Curvature Wavefront Sensing for the Large Synoptic Survey Telescope

Abstract: The Large Synoptic Survey Telescope (LSST) will use an active optics system (AOS) to maintain alignment and surface figure on its three large mirrors. Corrective actions fed to the LSST AOS are determined from information derived from 4 curvature wavefront sensors located at the corners of the focal plane. Each wavefront sensor is a split detector such that the halves are 1mm on either side of focus. In this paper we describe the extensions to published curvature wavefront sensing algorithms needed to address challenges presented by the LSST, namely the large central obscuration, the fast f/1.23 beam, off-axis pupil distortions, and vignetting at the sensor locations. We also describe corrections needed for the split sensors and the effects from the angular separation of different stars providing the intra- and extra-focal images. Lastly, we present simulations that demonstrate convergence, linearity, and negligible noise when compared to atmospheric effects when the algorithm extensions are applied to the LSST optical system. The algorithm extensions reported here are generic and can easily be adapted to other wide-field optical systems including similar telescopes with large central obscuration and off-axis curvature sensing.

• The paper presents algorithmic extensions for curvature wavefront sensing tailored for the Large Synoptic Survey Telescope (LSST), addressing unique challenges like central obscuration and fast optics.
• Key innovations include adapting algorithms using annular Zernike polynomials, implementing nonlinear wavefront mapping correction, and compensating for off-axis pupil distortions and vignetting.
• Simulation results confirm the robustness of the extended algorithms, demonstrating negligible algorithmic noise compared to atmospheric effects and validating their reliability for LSST's operational requirements.

Curvature Wavefront Sensing for the Large Synoptic Survey Telescope

The paper "Curvature Wavefront Sensing for the Large Synoptic Survey Telescope" presents algorithmic extensions crucial for deploying curvature wavefront sensing in the Large Synoptic Survey Telescope (LSST). As an instrumental component of the LSST's Active Optics System (AOS), curvature wavefront sensing is pivotal for maintaining the alignment and surface figure of the telescope's large mirrors. This summary provides an expert-level overview of the key methodologies, results, and implications detailed in the paper.

Overview of Curvature Wavefront Sensing Challenges

The LSST presents several unique challenges for curvature wavefront sensing. The significant central obscuration of the telescope, its fast optical $f$/1.23 beam, off-axis pupil distortions, and vignetting complicate the conventional wavefront sensing approach. This paper adapts two foundational curvature wavefront sensing algorithms—the iterative Fast Fourier Transform (FFT) method by Roddier and Roddier and the series expansion technique by Gureyev and Nugent—to the LSST's constraints. These modifications are broadly applicable to other wide-field optical systems experiencing similar issues.

Algorithmic Innovations

Key innovations include:

1. Annular Zernike Polynomials: For accuracy, the algorithms adopt annular Zernike polynomials to address the 60% central obscuration, thus maintaining orthogonality in decomposing wavefront errors.
2. Nonlinear Mapping: A correction for the non-linear mapping of wavefront errors is implemented, essential for LSST’s low $f$-number. The application of a non-linear transformation rescales the wavefront to account for distortions across the intra- and extra-focal planes.
3. Off-axis Distortion Compensation: Recognizing the pupil distortions and vignetting at off-axis curvature sensing locations, polynomial mappings based on detailed ZEMAX simulations correct the off-axis geometrical distortions.
4. Field-dependent Variations: The split sensor design is addressed by solutions that normalize and subtract background variations, ensuring consistent wavefront properties between differently placed intra- and extra-focal images.

Results and Implications

The paper corroborates the algorithmic extensions with simulation results using tools such as ZEMAX and LSST's Photon Monte Carlo Simulator. Notably, the simulations demonstrate that algorithmic noise is negligible compared to atmospheric effects, validating the robustness of the extended algorithms in an operational setting. The authors report strong linear correlations in wavefront measurements and minimal deviations, affirming the algorithm's reliability under varied conditions.

Theoretical and Practical Implications

The successful extension of curvature wavefront sensing algorithms has far-reaching implications for active optics in large-scale survey telescopes. The enhanced computational methods advance our capacity to manage complex optical systems with large degrees of freedom and significant aberration control requirements. Practically, these algorithms enable the LSST to achieve its ambitious survey goals by producing more consistent and precise optical results despite atmospheric and intrinsic system aberrations.

Future Prospects

Future work involves integrating these algorithms into the LSST's AOS control systems, potentially extending them to other major telescope systems. Moreover, alignment strategies, tomographic reconstruction, and further validation with empirical data will be explored. As telescope technologies and the computational demands of astronomical data continue to evolve, the adaptability of these algorithms to various optical configurations may be a significant research focus.

In conclusion, this paper presents crucial advancements in curvature wavefront sensing algorithms tailored for the LSST. These developments exemplify the intricate interplay between algorithmic sophistication and physical optics design, reinforcing the prospects for future adaptive optics endeavors in astronomy.