# How does light actually interact with different materials? - PBR

I am a computer graphics guy in the area of physically based rendering and recently I've been searching on the net to figure out how physical is Physically Based Rendering (PBR). The nature of the question lies somewhere between pure physics and pure graphics, so I'm hoping I find a someone familiar with graphics here.

For those who don't know, PBR aims to render the different materials in the same way it actually happens in real life, so it's a more physical approach. This lets us render highly realistic images than other approaches.

I want to check if my understanding is correct about how light actually interacts with different materials.

1. First of all when light first strikes a surface, the Fresnel equations directly come into play and they determine how much light gets reflected and transmitted. This is different for different wavelengths since the index of refraction depends on the wavelength.

2. The transmitted light may travel farther for refractive surfaces or may get absorbed quickly as in the case for metals. The transmitted light may also re-emerge from different positions. This is what we in graphics call "diffuse reflection". The counterpart being "specular reflection" (light just reflects off the surface. Note that the reflection doesn't necessarily have to be in the mirror direction).

3. In graphics we usually define the color of the object through RGB triples. I know this is inaccurate however I'll move on with this assumption. I think that the Fresnel equations are indirectly defining this RGB triple for different surfaces? Since Fresnel reflection is different at different wavelengths, then if we sample at the 3 main wavelengths R, G, B, we are actually getting the amount reflected for each wavelength, which in turn is our color of the object? However the color of the object should be independent of the view direction which clearly isn't the case with my assumption. Can anybody clear out this point?

4. The next difficulty is how much light do rough surfaces like an unpainted wall or wood etc, reflect light diffusely or specularly.

We have 2 parameters which we denote as the reflectivity of the surface. We say a surface might reflect light 60% diffusely ( that is 60% get transmitted then re-emerges) while 40% get reflected specularly. This doesn't need to always add up to 1 since some energy is also lost in the form of heat. We denote both of these parameters as $K_d$ and $K_s$ (diffuse and specular reflectivity).

But doesn't this sound the same as Fresnel reflectance? Basically doesn't $K_d$ seem like the amount of light transmitted (ignoring for the moment that a fraction of transmitted light may get lost in the form of heat) and $K_s$ the amount of light reflected? This implies that these parameters would vary w.r.t viewing direction but We normally set $K_d$ and $K_s$ to fixed value when we are defining the material in graphics or at least that's what I have seen so far.

If $K_d$ and $K_s$ really is the same as Fresnel reflectance, this would mean that rough surfaces such as wood will reflect light specularly when viewed at grazing angles and when viewed head-on, the light coming from the wood into our eye is more that had transmitted into the surface and re-emerged i.e. diffusely. Is this the case in real life as well?

5. Last but not least is the case of reflection.

In PBR we usually have microfacet based models according to which each surface has micro-bumps. From there comes the first important parameter for PBR that is roughness/smoothness. This parameter governs how much the specular reflection is concentrated in a single direction.

(5a) In point 2 I assumed specular reflection meant light just scattering off the surface not necessarily in the mirror direction. Is this true? Or light always reflects in the mirror direction, it's just that it isn't concentrated due to these microfacets?

(5b) This leads me to believe reflections are governed by 2 parameters. How smooth the surface is and how much the light reflects off the surface (specularly). Are there any other parameters that govern why we see reflections on surfaces of different objects?

• You might want to look into the Bidirectional Reflectance Distribution Function – garyp Sep 4 '18 at 16:29
• I have, Actually I have read all those and even written my own path traced renderer. I am consulting PBRT which is considered as one of the best books for PBR. However I just want a more physicist point of view to my questions. PBRT doesn't go into detail about physics. I want to know how thing actually happen in real life and whether the approximations we make in PBR are close to reality or not. – gallickgunner Sep 4 '18 at 16:31

## 2 Answers

On point 3, different frequencies of light get refracted at different angles. If you assume a color is achieved by means of a superposition exact R, G and B frequencies then you will not get the same directions as modelling reflection across a spectrum focused on R, on G and on B. Some of each color is reflected across a range of directions.

Fresnel Equations can be used to define the reflection of R, G and B light frequecies or to bound the reflection angles across a range modelling a spectrum focused on each one, if that is what you mean.

The colour of light reflected by an object most certainly does change based upon the colour of the light source and the viewing angle, however human brains learn to take this into account and try to derrive an understanding of the intrinsic colour of the object, which under most conditions with a relatively white/broad spectrum light source is quite successfull. Under, say, an orange light source, distinguishing an orange object from a white one can be difficult. If an abserver happens to align with the angle at which the majority of light form the light source is reflected, the intrinsic color of the object can be overwhelmed by that of the source, and they may observe an image of the source.

On point 4) It is the same effect as Fresnel, but you are modelling Fresnel on a rough surface at which light from the same direction now impacts different parts of the surface at a range of incedence angles.

Point 5a) sounds corrrect that light is always reflected in the mirror direction, but this varies due to "microfacets"

5b) Yes, the challenge is typically to get a model as accurate as possible with as few parameters as possible in order to maximise performance. There is not really a limit to how much detail might be applied, such as modelling individual photons and their quantum interaction with the media - I think that would be far too much for your purposes. However you might want to account for atmospheric scattering, and so called "ambient light" because modelling it by light rays is somewhat intensive.

• When you say correct about point 5a) do you mean reflected rays need not be in the mirror direction? or is it the reverse? – gallickgunner Sep 4 '18 at 17:43
• Also just wanted to add this, you might or might not know but we actually do model ambient light through light rays here in PBR :) I don't know if you already knew that. It's called global illumination and as you said it's a hell lot of an expensive process. – gallickgunner Sep 4 '18 at 17:51
• Calrified point 4. I guess I shouldn't be suprised, given the increasing capability of CPU and probably moreover GPUs. – JMLCarter Sep 4 '18 at 21:06
• I have marked this as answer and added a link. It's Naty Hoffman's paper discussing the basic light matter interaction in more detail presented at SIGGRAPH. It helped me greatly and will help anybody else who stumbles here. Please accept the edit. Thanks – gallickgunner Sep 5 '18 at 19:09
• GALLICKGUNNERS EDIT (did not get voted in) was as follows:- For people with similar questions and doubts [this][1] paper clears most of them. This is Naty Hoffman's presentation/paper describing light matter interactions from the physics and from the graphics side. In case the link gets broken, just search "Background: Physics and Math of Shading by Naty Hoffman" [1]: pdfs.semanticscholar.org/e8e9/… – JMLCarter Sep 5 '18 at 21:12

I can only address your point 3, like the existing answer, which I don't think goes far enough.

If you want to describe a dispersive material with significantly different refractive indices (and therefore significantly different Fresnel reflectivities) at different wavelengths, but your model of color is strictly that of an RGB triplet, then your model is fundamentally handicapped.

In particular, consider a beam of yellow light that hits your material. Should it split up? Should it change colour upon reflection and transmission? Well, it depends! If it is a spectrally pure yellow, then its color will be unchanged by the interaction, but if the beam is a mixture of red and green light, and the red and green components are reflected differently, then the reflected beam will be a different color. However, because your model of the beam is only that of an RGB triplet, you can't tell what the underlying reality is, and you have to fill in information you don't have.

Now, as you said in

I know this is inaccurate however I'll move on with this assumption,

this information clipping is generally a reasonable thing to do (you probably don't want to carry around full spectral information on every light beam in your simulation), but it is important to point out that with respect to your goal here,

how physical is Physically Based Rendering,

this inaccuracy of the RGB model is indeed one place that really does hurt how accurately physical your model can be, when it comes to the interaction with dispersive materials.

• Thanks, we do actually have a separate branch of rendering in PBR which is spectral rendering. There we do take into account of several wavelengths, however in non-spectral rendering which I am concerned with, we just assume the RGB model. Also what about points 1 and 2, I thought the first two ones were more closely related to physics than the other ones :) – gallickgunner Sep 4 '18 at 17:39
• Point 1 looks correct to me. Point 2 looks correct so long as you're not confusing specular reflection with absorption and re-emission. – Emilio Pisanty Sep 4 '18 at 17:41
• Ok about Point 5a. According to Wikipedia specular reflection is always in the mirror direction. My question, is it possible that light may reflect off the surface but not in the mirror direction? i.e. angle of incidence not equals angle of reflection. We used to learn early on that that is the case for rough surfaces, however as I said, that reflection of light rays not in mirror directions for rough surfaces is actually due to absorption and re-emission or so I've heard. Is this true? – gallickgunner Sep 4 '18 at 17:47
• As I said, I'll only address your point 3. I don't have the technical knowledge, nor the time to dig through your extensive text, to go beyond that. – Emilio Pisanty Sep 4 '18 at 18:01