The present invention relates generally to physical articles, e.g., such as documents, and authenticating physical articles. One claim recites a method of determining authenticity of an analog form (e.g., a printed document such as legal tender, currency or identification documents). The analog form includes a machine-detectable signal represented in printing formed thereon. The signal is based on a rotationally symmetric pattern and is machine-detectable from visible light reading of the analog form, but the signal is imperceptible upon human inspection of the analog form. The method includes acts of: collecting visible light data corresponding to the analog form; transforming the visible light data to a complementary domain; inspecting the transformed data for the rotationally symmetric pattern, wherein presence of said pattern indicates presence of the signal; and taking an action based on presence of the signal. Other combinations and physical articles are provided as well.