A diagnostic apparatus monitors a lithographic manufacturing system. First measurement data representing local deviations of some characteristic across a substrate is obtained using sensors within a lithographic apparatus, and/or a separate metrology tool. Other inspection tools perform substrate backside inspection to produce second measurement data. A high-resolution backside defect image is processed into a form in which it can be compared with lower resolution information from the first measurement data. Cross-correlation is performed to identify which of the observed defects are correlated spatially with the deviations represented in the first measurement data. A correlation map is used to identify potentially relevant clusters of defects in the more detailed original defect map. The responsible apparatus can be identified by pattern recognition as part of an automated root cause analysis. Alternatively, reticle inspection data may be used as second measurement data.