This paper is concerned with the construction of optimal filters for smoothing the photon noise that arises under low-light conditions in vision and under low-dose or short-exposure conditions in nuclear medicine. In the case of vision, the paper explores the hypothesis that the retina functions as an optimal filter. The consequences of this hypothesis for light adaptation are studied. In the case of nuclear medicine, a method for constructing optimal filters is introduced, and the method is tested by computer simulation.