Sensing and control of segmented mirrors with a pyramid wavefront sensor in the presence of spiders

Abstract

The secondary mirror unit of the European Extremely Large Telescope (ELT) is supported by six 50-cm wide spiders, providing the necessary stiffness to the structure while minimising the obstruction of the beam. The deformable quaternary mirror (M4) contains over 5000 actuators on a nearly hexagonal pattern. The reflective surface of M4 itself is composed of a segmented thin shell made of 6 discontinuous petals. This segmentation of the telescope pupil will create areas of phase isolated by the width of the spiders on the wavefront sensor (WFS) detector, breaking the spatial continuity of the wavefront data.The poor sensitivity of the Pyramid WFS (PWFS) to differential piston (or of any WFS sensitive to the derivative of the wavefront such as the Shack-Hartmann) will lead to badly seen and therefore uncontrollable differential pistons between these areas. In close loop operation, differential pistons between segments will settle around integer values of the average sensing wavelength lambda. The differential pistons typically range from one to tens of time the sensing wavelength and vary rapidly over time, leading to extremely poor performance. In addition, aberrations created by atmospheric turbulence will naturally contain some differential piston between the segments. This differential piston is typically a relatively large multiple of the sensing wavelength, especially for 40 m class telescopes. Trying to directly remove the entire piston contribution over each of the DM segments will undoubtedly lead to poor performance.In an attempt to reduce the impact of unwanted differential pistons that are injected by the AO correction, we compare three different approaches. A first step is to try to limit ourselves to use only the information measured by the PWFS, in particular by reducing the modulation. We show that using this information sensibly is important but it is only a prerequisite and will not be sufficient. We discuss possible ways of improvement by removing the unwanted differential pistons from the DM commands while still trying to maintain the atmospheric segment-piston contribution by using prior information. A second approach is based on phase closure of the DM commands and assumes the continuity of the correction wavefront over the entire unsegmented pupil. The last approach is based on the pair-wise slaving of edge actuators and shows the best results. We compare the performance of these methods using realistic end-to-end simulations. We find that pair-wise slaving leads to a small increase of the total wavefront error, only adding between 20-45 nm RMS in quadrature for seeing conditions between 0.45"-0.85". Finally, we discuss the possibility of combining the different proposed solutions to increase robustness.

Real-time adaptive optics with pyramid wavefront sensors: part I. A theoretical analysis of the pyramid sensor model

“…These are used in the upcoming second part of the paper [39] which will be devoted to the application of iterative algorithms to the problem of wavefront reconstruction from pyramid wavefront sensor data. An extension of the analysis (linearization and calculation of adjoints) to the full pyramid sensor operator as well as the adaption of the aperture mask to segmented pupils on ELTs [17,40,55,66,67] is dedicated to future work.…”

Review on methods for wavefront reconstruction from pyramid wavefront sensor data

“…8,27,[99][100][101][102][103] Furthermore, the modal basis is not as well-suited for pupils with spiders as the zonal approach, which allows significantly more degrees of freedom in the representation of wavefront. 49,69,[104][105][106][107] An alternative-decoupled-approach to AO loop control considers the two steps: wavefront reconstruction and DM fitting, separately and independently. In this situation, wavefront reconstruction can be based on a synthetic calibration (using a numerical implementation of the sensor's forward model) done independently from the shapes a DM can produce.…”

“…Because of such data fragmentation, most of the available wavefront reconstruction algorithms per se are not able to control fragmented piston modes of the wavefront. 49,69,104,105 This manifests itself via uncontrolled pistons on disjoint pupil "islands" seen in the residual screens and the dramatically reduced Strehl ratio.…”

“…A successful control of the island effect has been demonstrated using a zonal matrix vector multiplication, 49,116,142 with an adapted model-based reconstructor in the split approach, 49,116 and with edge actuator coupling for a modal matrix vector multiplication. 104,105,143 It has been acknowledged that the island effect becomes more severe at shorter wavelengths and larger seeing values. Accurate reconstruction of fragmented pistons is much more difficult in the visible compared to the NIR, despite the fact that in the calibration stage the pyramid WFS is sensitive to those modes.…”

Analysis and mitigation of pupil discontinuities on adaptive optics performance

“…The strength of the low wind effect will essentially depend on the height of the spiders. The second is the island effect [10]: a differential piston between the mirror segments created by the AO control loop (this is true for any badly seen modes (such as waffle) that will undergo amplification during the inversion/reconstruction). The strength of the island effect (IE) is mainly driven by the width of the telescope's spiders, in our case 50 cm.…”