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Improved Nonlinearity Correction Method for Homodyne Orthogonal Signals in Vibration Calibration
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摘要: 针对振动校准中零差干涉信号非线性误差修正的问题，叙述了一种改进的椭圆拟合算法，与传统的基于最小二乘的海德曼椭圆修正方法相比，所述方法做了两个改进，一个是对拟合的圆锥曲线方程增加椭圆参数的限定条件，另一个是将常规的基于最小距离准则下的参数计算转化为求数据矩阵特征值。所述方法能够确保零差干涉信号形成的李萨如图形在只是一个部分椭圆的条件下，依然能够拟合得到一个完整的椭圆，从而能够扩展零差干涉仪在振动校准中的工作频率范围，同时提高测量的准确度。Abstract: Addressing the issue of nonlinearity correction for homodyne interference signals in vibration calibration, this paper describes an improved ellipse fitting algorithm. Compared to the traditional Heydeman ellipse correction method based on least squares, the proposed method makes two improvements. First, it adds constraints on the ellipse parameters in the fitted conic equation. Second, it transforms the conventional parameter calculation based on the minimum distance criterion into solving the eigenvalues of the data matrix. The proposed method ensures that even when the Lissajous figure formed by the homodyne interference signal is only a partial ellipse, a complete ellipse can still be fitted. This extends the working frequency range of the homodyne interferometer in vibration calibration while improving the measurement accuracy.
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Key words:
- metrology /
- vibration calibration /
- homodyne interferometer /
- nonlinearity error /
- ellipse fitting
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图 3 不同干涉信号椭圆拟合的结果
Figure 3. Ellipse fitting results for different interference signals
图 7 100 Hz试验零差干涉信号李萨如图
Figure 7. Lissajous diagram of homodyne interference signal at 100 Hz
图 9 5 kHz试验零差干涉信号李萨如图
Figure 9. Lissajous diagram of homodyne interference signal at 5 kHz
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