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Register a new userGeneral formalism for Fourier based Wave Front Sensing: application to the Pyramid wave front sensors
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In this article, we compare a set of Wave Front Sensors (WFS) based on Fourier filtering technique. In particular, this study explores the class of pyramidal WFS defined as the 4 faces pyramid WFS, all its recent variations (6, 8 faces, the flattened PWFS, etc.) and also some new WFSs as the flattened cone WFS or the 3 faces pyramid WFS. In the first part, we describe such a sensors class thanks to the optical parameters of the Fourier filtering mask and the modulation parameters. In the second part, we use the unified formalism to create a set of performance criteria: size of the signal on the detector, efficiency of incoming flux, sensitivity, linear range and chromaticity. In the third part, we show the influence of the previous optical and modulation parameters on these performance criteria. This exhaustive study allows to know how to optimize the sensor regarding to performance specifications. We show in particular that the number of faces has influence on the number of pixels required to do the wave front sensing but no influence on the sensitivity and linearity range. To modify these criteria, we show that the modulation radius and the apex angle are much more relevant. Moreover we observe that the time spent on edges or faces during a modulation cycle allows to adjust the trade-off between sensitivity and linearity range.
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We introduce in this article a general formalism for Fourier based wave front sensing. To do so, we consider the filtering mask as a free parameter. Such an approach allows to unify sensors like the Pyramid Wave Front Sensor (PWFS) and the Zernike Wave Front Sensor (ZWFS). In particular, we take the opportunity to generalize this two sensors in terms of sensors class where optical quantities as, for instance, the apex angle for the PWFS or the depth of the Zernike mask for the ZWFS become free parameters. In order to compare all the generated sensors of this two classes thanks to common performance criteria, we firstly define a general phase-linear quantity that we call meta-intensity. Analytical developments allow then to split the perfectly phase-linear behavior of a WFS from the non-linear contributions making robust and analytic definitions of the sensitivity and the linearity range possible. Moreover, we define a new quantity called the SD factor which characterizes the trade-off between these two antagonist quantities. These developments are generalized for modulation device and polychromatic light. A non-exhaustive study is finally led on the two classes allowing to retrieve the usual results and also make explicit the influence of the optical parameters introduced above.
In this paper, we describe Fourier-based Wave Front Sensors (WFS) as linear integral operators, characterized by their Kernel. In a first part, we derive the dependency of this quantity with respect to the WFSs optical parameters: pupil geometry, filtering mask, tip/tilt modulation. In a second part we focus the study on the special case of convolutional Kernels. The assumptions required to be in such a regime are described. We then show that these convolutional kernels allow to drastically simplify the WFSs model by summarizing its behavior in a concise and comprehensive quantity called the WFSs Impulse Response. We explain in particular how it allows to compute the sensors sensitivity with respect to the spatial frequencies. Such an approach therefore provides a fast diagnostic tool to compare and optimize Fourier-based WFSs. In a third part, we develop the impact of the residual phases on the sensors impulse response, and show that the convolutional model remains valid. Finally, a section dedicated to the Pyramid WFS concludes this work, and illustrates how the slopes maps are easily handled by the convolutional model.
Advanced AO systems will likely utilise Pyramid wave-front sensors (PWFS) over the traditional Shack-Hartmann sensor in the quest for increased sensitivity, peak performance and ultimate contrast. Here, we wish to bring knowledge and quantify the PWFS theoretical limits as a means to highlight its properties and use cases. We explore forward models for the PWFS in the spatial-frequency domain for they prove quite useful since a) they emanate directly from physical-optics (Fourier) diffraction theory; b) provide a straightforward path to meaningful error breakdowns, c) allow for reconstruction algorithms with $O (n,log(n))$ complexity for large-scale systems and d) tie in seamlessly with decoupled (distributed) optimal predictive dynamic control for performance and contrast optimisation. All these aspects are dealt with here. We focus on recent analytical PWFS developments and demonstrate the performance using both analytic and end-to-end simulations. We anchor our estimates with observed on-sky contrast on existing systems and then show very good agreement between analytical and Monte-Carlo estimates for the PWFS. For a potential upgrade of existing high-contrast imagers on 10,m-class telescopes with visible or near-infrared PWFS, we show under median conditions at Paranal a contrast improvement (limited by chromatic and scintillation effects) of 2x-5x by replacing the wave-front sensor alone at large separations close to the AO control radius where aliasing dominates, and factors in excess of 10x by coupling distributed control with the PWFS over most of the AO control region, from small separations starting with the Inner Working Angle of typically 1-2 $lambda/D$ to the AO correction edge (here 20 $lambda/D$).
In this paper we report on the laboratory experiment we settled in the Shanghai Astronomical Observatory (SHAO) to investigate the pyramid wavefront sensor (WFS) ability to measure the differential piston on a sparse aperture. The ultimate goal is to verify the ability of the pyramid WFS work in closed loop to perform the phasing of the primary mirrors of a sparse Fizeau imaging telescope. In the experiment we installed on the optical bench we performed various test checking the ability to flat the wave-front using a deformable mirror and to measure the signal of the differential piston on a two pupils setup. These steps represent the background from which we start to perform full closed loop operation on multiple apertures. These steps were also useful to characterize the achromatic double pyramids (double prisms) manufactured in the SHAO optical workshop.
In tomographic adaptive-optics (AO) systems, errors due to tomographic wave-front reconstruction limit the performance and angular size of the scientific field of view (FoV), where AO correction is effective. We propose a multi time-step tomographic wave-front reconstruction method to reduce the tomographic error by using the measurements from both the current and the previous time-steps simultaneously. We further outline the method to feed the reconstructor with both wind speed and direction of each turbulence layer. An end-to-end numerical simulation, assuming a multi-object AO (MOAO) system on a 30 m aperture telescope, shows that the multi time-step reconstruction increases the Strehl ratio (SR) over a scientific FoV of 10 arcminutes in diameter by a factor of 1.5--1.8 when compared to the classical tomographic reconstructor, depending on the guide star asterism and with perfect knowledge of wind speeds and directions. We also evaluate the multi time-step reconstruction method and the wind estimation method on the RAVEN demonstrator under laboratory setting conditions. The wind speeds and directions at multiple atmospheric layers are measured successfully in the laboratory experiment by our wind estimation method with errors below 2 ms. With these wind estimates, the multi time-step reconstructor increases the SR value by a factor of 1.2--1.5, which is consistent with a prediction from end-to-end numerical simulation.
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