Abstract
.Significance: Monte Carlo (MC) light transport simulations are most often performed in regularly spaced three-dimensional voxels, a type of data representation that naturally struggles to represent boundary surfaces with curvature and oblique angles. Not accounting properly for such boundaries with an index of refractivity, mismatches can lead to important inaccuracies, not only in the calculated angles of reflection and transmission but also in the amount of light that transmits through or reflects from these mismatched boundary surfaces.Aim: A new MC light transport algorithm is introduced to deal with curvature and oblique angles of incidence when simulated photons encounter mismatched boundary surfaces.Approach: The core of the proposed algorithm applies the efficient preprocessing step of calculating a gradient map of the mismatched boundaries, a smoothing step on this calculated 3D vector field to remove surface roughness due to discretization and an interpolation scheme to improve the handling of curvature.Results: Through simulations of light hitting the side of a sphere and going through a lens, the agreement of this approach with analytical solutions is shown to be strong.Conclusions: The MC method introduced here has the advantage of requiring only slight implementation changes from the current state-of-the-art to accurately simulate mismatched boundaries and readily exploit the acceleration of general-purpose graphics processing units. A code implementation, mcxyzn, is made available and maintained at https://omlc.org/software/mc/mcxyzn/.
Highlights
The propagation of photons in a Monte Carlo (MC) simulation can be broken down in a few standard steps: propagation, absorption, scattering, and the Fresnel phenomena of transmission and reflection at boundaries, where the refractive index changes.1 When using a rectangular grid structure, the representation of curved, smooth, or slanted boundaries is discretized into voxels, referred to as a Cartesian grid.2 The drawbacks are aesthetic in nature and represent important deviations from the modeled structure
The MC method introduced here has the advantage of requiring only slight implementation changes from the current state-of-the-art to accurately simulate mismatched boundaries and readily exploit the acceleration of general-purpose graphics processing units
The angles of reflectance and transmittance and the corresponding event probabilities are determined through Fresnel equations using the angle of incidence as well as the normal angle to the boundary surface
Summary
The propagation of photons in a Monte Carlo (MC) simulation can be broken down in a few standard steps: propagation (hop), absorption (drop), scattering (spin), and the Fresnel phenomena of transmission and reflection at boundaries, where the refractive index changes. When using a rectangular grid structure, the representation of curved, smooth, or slanted boundaries is discretized into voxels, referred to as a Cartesian grid. The drawbacks are aesthetic in nature and represent important deviations from the modeled structure. When using a rectangular grid structure, the representation of curved, smooth, or slanted boundaries is discretized into voxels, referred to as a Cartesian grid.. The drawbacks are aesthetic in nature and represent important deviations from the modeled structure. The use of a finer grid can partially minimize the differences between the voxel-based representation and the modeled geometry. This works well to improve the precision of the propagation, absorption, and scattering steps; the trade-off being higher memory requirements to store the information and slower simulation performances due to the larger number of elements involved. The deviation addressed in this work is the representation of the surface boundary between
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