Subodh K. Sharma

Role of approximate phase functions in Monte Carlo simulation of light propagation in tissues

We examine the phase function dependence of Monte Carlo simulation for light propagation in biomedical tissues. Two discrete particle tissue models are considered. The model phase functions can be obtained using the Mie theory. Dependence on various approximate phase functions is then examined for fluence, angular variation of diffuse reflectance and diffuse transmittance and their average values. The diffuse reflectance as a function of source–detector separation is also examined. The tissue parameters varied are the thickness and the constituent particle size and concentration. The results of this study place the use of the Henyey–Greenstein phase function on a firmer footing.

Volume concentration and size dependence of diffuse reflectance in a fractal soft tissue model

Employing a fractal model for the particle size distribution, we examine the possibility of relating the size/volume concentration changes in the tissue to its diffuse reflectance. It is noted that for the practically interesting range of fractal dimension values α, the curves depicting the variation of diffuse reflectance (the ratio of diffuse reflectance at two suitably chosen source detector separations) with α at fixed volume concentration Tv, are single valued. The same is true if α is fixed and Tv is varied. This crucial observation shows that it should be possible to identify changes in the size/volume concentration of the tissue from the diffuse reflectance measurement at two source detector separations when either α or Tv is a priori known. Similar results have been obtained for ratio of fluence measured at two suitably chosen depths within the tissue.

New approximate phase functions: test for nonspherical particles

Abstract In a recent paper, we described two approximate phase functions for the scattering of light by monodisperse particles. One phase function for particles of size small or comparable to the wavelength of scattering radiation and the other for larger particles. Validity of these phase functions was established by comparing their predictions against Mie phase functions. In this paper we examine the validity of these phase functions for monodisperse aligned nonspherical particles. The nonspherical particles employed for examining approximate phase functions are spheroids and infinitely long cylinders. Results show that the predictions of our approximate phase functions are equally valid for nonspherical particles too.

NEW APPROXIMATE PHASE FUNCTIONS FOR SCATTERING OF UNPOLARIZED LIGHT BY DIELECTRIC PARTICLES

Abstract We present two new phase functions, one for particles small compared to the wavelength of the scattering radiation and the other for particles large compared to the wavelength of the scattering radiation. These phase functions have been validated for the case of Mie scatterers. For small particles, the results of the new phase function are found to be identical with the Mie results. For large particles, comparison with the Mie results show that the phase function presented here is an extremely good approximation to the Mie phase function. We believe that these phase functions can be expediently used in problems relating to solutions of the radiative transfer equations.

On the validity of the anomalous diffraction approximation

Abstract The derivation of the anomalous diffraction approximation from Mie theory has been re-examined. The usual requirement ¦m − 1¦ ≪ 1, m being the relative refractive index of the scatterer, is shown to be over-restrictive. A more appropriate requirement is found to be ¦m − 1¦2 ≪ ¦m + 1¦2. The relationship between the anomalous diffraction approximation and another m→1 approximation, namely the eikonal approximation, has been investigated.

Use of Monte Carlo simulations for propagation of light in biomedical tissues.

In problems relating to light propagation in biomedical tissues, the tissue is generally modeled as a turbid medium and Monte Carlo (MC) simulation is employed to compute quantities such as diffuse reflectance, fluence, and transmittance. Two prescriptions are available in the literature for MC simulations. The first prescription considers all input quantities, including phase function, as an average over the particle size distribution, and the second prescription considers the phase function of each scatterer individually. The two prescriptions have been compared and contrasted in this paper for a given soft tissue model. It is demonstrated that, in general, the two recipes do not yield identical results. The source of this disagreement has been traced.

A simple analysis of the extinction spectrum of a size distribution of Mie particles

In the context of the inverse scattering problem in optics, the extinction spectra generated by smooth size distributions of Mie particles are analysed. It is seen that an extinction spectrum, in general, has some easily identifiable characteristic regions where the extinction–frequency relationship can be approximated by simple empirical formulae involving the first four moments of the particle size distribution function. Also, some remarkable features associated with the symmetric (Gaussian) distributions are observed and explained in this context. This analysis clearly exhibits the manner in which essential features of a particle size distribution gets coded into its extinction spectrum.

Absorption and scattering of electromagnetic radiation by a large absorbing sphere with highly absorbing spherical inclusions

Abstract An approximate formula based on geometrical optics approximation has been examined for the scattering of light by a sphere with highly absorbing inclusions in it. The validity of an equivalent refractive index formulation has also been examined. Numerical comparisons demonstrate these to be useful in predicting the absorption efficiency, asymmetry parameter and albedo of the sphere. The investigation considers frequencies for which the host medium is absorbing.

Validity of a modified Born approximation for a pulsed plane wave in acoustic scattering problems.

The validity domain of a modified Born approximation (MBA) has been examined for the scattering of a pulsed plane wave (PPW). This new approximation has been compared with exact results and also with the conventional Born approximation (BA). Comparisons have been made for the scattering by a homogeneous sphere. Error charts have been presented for various scatterer sizes and acoustic properties for forward as well as back scattering. The pulse width has also been varied. Our study shows that the modified Born approximation is generally preferable to the conventional Born approximation in the forward direction. In the backward direction both approximations have a similar kind of validity domain. These observations are important in view of the fact that the Born approximation has been widely used in acoustic scattering problems.

On the validity of soft particle approximations for the light scattering by a homogeneous dielectric sphere

Abstract The validity of various soft particle approximations has been examined for the scattering of light by a homogeneous dielectric sphere. A scalar analogue of the S-approximation has been presented. It is shown that this much simpler approximation could be nearly as good as the sophisticated S-approximation itself. Numerical results for the extinction and the scattered intensities are examined over a wide refracted index and size parameter domain. The anomalous diffraction approximation has also been included in numerical comparisons.