All of the BRDF models provided by the SCATMECH library return a Mueller matrix BRDF, ${\bf f}_{\rm r}$, relating the scattered Stokes vector ${\rm d}{\bf \Phi}_{\rm s}$ to the incident Stokes vector power ${\bf \Phi}_{\rm i}$: \begin{equation} {\rm d}{\bf \Phi}_{\rm s}={\bf f}_{\rm r}\cdot{\bf \Phi}_{\rm i}\cos\theta_{\rm s}\;{\rm d}\Omega \end{equation} To obtain reflectance values, the incident Stokes powers should be normalized to unity. The following table describes some suitable incident polarizations:
| Incident polarization | Interpretation |
|---|---|
| (1,0,0,0) | unpolarized incident light |
| (1,1,0,0) | s-polarized incident light, electric field perpendicular to the plane of incidence |
| (1,-1,0,0) | p-polarized incident light, electric field parallel to the plane of incidence |
| (1,0,1,0) | 45° polarized incident light |
| (1,0,0,1) | left-circularly polarized incident light |
| (1,0,0,-1) | right-circularly polarized incident light |
| (1,cosd(2*inpol),sind(2*inpol),0) | linearly polarized incident light at an angle inpol from s-polarized |
To obtain the measured scattered power or the effective BRDF, the reflected Stokes vector is multiplied by a Stokes sensitivity vector ${\bf S}$: \begin{equation} \Phi_{\rm r}={\bf S}\cdot{\bf \Phi}_{\rm r} \end{equation} The Stokes sensitivity must reflect the loss that would be exhibited by a polarizer having the specific sensitivity. That is, a fully polarization sensitive detector will detect only half of unpolarized light incident upon it. Thus, the following table represents polarization sensitivities appropriate for use in MIST:
| Polarization Sensitivity | Interpretation |
|---|---|
| (1,0,0,0) | insensitive to polarization |
| (0.5,0.5,0,0) | sensitive to only s-polarized light |
| (0.5,-0.5,0,0) | sensitive to only p-polarized light |
| (0.5,0,0.5,0) | sensitive to only 45° polarized light |
| (0.5,0,0,0.5) | sensitive to only left-circularly polarized light |
| (0.5,0,0,-0.5) | sensitive to only right-circularly polarized light |
| (1/2,cosd(2*inpol)/2,sind(2*inpol)/2,0) | sensitive to linearly polarized light at an angle inpol from s-polarized |
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Latest MIST Version: 4.10 (October 2017)