Algorithm for calculating the optimal parameters of multilayer aperiodic mirrors for soft X-rays

A new algorithm is proposed for optimising the thickness of layers in multilayer aperiodic mirrors. An important feature of the algorithm is the separation of the explicit dependence of the reflection coefficient on the thickness of one layer. This reduces the amount of calculations required for the mirror optimisation by a factor of N (N is the number of layers of the mirror). The algorithm allows one to perform optimisation of different types: the obtaining of the maximum reflection coefficient at one frequency, the maximum of the integrated reflection coefficient within a specified frequency interval, the constant reflection coefficient in the working frequency or angular interval, etc. Examples of practical applications of the algorithm demonstrating its efficiency and versatility are presented.