Fractional Montgomery effect: a self-imaging phenomenon

Self-imaging means image formation without the help of a lens or any other device between object and image. There are three versions of self-imaging: the classical Talbot effect (1836), the fractional Talbot effect, and the Montgomery effect (1967). Talbot required the object to be periodic; Montgomery realized that quasiperiodic suffices. Classical means that the distance from object to image is an integer multiple of the Talbot distance Z(T) = 2p2/lambda, where p is the grating period. Fractional implies a distance that is a simple fraction of Z(T): say, Z(T)/2, Z(T)/4, 3Z(T)/2.... We explore the most general case of the fractional Montgomery effect.