Error correction for rotationally asymmetric surface deviation testing based on rotational shears

We present a practical method for absolute testing of rotationally asymmetric surface deviation based on rotation averaging, additional compensation, and azimuthal errors correction. The errors of angular orders kNθ neglected in the traditional multiangle averaging method can be reconstructed and compensated with the help of least-squares fitting of Zernike polynomials by an additional rotation measurement with a suitable selection of rotation angles. The estimation algorithm adopts the least-squares technique to eliminate azimuthal errors caused by rotation inaccuracy. The unknown relative alignment of the measurements also can be estimated through the differences in measurement results at overlapping areas. The method proposed combines the advantages of the single-rotation and multiangle averaging methods and realizes a balance between the efficiency and accuracy of the measurements. Experimental results show that the method proposed can obtain high accuracy even with fewer rotation measurements.