多波长加权回归准确计算F-P标准具的间隔

Accurate calculation of the spacing of F-P etalon under the multi-wavelength weighted regression

漫射单色光经F-P标准具产生一组干涉圆环,对环直径平方与干涉级次的经典一阶方程加上二阶修正项,从修正后的准直线方程能够确定圆环中心干涉级次的小数部分。实验采用波长相近的两条汞黄线、氦黄线和氖黄线作为光源,同时获得经F-P标准具的四组干涉圆环。对圆环的点位坐标数据作圆回归求得直径值及其标准差,进而用新的准直线模型作加权回归求得各波长的小数干涉级次,评定其扩展不确定度。将3个波长(两条贡黄线,一条氦黄线)的测量结果用于小数重合法计算,从厚度粗测值选定间隔数值计算的取值范围,步距小于0.01 nm,求得间隔d=1 655.331 67±0.000 45μm,相对误差限约为3×10-7。再用第4个氖波长作检验,由d求出的干涉级次与实测值的相对偏差为1.9×10-7,显著小于干涉级次测量值的相对不确定度7.4×10-7。

A set of interference concentric circles was formed when monochromatic light illuminated the F-P etalon.The relation of interference orders and the square of the diameters of interference circles was known in the first-order approximation.The fractional order at the centre of the interference fringes was determined by the revised quasi-linear equation in which the second-order term was added.The multi-spectral light source consisted of four similar yellow wavelengths,such as two Hg,one He and one Ne.The image of interference concentric circles was obtained by digital camera at the focal plane of lens simultaneously.The diameters and standard deviations were computed by the circular regression of coordinate data.The fractional order was calculated by a new quasi-linear weighted regression model,and the expanded uncertainties were solved corresponding to different wavelengths.Inducing three wavelengths to the process of excess fraction method,which was composed of two Hg and one He spectra,the integer interval and the fractional ranges could be confirmed under the condition that the estimated spacer of the F-P etalon was measured.The experimental results show that if the calculating step is less than 0.01 nm,the spacer d of the F-P etalon is 1 655.331 67±0.000 45 μm,and the relative error limit is not more than 3×10-7.Tested by the Ne spectrum,the relative deviation between the calculated and measured values of the interference order is 1.9×10-7 through the measured value of d,which is significantly less than the relative uncertainty of the measurements value of 7.4×10-7.