Catadioptic deep ultraviolet lithography objective took the mirror as active free-form surface to compensate thermal aberration. Mirror in compliance with the requirements of the system optical path had a rectangular aperture. For the purpose of describing the active deformation of mirror, it’s necessary for orthogonal polynomials in rectangle zone to fit the deformation data. For high accuracy of fitting surface deformation, it was needed to obtain higher order polynomial expressions. According to the properties of orthogonal polynomials, rectangular orthogonal polynomials formula was derived and the first 36 polynomial expressions were listed. And the polynomials were applied to fit the deformation data of active free-surface. The results showed that the minimum fitting residual error RMS is 0.024 nm when the deformation is 2 nm~5 nm in RMS. According to the characteristic of fitting residual map, the structure design of the active free surface could be improved.