Advanced wavefront reconstruction methods for segmented Extremely Large Telescope pupils using pyramid sensors

Abstract

The generation of Extremely Large Telescopes (ELTs) with mirror diameters up to 40 m has thick secondary mirror support structures (also known as spider legs), which cause difficulties in the wavefront reconstruction process. These spider legs create areas where the information of the phase is disconnected on the wavefront sensor detector, leading to pupil fragmentation and a loss of data on selected subapertures. The effects on wavefront reconstruction are differential pistons between segmented areas, leading to poor wavefront reconstruction. The resulting errors make the majority of existing control algorithms unfeasible for telescope systems having spider legs incorporated. A solution, named the split approach, is presented, which suggests to separate reconstruction of segment piston modes from the rest of the wavefront. Further, two methods are introduced for the direct reconstruction of the segment pistons. Due to the separate handling of the piston offsets on the segments, the split approach makes any of the existing phase reconstruction algorithms developed for nonsegmented pupils suitable for wavefront control in the presence of telescope spiders. We present end-to-end simulation results showing accurate, stable, and extremely fast wavefront reconstruction for the first light instrument mid-infrared ELT imager and spectograph of the ELT that is currently under construction.

Nonlinear wavefront reconstruction methods for pyramid sensors using Landweber and Landweber–Kaczmarz iterations

“…We will come back to this topic including detailed comparisons of pyramid and roof sensor models as basis in the reconstruction approach in an upcoming paper. At present, there already exist several methods that allow for accurate wavefront reconstruction such as MVM based approaches or the P-CuReD algorithm [65] with LE Strehl ratios around 0.89 as summarized in, e.g., [31]. Nevertheless, we want to emphasize the importance of the development of new algorithms since the high reconstruction performance with the linear methods is obtained in undisturbed closed loop AO systems.…”

Review on methods for wavefront reconstruction from pyramid wavefront sensor data

“…46 On the ELTs under design, the primary mirrors are so large that they need to be segmented, which poses the key challenge of cophasing the segments in order to produce a single optical surface. Here is another very valuable feature of the pyramid sensor: its ability to sense differential pistons of a segmented mirror, which has been successfully demonstrated in the laboratory, 48 supported by numerical simulations, 49 and validated on sky under seeing-limited conditions. 39 Moreover, it was found that among the available wavefront sensor types, the PWFS takes the most sensitive measurements of differential pistons on the segments.…”

“…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.…”

“…An extensive overview on numerous variants of these approaches can be found in Ref. 49. The algorithms are generally applicable to pyramid sensors with and without modulation.…”

Real-time adaptive optics with pyramid wavefront sensors: part II. Accurate wavefront reconstruction using iterative methods

“…For several telescope systems the pupil Ω is annular instead of circular since a shade created by the secondary mirror prevents measurements on these areas. Thus, the light in the area of the central obstruction possibly does not produce reliable measurements [20,37,56,69,70]. Hence, the last step is realized as a multiplication with a second characteristic function…”