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Some options are available only in Advanced mode.

Opacity^* – Specifies how opaque or transparent the material is. A texture map can be assigned to this channel. 

Custom Source – When enabled, V-Ray uses an alpha channel to control the material opacity. 

Diffuse Texture Alpha – The diffuse texture alpha channel controls the opacity. Diffuse Texture Alpha source works the same way as Diffuse Map Alpha as Transparency legacy option from the V-Ray versions before 3.60. 
Opacity Texture Alpha – The opacity texture alpha channel controls the opacity, instead of the default texture intensity. If there is no texture in the source slot, the option is ignored. 

Mode – Controls how opacity is sampled.

Clip – (Very fast) The surface is shaded as either fully opaque or fully transparent depending on the value of the opacity map (i.e. without any randomness). This mode also disables the filtering of the opacity texture. This is the fastest mode but it may increase flickering when rendering animations.
Stochastic – (Optimal) The surface is randomly shaded as either fully opaque or fully transparent so that on average it appears to be with the correct transparency. This mode reduces lightning calculations but might introduce some noise in areas where the opacity map has gray-scale values. The opacity texture is still filtered as normal.