Time-resolved nonlinear ghost imaging

Terahertz (THz) spectroscopy systems are widely employed to retrieve the chemical and material composition of a sample. This is single-handed the most important driving motivation in the field and has largely contributed to shaping THz science as an independent subject. The limited availability of high-resolution imaging devices, however, still represents a major technological challenge in this promising field of research. In this theoretical work, we tackle this challenge by developing a novel nonlinear Ghost Imaging (GI) approach that conceptually outperforms established single-pixel imaging protocols at inaccessible wavelengths. Our methodology combines nonlinear THz generation with time-resolved field measurements, as enabled by state-of-the-art Time Domain Spectroscopy (TDS) techniques. As an ideal application target, we consider hyperspectral THz imaging of semi-transparent samples with nonnegligible delay contribution and we demonstrate how time-resolved, full-wave acquisition enables accurate spatiotemporal reconstruction of complex inhomogeneous samples

Hyperspectral phase retrieval : spectral–spatial data processing with sparsity-based complex domain cube filter

Hyperspectral (HS) imaging retrieves information from data obtained across broadband spectral channels. Information to retrieve is a 3D cube, where two coordinates are spatial and the third one is spectral. This cube is complex-valued with varying amplitude and phase. We consider shearography optical setup, in which two phase-shifted broadband copies of the object projections are interfering at a sensor. Registered observations are intensities summarized over spectral channels. For phase reconstruction, the variational setting of the phase retrieval problem is used to derive the iterative algorithm, which includes the original proximity spectral analysis operator and the sparsity modeling of the complex-valued object 3D cube. We resolve the HS phase retrieval problem without random phase coding of wavefronts typical for the most conventional phase retrieval techniques. We show the performance of the algorithm for object phase and thickness imaging in simulation and experimental tests.publishedVersionPeer reviewe

Compressively sampling the optical transmission matrix of a multimode fibre (article)

This is the final version. Available on open access from Springer Nature via the DOI in this recordThe dataset associated with this article is available in ORE at : https://doi.org/10.24378/exe.3204The measurement of the optical transmission matrix (TM) of an opaque material is an advanced form of space-variant aberration correction. Beyond imaging, TM-based methods are emerging in a range of fields, including optical communications, micro-manipulation, and computing. In many cases, the TM is very sensitive to perturbations in the configuration of the scattering medium it represents. Therefore, applications often require an up-to-the-minute characterisation of the fragile TM, typically entailing hundreds to thousands of probe measurements. Here, we explore how these measurement requirements can be relaxed using the framework of compressive sensing, in which the incorporation of prior information enables accurate estimation from fewer measurements than the dimensionality of the TM we aim to reconstruct. Examples of such priors include knowledge of a memory effect linking the input and output fields, an approximate model of the optical system, or a recent but degraded TM measurement. We demonstrate this concept by reconstructing the full-size TM of a multimode fibre supporting 754 modes at compression ratios down to ∼5% with good fidelity. We show that in this case, imaging is still possible using TMs reconstructed at compression ratios down to ∼1% (eight probe measurements). This compressive TM sampling strategy is quite general and may be applied to a variety of other scattering samples, including diffusers, thin layers of tissue, fibre optics of any refractive profile, and reflections from opaque walls. These approaches offer a route towards the measurement of high-dimensional TMs either quickly or with access to limited numbers of measurements.National Natural Science Foundation of ChinaNational Science Foundation (NSF)European Regional Development Fund (ERDF)European Research Council (ERC)Royal Academy of Engineering (RAE

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal