This work presents a study of variance to rotation key encryption processors based on the Fourier transform. It was determined that the key in rectangular coordinates allows a tolerance level of less than 0.2 degrees of rotation of the key in the decryption process. Thus, the solution is to build the key in polar coordinates, by means of circular harmonics expansion; in this way, the tolerance threshold rises to about 40 degrees of rotation of the key in the decryption process. This solution is an added value for optical encryption processors. I have developed a computational tool for simulations and results obtained in this study.