Interference microscopy: Super-resolution particle tracking and velocimetry.

摘要

This dissertation describes the theory and applications of a new approach to imaging called Interference Microscopy (IM). Interfere Microscopy works by inserting a lens and axicon into the optical path of an imaging system. The lens and axicon serve to re-image the image produced by the original optical system. However, instead of imaging a point in the measurement plane to a point in an image plane, the IM system maps a point along a line produced by an interference pattern. This unique interference pattern, called a Bessel beam, allows for several unique applications of the IM system. The first chapter of this dissertation describes a rigorous derivation of the three dimensional point spread function of the IM system. Using the Frenel Diffraction Integral, light from a paraxial off axis point source is propagated through the axicon to an imaging plane. The resulting analytical expression for the diffraction pattern produced is then experimentally verified. Chapter 2 covers the use of IM for single view three dimensional particle locating. This application relies on the analytical expression for the three dimensional point spread function of the IM system. Once the properties of an interference pattern produced by a particle are determined, it is possible to directly calculate the three dimensional location of the particle that produced it. Image analysis algorithms to determine interference pattern properties are described and the method is experimentally verified and applied to pressure driven flow in a rectangular channel and to a particle carried by an electrothermal vortex. A measurement depth of 200 μm is demonstrated with an accuracy of ± 3 μm in calculating the height of the particle. In the third chapter the IM system is applied to another velocity measurement technique, Particle Image Velocimetry (PIV). Here, simulated images of a typical microscope and the same microscope with the IM attachment are used to investigate the resolution limits of PIV measurements. A clear increase in resolution is found, nearly double that of the base microscope. The last chapter discusses the ability of the IM system to resolve features that are smaller than the diffraction limit of the base microscope. The Reyleigh limit for the IM system is shown to be less than one third the base microscope. Diffraction simulations are performed to verify this limit and experimental images of sub-diffraction limit particles are presented.