arXiv subjects

Bastien Laville

Publications and source records attributed to Bastien Laville.

4 recordsLinked to original sources

arXiv2026

Robust optical design and closed-form tolerancing through autodiff-based Hessian spectral analysis

Robust optical design demands quantitative knowledge of how manufacturing and alignment tolerances degrade system performance. We show that analysing the perturbation eigenmodes of the Hessian matrix gives qualitative insight about the mechanisms of performance degradation (such as couplings) that is invisible to classical sensitivity-matrix analysis based on the Jacobian alone. Via the envelope theorem, we prove that the first-order sensitivity of the fully compensated system is identical to that of the uncompensated one; refocusing only acts at second order through the Schur complement of the Hessian. We propose the trace of the tolerance-scaled Hessian %,$\Tr(\mathbf{S}\mathbf{H}\mathbf{S})$, as a single scalar robustness metric. Demonstrated on an off-axis three-mirror anastigmat and scaled to a twenty-three-parameter surface-figure model, eigenmode decomposition reveals the dominant sensitivity directions and yields deterministic tolerance budgets that replace costly Monte Carlo sampling.

physics.optics↗

arXiv2025

The $N$-achromat and beyond: a unified variational framework for optimal chromatic aberration correction

In this article, we present novel and effective methods for reducing chromatic aberrations in cemented lens systems. We derive an analytical solution coined the pentachromat, which corrects five distinct colors. This method can naturally be extended to accommodate an arbitrary number of lenses and to correct for a customized selection of spectral lines. Since correcting for specific rays rather than the entire residual spectrum can overconstrain the system, we introduce a variational formulation. This approach tames the residual spectrum by several orders of magnitude compared to conventional designs like the superachromat, while giving theoretical guarantees to reach the optimal solutions. Furthermore, this innovative methodology opens up previously uncharted design possibilities, such as multiple-focal-length achromatic systems. This allows for the selection of specific optical powers paired with desired bandwidths, enabling the design of highly specialized and tailored optical systems. Finally, we couple our variational framework with a combinatorial search, allowing to find the type of glasses and their geometry such that it reaches the best residual spectrum over an available catalogue.

physics.optics↗

arXiv2025

Dynamic off-the-grid untangling of curves by Riemannian metric

We propose an improved strategy for point sources tracking in a temporal stack through an off-the-grid fashion, inspired by the Benamou-Brenier regularisation in the literature. We define a lifting of the problem in the higher-dimensional space of the roto-translation group. This allows us to overcome the theoretical limitation of the off-the-grid method towards tangled point source trajectories, thus enabling the reconstruction and untangling even from the numerical standpoint. We define accordingly a new regularisation based on the relaxed Reeds-Shepp metric, an approximation of the sub-Riemannian Reeds-Shepp metric, further allowing control on the local curvature of the recovered trajectories. Then, we derive some properties of the discretisation and prove a $Γ$-convergence result, fostering interest for practical applications of polygonal, Bézier, and piecewise geodesic discretisation. We finally test our proposed method on a localisation problem example, and give a fair comparison with the state-of-the-art off-the-grid method.

math.DG↗

arXiv2021

Off-the-grid covariance-based super-resolution fluctuation microscopy

Super-resolution fluorescence microscopy overcomes blurring arising from light diffraction, allowing the reconstruction of fine scale details in biological structures. Standard methods come at the expense of long acquisition time and/or harmful effects on the biological sample, which makes the problem quite challenging for the imaging of body cells. A promising new avenue is the exploitation of molecules fluctuations, allowing live-cell imaging with good spatio-temporal resolution through common microscopes and conventional fluorescent dyes. Several numerical algorithms have been developed in the literature and used for fluctuant time series. These techniques are developed within the discrete setting, namely the super-resolved image is defined on a finer grid than the observed images. On the contrary, gridless optimisation does not rely on a fine grid and is rather an optimisation of Dirac measures in number, amplitudes and positions. In this work, we present an off-the-grid problem accounting for the independence of fluctuations.

math.OC↗