Add more detailed definition for BRDF

[DavidJRitter904]

Describe your changes

Added a more detailed definition of the BRDF in the description field based on the references stated in #236 and Hapke.

Issue ticket number and link

#254

Mention a member

@KimuraDIVP @ClemensLinnhoff @lyndyRott @Norihito-Hiruma
Ready for review

Checklist before requesting a review

• I have performed a self-review of my code/documentation.
• My changes generate no new warnings during the documentation generation.

[lyndyRott]

Well done. It makes sense to me to use this definition which refers to an angle pair (collimated ray "input") as opposed to the albedo from remote-sensing, where the incoming direction might not be known or arbitrary and thus the entire half-space is used.

[TimoHinsemann]

Sounds very good, thank you very much! One thing I would like to add to the description - As far as I know, the part "...Could vary from 0 to infinity. It is symmetric in the incoming and outgoing direction, known as the Helmholtz reciprocity principle." is not part of the BRDF-Definition, but means that a BRDF is "physically plausible" (See Montes and Urena: https://digibug.ugr.es/bitstream/handle/10481/19751/rmontes_LSI-2012-001TR.pdf ; Page 3). So a BRDF is physically plausible, when it is non-negative (1), obeys symmetry (Helmholtz Reciprocity) (2) and no more radiant energy is reflected than the incident energy (3).

Thats why I would prefer to add these 3 mentioned properties as "requirements" for a "physically plausible" BRDF, and not the BRDF-Definition. Also we could have a problem with the "symmetry" when it comes to measured BRDFs, which would be another reason to exclude the properties from the BRDF-Definition.

[Norihito-Hiruma]

Thank you so much.
I think it's a very polite and good additional explanation.

[lyndyRott]

Sounds very good, thank you very much! One thing I would like to add to the description - As far as I know, the part "...Could vary from 0 to infinity. It is symmetric in the incoming and outgoing direction, known as the Helmholtz reciprocity principle." is not part of the BRDF-Definition, but means that a BRDF is "physically plausible" (See Montes and Urena: https://digibug.ugr.es/bitstream/handle/10481/19751/rmontes_LSI-2012-001TR.pdf ; Page 3). So a BRDF is physically plausible, when it is non-negative (1), obeys symmetry (Helmholtz Reciprocity) (2) and no more radiant energy is reflected than the incident energy (3).

Thats why I would prefer to add these 3 mentioned properties as "requirements" for a "physically plausible" BRDF, and not the BRDF-Definition. Also we could have a problem with the "symmetry" when it comes to measured BRDFs, which would be another reason to exclude the properties from the BRDF-Definition.

I agree with Timo. To provide the 3 properties makes sense, as it is done in various literature sources. Property (3) could also be shortened to the term "energy conservation", under which it is typically known.

[ClemensLinnhoff]

Okay, @DavidJRitter904 would you add this addition from Timo? Then I think we are ready to merge.

[DavidJRitter904]

Thank you for your feedback!
I have added the three properties for a physical plausible BRDF to the description.
The part with the variation of of the units between 0 and infinity is added as there can be high radiance in exit direction due to arbitrary small irradiance.

I think now we have a very elaborate definition.