Study of the aberration induced by an array of microlenses

Microlens arrays are often used to give an image array of a single light point source. Then the parts of the wavefront which are transmitted by each lens are mutually coherent and the spatial amplitude in the focal plane of the array is the sum of the individual contributions of every lens. The total image, that is the intensity spread function of the array, is thus different from the sum of the individual intensity spread functions of the lenses. Geometrically and photometrically this causes a kind of aberration because the main intensity maxima are shifted and have different values. So their contained energies are also different. The effect, which is existing for all shapes and distributions of lenses, are more easily predictable in the case of an array of square contiguous lenses because their own amplitude contribution in the focal plane contains which are periodically distributed in two orthogonal directions. The problem is studied in terms of the number of these zeros inside the step of the array. This number is proportional to the normalized phase difference between the pole and the corner of the lens. The authors also study the case of a partially used array as it is the case with an atmospheric wavefront sensor associated with a centrally obturated reflecting telescope.