Design of some achromatic imaging hybrid diffractive-refractive lenses

The authors consider only hybrid singlet lenses composed of a plano-convex or a plano- concave glass lens and of a volume phase holographic optical element (HOE) in dichromated gelatin, coated on the plane surface of the glass lens. A design method is described which combines usual ray-tracing through a refractive lens and, for the HOE, the method of Hasman and Friesem. This latter method is based on a ray-tracing procedure that uses the minimization of the mean-square difference of the propagation vector components between the actual output wave fronts and the desired output wave fronts. Considering the one-dimensional case and a given spectral bandwidth, the authors determine by simulation the image spot sizes, the distortions at the image plane, and the mean-square difference of the propagation vectors. At the end, the results are compared with the performance of the optimal HOE alone, the spherical HOE, the refractive lens alone, and a diffractive system made of two HOEs. In conclusion, the authors discuss the space bandwidth product of the optimal HOE used in the hybrid systems.