New physical quantities for radar and update on IOR for camera and lidar

[matteomarone]

-) The Index of refraction (IOR) was restructured for better gltf reprocessing. Dependency on temperature more readable.
-) Permittivity, permeability, and conductivity were added to extend the project towards radar sensor implementation. These quantities can be defined as a function of wavelength and temperature.

[LudwigFriedmann]

Hi @matteomarone. thanks for the comprehensive PR! In issue #4, we're discussing the (functional) relationship between index of refraction, permittivity and permeability.
Especially, parallel implementation of the complex IOR and the (complex) permitivity seems to be somehow redundant and therefore error-prone.
Because of the much wider distribution and availability of IOR data, we would tend to use these values and remove permittivity from the specification (i.e. leave it open to the implementation to derive these values). What do you think?

[LudwigFriedmann]

1. Restructuring of IOR (see Remove literals #3 ) would require change in documentation, schemes and the pathtracer/raytracer (glTF parsing)
2. The direct relationship between IOR and permittivity is probably only valid for the optical range and for non-magnetic materials. In this case, IOR, permittivity and permeability would not be related in a consistent manner and therefore have to be specified independently. This would be contradictive to refractive index, permittivity and permeability #4
3. The look-up tables for permittivity, permeability, and conductivity (non-complex) are structured based on the proposal for IOR (1.) again, documentation, schemes and the pathtracer/raytracer (glTF parsing) have to be adopted. On top, the extension OpenMaterial_material_parameters has to be adopted since relative_permittivity, relative_permeability require references to look-up tables. A look-up table for emissivity already exist. Conductivity is not yet incorporated in OpenMaterial_material_parameters. Again, a reference to the look-up table has to be added.

[hschoen]

@LudwigFriedmann : You write "The direct relationship between IOR and permittivity is probably only valid for the optical range and for non-magnetic materials. " I am not aware that the physical laws for IOR and permittivity are restricted to a certain frequency range. Before we make a distinction between regimes and materials we need a trustworthy source to rationalize this.

[matteomarone]

@hschoen @LudwigFriedmann In the optical range and for non-magnetic materials we can simply assume that the permeability ~1. In this way the formula n=sqrt(epsilon_r*mu_r) becomes a 1:1 dependency n=epsilon_r. For the radar and magnetic material the generic formula still stands, but it would not be possible to derive simultaneously the permittivity and permeability directly from the IOR, only their product.

[LudwigFriedmann]

Hi @hschoen and @matteomarone ,
I think we all agree there's a wide range for (relative) permeability μ_r (see https://en.wikipedia.org/wiki/Permeability_(electromagnetism).

The following cases can be distinguished (https://de.wikipedia.org/wiki/Magnetische_Permeabilit%C3%A4t):

• Diamagnetic Materials 0 <= μ_r < 1
• Paramagnetic Materials μ_r > 1
• Ferromagnetic Materials μ_r >> 1

As an example, for iron, the temperature-related range of μ_r is 300…10.000.

Now according to https://en.wikipedia.org/wiki/Refractive_index, generally, for electromagnetic radiation, the following condition is true:

n=sqrt(ε_r * μ_r)

(n being the complex refractive index, ε_r complex relative permittivity and μ_r complex relative permeability)

Obviously, for values of μ_r close to 1, this simplifies to

n=sqrt(ε_r)

Nevertheless, the relation in its general form is true at all times, or did I miss something?

So we need two of the three complex values in the data to derive the third one....

[LudwigFriedmann]

As the wiki page https://en.wikipedia.org/wiki/Refractive_index states, "the refractive index is used for optics in Fresnel equations and Snell's law; while the relative permittivity and permeability are used in Maxwell's equations and electronics". I think both user groups have their favorites. Nevertheless, I would rather rely on converters than write 3 directly dependant parameters into the materials.

[matteomarone]

@LudwigFriedmann Yes, the general relationship between IOR and (permittivity*permeability) is valid regardless the frequency, and simplified when mu_r is close to 1.
You are also suggesting to write a converter but in such a case it would only work in one direction (μr and εr -> IOR). If you only have the IOR you cannot derive the other two separately (just the product), and for the sensors there might be some models where the knowledge of the single μr,εr is mandatory.
I guess that the case where you have IOR and one between μr and εr is not that common. In most of the cases you have either the IOR or the other two (at least this is my small experience. As you said IOR is typically used/measured in optics while the other two with the Maxwell equations/electronics. Or do you have a different opinion on that?)

[hschoen]

@matteomarone, @LudwigFriedmann I don't think we have a problem: If we want to derive εr from IoR we simply need to know additionally μr.

[LudwigFriedmann]

Hi @matteomarone, concerning your proposal for conductivity, for the sake of reusability in implementation (i.e. interpolation algorithms), can we restructure the data to key value pairs of wavelength and conductivity (like IOR re/im part)?

[matteomarone]

Hi @LudwigFriedmann yes I agree, we can restructure the conductivity to match the IOR