Zeitschriftenaufsätze, Buchbeiträge

The size of the aperture stop of a lens is a major parameter to define, e.g., the depth of focus of an optical imaging system. In conventional systems, totally absorbing apertures are generally assumed. Their optical performance can be easily described by a geometric ray model. We propose an extended model to estimate the depth of focus with respect to a nontotally absorbing circular aperture, which may correspond to new concepts for tunable apertures, in particular for micro-optical systems. We present specifications to analyze and optimize the performance of those systems and verify the theoretical model by experimental depth of focus measurements with a partly transparent aperture.

An efficient algorithm for calculating nonparaxial scalar field distributions in the focal region of a lens is discussed. The algorithm is based on fast Fourier transform implementations of the first RayleighSommerfeld diffraction integral and assumes that the input field at the pupil plane has a larger extent than the field in the focal region. A sampling grid is defined over a finite region in the output plane and referred to as a tile. The input field is divided into multiple separate spatial regions of the size of the output tile. Finally, the input tiles are added coherently to form a summed tile, which is propagated to the output plane. Since only a single tile is propagated, there are significant reductions of computational load and memory requirements. This method is combined either with a subpixel sampling technique or with a chirp z-transform to realize smaller sampling intervals in the output plane than in the input plane. For a given example the resulting methods enable a speedup of approximately 800× in comparison to the normal angular spectrum method, while the memory requirements are reduced by more than 99%.

An innovative optical system for trapping particles in air is presented. We demonstrate an optical system specifically optimized for high precision positioning of objects with a size of several micrometers within a nanopositioning and nanomeasuring machine (NPMM). Based on a specification sheet, an initial system design was calculated and optimized in an iterative design process. By combining optical design software with optical force simulation tools, a highly efficient optical system was developed. Both components of the system, which include a refractive double axicon and a parabolic ring mirror, were fabricated by ultra-precision turning. The characterization of the optical elements and the whole system, especially the force simulations based on caustic measurements, represent an important interim result for the subsequently performed trapping experiments. The caustic of the trapping beam produced by the system was visualized with the help of image processing techniques. Finally, we demonstrated the unique efficiency of the configuration by reproducibly trapping fused silica spheres with a diameter of 10 [my]m at a distance of 2.05 mm from the final optical surface.