Monte Carlo method of calculating the derivatives of polarized radiation

Ukhinov, S. A.; Yurkov, D. I.

doi:10.1515/rnam.1998.13.5.425

Cited by 6 publications

(8 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Below we describe the general algorithm of the Monte Carlo method for estimation of such functionals in the case of a system of second-kind integral equations [4,5,8,12]. Below we describe the general algorithm of the Monte Carlo method for estimation of such functionals in the case of a system of second-kind integral equations [4,5,8,12].…”

Section: Weighted Vector Estimatesmentioning

confidence: 99%

The Monte Carlo method and analytic averaging for estimation of parameters of polarized radiation asymptotics

Mikhaı̆lov¹,

Tracheva²,

Ukhinov³

2008

Russian Journal of Numerical Analysis and Mathematical Modelling

Self Cite

View full text Add to dashboard Cite

A problem of estimation of parameters of polarized radiation time asymptotics is considered in the paper. Using the Monte Carlo method, precise estimates of such parameters are obtained for a half-infinite layer of a material based on the calculation of parametric time derivatives. For two variants of such problem: with a matrix of aerosol scattering and with a Rayleigh matrix of molecular scattering, it is shown that polarization does not influence the asymptotics of the reflected radiation intensity determining the 'back-scattering noise' in optical probing of material. P(ω ′ , ω) = L(π − i 2 )R(µ)L(−i 1 )

show abstract

Section: Weighted Vector Estimatesmentioning

confidence: 99%

The Monte Carlo method and analytic averaging for estimation of parameters of polarized radiation asymptotics

Mikhaı̆lov¹,

Tracheva²,

Ukhinov³

2008

Russian Journal of Numerical Analysis and Mathematical Modelling

Self Cite

View full text Add to dashboard Cite

show abstract

“…We consider the transport equation, taking into account polarization [2,4] in Ä ½´ µ: ³ ´Üµ ½ Ã ´Ü ¼ Üµ³ ´Ü ¼ µ Ü ¼ · Ë ´Üµ ½ (1.1) or in operator form¨ K¨· Ë, and its adjoint equation in Ä ½´ µ: (1.2) or in operator form¨£ K £¨· À.…”

Section: General Statementsmentioning

confidence: 99%

“…The operator K describes a variation of the vector function¨of the scattered photon density and is the composition of the operators I and C [4]:…”

Section: General Statementsmentioning

confidence: 99%

“…In what follows we mainly consider derivatives with respect to the aerosol scattering cross-section for the calculation of which the following algorithms [4] were used.…”

Section: Calculation Of the Local Characteristics Of Polarized Radiationmentioning

confidence: 99%

“…The conditions for the nonbias and variance finiteness of the estimates´ µ ´Ü £ µ and´ ¼ µ ´Ü £ µ are given by the following assertion [4].…”

Section: Calculation Of the Local Characteristics Of Polarized Radiationmentioning

confidence: 99%

See 2 more Smart Citations

Computation of the parametric derivatives of polarized radiation and the solution of inverse atmospheric optics problems

Ukhinov

Yurkov

2002

Russian Journal of Numerical Analysis and Mathematical Modelling

Self Cite

View full text Add to dashboard Cite

The authors consider problems of calculating the derivatives of polarized solar radiation parameters and the solution of inverse atmospheric optics problems, using the modified double local estimate of the Monte Carlo method in ground-based observations. We study the applicability of the Newton-Kantorovitch iterative process and propose a method based on minimizing the square of the difference norm in the calculated and observed characteristics of polarized radiation.

show abstract

Monte carlo estimate of backscattering noise asymptotics parameters with allowance for polarization

2011

View full text Add to dashboard Cite

Monte Carlo method of calculating the derivatives of polarized radiation

Cited by 6 publications

References 0 publications

The Monte Carlo method and analytic averaging for estimation of parameters of polarized radiation asymptotics

The Monte Carlo method and analytic averaging for estimation of parameters of polarized radiation asymptotics

Computation of the parametric derivatives of polarized radiation and the solution of inverse atmospheric optics problems

Monte carlo estimate of backscattering noise asymptotics parameters with allowance for polarization

Contact Info

Product

Resources

About