An apparatus for web monitoring in paper making machines comprises a row of two or more lookers (6, 8) which are spaced across the width of the moving paper web. Each looker is stationery, and continuously inspects one or more small areas of the web as the web passes beneath. Optical signals from each individual inspection area are digitized, and spatial filtering is used to remove from the signals the effects of variations in the web which are much larger or much smaller than the variations being studied. A number of power spectra are calculated from the spatially filtered signals, and analysis of these functions is then used to identify significant features. Plots or tables of such features can be used to provide detailed information for the machine operator on the types of variations that are occurring in the paper web, and the possible causes of these variations.