Mathematical Fundamentals

Egan, Walter G.; Hilgeman, T.

doi:10.1016/b978-0-12-232650-9.50005-9

Cited by 17 publications

(25 citation statements)

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“…It is also likely that some, if not all, of the absorption reported above for soluble aerosol is spurious, an artifact of absorption measurements on scattering media, and some of the work cited above has been criticized for such an oversight [Bergstrom, 1973;Egan and Hilgeman, 1979]. Accordingly, we will treat the soluble material in the composite particles as nonabsorbing sulfate compounds.…”

Section: Reported Absorption By the Soluble Atmospheric Aerosol Fractionmentioning

confidence: 80%

Effects of mixing on extinction by carbonaceous particles

Fuller¹,

Malm²,

Kreidenweis³

1999

J. Geophys. Res.

535

492

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Section: Reported Absorption By the Soluble Atmospheric Aerosol Fractionmentioning

confidence: 80%

Effects of mixing on extinction by carbonaceous particles

Fuller¹,

Malm²,

Kreidenweis³

1999

J. Geophys. Res.

535

492

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“…where Rf and ma, are the reflectance and the frequency of the last measured data point, respectively, and E is an adjustable exponent, typically taking on a value between zero and four. Above WA = 10 X 106 cm', free-electron behavior (11) R(W) = Rf'(wA/w) 4 was assumed.' 3 '1 5 Here Rf' is defined as…”

Section: High-frequency Extrapolationmentioning

confidence: 99%

Method for the determination of the optical properties of highly conjugated pigments

1993

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Measurements of the near-normal solid-state-pellet reflectance of five commercially available color pigments are used to calculate the frequency-dependent complex index of refraction with the Kramers-Kronig relationship. Although it is conceptually simple, the Kramers-Kronig analysis is very sensitive to the choice of extrapolation constants that describe the reflectance behavior outside the accessible frequency range, especially in the ultraviolet. We develop a method to obtain accurate optical property data in the visible region by minimizing the difference between the absorbance calculated from the refractive index and the separately measured absorption spectrum through an appropriate choice of the high-frequency extrapolation exponent. Root-meansquare differences as low as 3% can be achieved.

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“…where the internal reflection r d is given by [26] r d = −1.4399n −2 + 0.7099n −1 + 0.6681 + 0.0636n. Let us consider the corresponding surface Green's function G s (r, t; ρ , s), which satisfies Eq.…”

Section: Diffusion Theorymentioning

confidence: 99%

A Hybrid Inversion Scheme Combining Markov Chain Monte Carlo and Iterative Methods for Determining Optical Properties of Random Media

et al. 2019

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Near-infrared spectroscopy (NIRS) including diffuse optical tomography is an imaging modality which makes use of diffuse light propagation in random media. When optical properties of a random medium is investigated from boundary measurements of reflected or transmitted light, iterative inversion schemes such as the Levenberg-Marquardt algorithm are known to fail when initial guesses are not close to the true value of the coefficient to be reconstructed. In this paper, we investigate how this weakness of iterative schemes is overcome by the use of Markov chain Monte Carlo. Using time-resolved measurements performed against a polyurethane-based phantom, we present a case that the Levenberg-Marquardt algorithm fails to work but the proposed hybrid method works well. Then with a toy model of diffuse optical tomography we illustrate that the Levenberg-Marquardt method fails when it is trapped by a local minimum but the hybrid method can escape from local minima by using the Metropolis-Hastings Markov chain Monte Carlo algorithm until it reaches the valley of the global minimum. The proposed hybrid scheme can be applied to different inverse problems in NIRS which are solved iteratively. We find that for both numerical and phantom experiments optical properties such as the absorption and reduced scattering coefficients can be retrieved without being trapped by a local minimum when Monte Carlo simulation is run only about 100 steps before switching to an iterative method. The hybrid method is compared with simulated annealing.

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Mathematical Fundamentals

Cited by 17 publications

References 0 publications

Effects of mixing on extinction by carbonaceous particles

Effects of mixing on extinction by carbonaceous particles

Method for the determination of the optical properties of highly conjugated pigments

A Hybrid Inversion Scheme Combining Markov Chain Monte Carlo and Iterative Methods for Determining Optical Properties of Random Media

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