A method is provided for constructing a composite image having an authentication image formed therein. The authentication image is viewable using a decoder lens having one or more decoder lens frequencies. The method comprises 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 is configured to include a representation of the authentication image. The method further comprises determining a pattern of component image elements for each of the component images. The pattern having at least one element frequency that is equal to or a multiple of a decoder lens frequency. At least a portion of the content of each component image element is extracted and used to construct a composite image element.