Many experiments and devices in physics use static magnetic fields to guide charged particles from a source onto a detector, and we ask the innocent question: What is the distribution of particle intensity over the detector surface? One should think that the solution to this seemingly simple problem is well known. We show that, even for uniform guide fields, this is not the case, and we present analytical point spread functions (PSF) for magnetic transport that deviate strongly from previous results. The “magnetic” PSF shows unexpected singularities, which were recently also observed experimentally, and which make detector response very sensitive to minute changes of position, field amplitude, or particle energy. In the field of low-energy particle physics, these singularities may become a source of error in modern high precision experiments, or may be used for instrument tests.