Study On Resolution Enhancement Of Fourier Transform Spectroscopy

Main points of the dissertation 揝tudy on Resolution Enhancement of Fourier Transform Spectroscopy?are as following: 1. Super-Resolution Spectrum Estimation (SRSE) based on Eigenvalue Analysis and Linear Fitting (EALF) Treating SRSE in Fourier Transform Spectroscopy (FTS) as estimation of harmonic frequencies and amplitudes in the interferogram, the method EALF, inspired by Prony method in Signal and System domain is brought forward. EALF is composed of three parts: parameter estimation with Total Least Squares (TLS), frequency estimation with eigenvalue analysis and amplitude estimation with Least Squares (LS) fitting. 2. Parameter Estimation with TLS Every parameter estimation problem gives rise to an overdetermined set of linear equations. LS is the common approach to solve this set, but it gives unbiased solution only when noise in data vector has Gauss distribution. When the data matrix is also inaccurate, TLS can give strongly consistent estimation. Original ideas about TLS parameter estimation are presented through theoretical study on TLS and by means of Matrix Singular Value Decomposition. 3. Characteristics of Fourier Self-Deconvolution (FSD) FSD is not only a resolution enhancement technique by itself, but also an absolutely necessary step in SRSE based on Auto-Regressive (AR) model. We find in study that FSD performs like a band-pass filter with deconvolution function as the high-pass filter and apodization function as the low-pass filter. They together determine the filtering characteristics of FSD. Knowing line shape of the spectrum is the precondition for FSD. The particularities of line shape estimation in FTS are I? discussed. 4. Application of FTS Resolution Enhancement (FTSRE) in No Moving Parts Imaging FTS (NMM-IFTS) A flow chart of SRSE program is presented as the consideration to the application of FTSRE in NMM-IFTS. Two such instruments based on Lateral Shearing Interferometer (LSI) are developed by the author抯 group.