Understanding Fresnel Reflections

What we refer to in CG by the term “Fresnel Reflections” or “Fresnel Effect”, is the way Specular Reflection intensity changes according to light \ surface incident angle, and it is a basic optical property surfaces.

Specular reflection intensity changes according to light incident angle, and behaves almost like a perfect mirror at grazing view angle.
The reason we call this natural reflection behavior “Fresnel Effect” or “Fresnel Reflection” is that the equations describing the how reflection intensity changes according to incident angle were invented by the French Physicist Augustin-Jean Fresnel, and in early CG days, not all systems knew how to calculate natural reflections or reflections at all for that matter. So in CG we ended up treating this as something special, when in fact it’s not special in nature, it was just special in the early days of ray-tracing.

When rendering Fresnel Reflections, the reflection intensity isn’t determined by a linear blending percent like mixing a layer.
It’s determined by a factor called “Refractive Index” or “Index Of Refraction” i.e. IOR.
The IOR value is derived from the physical material’s density, which is the key factor determining both reflection intensity and refraction amount.

Examples of some physical IOR values*:
Air (vacuum): 1.0
Water: 1.33
Glass: 1.52
Diamond: 2.417
* Physical values differ between different measurements and samples of materials so you might see differences between different data sources.

This ball is rendered without “Fresnel Reflections”.
Its Specular reflection is blended consistently at 50% over the diffuse color (reflection), not affected by the light/view incident angle.
The result looks wrong for a natural material. It may look like a dielectric material (non metal) that’s coated with a silvery coating, but it can’t look correctly like glossy plastic or glass.

This ball is rendered with “Fresnel Reflections”.
The reflections look natural for a dielectric material (non metal), because they are dim at perpendicular incident angle and intense at grazing view angle, hence seen mostly at the sides of the ball accentuating its contour.

Theoretically Specular Reflection for all types of materials should be calculated using what we refer to in CG by the term “Complex Fresnel”, that is reflection equations that take into account both the Refractive Index (IOR) and Extinction Coefficient for 3 primary colors (spectrum wave lengths).
*Complex Fresnel component values for different materials can be found on https://refractiveindex.info/.
In practice, for Dielectric materials (non metals), most common production rendering systems use what we refer to in CG by the term “Simple Fresnel” or “Simple IOR”, that is calculating the reflection for all 3 primary colors using a single Refractive Index value, which is the surface’s Refractive Index for the Green primary color.
This method has proven itself to be very efficient for rendering non-metallic surfaces (dielectric materials).
Rendering metallic reflection using Complex IOR produces the most realistic color and reflection* for metals.
*In metallic surfaces the color is the reflection color itself and not a separate Diffuse component.
Some rendering systems like Arnold 5 for example have implemented a general form* of Complex IOR into their physical surface shader, Complex IOR reflection can also be rendered via OSL shaders that can be found on the web (or written..).
*I’m using the term ‘general form’ because these implementations don’t include input for Complex IOR values but just a general metallic reflection curve, that interpolates manual color selection.

This golden monkey statue (“Suzanne”) is rendered in Cycles using a Complex Fresnel procedural node:

Popular useful cheats for mimicking metallic reflection without complex IOR are to set a very high (non physical) simple IOR value, like 15 to 30 which forces the Fresnel reflection to become more metal-like, or turn Fresnel reflection completely off, turning the specular reflection into a perfect mirror reflection, or create a custom reflection/angle curve/ramp that produces the effect of the metallic reflection color and intensity changing by incident angle, see example here.

In many popular production renderers, the physical surface shader uses a single IOR parameter. Some rendering systems allow using 2 different IOR parameters, one for calculating reflections and the other for calculating Refraction.
* physically correct dielectric materials should be defined with the same IOR value for both reflections and refraction. using different IOR values for reflection and refraction allows useful cheats like creating transparent a material that is modeled without any thickness or defining a transparent glass that has silver reflective coating like sunglasses sometimes have.

Notes:

1. IOR lists on the web, that display only simple IOR values like this list, are not valid for metals, and produce wrong results.
*Using simple IOR values for dielectric materials however is very efficient.
2. There are parts in the CG industry where in daily slang language, the term “Fresnel” is used to refer to any shading effect that is view-angle dependent,
Usually referring to the shading properties appearing at the “sides” or contours of the model.
3. There are some CG systems that use the term Fresnel to refer to a simple linear or non-linear incident angle blending effect, that should actually be called “Facing ratio” or “Perpendicular-Parallel” blending (falloff).
This is wrong because IOR based Fresnel reflection intensity produces a specific physical Reflection intensity/view angle function curve, and not just a linear or simple power function.
See example in UE4’s Fresnel node.
4. Some PBR rendering systems using implementations of the Disney principled BRDF don’t use a Fresnel IOR input value for dielectric materials, but instead use a simpler 0 – 1 (or higher) Specular input parameter that produces dielectric reflections of approximately 1.0 to ~1.8 IOR value range, which generally covers the range between no reflection at all to common gemstones.
This approach may be inconvenient for rendering artists that are used to setting IOR values, but it has a significant advantage of allowing the usage of an LDR 0 – 1 range (regular image file) texture map for the Specular input, and that way be able to define different material reflections on the same object, rather than having to create a physical IOR map that has encode higher than 1 float values or be mapped to that range at the shading graph.
* See Blender’s Pricipled BSDF and Unreal Engine’s PBR Material.
* Blender’s Principled BSDF actually allows setting Specular values higher than 1 to render material denser than IOR 1.8 (like a diamond for example).
5. Many modern production renderers use Schlick’s Approximation to render Fresnel reflections, a simplified Fresnel formula that is both faster to compute and better suited for microfacet glossy reflection models.

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