Effect of host medium absorption on the radiative properties of dispersed media consisting of optically soft particles

Highlights

• The extinction coefficient, scattering coefficient, and phase function of the dispersed medium consisting of optically soft particles are investigated with considering the effect of host medium absorption on particle scattering.

• Neglecting the host medium absorption on particle scattering has a more significant influence on the scattering coefficient than the extinction coefficient in most cases.

• The relative error of scattering coefficients of polydisperse particles is larger than that of monodisperse particles.

• The differences in phase functions obtained by using the conventional Mie theory and modified Mie theory are negligible for particles with small size, but become obvious with the increase of particle size.

Abstract

Light scattering by particles immersed in an absorbing host medium has been an important issue in many fields, such as ocean optics, atmospheric radiation, remote sensing and so on. The traditional theory ignores the effect of host medium absorption on particle scattering, which may result in inaccurate results. In this paper, the scattering coefficient, extinction coefficient and phase function of the dispersed medium consisting of optically soft particles are investigated with considering the effect of host medium absorption on particle scattering. The results are based on the recently developed Mie theory for the absorbing host medium. It is found that neglecting the host medium absorption on particle scattering will result in a small change in extinction coefficients but a great change in scattering coefficients. Meanwhile, the relative error of scattering coefficients caused by using the conventional Mie theory increases obviously with the increase of particle size and the absorption index of the host medium, while the relative error of extinction coefficients fluctuates with the particle size. Moreover, the relative error of scattering coefficients of polydisperse particles is more significant than that of monodisperse particles.

Introduction

Particles with refractive index close to that of the surrounding medium refer to optically soft particles [1]. Radiative transfer in the dispersed medium consisting of optically soft particles plays an important role in many practical applications, such as remote sensing, ocean optics, atmospheric radiation, medicine and so on [2], [3], [4], [5], [6]. To study radiative transfer in such systems, the single scattering properties of particles should be calculated in advance. In general, the effect of host medium absorption on particle scattering is neglected, and the single scattering properties of particles can be derived by the conventional theory of electromagnetic scattering by particles [7,8]. However, there are many situations that the host medium surrounding the particles is absorbing. Some examples are light scattering by cloud particles surrounded by water vapor in the atmosphere, by air bubbles and biological particles in the ocean, by particles in polymers, and many others [9], [10], [11], [12], [13]. In such cases, the conventional theory of electromagnetic scattering by particles must be modified to get accurate results [14,15].

Scattering of light by an isolated spherical particle immersed in a non-absorbing host medium can be exactly solved by using the conventional Mie theory. However, when the host medium is absorbing, the conventional Mie theory need to be modified. Several studies have been carried out to generalize a theoretical treatment of light scattering by spherical particles immersed in an absorbing host medium [15], [16], [17], [18], [19], [20], [21]. Some researchers derived the scattering, absorption and extinction cross sections of an isolate particle by integrating the electromagnetic fields over a conceptual sphere concentric to the particle (i.e., the far field) [17,18]. Unfortunately, the extinction cross section derived by the far field depends on the radius of the integrating conceptual sphere. Therefore, the definition of extinction cross section of an isolate particle immersed in an absorbing medium is confusing. In order to avoid the difficulty in deriving the extinction cross section, Chylek et al. [19] and Sun et al. [20] calculated the single scattering properties of an isolate particle by integrating the electromagnetic fields on the surface of the particle (i.e., the near field). However, the meaning of the single scattering properties derived by this approach is different from that derived by the far field. Therefore, the single scattering properties derived by the near field cannot be applied to the radiative transfer equations [15].

Recently, Mishchenko et al. [22], [23], [24], [25] developed a practical program for the calculation of relevant far-field optical observables in the framework of the conventional Mie theory of light scattering by a spherical particle embedded in an unbounded absorbing host medium. The single scattering properties obtained by this method are able to enter the radiative transfer equation, which makes this method more useful for practical applications. Based on this method, some important results have been obtained [9,10,[26], [27], [28]]. Mishchenko and Dlugach [28] studied the single and multiple scattering of light by particles in an absorbing medium. Ma et al. [9] studied the radiative transfer characteristics with considering the effect of host medium absorption. The results revealed that the conventional theory is not accurate enough for many practical applications, such as particles in polymer coatings, solid dye films and so on. In these studies, the researchers focused mainly on the extinction coefficient and phase function, while the scattering coefficient of the dispersed medium was rarely mentioned. Moreover, the effects of the particle complex refractive index and particle volume fraction on the radiative properties of the dispersed medium need to be further investigated.

In this paper, the scattering coefficient, extinction coefficient and phase function of the dispersed medium are systematically investigated with considering the effect of the host medium absorption on particle scattering. The results are based on the conventional Mie theory for the non-absorbing medium (i.e., Mie theory), and the modified Mie theory developed by Mishchenko et al. [22,23] for the absorbing medium (i.e., modified Mie theory). The effects of host medium absorption index, particle complex refractive index, size parameter and size distribution, and particle volume fraction are discussed.