The technique of mapping an array of gray levels to some arrangement of dots such that it renders the desired gray levels is called halftoning. In this research, we present a refinement of our previously proposed new digital halftoning algorithm to achieve this goal based on an approach called the recursive multiscale error diffusion. Our main assumption is that the resulting intensity from a raster of dots is in proportion to the number of dots on that raster. In analogy, the intensity of the corresponding region of the input image is simply the integral of the (normalized) gray level over the region. The two intensities should be matched as much as possible. Since the area of integration plays an important role to how successful the matching of the two intensities can be, and since the area of integration corresponds to different resolutions (therefore to different viewing distances), we address the problem of matching the intensities, as much as possible for every resolution. We propose a new quality criterion for the evaluation of halftoned images, called local intensity distribution, that stems from the same principle i.e., how close the average intensities of the input and output images match for different resolutions. Advantages of our method include very good performance, both in terms of visual quality and when measured by the proposed quality criterion, versatility, and ease of hardware implementation.