First and second patterns are formed on a substrate. A spatial offset between the patterns is determined, and stored for later use in authenticating the substrate. (One or both of the patterns may convey steganographic information. One pattern may be printed, while the other may be embossed.) A smartphone can sense these patterns, determine the spatial offset, and check whether the determined offset matches the earlier-stored offset, to judge whether the substrate is authentic. Another arrangement effects serialization of product packaging by use of paired patterns (at least one of which is typically a watermark pattern) applied in a manner causing a spatial offset between the patterns to progressively vary along a length of a printed web. Still other arrangements involve substrates conveying patterns that degrade over time, e.g., indicating freshness or pressurization condition. A great variety of other features and arrangements are also detailed.