arXiv subjects

Mikhail Charnotskii

Publications and source records attributed to Mikhail Charnotskii.

9 recordsLinked to original sources

arXiv2023

Improper statistics of the radiation from a randomly rotating source

Our earlier work [J. Opt. 19. (2017) 0905603] showed that, in contrast to the four parameters of the traditional Stokes vector description of the statistics of the partially polarized light, the complete second-order statistics of the narrow-band polarized wave is characterized by thirteen parameters. Here we analyze the second-order statistics of the radiation from a randomly rotating source of the electromagnetic radiation, and show that it includes a covariance of the right and left circular polarizations that is not captured by the Stokes vector formalism. We illustrate this finding on a simple example of rotating quadrupole.

physics.optics↗

arXiv2022

Warp and blur model for imaging through turbulence

Point Spread Function (PSF) for imaging through inhomogeneous refractive medium, such as atmospheric turbulence is bounded by three constraints [Charnotskii, Opt. Eng., 52, 04600, (2013)]. PSF is non-negative, band-limited, and the third constraint, related to the energy conservation principle, warrants the absence of fluctuations in the image of a uniformly bright object. We develop a version of the common warp and blur model for the anisoplanatic image distortions by turbulence that satisfies these three constraints.

physics.optics↗

arXiv2022

Partially-coherent waves with binominal coherence

Comprehensive analysis of non-diffracting optical waves with binominal two-point coherence function (BCF) is presented. This coherence function consist of two terms, each depending on either separation of points or central point. We established the necessary and sufficient conditions for non-negative definiteness of the binominal coherence functions. Spectral analysis, including calculations of the eigenvalues and eigenfunctions for the general BCF case is presented. We considered two simple BCF examples of and analyzed the conditions leading to the maximum irradiance contrast.

physics.optics↗

arXiv2021

Passive scintillometer: Theory and proof of concept

We propose design of a low-cost passive scintillometer that measures the strength of optical turbulence by analyzing scintillation in the image of a straight edge between the two areas of uniform, but distinct brightness. Two theoretical approaches to scintillations description are developed that are based on the phase screen and rigorous path integral propagation imaging models. Asymptotic analysis of both models leads to four distinctive imaging situations. We propose two uniform approximations that cover the most promising conclusion for the passive scintillometer applications. Both the strength of scintillation and the width of the area where scintillations exist can be used to estimate the turbulence strength. We present the results of the proof-of-concept experiment where images of the specifically made target were taken by a consumer grade camera equipped with a telephoto lens. We describe the image processing that separates the target characteristics from the turbulence scintillations. The spatial profiles of the image variances at three spectral bands and for several apertures were calculated. As was expected, scintillations are concentrated around the sharp edge and are absent at the uniformly bright parts of the target. Observed edge scintillation variances are within the theoretical limits, and provide reasonable estimates for the turbulence structure constant across the three spectral bands. However, the width of the scintillation area and dependence on the aperture are inconsistent with the thin lens imaging theory for larger apertures. We attribute this to the Additional bench tests on bar targets revealed that the camera and lens resolution are well below the nominal thin lens diffraction limit, and a different optical setup should be used in order to exploit the spatial distribution and aperture dependence of fluctuations.

physics.optics↗

arXiv2019

Four methods for generation of turbulent phase screens: comparison

We introduce a new method for generation of the phase screen samples with arbitrary spatial spectrum: Sparse Spectrum with uniform wave vectors (SU). Similar to the known Sparse Spectrum (SS) technique, it uses trigonometric series with random discrete support on the wave vector plane, but, unlike the SS technique, the random wave vectors are uniformly distributed on the individual segments of the wave vector plane partition. We compare the accuracy and computational effectiveness of the SU technique with ubiquitous subharmonics complemented DFT method, SS method, and recently published, randomized DFT technique [J. Opt. Soc. Am. B 36, 3249 (2019)]. SSU and SS algorithms generate unbiased samples, for screens with bounded phase variance, and show the superior computational effectiveness for one megapixel and larger screens.

eess.IV↗

arXiv2019

Eight models for coherence of radiation from incoherent sources and coherence of sunlight

Eight models for the coherence of the quasi-monochromatic light from spherical incoherent sources are constructed by placing incoherent monopole and dipole sources on the surface of a sphere, inside a ball and on a plane circular disk. All models allow relatively simple numerical calculations of coherence functions for arbitrary source sizes and positions of observation points. We show that the far-field regime for transverse coherence is formed at the distances larger than the source size, regardless of the wavelength. Wide angle far field coherences have simple analytical representations in terms of the spherical and cylindrical Bessel functions. For very large sources the main and few first lobes of coherence function is well represented by paraxial approximation, which reduces the number of models to three. Based on the solar images corresponding to these three models the ball model emerges as the most appropriate. Ball model can be modified to match the limb darkening observations.

physics.optics↗

arXiv2018

Fluctuations of the aperture-averaged orbital angular momentum after propagation through turbulence

In the recent paper [1] it was shown that for paraxial propagation of scalar waves, the transverse linear momentum and orbital angular momentum (OAM) are related to the wave coherence function. Although both of these quantities are conserved during free-space propagation, they fluctuate for beam propagation in a random inhomogeneous medium. We hereby present an extension of this theory to the case of OAM fluctuations of a spherical wave intercepted by a finite aperture. A complete asymptotic theory for the aperture-averaged OAM variance is developed for both weak and strong fluctuation conditions, based on the asymptotic expansions of the Feynman path-integral solution for the fourth-order coherence function of a spherical wave propagating through a random inhomogeneous medium. We show that"square root" law, and that the weak/strong fluctuation conditions for the aperture-averaged OAM are not defined by the values of the scintillation index of the incident wave.

physics.optics↗

arXiv2017

Transverse linear and orbital angular momenta of beam waves and propagation in random media

For paraxial propagation of scalar waves the classic electromagnetic theory definition of transverse linear (TLM) and orbital angular (OAM) momenta of the beam wave are represented in terms of the coherence function. We show in examples that neither the presence of optical vortices is necessary for the intrinsic OAM, nor does the presence of optical vortices warrant the non-zero intrinsic OAM. The OAM is analyzed for homogeneously coherent and twisted partially coherent beam waves. A twisted Gaussian beam has an intrinsic OAM with a per-unit power value that can be continuously changed by varying the twist parameters. Using the parabolic propagation equation for the coherence function, we show that both total TLM and OAM are conserved for the free-space propagation, but not for propagation in an inhomogeneous medium. In the presence of the random inhomogeneous medium, the total TLM and OAM are conserved in average, but the OAM fluctuations grow with the propagation path. This growth is slower for beams with rotation-symmetric irradiance.

physics.optics↗

arXiv2017

Statistics of narrow-band partially polarized light

A complete single-point statistical description of a narrow-band partially polarized optical field is developed in terms of the 2-D Period-Averaged Probability Density Function (PA-PDF) of the electrical field vector. This statistic can be measured using the coherent (heterodyne) detection. PA-PDF carries more information about the partially-polarized light than the traditional Stokes vector. For a simple Gaussian partially polarized field the PA-PDF depends on 13 real parameters in contrast to the four parameters of the Stokes vector or coherence tensor

physics.optics↗