Measurement of highly reflective surface shape using wavelength tuning Fizeau interferometer and polynomial window function
Measurement of highly reflective surface shape using wavelength tuning Fizeau interferometer and polynomial window function
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DOI：
10.1016/j.precisioneng.2016.02.011
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发表时间：
2016-07
影响因子：
3.6
通讯作者：
Yangjin Kim;N. Sugita;M. Mitsuishi
中科院分区：
文献类型：
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作者：
Yangjin Kim;N. Sugita;M. Mitsuishi
本文提出了一种包括多项式窗函数和离散傅立叶变换的5N−-4相移算法，用于干涉测量硅片的表面形状，抑制了高次谐波与相移误差之间的耦合误差。在特征多项式理论的基础上，通过在特征图上定位5个重根，得到了一种新的多项式窗函数。相对于频域中的傅里叶表示来估计5N−-4算法的特性。讨论了使用5N−-4算法进行测量的相位误差，并与使用其他传统相移算法获得的测量结果进行了比较。最后，4英寸的表面形状。使用5N−-4算法和波长调谐菲佐干涉仪测量硅片。通过比较其他算法计算出的串扰噪声的幅度，讨论了测量的精度。整个测量的不确定度为34 nm，比任何其他传统的相移算法都要好。
In this study, a 5N− 4 phase shifting algorithm comprising a polynomial window function and a discrete Fourier transform is developed to measure interferometrically the surface shape of a silicon wafer, with suppression of the coupling errors between the higher harmonics and the phase shift error. A new polynomial window function is derived on the basis of the characteristic polynomial theory by locating five multiple roots on the characteristic diagram. The characteristics of the 5N− 4 algorithm are estimated with respect to the Fourier representation in the frequency domain. The phase error of the measurements performed using the 5N− 4 algorithm is discussed and compared with those of measurements obtained using other conventional phase shifting algorithms. Finally, the surface shape of a 4-in. silicon wafer is measured using the 5N− 4 algorithm and a wavelength tuning Fizeau interferometer. The accuracy of the measurement is discussed by comparing the amplitudes of the crosstalk noise calculated by other algorithms. The uncertainty of the entire measurement was 34 nm, better than that of any other conventional phase shifting algorithms.