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 includes generating two gray-scale component images having tonal areas that are tonally balanced around at least one tonal value. At least one of the two gray-scale component images includes a representation of the authentication image. The method further includes determining a first pattern of the component image elements for the two gray-scale component images, the first pattern including a first element configuration and at least one element frequency that is equal to or a multiple of one of the decoder lens frequencies. The method includes extracting at least a portion of the content from the component image elements of the two gray-scale component images and constructing a composite image having a second pattern of composite image elements.