It is well known that speckle reduction can be achieved by the noncoherent addition of independent image samples. Sampling can occur at either an image plane or at a Fresnel or Fraunhofer plane of a coherent imaging system. In the literature various comparisons have been made between continuous and discrete sampling methods which take place at a Fraunhofer plane. Because of difficulties in obtaining general closed form expressions in these calculations, no sampling function with optimum characteristics has been specified. This paper shows that continuous sampling at a Fresnel or Fraunhofer plane is precisely equivalent to image plane sampling, provided certain simple criteria are satisfied. This result is valuable since the degree of speckle reduction for a given resolution loss in image plane sampling can be easily calculated and optimized.