DIFFERENTIAL INTERFEROMETRY

干涉法是高精度测量镜面形状的一种典型技术，但它只能得到物体与参考波前的差值，而不能得到绝对形状。在这项研究中，我们提出了微分干涉法来获得反射镜的绝对形状。该方法是测量物体移动前后的两个相位分布，并取它们的差值来减去参考相位的影响。我们使用带板干涉仪进行测量，以减少振动和空气湍流的影响，并使用电光相位调制器来改变相移技术的参考相位。研究结果如下：为了验证该方法的有效性，将其应用于凹面镜半径的测量中，并提出了一种新的光学系统，该系统增加了一个干涉仪来测量平台的倾角，并给出了一个减小倾角误差的公式。对比了垂直于干涉仪光轴平行于干涉仪光轴的物体位移方向，发现后者的精度更高。提出了一种测量抛物面镜形状的方法，该方法将反射镜旋转到曲率中心，而不是直线平移。实验表明，对于半径为1m、直径为100mm的凹面镜，测量凹面镜半径的精度约为0.1%。

Interferometry is a typical technique for high precision measurement of mirror shapes, but one can only get the defference between the object and the reference wavefronts, rather than the absolute shape. In this research, we propose differential interferometry to get absolute shapes of the mirrors.The method consists of the measurement of two phase distributions before and after shifting the object, and taking the difference of them to subtract out the influence of the reference phase. We used a zone plate interferometer for the measurement to reduce the influences from vibration and air turbulence, and employed an electro-optical phase modulator to change the reference phase for the phase shifting technique. The following results are obtained in the research.1.To verify this technique experimentally, it is applied in the measurement of the radius of a concave mirror, and we propose a new optical system with an additional interferometer to measure the inclination of the stage, and an equation to reduce the error due to the inclination.2.We compare the object shifting direction, perpendicular to and parallel to the optical axis of the interferometer, and achieve better accuracy by the latter technique.3.A technique to measure a parabolic mirror's shape is proposed, in which the mirror is rotated to the center of the curvature, instead of linear translation.4.Experiments show the accuracy of the measurement of a concave mirror's radius is about 0.1% for a mirror of 1m radius and 100mm diameter.