When the polymethyl methacrylate (PMMA) layer is placed between the gold nanoparticles and gold substrate, we study the effects of metal nanoparticles on the total emission rates and radiative emission rates and far-field radiation pattern of the radiation source of molecular or quantum dots in the PMMA layer. Compared with single gold nanoparticle, when two, three, five and nine gold nanoparticles are put on the PMMA layer with the same distance, the total radiation rates and radiative emission rates are enhanced. By measuring the far-field radiation pattern, the number of nanoparticles and the distance between nanoparticles can be inversely deduced, thus realizing the high precision measurement of nanoparticles.