scholarly journals Variant-Coherence Gaussian Sources

Photonics ◽  
2021 ◽  
Vol 8 (9) ◽  
pp. 403
Author(s):  
Franco Gori ◽  
Massimo Santarsiero

The celebrated Gaussian Schell model source with its shift-invariant degree of coherence may be the basis for devising sources with space-variant properties in the spirit of structured coherence. Starting from superpositions of Gaussian Schell model sources, we present two classes of genuine cross-spectral densities whose degree of coherence varies across the source area. The first class is based on the use of the Laplace transform while the second deals with cross-spectral densities that are shape-invariant upon paraxial propagation. For the latter, we present a set of shape-invariant cross-spectral densities for which the modal expansion can be explicitly found. We finally solve the problem of ascertain whether an assigned cross-spectral density is shape-invariant by checking if it satisfies a simple differential constraint.

Photonics ◽  
2021 ◽  
Vol 8 (4) ◽  
pp. 134
Author(s):  
Rosario Martínez-Herrero ◽  
Massimo Santarsiero ◽  
Gemma Piquero ◽  
Juan Carlos González de Sande

A new class of sources presenting structured coherence properties is introduced and analyzed. They are obtained as the incoherent superposition of coherent Laguerre-Gaussian modes with suitable coefficients. This ensures that the shape of the intensity profile and the spatial coherence features of the propagated beams are invariant during paraxial approximation. A simple analytical expression is obtained for the cross-spectral density of the sources of this class, regardless of the number of superposed modes. Properties of these sources are analyzed and described by several examples.


1974 ◽  
Vol 96 (2) ◽  
pp. 676-679 ◽  
Author(s):  
J. C. Wambold ◽  
W. H. Park ◽  
R. G. Vashlishan

The initial portion of the paper discusses the more conventional method of obtaining a vehicle transfer function where phase and magnitude are determined by dividing the cross spectral density of the input/output by the power spectral density (PSD) of the input. The authors needed a more descriptive analysis (over PSD) and developed a new signal description called Amplitude Frequency Distribution (AFD); a discrete joint probability of amplitude and frequency with the advantage of retaining amplitude distribution as well as frequency distribution. A better understanding was obtained, and transfer matrix functions were developed using AFD.


2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Mozamel Musa Saeed ◽  
Mohammed Alsharidah

AbstractBoth software-defined networking and big data have gained approval and preferences from both industry and academia. These two important realms have conventionally been addressed independently in wireless cellular networks. The discussion taken into consideration in this study was to analyze the wireless cellular technologies with the contrast of efficient and enhanced spectral densities at a reduced cost. To accomplish the goal of this study, Welch's method has been used as the core subject. With the aid of previous research and classical techniques, this study has identified that the spectral densities can be enhanced at reduced costs with the help of the power spectral estimation methods. The Welch method gives the result on power spectrum estimation. By reducing the effect of noise, the Welch method is used to calculate the power spectral density of a signal. When data length is increased, Welch's method is considered the best as a conclusion to this paper because excellent results are yielded by it in the area of power spectral density estimation.


1969 ◽  
Vol 59 (3) ◽  
pp. 1071-1091
Author(s):  
Dean V. Power

abstract Ground motion records from six high-explosive cratering events in northeastern Montana, ten contained nuclear explosive events at the Nevada Test Site, and motions of an earth-fill dam during the Gasbuggy underground nuclear explosion in New Mexico were analyzed for power spectral density, peak velocity and velocity spectra. The high-explosive events included four 20-ton single charges at depths of burst which varied between 42 to 57 feet, a 140-ton row charge consisting of three 20-ton and two 40-ton charges at optimum cratering depths of burst, and a 0.5-ton charge at the optimum depth of burst. It was found that at these depths and charge weights an increase in depth of burst resulted in an increase in peak velocities and power-spectral densities as measured at distant points (> 5 km). Power spectral density was found to be approximately proportional to the first power of yield. For this region it was determined that power spectral density varied inversely as radial distance to the 3.55 power. Three analysis techniques—peak velocity, velocity spectra and power spectral density—are compared, and it is shown that power spectral density is the most consistent method when comparing records from different measuring stations. An analysis of power-spectral density measured at one station for the ten events at the Nevada Test Site shows that a significant shift in the frequency of the energy in the seismogram occurs when the source location changes. For events in the Yucca Flat area the peak energy at Mercury was consistently at 1.0 Hz, while for events in the Pahute Mesa area this peak occurs at 2.5 Hz. A comparison of the power spectral densities on and near the Navajo Dam revealed that the natural frequencies and first harmonics of the dam are 1.4, 2.0 and 2.5 Hz in the mode where motion is parallel to the canyon axis. A simple model makes use of these frequencies to calculate a shear-wave velocity of 1130 ft/sec. A method of using power spectral density to measure earthquake magnitudes and measure the yield of underground explosions is proposed.


1997 ◽  
Vol 119 (2) ◽  
pp. 277-280 ◽  
Author(s):  
B. A. Singer

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.


Optics ◽  
2020 ◽  
Vol 1 (1) ◽  
pp. 97-113
Author(s):  
Milo W. Hyde IV

We present a method to generate any genuine electromagnetic partially coherent source (PCS) from correlated, stochastic complex screens. The method described here can be directly implemented on existing spatial-light-modulator-based vector beam generators and can be used in any application which utilizes electromagnetic PCSs. Our method is based on the genuine cross-spectral density matrix criterion. Applying that criterion, we show that stochastic vector field realizations (corresponding to a desired electromagnetic PCS) can be generated by passing correlated Gaussian random numbers through “filters” with space-variant transfer functions. We include step-by-step instructions on how to generate the electromagnetic PCS field realizations. As an example, we simulate the synthesis of a new electromagnetic PCS. Using Monte Carlo analysis, we compute statistical moments from independent optical field realizations and compare those to the corresponding theory. We find that our method produces the desired source—the correct shape, polarization, and coherence properties—within 600 field realizations.


1988 ◽  
Vol 68 (4) ◽  
pp. 239-243 ◽  
Author(s):  
F. Gori ◽  
G. Guattari ◽  
C. Palma ◽  
C. Padovani

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