摘要
波长扫频干涉测量系统的深度分辨率受限于波数扫频带宽,当激光器的非连续输出导致可用的带宽受限时,测量系统的深度分辨率会显著下降。针对该问题,国际上通用的解决方案是合成非连续波长扫频前后的波数序列,但该方案会导致旁瓣异常,影响后续的深度分辨与相位重构。提出了基于最小二乘谱的非连续波长扫频干涉信号校正方法,抑制了非连续扫频合成引起的异常旁瓣,提高了波长扫频干涉技术的适用性。最小二乘谱通过最小化误差平方和,判断信号的周期变换趋势并评估拟合模型的置信度,使所提方法在非均匀采样的情况下仍能获得精确的频谱信息。在仿真实验中,利用最小二乘谱计算的干涉相位与理想相位的平均误差和标准误差均小于0.036 rad。在实际实验结果中,最小二乘谱解调的多表面高精度参数为:光楔倾角误差为0.34′,平凸透镜平面标准误差为21.66 nm,平凸透镜曲率半径误差为13μm。所提出的最小二乘谱方法能够有效校正非连续波长扫频干涉信号,提高深度分辨率,正确重构相位,从而实现高精度的多表面测量。
Objective The depth resolution of a wavelengthscanning interferometric measurement system is limited by the wavenumber scanning bandwidth.When the laser discontinuous output restricts the available bandwidth,the depth resolution of the measurement system significantly decreases.Currently,the mainstream solution internationally is to synthesize the wavenumber sequences before and after the discontinuous wavelength scanning.Under discontinuous wavelength output,the initial phase of the scanning interferometric signal experiences jumps,leading to abnormal sidelobe amplitudes,which can cause interference between adjacent sidelobe peaks and affect subsequent depthresolved phase reconstruction.This paper proposes a multisurface interferometric measurement method suitable for discontinuous wavelength scanning.By constructing a leastsquares spectrumbased phase reconstruction method for scanning interferometry,the impact of phase jumps in discontinuous scanning interferometric signals is eliminated,thereby suppressing the abnormal sidelobes caused by the discontinuous sweep synthesis and improving the applicability of wavelengthscanning interferometry.Methods The algorithm proposed in this paper,based on leastsquares spectrum correction of discontinuous interferometric signals,aims to suppress abnormal sidelobes caused by discontinuous laser wavelength scanning,thereby fully utilizing the spectral information from the discontinuous bands to achieve highresolution and highprecision phase reconstruction.First,a constant drive current,temperature tuning range,and acquisition frame rate are set.Using the principle of scanning interferometric imaging,interference patterns from multiple surfaces are obtained on a selfbuilt multisurface scanning interferometric measurement hardware system.After removing the direct current component and synthesizing the wavenumber sequences before and after the discontinuous wavelength scanning,the necessary preprocessing is carried out to obtain the discontinuous scanning interferometric signals required for the experiment.The discontinuous interferometric signals are decomposed into a linear combination of sine and cosine basis functions using the leastsquares error minimization,and the amplitude parameters of the sine and cosine basis functions,which contain the frequency and phase information of the scanning interferometric signal,are estimated using matrix leastsquares estimation to demodulate the interference phase.Two experimental sets are designed in this paper.In the numerical simulation comparison experiments,the mean difference and standard deviation between the interferometric phase and the ideal phase are used as evaluation metrics for quantitative analysis.In the actual experimental results,highprecision parameter estimation for multiple surfaces is achieved,validating the effectiveness of the proposed method.Results and Discussions In the numerical simulation experiment,this paper compares the interference phase maps before and after the synthesis of discontinuous scanning wavenumber sequences(Fig.6).Due to the limited bandwidth of continuous scanning wavenumber sequences,Fourier transforms struggle to effectively separate the spectral components of the interferometric signal,leading to inadequate phase reconstruction accuracy.To improve depth resolution,this paper synthesizes discontinuous scanning wavenumber sequences.However,the initial phase jumps introduced by these sequences cause abnormal sidelobes during Fourier transform demodulation,leading to errors in peak frequency extraction and ultimately resulting in phase aliasing.To suppress the impact of these sidelobe anomalies,an algorithm based on the leastsquares spectrum is used to correct the discontinuous interferometric signals,reducing the sidelobe amplitudes,minimizing their influence on the main peak,and ensuring accurate peak frequency extraction for correct phase reconstruction.To assess phase quality,error analysis is conducted on the results of the discontinuous interferometric phase(Table 1 and Table 2),calculating the average error and standard deviation between each interferometric phase and the ideal phase.The interference phase errors calculated by the leastsquares spectrum are all less than 0.036 rad,significantly smaller than those obtained from Fourier transform calculations.In the multisurface scanning interferometric measurement experiment,the interferometric phase results for each surface are consistent with those from the numerical simulation experiment(Fig.10 and Fig.11),demonstrating the robustness of the algorithm.Highprecision parameter estimation for each surface are as follows(Fig.12):the light wedge tilt angle is 6.34′,with an error of 0.34′,corresponding to a percentage error of 5.67%;the standard error for the planoconvex lens surface is 21.66 nm;and the radius of curvature of the convex surface of the planoconvex lens is 516.8130 mm,with an error of 13μm,corresponding to a percentage error of 0.0025%.Conclusion The leastsquares spectrum method proposed in this paper significantly enhances the applicability of wavelengthscanning interferometry under discontinuous laser output.The method effectively suppresses abnormal sidelobes caused by discontinuous wavelength scanning,improves depth resolution,and accurately reconstructs the phase.Both numerical simulation and multisurface interferometric experimental results demonstrate that the leastsquares spectrum has good robustness in correcting discontinuous interferometric signals to achieve highprecision multisurface measurements,providing an effective solution for highprecision optical measurements.
作者
裘昊
董博
谢胜利
白玉磊
Qiu Hao;Dong Bo;Xie Shengli;Bai Yulei(School of Automation,Guangdong University of Technology,Guangzhou 510006,Guangdong,China;Key Laboratory of Inteligent Information Processing and System Integration of IoT,Ministry of Education,Guangzhou 510006,Guangdong,China)
出处
《中国激光》
北大核心
2025年第11期130-141,共12页
Chinese Journal of Lasers
基金
国家自然科学基金(62475048)
广东省自然科学基金(2024A1515010230)。
关键词
干涉测量
非连续波长扫频
最小二乘谱
多表面测量
interferometric measurement
discontinuous wavelength scanning
leastsquares spectrum
multisurface measurement
