Simulation of an optimized holographic wavefront sensor for realistic turbulence scenarios

Atmospheric turbulence limits the performance of laser systems operating within the atmosphere. Therefore, adaptive optics systems are designed to measure and correct the effects of turbulence in real-time. A crucial part of such a system is the wavefront sensor. The modal holographic wavefront sensor is a promising alternative to well-established sensor types (e.g. Shack-Hartmann wavefront sensor). It measures the strength of individual aberration modes directly. Since there is no need for complex calculations, bandwidths in the megahertz range are possible. However, different aberration modes present in the laser beam influence each other's measurements. This inter-modal crosstalk has a very significant impact on the performance of the sensor. Careful design of the holographic sensor can reduce this influence. In this paper we show a method to optimize the sensor design for a given turbulence strength. We use a merit function to find the optimal combination of two design parameters: the detector size and the phase bias. This optimization is done on a mode-by-mode basis. We simulate realistic turbulence scenarios and evaluate the performance of the optimized holographic sensor. By considering the expected turbulence strength during the design process, we can increase the measurement accuracy significantly. We also compare two different modal bases and achieve a further improvement in accuracy when using Karhunen-Lòeve instead of Zernike modes. We evaluate the efficiency of an open-loop adaptive optics system based on the optimized holographic sensor and show that it can be used to correct the effects of realistic dynamic atmospheric turbulence.