CAJ | 학술논문

基于最小二乘拟合的传统干涉子孔径拼接方法实现了小口径干涉仪对大口径光学元件的检测，然而在子孔径测试过程中，由于干涉仪上的参考面存在面形误差，将使获得的各子孔径的面形数据偏离真实值，所以在进行高精度面形测量时，获得参考面的面形误差并将其补偿掉是非常必要的。因此，提出了一种在拼接过程中用Zernike项对子孔径间重叠区域数据进行拟合的方法来求得参考面面形。首先在传统的目标函数上加入一系列Zernike项表征待求参考面，然后按照最小二乘法对函数进行求解得到各项系数，从而得到拟合的参考面。对平面和球面分别进行了子孔径拼接实验，拟合得到的参考面面形与QED拼接干涉仪计算得到的参考面面形的PV值偏差小于5 nm，RMS值偏差小于0.2 nm，拼接后的重叠区域不匹配误差值小于10 nm。实验结果表明，在子孔径拼接过程中可以补偿参考面误差而得到更真实的拼接面形。
기우최소이승의합적전통간섭자공경병접방법실현료소구경간섭의대대구경광학원건적검측，연이재자공경측시과정중，유우간섭의상적삼고면존재면형오차，장사획득적각자공경적면형수거편리진실치，소이재진행고정도면형측량시，획득삼고면적면형오차병장기보상도시비상필요적。인차，제출료일충재병접과정중용Zernike항대자공경간중첩구역수거진행의합적방법래구득삼고면면형。수선재전통적목표함수상가입일계렬Zernike항표정대구삼고면，연후안조최소이승법대함수진행구해득도각항계수，종이득도의합적삼고면。대평면화구면분별진행료자공경병접실험，의합득도적삼고면면형여QED병접간섭의계산득도적삼고면면형적PV치편차소우5 nm，RMS치편차소우0.2 nm，병접후적중첩구역불필배오차치소우10 nm。실험결과표명，재자공경병접과정중가이보상삼고면오차이득도경진실적병접면형。
Sub-aperture stitching can be used to measure large optical aperture with a relatively smaller aperture interferometer. In the process of sub-aperture testing, if reference surface error is taken into consideration, the stitching result will deviate from truth. As a result, obtaining and compensating reference surface error is necessary. An approach was proposed to obtain and compensate reference surface error by fitting overlap data of each sub-aperture with Zernike terms. A series of Zernike terms were added into traditional stitching function, the form of reference surface that characterized by a Zernike polynomial was obtained by using the least-square method. Experiments had been done on flat and sphere sub-aperture stitching, which were then compared with QED′s result. The deviation of PV and RMS of these two results are less than 5 nm and 0.2 nm respectively. At the same time, the mismatch of stitching aperture is less than 10 nm. Experimental result proves that reference surface error can be compensated in the process of sub-aperture stitching and stitching aperture is more accurate.