This function provides the basic arithmetic operations being
applicable, if at least two 2D data objects are merged into a data view.
These spectra can undergo the following arithmetic operations:

Adding two spectra

Subtracting two spectra

Multiplying two spectra

Dividing two spectra

Power spectra

The spectrum arithmetics submenu also contains links to the
functions Average spectra and Thickness
Correction which may be applied to two or more spectra merged into
a 2D data view.

Arithmetic operations can be performed either on the whole
spectral range or just on a selected region. In all cases the result will
be a new 2D data object. The reference spectrum is the spectrum that will
stay untouched. It is the spectrum that will be added to/subtracted from
the other spectra - or the other spectra will be multiplied with/divided
by.

How can I identify the reference spectrum?

The current active object is considered as the reference
spectrum. Switching of the reference spectrum is possible by simply selecting
a different spectrum before the calculation is carried out.

What happens to the spectrum outside
the selected region?

The current active object is meant to be the reference spectrum.
Data points outside the selected spectral region will simply be copied
into the new data object from the reference spectrum.

Arithmetic operations will be applied to the selected spectral
regions of multiple 2D data objects. The 2D data sets must be equidistant
and must have the same resolution to run this operations. Exceeding data
points will be copied from the reference spectrum by default.

For convenience, the spectrum arithmetics parameters can be adjusted
interactively in the mathematics tab while the results are displayed in
the dataview. The mathematics tab for the spectrum arithmetics function
looks like this:

The following parameters are available for spectrum arithmetics:

Operation

The following mathematic operations are available:

Addition - Adding two Spectra
The intensity values of both data objects are summed for each data
point in the selected spectral region. Exceeding data points will be just
copied from the current active spectrum. The intensities of the reference
object are scaled by the scaling factor in advance.

Substraction - Subtracting
two Spectra
The intensities of the inactive 2D data object are subtracted by the
intensities of the current active 2D data object (reference spectrum)
in the selected spectral region. Exceeding data points will be just copied
from the current active spectrum. The intensities of the reference object
are scaled by the scaling factor in advance.

Multiplication - Multiplying
two spectra
The intensity values of both data objects are multiplied for each data
point in the selected spectral region. Exceeding data points will be just
copied from the current active spectrum. The intensities of the reference
object are scaled by the scaling factor in advance.

Division - Dividing two
spectra
The intensity values of the current inactive 2D data set are divided
by the intensities of the active 2D data object (reference spectrum) for
each data point in the selected spectral region. Exceeding data points
will be just copied from the current active spectrum. The intensities
of the reference object are scaled by the scaling factor in advance.

Division by zero is not allowed!

Power spectra
The intensity values of the current inactive 2D data set are raised
to the power of the intensity of the active data object (reference spectrum),
e.g. I^A. Exceeding data points will be just copied from the reference
spectrum.

Potentiation This is the inverse of the power
operation. The intensity values of the current active 2D data set are
raised to the power of the intensity of the inactive data object (reference
spectrum), e.g. A^I.

Zero negative values

This parameter controls whether all negative values in the result data
object of arithmetic calculation will be set to zero automatically or
not. This can be useful when searching
residual spectra in libraries. The following settings are available:

Checked
Enables auto-zero function for negative values in the defined spectral
range of the resulting data object.

Unchecked
Disables the auto-zero function.

Scaling Factor

The scaling factor is used to scale the reference spectrum with a scalar
value before the arithmetic calculation is carried out. All intensities
in the specified spectral region are multiplied by the scaling factor
before arithmetic calculation. The value is set to 1 by default. For normal
spectrum arithmetic operations it should stay untouched.
If an adjustment of the scaling factor is necessary, it can be done by
simply entering a numerical value or by using the slider. In both cases
the preview spectrum will be adjusted to show the result.

Full Range

This parameter controls whether only the selected spectral region is
applied or the whole spectral range. The following settings are available:

Unchecked
Only the specified part of the spectral range is applied. It is defined
by Minimum and Maximum
values as well as indicated by the light grey graphical section in the
graph view.

Checked
The maximum applicable spectral range of both objects is applied.

Minimum

This parameter denotes the lower boundary (on the x-axis) taken into
account for the arithmetic calculation. It may be adjusted by entering
a numerical value or graphically by adjusting the selection area in the
data view.

Maximum

This parameter denotes the upper boundary (on the x-axis) taken into
account for the arithmetic calculation. It may be adjusted by entering
a numerical value or graphically by adjusting the selection area in the
data view.

The spectrum arithmetics are interactive, changes made to the parameters
will directly be show in a preview window:

The upper part of the window shows the dataview
with the merged original spectra being used for calculation. The red spectrum
is the active (highlighted) spectrum and therefore the reference spectrum.
In the lower spectrum view the calculation result preview spectrum is
shown.

You can switch the active spectrum
by selecting another spectrum in the legend or by clicking the curve directly!

Any changes to the calculation parameters
will be directly reflected in the preview spectrum.Click the Calculate button in the mathematics tab to run
the calculation. All spectra in the upper dataview except the reference
spectrum will be replaced by the resulting spectra.