Holographic optical elements (HOE) have classically been designed using grating theory [ E.B.-Champagne, J.Opt.Soc.Am. 57,51(1967)]; logically so, since an HOE is a grating produced on film by two interfering beams of coherent light. This paper describes an equivalent refracting lens, which exactly duplicates the focusing properties of an HOE. This analog allows optical systems containing holographic optical elements to be completely designed with a common lens design computer code. The thickness of the analogous lens approaches zero and its index approachs infinity. In this paper the ray tracing equations for a thin lens are specialized to the infinite index case. The resulting equation has exactly the same form as the diffraction equation; thereby verifying the analog. The analogous lens for a grating a curved mirror is also described.
© 1979 Optical Society of America
William C. Sweatt, "Mathematical equivalence between a holographic optical element and an ultra-high index lens," J. Opt. Soc. Am. 69, 486-487 (1979)