When ambient light is used, the objects in your scene may appear to be too bright and geometric detail may become lost. Ambient occlusion solves this problem by subtracting ambient light and adding shadowing.
For more information on ambient occlusion, see Ambient occlusion concepts.
Final gather adds details to your scene by adding bounced light. Ambient occlusion, however, adds shadowing to your scene to show surface details.
With ambient occlusion, rays are emitted from the shading point. Final gather, on the other hand, emits rays from special final gather points created during the precomputation phase. The final gather results are then smoothed and filtered.
Ambient occlusion treats semi-transparent objects as if they were opaque. Occlusion rays do not penetrate through these objects. Final gather, on the other hand, uses the trace depth option to determine the number of reflection/refraction bounces that should be traversed through each object.
Of the two, ambient occlusion is easier to use and cheaper to incorporate, particularly if baked to an object. Ambient occlusion is also more predictable because it does not involve bouncing of light; objects only become darker. Final gather involves the bouncing of light, and thus the results can be either brighter or darker.
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