Boots – shoes – and leggings
Patent
1993-06-30
1995-03-21
Voeltz, Emanuel T.
Boots, shoes, and leggings
356346, 364498, 364574, G06J 345, G01R 2316
Patent
active
054002656
DESCRIPTION:
BRIEF SUMMARY
The present invention concerns a procedure performed entirely in the time domain, for increasing the resolution of spectral information, or for reducing the width of spectral lines, in FTIR, IR, NMR or other spectroscopy.
For instance when the quantities of gaseous impurities are monitored in industrial areas, factory halls, switching yards or other critical locations, or when air quality in general is studied, one has to be able to observe concentrations on the order of a few ppb. It is typical, in apparatus constructed for this purpose, to use chemical or semiconductor detectors which are sensitive to a single gas or a few gases only. Since infrared spectroscopy, at its best, enables the same sensitivity to be reached, it becomes possible to monitor simultaneously almost all measurable gases, and this being furthermore a comparatively rapid method of analysis, it is a noteworthy alternative in applications of this type.
However, the spectra obtained as results of measurement may be difficult of their interpretation. The gas which is being measured may contain many different constituents and various interference factors which impede the interpretation of the spectrum. The object of the present invention is to disclose a design which enables more accurate and more detailed interpretation of measured spectral information than before, and elimination of disturbances of the measurement.
Fourier Self-Deconvolution (FSD) and the Maximum Entropy Method (MEM) are both well-established procedures serving spectral line stabilizing (spectral information resolution enhancing). FSD is at present mainly employed in infrared .spectroscopy of solid or liquid state, while MEM has been applied in numerous other branches of science as well.
FSD constitutes a linear method of deconvolution which is exclusively based on multiplication of the measured information in the time domain. In the present application text the FT-IR convention is followed, referring to the interferogram domain as the time domain and the spectral domain, as the frequency domain. MEM, on the other hand, represents a non-linear fitting method maximizing the information entropy of the output data. It is typical of this method that minor changes at the input cause powerful distortions in the output, and the results may even depend on the algorithm used. Furthermore, MEM gives only one of a plurality of possible solutions, whereas FSD yields an exact solution containing noise. While MEM is a well-approved procedure today, many practitioners of this method add a warning that it generates ghost lines or fails to find real, small lines.
In the following we shall first compare the FSD and MEM procedures as regards their efficiency to narrow spectral lines.
We shall use the following pair of Fourier transformations in this text: ##EQU1## where E(.nu.) is the spectrum (i.e., intensity as a function of wave number), I(x) is the interferogram (i.e., intensity as a function of optical path difference), and { } and .sup.-1 { } are the Fourier transform and the inverse Fourier transform, respectively.
Fourier self-deconvolution (FSD) takes as input a spectrum E(.nu.), consisting of lines with assumed line shapes W(.nu.). These input line shapes are converted to a desired output line shape W.sub.o (.nu.) by the time domain operation specified in Formula 2: ##EQU2## where W'(.nu.) is the deconvolved spectrum having the output line shape W.sub.o (.nu.). If the desired line shape is narrower than the initial line shape, line narrowing has been achieved. The line shape, line narrowing has been achieved. The line narrowing factor K, loosely referred to as "resolution enhancement factor", is given by the formula: ##EQU3## where FWHH(W) and FWHH(W.sub.o ) are the full width at half height of W(.nu.) and W.sub.o (.nu.), respectively.
The main advantage of FSD is that it is a linear procedure, that is, the Fourier self-deconvolutions of E.sub.1 (.nu.) and E.sub.2 (.nu.):
It is well-known (notably in electronics) that an output signal S' (t) can be defined as the convolution of t
REFERENCES:
patent: 5039222 (1991-08-01), Izumi
Fourier & Computerized Infrared Spectroscopy, vol. 553, 1985 (Canada) K. H. Michaelian et al: "Resolution Enhancement of Photoacoustic FTIR Spectra", See pp. 260-261.
Electronics & Communications in Japan, vol. 72, No. 9, 1989 Kiyoshi Nishiyama et al: "Super-Resolution NMR Spectrum Estimation Method", see pp. 25-33.
Journal of Magnetic Resonance, vol. 43, 1981 R. G. Brereton et al: "The Application of Adjustable-Parameter Sine Bell Apodizationto Carbon 13 NMR Spectra", see pp. 224-233.
Journal of Magnetic Resonance, vol. 24, 1976 Antonio De Marco et al: "Digital Filtering with a Sinusoidal Window Function: An Alternative Technique for Resolution Enhancement in FT NMR", see pp. 201-204.
Pipala Edward
Temet Instruments Oy
Voeltz Emanuel T.
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