Monte Carlo implementation of Schiff׳s approximation for estimating radiative properties of homogeneous, simple-shaped and optically soft particles: Application to photosynthetic micro-organisms

- Radiative properties of axisymmetric, homogeneous, soft particles are studied.
- The model is Schiff׳s approximation or anomalous diffraction approximation.
- The integral formulation is solved using an original Monte Carlo algorithm.
- Comparisons with T-Matrix results are presented.
- Our approach opens perspectives for particles with more complex shapes.

In the present paper, Schiff׳s approximation is applied to the study of light scattering by large and optically-soft axisymmetric particles, with special attention to cylindrical and spheroidal photosynthetic micro-organisms. This approximation is similar to the anomalous diffraction approximation but includes a description of phase functions. Resulting formulations for the radiative properties are multidimensional integrals, the numerical resolution of which requires close attention. It is here argued that strong benefits can be expected from a statistical resolution by the Monte Carlo method. But designing such efficient Monte Carlo algorithms requires the development of non-standard algorithmic tricks using careful mathematical analysis of the integral formulations: the codes that we develop (and make available) include an original treatment of the nonlinearity in the differential scattering cross-section (squared modulus of the scattering amplitude) thanks to a double sampling procedure. This approach makes it possible to take advantage of recent methodological advances in the field of Monte Carlo methods, illustrated here by the estimation of sensitivities to parameters. Comparison with reference solutions provided by the T-Matrix method is presented whenever possible. Required geometric calculations are closely similar to those used in standard Monte Carlo codes for geometric optics by the computer-graphics community, i.e. calculation of intersections between rays and surfaces, which opens interesting perspectives for the treatment of particles with complex shapes.