arXiv subjects

Victoria Laidlaw

Publications and source records attributed to Victoria Laidlaw.

3 recordsLinked to original sources

arXiv2026

A self-adjoint Fourier-type model for the iQuad wavefront sensor

Advanced adaptive optics (AO) systems can use Fourier-type wavefront sensing to correct optical distortions encountered in ground-based telescopes, AO-assisted retinal imaging, and free-space optical communications (FSOC). Recently, a novel Fourier-type wavefront sensor (WFS) known as the iQuad WFS has been introduced. Its design features a focal plane tessellation with a four-quadrant phase mask (FQPM) that incorporates a $\pm \pi/2$ phase shift between adjacent quadrants. In this work, we establish a comprehensive mathematical framework for the iQuad WFS, including its forward models and linearizations based on the Fr\'echet derivative. We reveal a connection between the iQuad WFS and the 2d finite Hilbert transform and demonstrate that the linear iQuad WFS operator is self-adjoint - a unique property among Fourier-type WFSs. Additionally, we introduce the double iQuad WFS, a two-path configuration that combines two rotated iQuad WFSs. This design addresses the limitations of the single iQuad WFS by suppressing poorly-seen phase components. Moreover, the double setup simplifies the mathematical modeling. We also highlight iQuad similarities to the widely used pyramid wavefront sensor (PWFS). Finally, we extend the concept of modulation to the iQuad WFS, further enhancing its versatility. The theoretical analysis presented here lays the groundwork for the development of fast and robust model-based wavefront reconstruction algorithms for the iQuad WFS, paving the way for future applications in AO instruments.

math-ph↗

arXiv2025

A generalised non-linear reconstructor for all Fourier-type wavefront sensors

State-of-the-art adaptive optics (AO) systems perform non-linear Fourier-type wavefront sensing for real-time corrections of dynamic wavefront aberrations. This general class of sensors uses a filtering mask in the focal plane that converts phase fluctuations of the incoming light into intensity variations in the subsequent pupil plane. Due to their high sensitivity, Fourier-type wavefront sensors (WFSs) are the sensors of choice for many current and upcoming AO systems in ophthalmic imaging, free-space optical communications (FSOC) and astronomical ground-based telescopes such as the forthcoming generation of extremely large telescopes (ELTs). Conventionally, linear methods, like a matrix-vector-multiplication (MVM), are used for the inversion of Fourier-type WFSs. However, their non-linear behavior gives rise to severe performance degradations when significant channel perturbations are observed. They are expected to occur during strong atmospheric turbulence conditions, which are commonplace for non-rural sites and daytime observations. This study presents a novel type of iterative reconstructor to overcome non-linear wavefront sensing regimes. The underlying method is the non-linear Landweber iteration with Nesterov acceleration, well known in the field of inverse problems. A significant advantage of the new approach is its direct applicability to any Fourier-type WFS. This is implemented by adapting the filtering mask of the specific Fourier-type WFSs in the model-based algorithm. Several Fourier-type wavefront sensors are considered for ELT-scale instruments and their performance with the new algorithm is compared. The study goes on to concentrate on the pyramid wavefront sensor (PWFS), one of the most well-known Fourier-type WFSs. We demonstrate in end-to-end simulations that this novel approach outperforms linear methods in non-linear sensing regimes.

astro-ph.IM↗

arXiv2024

On Phase Unwrapping via Digital Wavefront Sensors

In this paper, we derive a new class of methods for the classic 2D phase unwrapping problem of recovering a phase function from its wrapped form. For this, we consider the wrapped phase as a wavefront aberration in an optical system, and use reconstruction methods for (digital) wavefront sensors for its recovery. The key idea is that mathematically, common wavefront sensors are insensitive to whether an incoming wavefront is wrapped or not. However, typical reconstructors for these sensors are optimized to compute smooth wavefronts. Thus, digitally "propagating" a wrapped phase through such a sensor and then applying one of these reconstructors results in a smooth unwrapped phase. First, we show how this principle can be applied to derive phase unwrapping algorithms based on digital Shack-Hartmann and Fourier-type wavefront sensors. Then, we numerically test our approach on an unwrapping problem appearing in a free-space optical communications project currently under development, and compare the results to those obtained with other state-of-the-art algorithms.

math.NA↗