The usefulness of a lens depends on its imaging performance over its entire field of view. An effective test must measure image quality at off-axis positions, as well as on axis. An automated system is described which quantifies image quality at several different field positions more quickly and precisely than is possible with a manual system. In addition to the Modulation Transfer Function (MTF), the Phase Transfer Function (PTF), field curvature and lens distortion can be measured. Algorithms used to find the off-axis image are discussed in detail, including trade-offs between speed and generality. It is shown that a well designed algorithm must take into account the expected characteristics of the off-axis image, with allowances for uncertainties. The operation of the test system is illustrated with examples.