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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5nm,RMS值偏差小于0.2nm,拼接后的重叠区域不匹配误差值小于10nm。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。
The traditional interferometric sub-aperture stitching method based on least-square fitting realizes the detection of large-aperture optical components by the small-aperture interferometer. However, in the process of sub-aperture testing, because of the surface shape error of the reference surface on the interferometer, Of the sub-aperture surface shape data deviation from the true value, so the high-precision surface measurement, the reference surface to obtain the surface error and compensate for it is very necessary. Therefore, a method of fitting Zernike data of overlapping regions between subapertures in the splicing process is proposed to obtain the reference surface shape. Firstly, a series of Zernike terms are added to the traditional objective function to represent the reference surface to be solved, and then the coefficients are obtained by solving the function according to the least square method to obtain the fitted reference surface. The experiments of subaperture splicing were carried out on the plane and the spheres respectively. The deviation of the PV value of the reference plane obtained by the fitting of the reference plane and the QED splicing interferometer was less than 5 nm, and the deviation of the RMS value was less than 0.2 nm. The area mismatch error value is less than 10nm. Experimental results show that in the process of sub-aperture splicing, the reference surface error can be compensated to obtain a more realistic splicing profile.