scholarly journals Characteristics of Partially Coherent Circular Flattened Gaussian Vortex Beams in Turbulent Biological Tissues

2019 ◽  
Vol 9 (5) ◽  
pp. 969 ◽  
Author(s):  
Yongzhou Ni ◽  
Yimin Zhou ◽  
Guoquan Zhou ◽  
Ruipin Chen
Keyword(s):  
Spectral Density ◽  
Analytical Formula ◽  
Biological Tissues ◽  
Degree Of Polarization ◽  
Average Intensity ◽  
Partially Coherent ◽  
Spectral Density Matrix ◽  
Cross Spectral Density ◽  
Vortex Beams ◽  
The Cross

The characteristics of partially coherent circular flattened Gaussian vortex beams in turbulent biological tissues are investigated, and the analytical formula for the cross-spectral density of this beam is derived. According to the cross-spectral density matrix, the average intensity and degree of polarization can be obtained. By numerical simulation, the distributions of the normalized average intensity and degree of polarization of partially coherent circular flattened Gaussian vortex beams are demonstrated on the research plane of turbulent biological tissues. The effects of the two beam parameters, the topological charge, the two transverse coherent lengths, and the structural constant of biological turbulence on the normalized average intensity and degree of polarization are analyzed. This study is of great significance for the potential application of partially coherent circular flattened Gaussian vortex beams in medical imaging and medical diagnosis.

scholarly journals Matrix Methods for Estimating the Coherence Functions from Estimates of the Cross-Spectral Density Matrix

1996 ◽  
Vol 3 (4) ◽  
pp. 237-246 ◽  
Author(s):  
D.O. Smallwood
Keyword(s):  
Density Matrix ◽  
Spectral Density ◽  
Multiple Input Multiple Output ◽  
Spectral Density Matrix ◽  
Multiple Input ◽  
Cross Spectral Density ◽  
Input Multiple Output ◽  
The Cross ◽  
Value Decomposition ◽  
Physical Order

It is shown that the usual method for estimating the coherence functions (ordinary, partial, and multiple) for a general multiple-input! multiple-output problem can be expressed as a modified form of Cholesky decomposition of the cross-spectral density matrix of the input and output records. The results can be equivalently obtained using singular value decomposition (SVD) of the cross-spectral density matrix. Using SVD suggests a new form of fractional coherence. The formulation as a SVD problem also suggests a way to order the inputs when a natural physical order of the inputs is absent.

scholarly journals Generation of Stationary Non-Gaussian Time Histories with a Specified Cross-spectral Density

1997 ◽  
Vol 4 (5-6) ◽  
pp. 361-377 ◽  
Author(s):  
David O. Smallwood
Keyword(s):  
Density Matrix ◽  
Spectral Density ◽  
Probability Density ◽  
Complex Frequency ◽  
Spectral Density Matrix ◽  
Cross Spectral Density ◽  
Time Histories ◽  
The Cross ◽  
Non Gaussian ◽  
Skewness And Kurtosis

The paper reviews several methods for the generation of stationary realizations of sampled time histories with non-Gaussian distributions and introduces a new method which can be used to control the cross-spectral density matrix and the probability density functions (pdfs) of the multiple input problem. Discussed first are two methods for the specialized case of matching the auto (power) spectrum, the skewness, and kurtosis using generalized shot noise and using polynomial functions. It is then shown that the skewness and kurtosis can also be controlled by the phase of a complex frequency domain description of the random process. The general case of matching a target probability density function using a zero memory nonlinear (ZMNL) function is then covered. Next methods for generating vectors of random variables with a specified covariance matrix for a class of spherically invariant random vectors (SIRV) are discussed. Finally the general case of matching the cross-spectral density matrix of a vector of inputs with non-Gaussian marginal distributions is presented.

scholarly journals Nonparaxial Propagation Properties of Specially Correlated Radially Polarized Beams in Free Space

2019 ◽  
Vol 9 (5) ◽  
pp. 997
Author(s):  
Lina Guo ◽  
Li Chen ◽  
Rong Lin ◽  
Minghui Zhang ◽  
Yiming Dong ◽  
...  
Keyword(s):  
Free Space ◽  
Degree Of Polarization ◽  
Average Intensity ◽  
Polarized Beams ◽  
Diffraction Integral ◽  
Spectral Density Matrix ◽  
Potential Applications ◽  
Spectral Degree ◽  
Propagation Properties ◽  
Radially Polarized

A specially correlated radially polarized (SCRP) beam with unusual physical properties on propagation in the paraxial regime was introduced and generated recently. In this paper, we extend the paraxial propagation of an SCRP beam to the nonparaxial regime. The closed-form 3 × 3 cross-spectral density matrix of a nonparaxial SCRP beam propagating in free space is derived with the aid of the generalized Rayleigh–Sommerfeld diffraction integral. The statistical properties, such as average intensity, degree of polarization, and spectral degree of coherence, are studied comparatively for the nonparaxial SCRP beam and the partially coherent radially polarized (PCRP) beam with a conventional Gaussian–Schell-model correlation function. It is found that the nonparaxial properties of an SCRP beam are strikingly different from those of a PCRP beam. These nonparaxial properties are closely related to the correlation functions and the beam waist width. Our results may find potential applications in beam shaping and optical trapping in nonparaxial systems.

Turbulent Wall-Pressure Fluctuations: A New Model for Off-Axis Cross-Spectral Density

1997 ◽  
Vol 119 (2) ◽  
pp. 277-280 ◽  
Author(s):  
B. A. Singer
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Spectral Density ◽  
Flow Direction ◽  
Wall Pressure ◽  
Mean Flow ◽  
New Approach ◽  
Cross Spectral Density ◽  
The Mean ◽  
The Cross

Models for the distribution of the wall-pressure under a turbulent boundary layer often estimate the coherence of the cross-spectral density in terms of a product of two coherence functions. One such function describes the coherence as a function of separation distance in the mean-flow direction, the other function describes the coherence in the cross-stream direction. Analysis of data from a large-eddy simulation of a turbulent boundary layer reveals that this approximation dramatically underpredicts the coherence for separation directions that are neither aligned with nor perpendicular to the mean-flow direction. These models fail even when the coherence functions in the directions parallel and perpendicular to the mean flow are known exactly. A new approach for combining the parallel and perpendicular coherence functions is presented. The new approach results in vastly improved approximations for the coherence.

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