Mathematical analysis of hexagonal source arrangement for making uniform reflective aluminum coatings

This paper presents modeling results for coating thickness as a function of position, for aluminum films made with a hexagonal array of evaporation sources. The computer simulation is based on measured plume data from a single evaporation source. The model is used to determine optimum source spacing for a given plume shape. The analysis revealed that arrangement of multiple sources in a hexagonal array can produce uniform coatings while utilizing a reasonable number of evaporation sources per square meter of coating area. Monte Carlo simulations followed by gradient descent optimization methods were used to determine optimal flatness solutions for groups of deposition sources with varied deposition times. Thin aluminum films with exceptional coating flatness are needed to meet the wavefront error requirements of future space-based telescope concepts such as HabEx, LUVOIR, CETUS and others.