Recursive algorithm for modeling non-linear etching rates in reactive plasma jet based optical surface machining of borosilicate crown glass

Abstract

Application-specific optical glass properties are achieved by utilizing complex material compositions. This can be problematic in reactive plasma-assisted deterministic surface processing since a non-volatile surface layer may form depending on the glass composition, which affects the etch rate and thereby the local etching depth. In this investigation, a model algorithm is proposed to tackle some restrictions in applying fluorine-based plasma jet as etching tool utilized for freeform surface machining of optics made of complex glass composition, like borosilicate crown glass (e.g., N-BK7®). In this regard, firstly an analytical model is proposed for estimating the depth-dependent etch rate function. Subsequently, a recursive simulation algorithm is introduced for convolving the derived depth-dependent etch rate function with the given dwell time matrix to simulate a deterministic freeform generation process. By the proposed simulation algorithm, the impeding influence of the residual layer on the reduction of etching depth is computed prior to a real experiment in order to scale the local dwell time to ensure the targeted local removal. Finally, the simulated freeform shape is compared with the corresponding result of an etching experiment to validate the feasibility of the proposed approach.