Abstract: The basic concepts of selective multiscale reconstruction of functions on the sphere from error-affected data is outlined for scalar functions. The selective reconstruction mechanism is based on the premise that multiscale approximation can be well-represented in terms of only a relatively small number of expansion coefficients at various resolution levels. A new pyramid scheme is presented to efficiently remove the noise at different scales using a priori statistical information.
The great flexibility of direct laser writing (DLW) arises from the possibility to fabricate precise three-dimensional structures on very small scales as well as the broad range of applicable materials. However, there is still a vast number of promising materials, which are currently inaccessible requiring the continuous development of novel photoresists. Herein, a new bio-sourced resist is reported that uses the monomeric unit of chitin, N-acetyl-D-glucosamine, paving the way from existing hydrogel resists based on animal carbohydrates to a new class of non-hydrogel ones. In addition, it is shown that the combined use of two photoinitiators is advantageous over the use of a single one. In this approach, the first photoinitiator is a good two-photon absorber at the applied wavelength, while the second photoinitiator exhibits poor two-photon absorbtion abilities, but is better suited for cross-linking of the monomer. The first photoinitiator absorbs the light acting as a sensitizer and transfers the energy to the second initiator, which subsequently forms a radical and initializes the polymerization. This sensitization effect enables a new route to utilize reactive photointiators with a small two-photon absorption cross section for DLW without changing their chemical structure.