Simulations on Hartmann wavefront sensors for the use in a gravitational wave detector

In this paper, a simulation environment for a Hartmann wavefront sensor is presented and discussed in the context of a gravitational wave detectors. Thermal effects occur in the optics of the gravitational wave detector and precise measurements is crucial. Hartmann wavefront sensors have been used for this purpose but need to be configured individually. In this work, an optical simulation is implemented to test different Hartmann wavefront sensor configurations. A figure of merit is developed allowing to quantize the wavefront sensor perfor-mance. Theoretical evaluations allow to define parameter sets of common measurement range and to fairly compare them across the parameter space. Core parameters are the number of apertures, aperture diameter, and the Hartmann-plate-to-camera distance. The approach is demonstrated based on a thermal deformation estimate with a measurement range represented by a maximum displacement angle of 𝛼𝑚𝑎𝑥=4 mrad. A parameter set including sixty-one apertures is derived allowing best resolution of 𝑟𝑒𝑠=3 pm for ten-fold averaging. This work can be used to find parameters for an optimal Hartmann wavefront sensor for a third-generation gravitational wave detector such as the Einstein Telescope once the thermal deformation due to the coating and the material of the gravitational wave detector test masses is known.