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- Gauss(vGrid, gamma=1.0)
- Gauss profile normalized to one (gamma is HWHM).
- HyperGauss(vGrid, gamma=1.0)
- 'hyper-Gauss' profile with power of six in the exponent normalized to one (gamma is HWHM).
- Hyperbolic(vGrid, gamma=1.0)
- Hyperbolic profile normalized to one (gamma is HWHM).
- Lorentz(vGrid, gamma=1.0)
- Lorentz profile normalized to one (gamma is HWHM).
- Sinc(x)
- SuperGauss(vGrid, gamma=1.0)
- 'super-Gauss' profile with power of four in the exponent normalized to one (gamma is HWHM).
- Triangle(xGrid, hwhm=1.0)
- Triangular profile normalized to one (the triangle goes from -2*hwhm to +2*hwhm).
- fts(vGrid, mopd=1.0, apodize='', vShift=0.0, sigma=1.0)
- Instrument Line Shape (spectral response function) for Fourier transform spectrometer.
Default: ils = 2 mopd sinc(2 pi mopd v) = sin(2 pi mopd v)/(pi v) unapodized;
ARGUMENTS:
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vGrid: wavenumber grid
mopd: L = mopd = maximum optical path difference [cm]
apodize: type of apodization function, default None, i.e. ILS = 2*L*sinc(2 pi L vGrid)
triangle, cosine, weak|medium|strong Norton-Beer, Hamming, Hanning, quartic, Gaussian, ...
In most cases case-insensitive, the first letter is sufficient (e.g. 't' for triangular)
except for:
"H" Hamming
"h" hanning
vShift: wavenumber shift (default 0.0)
sigma: width for Gaussian apodization
RETURNS:
--------
ils: a ndarray of response function values with size=len(vGrid)
REFERENCES:
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Weisstein, Eric W. "Apodization Function." From MathWorld -- A Wolfram Web Resource.
http://mathworld.wolfram.com/ApodizationFunction.html
R.H. Norton and C.P. Rinsland. New apodozing functions in Fourier spectrometry.
J. Opt. Soc. Am., 66:259-264, 1976. doi: 10.1364/JOSA.66.000259.
R.H. Norton and R. Beer. Errata: New apodozing functions in Fourier spectrometry.
J. Opt. Soc. Am., 67:419, 1977. doi: 10.1364/JOSA.67.000419.
- gauss4quad(x)
- # ... and the gaussian required for the integral defining the Gaussian apodization function, to be solved by quadpack
- hamming(t)
- Hamming instrument function for apodization (without the MOPD prefactor!).
- hanning1(t)
- Hanning instrument function for apodization (without the MOPD prefactor!).
- hanning2(t)
- Hanning instrument function for apodization (without the MOPD prefactor!).
- srf(vGrid, srFunction='Gauss', value=1.0)
- Evaluate spectral response function on given wavenumber grid and return array of data values.
vGrid: wavenumber grid
srFunction: name of the spectral reponse function (default Gauss)
G = Gauss | L = Lorentz | H = Hyperbolic | T = Triangle | S = SuperGauss | HG = HyperGauss
FTS = Fourier transform spectrometer (apodization selected by second 'word' in this string)
value hwhm OR mopd characterizing the spectral response function:
hwhm (half width @ half maximum) [1/cm] of (super/hyper) Gauss / Lorentz / Hyperbolic / Triangle
mopd (maximum optical path difference) [cm] of FTS
NOTE: FTS default without apodization, i.e. sinc
add a letter indicating type of apodization function, e.g. "FTS T" for triangular apodization
(see function fts documentation)
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