A mathematical model that describes the behavior of low-resolution Fresnel lenses encoded in any low-resolution device (e.g., a spatial light modulator) is developed. The effects of low-resolution codification, such the appearance of new secondary lenses, are studied for a general case. General expressions for the phase of these lenses are developed, showing that each lens behaves as if it were encoded through all pixels of the low-resolution device. Simple expressions for the light distribution in the focal plane and its dependence on the encoded focal length are developed and commented on in detail. For a given codification device an optimum focal length is found for best lens performance. An optimization method for codification of a single lens with a short focal length is proposed.
© 1994 Optical Society of America
Original Manuscript: March 1, 1993
Published: January 10, 1994
E. Carcolé, J. Campos, and S. Bosch, "Diffraction theory of Fresnel lenses encoded in low-resolution devices," Appl. Opt. 33, 162-174 (1994)