Successive order, multiple scattering of two-term Henyey-Greenstein phase functions

Pfeiffer, Nick; Chapman, Glenn H.

doi:10.1364/oe.16.013637

Cited by 30 publications

(28 citation statements)

References 6 publications

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“…As discussed by many Authors [5,7], OTHG is suitable for the fitting of the phase function for biological tissues only at angles smaller than 60°. To overcome this issue, a TTHG can be employed, which is defined as [15,16]:…”

Section: Methodsmentioning

confidence: 99%

Estimation of anisotropy coefficient of swine pancreas, liver and muscle at 1064 nm based on goniometric technique

Saccomandi

Vogel

Bazrafshan

et al. 2014

Journal of Biophotonics

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Optical properties of tissues are required for theoretical modeling of Laser Ablation in tumor therapy. The light scattering characteristic of tissues is described by the anisotropy coefficient, g. The relationship between the angular distribution of scattered light and g is given by the Henyey‐Greenstein (HG) phase function. This work describes the estimation of anisotropy coefficients of ex vivo swine pancreas, liver and muscle at 1064 nm. The intensities of scattered light at fixed angles were measured under repeatability conditions. Experimental data were fitted with a two‐term HG, estimating the anisotropy coefficients for the forward (e.g., 0.956 for pancreas, 0.964 for liver and 0.968 for muscle) and the backward (e.g., –0.481 for pancreas, –0.414 for liver and –0.372 for muscle) scattering.

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Section: Methodsmentioning

confidence: 99%

Estimation of anisotropy coefficient of swine pancreas, liver and muscle at 1064 nm based on goniometric technique

Saccomandi

Vogel

Bazrafshan

et al. 2014

Journal of Biophotonics

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“…To address this, we apply a two-term Henyey-Greenstein (TTHG) function (e.g. Pfeiffer & Chapman 2008;Cahoy et al 2010;Dyudina et al 2016) given by…”

Section: Scattering Of L-packets By Dust and Gasmentioning

confidence: 99%

“…To determine the scattering angle of a TTHG event, the probability of forward scattering is simply given by ζ < α (Pfeiffer & Chapman 2008) after which Eq. (13) with g λ = g a can be used, otherwise the scattering is a backscattering event in which g λ = g b is applied.…”

Section: Scattering Of L-packets By Dust and Gasmentioning

confidence: 99%

Dynamic mineral clouds on HD 189733b

Lee

Wood

Dobbs-Dixon

et al. 2017

A&A

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Context. As the 3D spatial properties of exoplanet atmospheres are being observed in increasing detail by current and new generations of telescopes, the modelling of the 3D scattering effects of cloud forming atmospheres with inhomogeneous opacity structures becomes increasingly important to interpret observational data. Aims. We model the scattering and emission properties of a simulated cloud forming, inhomogeneous opacity, hot Jupiter atmosphere of HD 189733b. We compare our results to available Hubble Space Telescope (HST) and Spitzer data and quantify the effects of 3D multiple scattering on observable properties of the atmosphere. We discuss potential observational properties of HD 189733b for the upcoming Transiting Exoplanet Survey Satellite (TESS) and CHaracterising ExOPlanet Satellite (CHEOPS) missions. Methods. We developed a Monte Carlo radiative transfer code and applied it to post-process output of our 3D radiative-hydrodynamic, cloud formation simulation of HD 189733b. We employed three variance reduction techniques, i.e. next event estimation, survival biasing, and composite emission biasing, to improve signal to noise of the output. For cloud particle scattering events, we constructed a log-normal area distribution from the 3D cloud formation radiative-hydrodynamic results, which is stochastically sampled in order to model the Rayleigh and Mie scattering behaviour of a mixture of grain sizes. Results. Stellar photon packets incident on the eastern dayside hemisphere show predominantly Rayleigh, single-scattering behaviour, while multiple scattering occurs on the western hemisphere. Combined scattered and thermal emitted light predictions are consistent with published HST and Spitzer secondary transit observations. Our model predictions are also consistent with geometric albedo constraints from optical wavelength ground-based polarimetry and HST B band measurements. We predict an apparent geometric albedo for HD 189733b of 0.205 and 0.229, in the TESS and CHEOPS photometric bands respectively. Conclusions. Modelling the 3D geometric scattering effects of clouds on observables of exoplanet atmospheres provides an important contribution to the attempt to determine the cloud properties of these objects. Comparisons between TESS and CHEOPS photometry may provide qualitative information on the cloud properties of nearby hot Jupiter exoplanets.

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“…The two-term Henyey-Greenstein (TTHG) phase function is the composition of two single HG phase functions and is commonly used in situations where the regular HG phase function does not describe the backward component of the actual phase function satisfactory [17,18]. The TTHG phase function [p TTHG θ] is given by Eq.…”

Section: B Two-term Henyey-greenstein Phase Functionmentioning

confidence: 99%

Estimation of the effective phase function of bulk diffusing materials with the inverse adding-doubling method

Leyre¹,

Meuret²,

Durinck³

et al. 2014

Appl. Opt.

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The accuracy of optical simulations including bulk diffusors is heavily dependent on the accuracy of the bulk scattering properties. If no knowledge on the physical scattering effects is available, an iterative procedure is usually used to obtain the scattering properties, such as the inverse Monte Carlo method or the inverse adding-doubling (AD) method. In these methods, a predefined phase function with one free parameter is usually used to limit the number of free parameters. In this work, three predefined phase functions (Henyey-Greenstein, two-term Henyey-Greenstein, and Gegenbauer kernel (GK) phase function) are implemented in the inverse AD method to determine the optical properties of two strongly diffusing materials: low-density polyethylene and TiO₂ particles. Using the presented approach, an estimation of the effective phase function was made. It was found that the use of the GK phase function resulted in the best agreement between calculated and experimental transmittance, reflectance, and scattered radiant intensity distribution for the LDPE sample. For the TiO₂ sample, a good agreement was obtained with both the two-term Henyey-Greenstein and the GK phase function.

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Successive order, multiple scattering of two-term Henyey-Greenstein phase functions

Cited by 30 publications

References 6 publications

Estimation of anisotropy coefficient of swine pancreas, liver and muscle at 1064 nm based on goniometric technique

Estimation of anisotropy coefficient of swine pancreas, liver and muscle at 1064 nm based on goniometric technique

Dynamic mineral clouds on HD 189733b

Estimation of the effective phase function of bulk diffusing materials with the inverse adding-doubling method

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