MATHEMATICAL ENCHANCEMENT OF THE SPECTRAL RESOLUTION OF FOURIER SPECTROSCOPY TECHNIQUES,
Abstract
The problem of mathematically increasing the spectral resolution of Fourier spectroscopy techniques is examined. The use of prolate spheroidal wave functions in a series expansion of an interferogram is investigated in detail in order to improve spectral resolution while allowing a decrease in superfluous signal-to-noise ratio. Resolution gain is shown to be proportional to the number of terms in the series: 4WT'/T terms essentially extrapolates the signal from T to T' and gives a resolution gain of T'T=K. The integral square error due to series truncation, interferogram noise, timelimiting, and computer programming limitations is formulated quantitatively. When exact analytical extrapolation of the noisy interferogram is assumed, an approximate one-to-one tradeoff between signal-to-noise ratio and resolution may theoretically be achieved. Practicalities involved in the numerical generation of the spheroidal functions and the numerical correlation are shown to be serious limitations to the application of the theory. Thus, only problems dealing with small time-bandwidth products (2 piWT<10) may be expected to yield resolution gains much greater than two. A method using small portions of the band, and, therefore a small time-bandwidth product, is introduced which is applicable if the major part of the signal energy is concentrated in that band. The theory presented is equally applicable to optical resolution problems. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 01, 1968
- Accession Number
- AD0688504
Entities
People
- Alvin M. Despain
- R. Lynn Kirlin
Organizations
- Utah State University