We propose a phase-retrieval method based on the numerical optimization of a new objective function using coherent phase-diversity images as inputs for the characterization of aberrations in coherent imaging systems. By employing a spatial light modulator to generate multiple-order spiral phase masks as diversities, we obtain an increase in the accuracy of the retrieved phase compared with similar state-of-the-art phase-retrieval techniques that use the same number of input images. We present simulations that show a consistent advantage of our technique, and experimental validation where our implementation is used to characterize a highly aberrated 4F optical system.