镜面对称法绝对测量中的误差补偿方法

Error Compensation Method for Mirror Symmetry Absolute Measurement

提出了一种对镜面对称法绝对测量中的原理性误差进行补偿的方法。镜面对称法绝对测量中,需要旋转其中一块平板,由于旋转次数的有限性,重构的三板波前均存在缺失cNθ项的原理性误差。通过增加一次不同角度的旋转,根据Zernike多项式在极坐标系中形式的旋转不变性,对旋转前后的波前差值求解多项式系数方程,获得了cNθ项的多项式系数,进而对原理性误差进行了补偿。由于cNθ项包含无穷多项,根据精度的需要和计算开销决定补偿的项数。模拟实验证明了该补偿方法的有效性。

A method is proposed to compensate intrinsic error in mirror symmetry absolute measurement. Because of the limitation of rotation times in mirror symmetry absolute measurement, intrinsic error of cNO terms occurs in reconstructed wavefronts of three flats. By adding a rotation with a different angle, the wavefront difference between two measurements before and after rotation is calculated, and the Zernike coefficients of cNO terms can be obtained by coefficient equations due to rotation invariability of the form of Zernike polynomials in polar coordinates. Therefore the intrinsic error of cNθ terms may be compensated. Because the amount of cNθ terms is infinite, the compensated terms are decided in terms of the balance between accuracy and computing capacity. Computer simulation proves the validity of the proposed method.