Question about BRDF in smuthi

[马小宙]

Dear All,

The question is, in the example: beam_reflection.py, we create a system as you shown in the last part of the paper "SMUTHI: A python package for the simulation of light scattering by multiple particles near or between planar interfaces", is it possible that we can get the BRDF instead of total field of the system which you described in the example?

Hoping to get yours answers.

All the best!

MA Xiaozhou

[Amos Egel]

Dear Ma Xiaozhou,

in principle it is possible to estimate the BRDF of a system based on Smuthi simulations.

There are, however, two complications:

• Finiteness: One needs to make sure the sample is large enough such that finte size effects can be neglected (one option are periodic boundary conditions)
  
• Specular signal: In theory, the specular reflection is only one direction. However, in Smuthi it has a finite width in direction space (in case of Gaussian beam illumination that is the beam divergence and in case of plane wave illumination that is the refraction at the boundary of the sample).The specular part of the reflection therefore needs to be separated from the diffuse background in the simulated far fields.

In the following I give a rough sketch of a path that I have used to evaluate the BRDF of nano-strucutred OLED thin film stacks. See my PhD thesis or this paper (free download from here). The following figures are from that paper.

The steps are:

• Run a simulation with Gaussian beam for fixed incident angle
• Evaluate the initial power P0 of the Gaussian beam
• Evaluate the total far field pattern in the top hemisphere (i.e. reflection)
• Separate the specular part from the diffuse part by definig a ring in direction space that you consider as specular reflection
• Get the specular power P_spec by integrating the total far field in the specular direction ring
• Get the diffuse power per solid angle dP_diff(theta,phi) / dOmega from the total far field outside the specular ring

I think the BRDF is then 1/P0 1/cos(theta) dP_diff(theta,phi) / dOmega. Please double check the cos(theta) factor, I am not so sure about it. (The definition of a BRDF always gets me confused.)

You can then

• Vary the incident direction to cover all incident directions of your BRDF
• Maybe you want to average over different random realizations to get information about the statistical uncertaincy in your estimation.
  

If you need further advice, don't hesitate to ask back. However, a full demonstration script of how to calculate the BRDF with Smuthi would be a lot of effort, which is why I cannot offer that for free. Maybe a paid consulting assignment could be an option.

Cheers, Amos

--
Smuthi project repository: https://gitlab.com/AmosEgel/smuthi
Online documentation https://smuthi.readthedocs.io/en/latest/
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