| Fluorescence microscopes are valuable tools in determining the structure of the objects they image, typically, fixed and living cells and their components. However, the axial resolution of such microscopes is much worse than their transverse resolution. In addition, due to the finite aperture of the lenses used in all microscopes, not all the light emitted from the object is collected by the microscope. Every microscope acts like a low-pass filter and is therefore characterized by a transfer function, known as the optical transfer function (OTF). The bandpass region of OTF that determines which frequency components of the object will be transmitted has a characteristic shape with a cone shaped region in the middle in addition to bandlimits. Any object frequency components that fall in this cone shaped region, or outside the bandlimits are lost during imaging.; The standing-wave fluorescence microscope (SWIM) uses interference of two beams, resulting in a non-uniform, planar excitation pattern in the specimen. The optical transfer function of this microscope (SWOTF) has three distinct bands, a central band that is identical to the optical transfer function (OTF) in a conventional fluorescence microscope, and two additional sidebands that are offset from the central band. Therefore, the SWOTF has gaps between the central band and the sidebands, and information about the object that falls in the gaps or outside the three bands is lost when imaging. The principal questions answered by this thesis are: (1) Do the data in the sidebands of the SWOTF contribute additional information about the object? (2) Can the information about the object lost in the gaps in the SWOTF be recovered using computational means?; In SWFM, three images per plane of focus are required to capture all the information about the object. In the case of multiple plane data sets, there are three stacks of such triplets. In order to answer the questions posed above, the three SWFM images (or stacks) have to be first combined to generate a composite data set. This thesis describes the mathematical theory and procedure to combine the images obtained by the SWFM. Also, processing the combined data using a non-linear algorithm recovers the information lost in the gaps. This leads to improved resolution, both axial and transverse, after processing, and is demonstrated by the results shown in the thesis, from simulated as well as biological data. |
