Realization of phase Fresnel lenses by multiple beam interferometry

Multiple interference fringes generated by a Fabry-Perot interferometer are used for realizing phase Fresnel lenses. The authors deal with a parallelism between the decomposition of a spherical wavefront in Fresnel zones and a multiple interference pattern obtained with a FP cavity with specially designed mirrors. In the first section, the authors show that the phase profile of a Fresnel lens can be described as the superposition of pseudo-sinusoidal functions whose amplitude and phase are given by a Fourier decomposition. Synthesis of the Fresnel lens profile can be carried out by multiple interference fringes formed by a FP cavity observed in reflection. The reflection coefficients of the mirrors of the cavity make the amplitude and the phase of multiple waves proportional to the Fourier terms. Experimental results are reported in the second section. Multiple fringe patterns are recorded on bleached holographic plates. The diffraction efficiency of Fresnel lenses thus obtained is 65%.