Compensation of Beer-Lambert attenuation using non-diffracting Bessel beams

We report on a versatile method to compensate the linear attenuation in a medium, independently of its microscopic origin. The method exploits diffraction-limited Bessel beams and tailored on-axis intensity profiles which are generated using a phase-only spatial light modulator. This technique for compensating one of the most fundamental limiting processes in linear optics is shown to be efficient for a wide range of experimental conditions (modifying the refractive index and the attenuation coefficient). Finally, we explain how this method can be advantageously exploited in applications ranging from bio-imaging light sheet microscopy to quantum memories for future quantum communication networks

Diffusion is All You Need for Learning on Surfaces

We introduce a new approach to deep learning on 3D surfaces such as meshes or point clouds. Our key insight is that a simple learned diffusion layer can spatially share data in a principled manner, replacing operations like convolution and pooling which are complicated and expensive on surfaces. The only other ingredients in our network are a spatial gradient operation, which uses dot-products of derivatives to encode tangent-invariant filters, and a multi-layer perceptron applied independently at each point. The resulting architecture, which we call DiffusionNet, is remarkably simple, efficient, and scalable. Continuously optimizing for spatial support avoids the need to pick neighborhood sizes or filter widths a priori, or worry about their impact on network size/training time. Furthermore, the principled, geometric nature of these networks makes them agnostic to the underlying representation and insensitive to discretization. In practice, this means significant robustness to mesh sampling, and even the ability to train on a mesh and evaluate on a point cloud. Our experiments demonstrate that these networks achieve state-of-the-art results for a variety of tasks on both meshes and point clouds, including surface classification, segmentation, and non-rigid correspondence

Deep Point Correlation Design

Designing point patterns with desired properties can require substantial effort, both in hand-crafting coding and mathematical derivation. Retaining these properties in multiple dimensions or for a substantial number of points can be challenging and computationally expensive. Tackling those two issues, we suggest to automatically generate scalable point patterns from design goals using deep learning. We phrase pattern generation as a deep composition of weighted distance-based unstructured filters. Deep point pattern design means to optimize over the space of all such compositions according to a user-provided point correlation loss, a small program which measures a pattern’s fidelity in respect to its spatial or spectral statistics, linear or non-linear (e. g., radial) projections, or any arbitrary combination thereof. Our analysis shows that we can emulate a large set of existing patterns (blue, green, step, projective, stair, etc.-noise), generalize them to countless new combinations in a systematic way and leverage existing error estimation formulations to generate novel point patterns for a user-provided class of integrand functions. Our point patterns scale favorably to multiple dimensions and numbers of points: we demonstrate nearly 10 k points in 10-D produced in one second on one GPU. All the resources (source code and the pre-trained networks) can be found at https://sampling.mpi-inf.mpg.de/deepsampling.html