Real-time Adaptive Optics with pyramid wavefront sensors: A theoretical analysis of the pyramid sensor model

Abstract

We consider the mathematical background of the wavefront sensor type that is widely used in Adaptive Optics systems for astronomy, microscopy, and ophthalmology. The theoretical analysis of the pyramid sensor forward operators presented in this paper is aimed at a subsequent development of fast and stable algorithms for wavefront reconstruction from data of this sensor type. In our analysis we allow the sensor to be utilized in both the modulated and non-modulated fashion. We derive detailed mathematical models for the pyramid sensor and the physically simpler roof wavefront sensor as well as their various approximations. Additionally, we calculate adjoint operators which build preliminaries for the application of several iterative mathematical approaches for solving inverse problems such as gradient based algorithms, Landweber iteration or Kaczmarz methods.

References in corpus (9)

• Large Binocular Telescope Adaptive Optics System: New achievements and perspectives in adaptive optics
• Efficient, Nonlinear Phase Estimation with the Non-Modulated Pyramid Wavefront Sensor
• The Mid-infrared E-ELT Imager and Spectrograph (METIS)
• Non-linear wavefront reconstruction methods for pyramid sensors using Landweber and Landweber-Kaczmarz iteration
• METIS - the Mid-infrared E-ELT Imager and Spectrograph
• The adaptive optics modes for HARMONI: from Classical to Laser Assisted Tomographic AO
• High Contrast Imaging in the Visible: First Experimental Results at the Large Binocular Telescope
• Sensing and control of segmented mirrors with a pyramid wavefront sensor in the presence of spiders
• Real-time Adaptive Optics with pyramid wavefront sensors: Accurate wavefront reconstruction using iterative methods

Cited by in corpus (2)

• Pyramid wavefront sensor optical gains compensation using a convolutional model
• Adaptive optics imaging with a pyramid wavefront sensor for visual science