1. An automated method for constructing a composite image having an authentication image formed therein, the authentication image being viewable by placement of a decoder lens having a plurality of lens elements defining one or more decoder lens frequencies over an object to which the composite image has been applied, the method comprising: generating a first plurality of component images in which corresponding tonal areas are tonally balanced around at least one tonal value, at least one of the component images being configured to include a representation of the authentication image; determining a pattern of component image elements for each of the component images, the pattern including an element configuration and at least one element frequency that is equal to or a multiple of one of the decoder lens frequencies, the component image elements for a given component image collectively carrying all the content of that component image; extracting at least a portion of the content of each component image element of each component image; and constructing a composite image having a pattern of composite image elements having the at least one element frequency that is equal to or a multiple of one of the decoder lens frequencies, each composite image element including the extracted content from a component image element from each component image in a location in the component image that corresponds to the location in the composite image.