相移光腔衰荡高反射率测量中的拟合方法
Fitting method for high reflectivity measurement with phase-shift cavity ring-down technique
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摘要: 分析了相移光腔衰荡技术中由锁相放大器探测光腔输出信号一次谐波的振幅和相位随调制频率的变化曲线。拟合结果发现，联合幅频和相频曲线构造同时含有振幅和相位信息的均方差拟合函数，不同频率拟合范围得到的衰荡时间平均值为0.791 μs，最大误差由分别用幅频或相频曲线拟合得到的衰荡时间误差的8%减小到1.3%，均方差仅为0.5%。通过在拟合函数中加入系统响应时间、系统初始相位等参数，避免了相移光腔衰荡中直腔实验时测量系统频率响应曲线，提高了测量精度。Abstract: The frequency dependences of both amplitude and phase-shift of the first harmonic of the ring-down signal are measured by a lock-in amplifier in a phase-shift cavity ring-down technique (PS-CRD). With different frequency ranges, the cavity decay time values fitted with either amplitude-frequency curve or phase-shift-frequency curve differ in a wide range, with a maximum error of roughly 8%. By defining a root-mean-square error function including both the amplitude error term and phase-shift error term, the maximum error is significantly diminished to 1.3% and the root-mean-square error is as small as 0.5%. The cavity decay time is statistically determined to be 0.791 μs with different frequency ranges. On the other hand, experimental parameters (i.e., the instrumental response time and th
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