To provide a comprehensive quantitative model of contrast discrimination, we measured contrast discrimination functions at four mean luminances, four spatial frequencies, three phase relations between tests and pedestal gratings, and two temporal frequencies for the test grating. The results confirm previous findings that the shape of the contrast discrimination function varies with three of these variables but is independent of luminance when each discrimination threshold is divided by the detection threshold for the test grating presented alone. The data in this 5-dimensional space can be described quantitatively if expressed in amplitudes instead of contrasts. The resulting model of visual amplitude sensitivity has seven parameters that are specific to a particular observer and are tied to identifiable visual properties. The "pedestal effect" and tests with the pedestal and test gratings out-of-phase can be explained by subthreshold summation but not stimulus uncertainty. © 1995 Elsevier Science Ltd.