Аннотация:This work addresses the problem of the calculation of limited-resolution maps from an atomic model in cryo-electron microscopy and in X-ray and neutron crystallography, including the cases when the resolution varies from one molecular region to another. Such maps are necessary in real-space refinement for comparison with the experimental maps. For an appropriate numeric comparison, the calculated maps should reproduce not only structural features contained in the experimental maps but also principal map distortions. These model maps can be obtained with no use of the Fourier transforms but, similar to the density distributions, as a sum of individual atomic contributions. Such contributions, referred to as atomic density images, are atomic densities morphed to reflect distortions of the experimental map, in particular, the loss of resolution. They are described by functions composed from a central peak surrounded by Fourier ripples. For practical calculations, atomic images should be cut at some distance. We show that to reach a reasonable accuracy such distance should be significantly larger than the distance customary applied when calculating density distributions. This is a consequence of a slow rate with which the amplitude of the Fourier ripples decreases. Such large distance means that at least a few ripples should be included in calculations in order to get a map accurate enough. Oscillating functions describing these atomic contributions depend, for a given atomic type, on the resolution and on the atomic displacement parameter values. To express both the central peak and the Fourier ripples of the atomic images, we represent these functions by the sums of especially designed terms, concentrated each in a spherical shell and depending analytically on the atomic parameters. In this work, we analyze how strong the accuracy of resulting map depends on the accuracy of the atomic displacement parameters and on the truncation distance, i.e., the number of ripples included into atomic density images. We complete this analysis by practical aspects of the calculation of the maps of an inhomogeneous resolution.