Blurry reflectors, such as partially polished metals, can be approximated by accumulating several reflected images for which the reflected surface normal is perturbed according to the reflected ray distribution. This distribution can be sampled from a BRDF, for example.
For planar surfaces, the eyepoint is perturbed to simulate the perturbed normal. In this way, objects close to the mirror remain sharp while objects farther away are more blurred, which is what the viewer expects.
Similar techniques may be applied for curved reflectors and refractions.
Care must be taken to render enough samples to reduce visible error, otherwise reflected images tend to appear only like several images overlaid. The accumulation buffer may be used to average several reflection images before copying to texture in the texturing algorithm presented above.