Radio Telescope Design Optimization Using Costing Constraints: Extrapolating LOFAR Costing to the Square Kilometre Array

In this paper we present a methodology for creating a system design for radio telescopes based on a fixed cost budget. This methodology builds on the idea to optimize a figure of merit such as sensitivity or survey speed given a model for the scaling of the cost of the components of a radio telescope. We applied the method of Lagrange multipliers to find the optimal design and we used cost scaling models based on our experience with the construction of the Low Frequency Array (LOFAR) telescope. We have extrapolated the LOFAR designs to the SKA1-Low telescope and have assessed the current SKA1-Low design in terms of figure of merit maximization. We have shown that, in the absence of other systems constraints such as point spread function requirements, in general, the chosen designs would be more sensitive if larger bandwidths and fewer and larger antenna stations would have been chosen. We have demonstrated that costs can be explicitly incorporated in the designs without adding too much complexity, so that it still is possible to find causal relations between cost, system design, and performance.