Fibre Bragg Gratings have become widespread measurement devices in engineering and other fields of application. In all but a few cases, the relation between cause and effect is simplified to a proportional model. However, at its mathematical core lies a nonlinear inverse problem which appears not to have received much attention in the literature. In this paper, we present this core problem to the mathematical community and provide a first report on opportunities and limitations of a regularization approach. In particular, we show that difficulties arise from non-uniqueness and the absence of established parameter selection rules for nonlinear inverse problems with multiple regularization parameters. Nevertheless, the paper takes a first step toward extracting more information from a single FBG measurement.

光纤布拉格光栅已成为工程和其他应用领域中广泛使用的测量设备。除少数情况外，因果关系被简化为比例模型。然而，其数学核心是一个非线性逆问题，在文献中似乎没有受到太多关注。在本文中，我们向数学界提出了这个核心问题，并提供了关于正则化方法的机会和局限性的第一份报告。特别是，我们表明，对于具有多个正则化参数的非线性逆问题，非唯一性和缺乏已建立的参数选择规则会产生困难。尽管如此，本文迈出了从单个 FBG 测量中提取更多信息的第一步。