Diffractive optical elements are ultra-thin optical components required for a variety of applications because of their high design flexibility. We introduce a gradient-based optimization method based on a step-transition perturbation approach which is an efficient approximation method using local field perturbations due to sharp surface profile transitions. Step-transition perturbation approach be available to calculate the gradient of figure of merit straightforwardly, we implemented optimization method based on this gradient. This fast and accurate inverse design creates binary (2-level) diffractive elements with small features generating the wide angle beam arrays. The results of the experimental characterization confirm that the optimization based on the perturbation method is valid for 1-to-117 fan-out grating generating beam pattern of linear array.