; Gupta, K. K.; Singh, Kehar

doi:10.1364/josa.70.000874

Cited by 11 publications

(3 citation statements)

References 5 publications

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“…For example, his results include processes with an exponential, Rayleigh, gamma, Maxwell, and Laplace distribution. Subsequently, several other authors have independently derived several of Khimenko's results including the exponential distribution, as the level-crossing rate of the intensity of speckle patterns have been the subject of both theoretical [7][8][9][10] and experimental [11,12] interest over the past several years. Barakat [4], based on the gamma distribution, obtained analytic results for the mean level crossing rate of aperture-integrated speckles.…”

Section: ͑2͒mentioning

confidence: 99%

Mean level signal crossing rate for an arbitrary stochastic process

Yura

Hanson²

2010

J. Opt. Soc. Am. A

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The issue of the mean signal level crossing rate for various probability density functions with primary relevance for optics is discussed based on a new analytical method. This method relies on a unique transformation that transforms the probability distribution under investigation into a normal probability distribution, for which the distribution of mean level crossings is known. In general, the analytical results for the mean level crossing rate are supported and confirmed by numerical simulations. In particular, we illustrate the present method by presenting analytic expressions for the mean level crossing rate for various probability distributions, including ones that previously were unavailable, such as the uniform, the so-called gamma-gamma, and the Rice-Nakagami distribution. However, in a limited number of cases the present results differ somewhat from the result reported in the literature. At present, this discrepancy remains unexplained and is laid open for future discussion.

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Section: ͑2͒mentioning

confidence: 99%

Mean level signal crossing rate for an arbitrary stochastic process

Yura

Hanson²

2010

J. Opt. Soc. Am. A

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“…Rice introduced level crossing or generally crossing statistics [3]. Soon after that, in various disciplines raging from com-plex systems [4][5][6][7][8], material sciences [9][10][11] optics [12][13][14][15][16][17][18][19][20][21][22][23][24][25] to cosmology and early universe [26][27][28][29][30], mentioned method has been used and improved. Crossing statistics represents geometrical properties of a typical stochastic process, therefore, it has proper capability in order to quantify fluctuations in a robust manner.…”

Section: Theoretical Model: Up-and Down-crossing Statisticsmentioning

confidence: 99%

“…surface height fluctuations based on crossing statistics has been done in [11]. The crossing statistics of the amplitude and the intensity of a monochromatic speckle pattern as well as the behavior of the spatial derivatives of these quantities have been studied theoretically in [12][13][14], and a theoretical limits on the light distributions with random phase diffusers were derived in [15,16]. Laser speckle velocimetry based on the zero-crossing rate of the spatially integrated speckle intensity variations under various optical configurations of illumination and detection has been studied in [17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

Crossing statistics of laser light scattered through a nanofluid

Pirlar¹,

Movahed

Razzaghi

et al. 2017

J. Opt. Soc. Am. A

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In this paper, we investigate the crossing statistics of speckle patterns formed in the Fresnel diffraction region by a laser beam scattering through a nanofluid. We extend zero-crossing statistics to assess the dynamical properties of the nanofluid. According to the joint probability density function of laser beam fluctuation and its time derivative, the theoretical frameworks for Gaussian and non-Gaussian regimes are revisited. We count the number of crossings not only at zero level but also for all available thresholds to determine the average speed of moving particles. Using a probabilistic framework in determining crossing statistics, a priori Gaussianity is not essentially considered; therefore, even in the presence of deviation from Gaussian fluctuation, this modified approach is capable of computing relevant quantities, such as mean value of speed, more precisely. Generalized total crossing, which represents the weighted summation of crossings for all thresholds to quantify small deviation from Gaussian statistics, is introduced. This criterion can also manipulate the contribution of noises and trends to infer reliable physical quantities. The characteristic time scale for having successive crossings at a given threshold is defined. In our experimental setup, we find that increasing sample temperature leads to more consistency between Gaussian and perturbative non-Gaussian predictions. The maximum number of crossings does not necessarily occur at mean level, indicating that we should take into account other levels in addition to zero level to achieve more accurate assessments.

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A Survey of Recent Progress on Level-Crossing Problems for Random Processes

Abrahams

1986

Communications and Networks

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Expected number of intensity level crossings in a normal speckle pattern

Cited by 11 publications

References 5 publications

Mean level signal crossing rate for an arbitrary stochastic process

Mean level signal crossing rate for an arbitrary stochastic process

Crossing statistics of laser light scattered through a nanofluid

A Survey of Recent Progress on Level-Crossing Problems for Random Processes

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