Polarization #2: Emissive Polarization

The Simple atmosphere model was used in this simulation. It provides the simulation with a uniform sky with an unpolarized apparent temperature of 250 K. Note that scattering is what leads to polarization in the atmosphere and scattering in the LWIR is very low. Hence, an unpolarized atmosphere is not an unreasonable approximation.

The scene is constructed using DIRSIG’s built-in geometry primitives. Specifically, three SPHERE objects are created in the sphere.odb file. The left, center and right spheres are assigned temperatures of 360 K, 320 K and 0 K, respectively. The spheres hover above a GROUND_PLANE object that is also assigned a temperature of 320 K. All three objects are attributed with the same "glossy black paint" material.

The "glossy black paint" material uses the ShellTarget polarized BRDF (pBRDF) model. The pBRDF can be hemispherically integrated to arrive at a polarized directional hemispherical reflectance (pDHR) for a given viewing geometry. For that same view geometry, the polarized directional emissivity (pDE) can be computed as pDE = 1 - pDHR. Hence, the pBRDF models commonly used in the reflective wavelength regions can also be employed to compute polarized emission in the thermal wavelength regions. The material is configured with the Generic radiometry solver, which is required for polarization simulations because it accounts for the local/global polarization orientation transforms when scene surfaces are not parallel to the Earth. The details of the material configuration can be found in sphere.mat.

The camera for this scenario is a simple 320 x 240 (QVGA) format array. The focal plane is sensitive from 8 - 12 microns, with a spectral flat response. Rather than output a single radiance band image, DIRSIG has an option to generate "Stokes Vector" output for a given band. Although there is not a direct method to perform this task in the real world (a combination of 3 or more linear and circular polarizations must be used to estimate the Stokes Vector), this option allows the user to quickly observe polarization phenomenology. When this option is enabled in the Polarization tab of the channel configuration the output is a 4-band Stokes Vector set (SO, S1, S2 and S3) for that spectral channel.

The output of the simulation is a 4-band image cube. The 4 bands are a result of the special "Stokes Vector" output produced by DIRSIG.

The S0 image below depicts the three spheres (the "hot", "warm" and "cold" spheres on the left, center and right, respectively). Basic unpolarized radiometric phenomenology can be observed in the relative contrast of the two spheres and their reflections in the background plate they are positioned over. Although the "hot" sphere and background plate are the same temperature, the leaving radiance for the background is lower because the directional emissivity is much lower at the view angles it is observed at. Also note that the reflection of the nearby sphere can be seen in the adjacent sphere.

The S1 and S2 images capture the linearly polarized radiance. Due to Kirkoff’s Law, the polarization orientation of emitted and reflected radiation are opposite. The contrast patterns across the surface of the spheres are due to the orientation of the radiation leaving the sphere. In the case of the "hot" sphere (dominated by emission) the polarization leaves the sphere parallel to the surface. The "cold" sphere (dominated by reflection) the polarization leaves the sphere normal to the surface. Therefore, the orientation of polarized energy for the two warmer spheres is the opposite of the colder sphere. This can be observed in the relative contrast patterns around the edge of the spheres in the S1 and S2 images.

The Polarization truth was enabled for this simulation, which produces the following truth images bands:

The degree of polarization (DoP) image is shown below. Remember that the DoP describes what fraction of the signal at a given location is polarized and does not capture the absolute magnitude of the total radiance. Even though the "cold" sphere has a lower total radiance, the radiance from this object has a significantly higher DoP because it is dominated by reflected radiance (the emission is 0 due to the temperature being 0 K) and the reflectance is highly polarized. In contrast, the "hot" sphere is emitting polarized radiance at 320 K and reflecting polarized radiance from 320 K backgrounds. As a result, some of the linearly polarized reflected radiance is "washed out" by the linearly polarized emissive radiance because these linear polarizations are orthogonal.

The angle of polarization (AoP) is heavily influenced by the surface geometry and the relative magnitude. Because the angles range from -90 to 90, scaling the angles for display results in some discontinuities where the angle quickly jumps from +90 to -90 degrees (which, is actually a continuum if the angles were not limited to this range).