Matched filters with signal-to-noise ratios that are space-invariant and rotation-invariant with respect to the target have been developed. Our approach has been to extract from the target one or more circular harmonic components and to use a filter matched to these components. The technique has been implemented both digitally and with an optical processor using com-puter-generated holograms. To discriminate between objects that are almost similar, a pseudo-object is used to generate the matched filter. The technique was introduced previously as an ad hoc method; a more systematic approach based on system constraints suggests the existence of other rotation-invariant linear filters.