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Some options are available only in Advanced mode.

Base material – Specifies the surface material.

Alpha contribution  – Determines the appearance of the object in the alpha channel of the rendered image.

Normal (1) – A value of 1.0 means the alpha channel is derived from the transparency of the base material.
Ignore in Alpha (0) –  A value of 0.0 means the object does not appear in the alpha channel at all and shows the alpha of the objects behind it.
Black Alpha (-1) – A value of -1.0 means that the transparency of the base material cuts out from the alpha of the objects behind. Matte objects are typically given an alpha contribution of -1.0. Note that this option is independent of the Matte surface option (i.e. a surface can have an alpha contribution of -1.0 without being a matte surface).

Ignore Objects in Secondary – When enabled, no other scene project objects are reflected or refracted by this material. All reflection and refraction rays instead sample the corresponding environment color or texture.

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Matte – When enabled, the material appears as a matte material, which shows the background, instead of the base material, when viewed directly. Note that the base material is still used for things like GI, caustics, reflections etc.

Matte for Secondaries – Normally the base material is used when an object with a Wrapper Material is seen through reflections/refractions. When enabled, the Wrapper Material shows the environment when seen through reflections/refractions, and the environment map is projected on the matte geometry.

Disabled – The base material is seen in reflections or through refractions.
Matte for Reflection and Refractions – The material is a matte when seen in reflection or through refractions.
Environment Projection – A material with environment projection is seen in reflections or through refractions.

Affect Other Mattes – When enabled, the object appears as a matte object in reflections, refractions, GI, etc. for other matte objects. Note that if this is on, refractions for the matte object might not be calculated (the object appears a matte object to itself and is not able to "see" the refractions on the other side).

Shadows  – When enabled, shadows are visible on the matte surface.

Affect Alpha  – When enabled, shadows affect the alpha contribution of the matte surface. Areas in perfect shadow produce white alpha, while completely unoccluded areas produce black alpha. Note that GI shadows (from skylight) are also computed. However, GI shadows on matte objects are not supported by the photon map and the light map GI engines when used as primary engines. Those with matte surfaces can be safely used as secondary engines.

Shadow Tint – Specifies a tint for the shadows on the matte surface.

Shadow Opacity – Specifies an optional brightness value for shadows on the matte surface. A value of 0.0 makes the shadows completely invisible, while a value of 1.0 produces the full shadows. 

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Generate GI – Controls the Global Illumination created by the material.

Receive GI – Controls the Global Illumination received by the material.

GI Quality Multiplier – Specifies the quality of GI for specific objects and allows adjustments to the render quality.

Use Irradiance Map – Determines whether the object with this material should use the pre-calculated irradiance map. When disabled, Brute Force primary GI rays is traced instead. The number of samples for this local calculation are controlled by the Irradiance Map Subdivs parameter. The option only has an effect if Irradiance Map is used.

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Generate caustics – – When enabled, the material generates caustics.

Receive caustics – When enabled, the material receives caustics.