New methods and apparatus for authenticating security documents such as banknotes, passports, etc. which may be printed on any support, including transparent synthetic materials and traditional opaque materials such as paper. The invention is based on moire patterns occuring between superposed dot-screens. By using a specially designed basic screen and master screen, where at least the basic screen is comprised in the document, a moire intensity profile of a chosen shape becomes visible in their superposition, thereby allowing the authentication of the document. If a microlens array is used as a master screen, the document comprising the basic screen may be printed on an opaque reflective support, thereby enabling the visualization of the moire intensity profile by reflection. Different variants of the invention are disclosed, some of which are specially adapted for use as covert features. Automatic document authentication is supported by an apparatus comprising a master scre en, an image acquisition means such as a CCD camera and a comparing processor whose task is to compare the acquired moire intensity profile with a prestored reference image. Depending on the match, the document handling device connected to the comparing processor accepts or rejects the document. An important advantage of the present invention is that it can be incorporated into the standard document printing process, so that it offers high security at the same cost as standard state of the art document production.