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In RenderMan, you can control the opacity of an object using the Presence Parameter on the materials. Typically designed to work as a 0 or 1 "cutout" effect, values in-between can be used for semi-transparent objects or ghost-like effects.
If using a value between 0 and 1 (or a pattern with middle gray values) you will notice noise by default since we use a stochastic sampling technique. However, integrators allow for smoother effects by specifying a depth in the Stoachastic Opacity Depth parameter. Where each intersection counts as a depth limit. This will be explained below.
The simplest example is that of a leaf. Rather than physically model a leaf which can be painful for the artist and increase geometric complexity in a scene, typically a plane is used to represent the leaf and a map is used to provide the shape. This map is then connected to the Presence Parameter.