Fluorescence microscopy is an important and ubiquitous tool in biological imaging due to the high specificity with which fluorescent molecules can be attached to an organism and the subsequent nondestructive in-vivo imaging allowed. Focused-light microscopies allow three-dimensional fluorescence imaging but their resolution is restricted by diffraction. This effect is particularly limiting in the axial dimension as the diffraction-limited focal volume produced by a lens is more extensive along the optical axis than perpendicular to it. Approaches such as confocal microscopy and 4Pi microscopy have been developed to improve the axial resolution. Spectral Self-Interference Fluorescence Microscopy (SSFM) is another high-axial-resolution technique and is the principal subject of this dissertation. Nanometer-precision localization of a single fluorescent layer has been demonstrated using SSFM. This accuracy compares favorably with the axial resolutions given by confocal and 4Pi systems at similar operating parameters (these resolutions are approximately 350nm and 80nm respectively).; This theoretical work analyzes the expected performance of the SSFM system when imaging a general object, i.e. an arbitrary fluorophore density function rather than a single layer. An existing model of SSFM is used in simulations to characterize the system's resolution. Several statistically-based reconstruction methods are applied to show that the expected resolution for SSFM is similar to 4Pi microscopy for a general object but does give very high localization accuracy when the object is known to consist of a limited number of layers. SSFM is then analyzed in a linear systems framework and shown to have strong connections, both physically and mathematically, to a multi-channel 4Pi microscope. Fourier-domain analysis confirms that SSFM cannot be expected to outperform this multi-channel 4Pi instrument. Differences between the channels in spatial-scanning, multi-channel microscopies are then exploited to show that such instruments can operate at a sub-Nyquist scanning rate but still produce images largely free of aliasing effects. Multi-channel analysis is also used to show how light typically discarded in confocal and 4Pi systems can be collected and usefully incorporated into the measured image.
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