We deduce the equation describing the refractive index perturbation in photovoltaic photorefractive crystals produced by the incidence of a focused laser beam and an incoherent uniform illumination. Under short-circuit conditions the equation shows a saturable Kerr-type nonlinearity that can be controlled by the intensity of the uniform background illumination. Z-scan experiments in an iron doped lithium niobate crystal are carried out using a 532 nm wavelength laser line to evaluate its self-lensing properties and to measure its photovoltaic field.782140354038