Modal wavefront reconstruction from slope measurements for rectangular apertures

We present a modal wavefront reconstruction from slope measurements for rectangular optical components of high-power laser systems. Wavefront reconstruction with slope data is an important approach used for wavefront control or correction in high-power systems. In this work, we derive a complete set of orthonormal wavefront slope polynomials for rectangular apertures and describe the modal method for obtaining wavefront representation with the aberration balancing property. Error propagation properties for the modal method are evaluated and compared with the Southwell method. The cross-coupling error is also discussed. Numerical experiments are conducted to illustrate that the modal method can achieve a higher accuracy than the Southwell method. In addition, we also investigate the influence of noise on the modal method compared with that of the Southwell method.