The ideal observer signal-to-noise ratio has been derived from statistical decision theory for all of the major medical imaging modalities. This yields an absolute scale for image performance assessment and instrumentation design and optimization. Applications include: the functional dependence of detectable detail size on exposure or imaging time; a framework for comparing data acquisition techniques, e.g., Fourier methods vs reconstruction from projections in NMR imaging; calculations of realizable limits, e.g., the limiting gain of time-of-flight PET scanning. Measurements on human observers show that they can come close to ideal performance, except when the noise has negative correlations as in images reconstructed from projections. In this latter case they suffer a small but significant penalty.