非线性动态特性的逆推演方法及其在干涉术中的应用

Inverse Evolution Method for Nonlinear Dynamics of Objects and Its Application to Interferometry

提出了研究对象非线性动态特性的逆推演新方法 ,它的特点是从已知对象的非微分方程解析解导出该对象可能的微分方程 ,从而开拓它的解域或解空间 ,或者说恢复丢失的解。同时讨论了当对象为法布里珀罗干涉(F P)或迈克耳孙干涉时该方法的应用过程 ,并且对法布里珀罗定义新的不透过系数 (u =1/τ) ,从而给出更简洁和易分析的对象动态特性微分方程 ,以及由此导出测量法布里珀罗干涉相位的过程。值得注意的是由新方法导出的微分方程揭示对象更一般的时空演化特征 ,而且在现有的经验和知识基础上可以进一步唯象地拓展至其他可能的非线性形式 ,从而使对象的表达方式更接近它的实际情况。

An inverse evolution method for studying the nonlinear dynamics of an object was suggested. Its main process is to deduce a probability differential (or partial differential) equation to the object by using known solution from non-differential equation, therefore the solution domain or space would be extended, so that the lost solutions are restored. Its application to Fabry-Perot (F-P) interferometer (also suitable to Mechelson interferometer) was described. A new parameter definition, opaqueness of F-P, is recommended. The dynamic property of F-P and other methods for measuring the fineness and optical phase of F-P were given. Not only an extended solution space is contained in the differential equation, but also some other nonlinear forms can be obtained according to the known typical nonlinear evolution equations or current experience and knowledge, hence the representation for object would be more close to its true state.