The present disclosure relates to specification, optimization and matching of optical systems by use of orientation Zernike polynomials. In some embodiments, a method for assessing the suitability of an optical system of a microlithographic projection exposure apparatus is provided. The method can include determining a Jones pupil of the optical system, at least approximately describing the Jones pupil using an expansion into orientation Zernike polynomials, and assessing the suitability of the optical system on the basis of the expansion coefficient of at least one of the orientation Zernike polynomials in the expansion.