A technique for characterizing and correcting the linearity of radiometric instruments is known by the names the "flux-addition method" and the "combinatorial technique". In this paper, we develop a rigorous uncertainty quantification method for use with this technique and illustrate its use with both synthetic data and experimental data from a "beam conjoiner" instrument. We present a probabilistic model that relates the instrument readout to a set of unknown fluxes via a set of polynomial coefficients. Maximum likelihood estimates (MLEs) of the unknown fluxes and polynomial coefficients are recommended, while a non-parametric bootstrap algorithm enables uncertainty quantification (e.g., it can return standard errors). The synthetic data represent plausible outputs of a radiometric instrument and enable testing and validation of the method. The MLEs for these data are found to be approximately unbiased, and confidence intervals derived from the bootstrap replicates are found to be consistent with their target coverage of 95 %. For the polynomial coefficients, the relative bias was less than 1 % and the observed coverages range from 90 % to 97 %. The experimental data set is used to illustrate how a complete calibration with uncertainties can be achieved using the method plus one well-known flux level. The uncertainty contribution attributable to estimation of the instrument's nonlinear response is less than 0.02 % over most of its range.
翻译:用来描述和纠正辐射测量仪器的线性特征和纠正辐射测量仪器的线性的技术以名称为“ 通量增加法” 和“ combinator 技术” 。 在本文中,我们开发了一种严格的不确定性量化方法,用于使用这种技术,并用合成数据和“ baam conjoiner” 仪器的实验数据来说明其使用情况。我们提出了一个概率模型,将仪器的读读数与一组通过一套多元系数的一组未知通量相挂钩;建议了未知通量和多元系数的最大概率估计值(MLEs),而一个非参数陷阱算法则能够进行不确定性量化(例如,它可以返回标准错误) 。合成数据代表了辐射测量仪器的可信输出,并能够测试和验证该方法。发现这些数据的MLE值大致没有偏差,而从靴杆复制中得出的信任度间隔与95%的目标覆盖率相符。对于多元系数的范围来说,相对偏差小于1%,而观测到的覆盖范围从90%至97%不等。 使用一个精确度的精确度方法来说明其精确度的精确度。