Non-modulated pyramid wavefront sensor: Why, how and when to use it to sense and correct atmospheric turbulence

Context. The diffusion of adaptive optics systems in astronomical instrumentation for large ground based telescopes is rapidly increasing and the pyramid wavefront sensor is replacing the Shack-Hartmann as standard solution for single conjugate adaptive optics systems. The pyramid wavefront sensor is typically used with a tip/tilt modulation to increase the linearity range of the sensor, but the non-modulated case is interesting because it maximizes the sensor sensitivity. The latter case is generally avoided for the reduced linearity range that prevents robust operation in the presence of atmospheric turbulence. Aims. We aim to solve part of the issues of the non-modulated pyramid wavefront sensor by reducing the model error in the interaction matrix. We linearize the sensor response in the working conditions without extending the sensor linearity range. Methods. We introduce a new calibration approach to model the response of pyramid wave front sensor in partial correction, where the working conditions in the presence of residual turbulence is considered. Results. We show how in simulations, through the new calibration approach, the pyramid wave front sensor without modulation can be used to sense and correct atmospheric turbulence and when this case is preferable to the modulated case.