| GNXAS DOCUMENTATION |
| Program deconv: deconvolution of lifetime broadening |
| by A. Filipponi, Aug 2000 |
Deconvolution procedures are particularly attractive for the possibility to deconvolve the Lorentzian core-hole lifetime width. In particular, the algorithm implemented in the deconv program, applied to high quality spectra with typical noise levels of the order of 10-4, is able to deconvolve the entire core-hole lifetime broadening using a Gaussian filter with a standard deviation s » G/3 (where G is the Lorentzian half width at half maximum). In these conditions any Lorentzian resonance is converted into a much narrower Gaussian peak and, similarly, an arc-tangent step is converted into an ``erf'' step function. Both reduced width and improved functional shapes, in which the long-range tails are eliminated, contribute to the sharpening of the spectral features.
The users of the program should be aware that the suggested deconvolution procedure is based on the assumption that the effect of the finite lifetime of the excited state is to introduce a Lorentzian broadening. While this is quite reasonable, especially for high energy edges, it is know that in several cases this is a over-simplified assumption. For instance, non-Lorentzian profiles occur in the case of autoionizing Fano resonances. Consequently the deconvolved spectra have to be always interpreted with caution.
The exact values of the core-hole widths may not be known with a sufficient accuracy. Useful tabulations of the known core-hole widths for most of the inner-shell excitations have been published by Krause and Oliver [2].
data_file_name
out_string
0
E_tail, W_tail, E_match
D_Gamma,D_sigma
filter_parameters
These parameter input lines are described in details below:
data_file_name is the name of the input data file to be deconvolved.
out_string Is a string of a maximum length of 10 characters used to generate output file names.
0 This input is left for future running options the integer number 0 should be supplied at present.
E_tail, W_tail, E_match These are the energy parameters in (keV) used for the automatic determination of a smoothed step function to eliminate the discontinuity at the high energy side of the spectrum to be deconvolved numerically. The functional form is that of eq. (5) in Ref. [1] or a simpler arctangent function. E_tail is the position of the step and it should be normally chosen well above the energy region of interest (It should not be the edge energy!!). W_tail is the Lorentzian width of this step contribution, it should be taken larger than the core-hole width to be deconvolved!! Finally E_match is the energy at which the matching in amplitude and slope between the step function and actual spectrum is made. This number should be greater that E_tail by at least a few W_tail widths.
D_Gamma,D_sigma are the Lorentzian (half width at half maximum) and Gaussian widths to be deconvolved. In order to deconvolve only a Lorentzian width, which is the normal program usage, the second parameter should be set to 0.
filter_parameters A filter is necessary to avoid noise blow up after deconvolution [1]. The Fourier transform of the filter should beat that of the deconvolved shape for high values of the conjugate variable value. The normal (and suggested) usage is to adopt a Gaussian filter for a Lorentzian deconvolution. A few other filters are available. The filter type is selected by the first character between quotes, the relevant parameters are entered on the same record in free format. Examples:
a) Gaussian filter, standard deviation 0.67 eV. Any positive number can be input, however, below a minimum value the high-frequency noise will not be suppressed. Reasonable values are in the range G/3 < s < G/2.
'G',0.67
b) Filter, w(q) = exp[-(q-q0)2s2/2 -((q-q0)/q3)3-((q-q0)/q4)4 ] , (w(q) = 1 for |q| < q0). The corresponding parameters are entered as:
'S',q0,s,q3,q4
If q0 = 0 and 1/q3,4 @ 0 the Gaussian filter is retrieved, a small q0 or a finite q3 term will introduce side ripples. Notice that q3 and q4 should be very large numbers to be ineffective.
2) Raw absorption data minus preliminary linear pre edge extrapolation,
3) Raw absorption data minus final linear pre-edge background,
4) Tail step function,
5) Absorption minus tail function (input for the numerical deconvolution).
2+3) Real and Imaginary part of Fourier transformed signal,
4+5) Real and Imaginary part of signal after deconvolution,
6) Fourier Transform of the filter (real).
2) Original spectrum on the same baseline of the deconvolved one,
3) Part of the spectrum numerically deconvolved, to be compared with col. 5 of .bkg,
4) Complete deconvolved spectrum (to be compared with column 2),
5) Filter in real space, (centered at the edge energy).
Most high quality spectra should be suitable for the application of this algorithm, however we recommend:
a) to improve as much a possible the energy resolution, using a suitable monochromator crystal and slits, possibly down to 1/10 of the core-hole width.
b) to collect a suitably long pre-edge up to 100 times the core-hole width (a coarse spacing is anyway sufficient).
c) to adopt a fine energy sampling in the edge region possibly down to 1/20 of the core-hole width.
d) to achieve a noise to signal level of the order of 10-4 or better.
e) to make sure that the monochromator energy is calculated with a sufficient accuracy for the finite motor steps [1,3]. Notice that a 0.1 eV error on an absorption edge rising by 1 within 2 eV corresponds to an equivalent noise of 0.05. Noise in the 10-4 range requires energy accuracy of 0.001 eV or better!
Similar performances and procedures are normally achieved at the BM29 beamline of the ESRF [3].
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On 26 Sep 2000, 09:12.