Conference Agenda

Wavefront shaping allows focusing and imaging at depth in disordered media such as biological tissues, exploiting the ability to control multiply scattered light. Many so-called guide-star mechanisms have been investigated to deliver light and image non-invasively, among which incoherent processes such as non-linear fluorescence feedback. However, the most common microscopy contrast mechanism, linear fluorescence, remains extremely challenging. I will discuss some of our recent works, exploiting signal processing and machine learning frameworks, to recover images behind scattering layers exploiting linear fluorescence.

Structured illumination microscopy (SIM) is a technique that employs non-uniform illumination to shift spatial frequencies that are normally unobservable into the region of the non-zero optical transfer function (OTF). Several images are combined to reconstruct these spatial frequencies, yielding up to twofold increase in resolution beyond the diffraction limit. However, the reconstruction process is affected by noise, and spatial frequencies can only be estimated with a certain precision and accuracy that depends on the procedure used. The spectral signal-to-noise ratio (SSNR) serves as an indicator of the possible quality of a reconstruction. Conventional SIM reconstruction is based on a least-squares estimate; while this approach yields high SSNR, it is performed in the Fourier domain and assumes uniform imaging conditions (illumination brightness, modulation depth, aberration coefficients) across the field of view (FOV). In large FOVs, this assumption is often violated, resulting in artifacts. An existing spatial-domain procedure produces low SSNR at high spatial frequencies, rendering these effectively unresolvable under low-light conditions. In this work, we present a local SIM reconstruction procedure with an order-of-magnitude higher SSNR. We demonstrate that it nearly achieves the SSNR of Fourier domain reconstruction, and we also show that further improvement is not possible.

Novel formulas have been derived for the primary spherical aberration, coma and axial color of systems of thin lenses in contact. Even in complex optical systems, groups of lenses can be modelled as thin lenses in contact. The new mathematical formalism helps explaining significant qualitative properties of the lens design landscape.

Distortion is a common annoyance in optical imaging. Learning from computer vision, many distortion correction algorithms are developed, mostly based on the Brown-Conrady model. An analysis of the field dependence of aberrations in terms of the zero aberration points in the field of view, the so-called nodes, provides another inroad to study distortion. Using the Nodal Aberration Theory, we show that the distortion field is the gradient of a scalar field. Structural changes in the distortion field are characterized by a complex sequence of creation, annihilation and reorganization of up to five nodes driven by tilt and decenter misalignments of the optical components. This description can be fruitfully applied in alignment protocols for complex optical systems, in image registration of multi-color localization microscopy, and of correlative light and electron microscopy.

Elevation topography equipment measures freeform surfaces by representing the surface with elevation maps, maximum curvature, minimum curvature, mean curvature, and Gaussian curvature. From a geodetic point of view, every regular point on a parametric surface can be described as a function of the principal curvatures and the local torsion concerning a reference path at each point. Here, we present some fundamentals required to create these density maps to represent the absolute torsion and the local conic constant of all points on a regular freeform surface.