This algorithm uses a numerical integration method to calculate attenuation factors resulting from absorption and single scattering in a sample with the material properties given. Factors are calculated for each spectrum (i.e. detector position) and wavelength point, as defined by the input workspace. The sample is first bounded by a cuboid, which is divided up into small cubes. The cubes whose centres lie within the sample make up the set of integration elements (so you have a kind of 'Lego' model of the sample) and path lengths through the sample are calculated for the centre-point of each element, and a numerical integration is carried out using these path lengths over the volume elements.
Note that the duration of this algorithm is strongly dependent on the element size chosen, and that too small an element size can cause the algorithm to fail because of insufficient memory.
Note that The number density of the sample is in
This flow chart is given as a way of selecting the most appropriate of the absorption correction algorithms. It also shows the algorithms that must be run first in each case. Note that this does not cover the following absorption correction algorithms: algm-MonteCarloAbsorption (correction factors for a generic sample using a Monte Carlo instead of a numerical integration method), algm-MultipleScatteringCylinderAbsorption & algm-AnvredCorrection (corrections in a spherical sample, using a method imported from ISAW). Also, HRPD users can use the algm-HRPDSlabCanAbsorption to add rudimentary calculations of the effects of the sample holder. 
This algorithm assumes that the (parallel) beam illuminates the entire sample unless a 'gauge volume' has been defined using the algm-DefineGaugeVolume algorithm (or by otherwise adding a valid XML string defining a shape to a Run property called "GaugeVolume"). In this latter case only scattering within this volume (and the sample) is integrated, because this is all the detector can 'see'. The full sample is still used for the neutron paths. (N.B. If your gauge volume is of axis-aligned cuboid shape and fully enclosed by the sample then you will get a more accurate result from the algm-CuboidGaugeVolumeAbsorption algorithm.)
The input workspace must have units of wavelength. The instrument associated with the workspace must be fully defined because detector, source & sample position are needed.
Example: A simple spherical sample
ExSimpleSpere
#setup the sample shape sphere = '''<sphere id="sample-sphere"> <centre x="0" y="0" z="0"/> <radius val="0.1" /> </sphere>'''
ws = CreateSampleWorkspace("Histogram",NumBanks=1) ws = ConvertUnits(ws,"Wavelength") CreateSampleShape(ws,sphere) SetSampleMaterial(ws,ChemicalFormula="V")
#restrict the number of wavelength points to speed up the example wsOut = AbsorptionCorrection(ws,NumberOfWavelengthPoints=5)
print "The created workspace has one entry for each spectra: %i" % wsOut.getNumberHistograms()
Output:
ExSimpleSpere
The created workspace has one entry for each spectra: 100