Designing efficient aberration-free holographic lenses in the presence of a construction–reconstruction wavelength shift

We have derived an analytic procedure for recording a flat, volume-phase-transmission holographic optical element at a wavelength different from that at which it is to be used. The procedure guarantees that the resulting element will have diffraction-limited aberration performance. Furthermore it guarantees, to a first order, that the Bragg condition for high diffraction efficiency will be satisfied. The technique gives simple analytic expressions for the required object and reference construction-beam phases at the element. In general, the object and reference construction beams must be realized by using computer-generated holograms in conjunction with conventional refractive or reflective optics.