A newly designed scanning electron microscope with polarization analysis (SEMPA or spin-SEM) for the acquisition of magnetic images is presented. Core component is the spin detector, based on the scattering of low-energy electrons at a W(100) surface in ultrahigh vacuum. The instrument has been optimized with respect to ease of handling and efficiency. The operation and performance of a general low-energy electron diffraction (LEED) detector for SEMPA have been modeled in order to find the optimum operating parameters and to predict the obtainable image asymmetry. Based on the energy dependence of the secondary electron polarization and intensity, the detector output is simulated. For our instrument with optimized performance we demonstrate experimentally 8.6% polarization asymmetry in the domain structure of an iron whisker. This corresponds to 17.2% image contrast, in excellent agreement with the predicted simulated value. A contrast to noise ratio of 27 is achieved at 5 ms acquisition time per pixel.