30 years of Data Processing:
The Rise and Fall of Deconvolution
Dr AF Carley, Cardiff University
Dr Carley highlighted the advances in computing, using the evolution of
deconvolution as an analytical tool as an example. The basic convolution integral is as
follows:
A shorthand form of the convolution integral is f = g * h, which has to
be converted to matrix notation to perform the calculations. The matrix form is as, f
= G h. This method of analysis enhanced the level of chemical state
information that could be obtained from a given set of spectra. Particular areas of
application included:
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Self Convolution
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CVV Auger data
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INS
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APS
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HREELS – Fuchs-Kliever phonon loss peaks from oxides
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ARXPS & sputter depth profiling
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Polynomial smoothing
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Spectral broadening and X-ray satellites
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Figure 1:
Digico M16V microcomputer |
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Early data processing programmes were written for ICL
mainframes, but the data had to be initially collected on chart recorders then inputted to
software. However, the advent of microcomputers really moved things forward. These
"powerful" instruments could be directly interfaced to the instruments, so for
the first time they could collect and process the data. An Early system cost around £5000
pounds which was enough to buy a family house.
This quantum leap in data processing still had no visual displays and
the data transfer was only10 bytes/sec. The standard computer came with a huge 4KB and had
a graphical output. Given these new "powerful" computers, it was now possible to
do some powerful data processing. What was the main interest in Cardiff at the time,
deconvolution!
What methods were available, well
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Hagstrom method - self
deconvolution
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Matrix inversion h=G-1f
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Fourier transform methods
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Iterative methods - Van Cittert
1931
This latter was the preferred choice since it was the easiest to programme |
Using this method of analysis it was possible to extract information
from relative poor resolution data. Below is an example of the enhancement in resolution
on the valence band spectra from gold.
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Figure 2:
a) "as received" data and b) deconvoluted spectrum |
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When data of this type was first shown in the open
literature, it appeared to be a major breakthrough. However there are clear limitations
with the technique.
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Non-unique solution
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Noise in the deconvolute
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Choosing the right one - maximum entropy
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Need excellent signal-to-noise
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Need accurate broadening functions |
These problems have restricted the use of the technique, even though we
now have computers, which are cheap enough and powerful enough to do the analysis. Using
the maximum entropy method it is possible to do the analysis with sufficient accuracy,
however with the development of high intensity monochromators, is there any point in
deconvoluting your data!
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