Aligning data

DEMETER uses a rather simple alignment algorithm. First, one Data object is chosen as the alignment standard. The standard is one that doesn't move -- other data are aligned to the standard by applying an E₀ shift. The derivative spectrum is computed for both the standard and the data. An E₀ shift and an overall amplitude are the variable parameters used to fit the data to the standard. The amplitude value is discard, but the fitted E₀ shift is set as the bkg_eshift attribute of the aligned data.

This algorithm work quite well for good quality data. Although, even for very good data, if it starts of many volts out of alignment, the fit is likely to find a false minimum. If data start very far out of alignment, you will likely need to set the bkg_eshift attribute by hadn to something close before calling the align method.

Here is a simple example:

#!/usr/bin/perl

my $prj = Demeter::Data::Prj -> new(file=>'U_DNA.prj');
my @data = $prj -> records(1, 2, 3, 4);

## ... set background removal and Fourier transform attributes for
##     each data set ...

## align to the standard
$data[0]->align(@data);
## make all the E0 values the same
$_->e0($data[0]) foreach @data[1..3];

Four data sets are imported at lines 3 and 4. By calling the align method on the first data set in the list at line 10, it is chosen as the standard, i.e. the one that stays in place while the others are shifted. It is not a problem that the standard is passed as an argument of the method. DEMETER will notice this and do the right thing.

Aligning does not also force the E₀ values to be the same, so that is done as a separate step at line 12.

There is also an align_with_reference method (which has an alias of alignwr). This will use the Data objects specified in the reference attribute of the standard and the data to perform the alignment. Here is how that works:

#!/usr/bin/perl

my $prj = Demeter::Data::Prj -> new(file=>'U_DNA.prj');
my @data = $prj -> records(1, 2, 3, 4);

$data[0]->reference($data[1]);
$data[2]->reference($data[3]);

## align to the standard using the reference
$data[0]->alignwr($data[2]);
## make the E0 values the same
$data[2]->e0($data[0]);

Smoothing the derivative spectra before aligning is not yet implemented.