Incoherent convergence of diffraction free fields

We describe a method for the synthesis of diffraction free fields by means of an ensemble of optical fields mutually incoherent. The constituent optical fields are generated by controlling the angular correlation function between two points distributed on a circle in the frequency space. The angular position and the separation between the points are considered as random variables. The implicit probability density function allows us to generate diffraction free beams with easily tunable profiles. Inverse problems are also analyzed, which consists in finding the joint probability density function for a known irradiance distribution. Experimental and computational results are shown.