Recently novel types of imaging spectrometers have been successfully demonstrated, where photonic crystals filters are placed onto a detector. For focused beams, it is however unclear how numerical aperture (NA), aperture shape and aberrations affect the transmission of these filters and there is currently no established and computational efficient method to assess this. In this work we present an angular spectrum method to reconstitute focused beam fields and transmissions based on plane wave simulations. Once these plane wave simulations have been performed, the transmission of arbitrary pupils, aberrations and NA can be directly computed. We investigate the accuracy of this method by comparing the synthesized transmission and Poynting vectors with a fully simulated focused Gaussian beam. These results show that an angular sampling between 0.5° and 0.8° is required to achieve an accurate result depending on the mesh sampling of the simulation. Lastly, we demonstrate how this method can be used to investigate the effect of the pupil shape and aberrations on the transmission profiles. This analysis enables the identification of spectral regions which are sensitive to the instrument design but also regions which appear robust. We believe that the method described in this work can provide scientists and optical engineers a tool to perform detailed performance studies on these promising new instruments.

As global climate change severely impacts our world, there is an increasing demand to monitor trace gases with a high spatial resolution and accuracy. At the same time, these instruments need to be compact in order have constellations for short revisit times. Here we present a new spectrometer instrument concept for trace gas detection, where photonic crystals filters replace traditional diffraction based optical elements. In this concept, 2D photonic crystal slabs with unique transmission profiles are bonded on a detector inside a regular telescope. As the instrument flies over the earth, different integrated intensities for each filter are measured for a single ground resolution element with a regular telescope. From this detector data, trace gas concentrations are retrieved. As an initial test case we focused on methane and carbon dioxide retrieval and estimated the performance of such an instrument. We derive the Cramér-Rao lower bound for trace-gas retrieval for such a spectrometer using Fisher information and compare this with the achieved performance. We furthermore set up a framework how to select photonic crystal filters based on maximizing the Fisher information carried by the filters and how to use the Cramér-Rao lower bound to find good filter sets. The retrieval performance of such an instrument is found to be between 0.4% to 0.9% for methane and 0.2% to 0.5% for carbon dioxide detection for a 300×300 m² ground resolution element and realistic instrument parameters.

High-NA light sheet illumination can improve the resolution of single-molecule localization microscopy (SMLM) by reducing the background fluorescence. These approaches currently require custom-made sample holders or additional specialized objectives, which makes the sample mounting or the optical system complex and therefore reduces the usability of these approaches. Here, we developed a single-objective lens-inclined light sheet microscope (SOLEIL) that is capable of 2D and 3D SMLM in thick samples. SOLEIL combines oblique illumination with point spread function PSF engineering to enable dSTORM imaging in a wide variety of samples. SOLEIL is compatible with standard sample holders and off-the-shelve optics and standard high NA objectives. To accomplish optimal optical sectioning we show that there is an ideal oblique angle and sheet thickness. Furthermore, to show what optical sectioning delivers for SMLM we benchmark SOLEIL against widefield and HILO microscopy with several biological samples. SOLEIL delivers in 15 μm thick Caco2-BBE cells a 374% higher intensity to background ratio and a 54% improvement in the estimated CRLB compared to widefield illumination, and a 184% higher intensity to background ratio and a 20% improvement in the estimated CRLB compared to HILO illumination.

MINFLUX offers a breakthrough in single molecule localization precision, but is limited in field of view. Here we combine centroid estimation and illumination pattern induced photon count variations in a conventional widefield imaging setup to extract position information over a typical micrometer-sized field of view. We show a near two-fold improvement in precision over standard localization with the same photon count on DNA-origami nanostructures and tubulin in cells, using DNA-PAINT and STORM imaging.