Solutions to Limitations on Spatially Varying Super-Resolution Methods

In this work we focused on Super-Resolution imaging methods which use active manipulation of spatially varying patterns on high resolution samples. We found solutions to the main limitations on known methods that use different ways to form patterns on the samples.

Approaches that use spatially varying illumination, such as structured illumination microscopy etc., encode high spatial-frequency features of samples which can later be decoded using post processing. A strong requirement is to have a-priori high spatial-frequency knowledge of the encoding patterns. We addressed this problem and proposed a method in which the sample is illuminated by an ensemble of unknown, high-resolution speckle patterns. The patterns themselves are unknown, but are connected by a known transformation. This set of illuminated sample images is limited in its spatial frequency because of the non-ideal imaging system. Using the set and the knowledge of the known transformation, the sample and the ensemble are reconstructed with higher resolution than the limited imaging system.

The concept of most super-resolution techniques is to perfect focusing or synthetically enlarge the aperture. However, the diffraction limit still determines the resolution boundary and resolution enhancement beyond 200 nm with visible light is hard to achieve. A new approach called linear optics nanoscopy managed to break beyond the diffraction limit by forming patterns on the sample using manipulation of disturbances to the global illumination. Subwavelength nanoparticles are suspended next to the object, and evanescent waves are encoded into the nanoparticles scattered light. A major limitation comes from the fact that the nanoparticles undergo Brownian motion. Based on passive scanning, the method suffers from long measurement times and other significant limitations; for example, only nanoparticles located closer than the illumination wavelength to the sample contribute to the signal. To overcome these limitation we developed a method that manipulates sub-wavelength particles using optical trapping which actively manipulated the disturbance. Optical tweezers both force the particle to subwavelength distances from the sample and control the scan. A new mathematical variation on the original method was also developed due to the fact that the disturbance reflected the light instead of absorbing it.