.. algorithm:: .. summary:: .. relatedalgorithms:: .. properties:: Description ----------- This algorithm is a port to C++ of a multiple scattering absorption correction, used to correct the vanadium spectrum for the GPPD instrument at the IPNS. The correction calculation was originally worked out by Jack Carpenter and Asfia Huq and implemented in Java by Alok Chatterjee. The java code was translated to C++ in Mantid by Dennis Mikkelson. * Elastic scattering is assumed In [1]_ we see that the calculation of the attenuation factor F involves an integral over the sample cylinder. By expanding the integrands as a power series, we can factor out any dependence on scattering cross section and radius. These integral terms are denoted by :math:`Z_{mn}` and so we may write: .. math:: \frac{1}{F} = \sum_{m=0}^\infty\sum_{n=0}^\infty\frac{(-1)^{m+n}}{m!n!}(\mu R)^{m+n} Z_{mn}(\theta) where :math:`\mu` is the inverse scattering length. The functions :math:`Z_{mn}(\theta)` are written in terms of Chebyshev expansion coefficients: .. math:: Z_{mn}(\theta) = \sum_{s=0}^\infty c_{s}(m,n)cos(s\theta) where the Chebyshev coefficients :math:`c_{s}(m,n)` up to m + n :math:`\leqslant` 5 have been tabulated and are stored as an array by the algorithm. This version of the correction follows the implementation in [1]_ in that it only calculates for the correction in-plane, unlike [2]_, [3]_ that generalizes the correction to out-of-plane. This algorithm calculates and outputs the absorption and/or multiple scattering correction workspaces to be applied to the InputWorkspace. Thus, there are, at most, two workspaces in the OutputWorkspaceBaseName group workspace. This allows for flexibility of applying either correction to a workspace without having to apply both (as is the case with :ref:`algm-CarpenterSampleCorrection`). For the case where both corrections are calculated, the output will be the following: 1. The absorption correction workspace will be OutputWorkspaceBaseName + `_abs` and will be in `.getItem(0)`. 2. The multiple scattering correction workspace will be OutputWorkspaceBaseName + `_ms` and will be in `.getItem(1)`. This is the child algorithm that :ref:`algm-CarpenterSampleCorrection` (previously known as *MultipleScatteringCylinderAbsorption*) uses to calculate and apply the correction to a sample workspace. Usage ----- **Example: Calculate corrections for a simple cylindrical sample** .. testcode:: ExCalculateCarpenterSampleCorrection_corrections ws = CreateSampleWorkspace("Histogram",NumBanks=1,BankPixelWidth=1) ws = ConvertUnits(ws,"Wavelength") ws = Rebin(ws,Params=[1]) SetSampleMaterial(ws,ChemicalFormula="V") #restrict the number of wavelength points to speed up the example wsOut = CalculateCarpenterSampleCorrection(ws,CylinderSampleRadius=0.2) print("Absorption Correction Output: {}".format(wsOut.getItem(0).readY(0))) print("Multiply Scattering Correction Output: {}".format(wsOut.getItem(1).readY(0))) Output: .. testoutput:: ExCalculateCarpenterSampleCorrection_corrections Absorption Correction Output: [0.85283805 0.79620318 0.74348494 0.69440412 0.64870017 0.62121997] Multiply Scattering Correction Output: [0.09633662 0.09991619 0.1034959 0.10705826 0.11058382 0.11280196] To reproduce what :ref:`algm-CarpenterSampleCorrection` does, you can calculate and apply the correction as follows **Example: Apply correction for a simple cylindrical sample using getItem** .. testcode:: ExCalculateCarpenterSampleCorrection_apply1 ws = CreateSampleWorkspace("Histogram",NumBanks=1,BankPixelWidth=1) ws = ConvertUnits(ws,"Wavelength") ws = Rebin(ws,Params=[1]) SetSampleMaterial(ws,ChemicalFormula="V") corrections = CalculateCarpenterSampleCorrection(ws,CylinderSampleRadius=0.2) # Get absorption correction absCorr = corrections.getItem(0) # Get multiple scattering correction msFactor = corrections.getItem(1) msCorr = Multiply(ws, msFactor) # Apply absorption correction to workspace ws_abs_corrected = Divide(ws, absCorr) # Apply multiple scattering correction to workspace ws_ms_corrected = Minus(ws, msCorr) # Apply both corrections wsOut = Minus(ws_abs_corrected, msCorr) print("Absorption Corrected Output: {}".format(ws_abs_corrected.readY(0))) print("Multiple Scattering Corrected Output: {}".format(ws_ms_corrected.readY(0))) print("Combined Corrected Output: {}".format(wsOut.readY(0))) Output: .. testoutput:: ExCalculateCarpenterSampleCorrection_apply1 Absorption Corrected Output: [ 6.66892661 7.14329517 21.0999759 8.1904963 8.76755487 2.51509668] Multiple Scattering Corrected Output: [ 5.13959844 5.11923959 14.06392099 5.07861898 5.05856725 1.38618331] Combined Corrected Output: [ 6.1210107 6.57502041 19.47638255 7.58160094 8.13860778 2.33885171] **Example: Apply correction for a simple cylindrical sample using getItem** .. testcode:: ExCalculateCarpenterSampleCorrection_apply2 ws = CreateSampleWorkspace("Histogram",NumBanks=1,BankPixelWidth=1) ws = ConvertUnits(ws,"Wavelength") ws = Rebin(ws,Params=[1]) SetSampleMaterial(ws,ChemicalFormula="V") #restrict the number of wavelength points to speed up the example basename = "corrections" CalculateCarpenterSampleCorrection(ws,OutputWorkspaceBaseName=basename, CylinderSampleRadius=0.2) # Get absorption correction absCorr = mtd[basename+"_abs"] # Get multiple scattering correction msFactor = mtd[basename+"_ms"] msCorr = Multiply(ws, msFactor) # Apply absorption correction to workspace ws_abs_corrected = Divide(ws, absCorr) # Apply multiple scattering correction to workspace ws_ms_corrected = Minus(ws, msCorr) # Apply both corrections wsOut = Minus(ws_abs_corrected, msCorr) print("Absorption Corrected Output: {}".format(ws_abs_corrected.readY(0))) print("Multiple Scattering Corrected Output: {}".format(ws_ms_corrected.readY(0))) print("Combined Corrected Output: {}".format(wsOut.readY(0))) Output: .. testoutput:: ExCalculateCarpenterSampleCorrection_apply2 Absorption Corrected Output: [ 6.66892661 7.14329517 21.0999759 8.1904963 8.76755487 2.51509668] Multiple Scattering Corrected Output: [ 5.13959844 5.11923959 14.06392099 5.07861898 5.05856725 1.38618331] Combined Corrected Output: [ 6.1210107 6.57502041 19.47638255 7.58160094 8.13860778 2.33885171] References ---------- .. [1] J.M. Carpenter *Attenuation Correction Factor for Scattering from Cylindrical Targets* Review of Scientific Instruments **40.4** (1969): 555. doi: `10.1063/1.1684003 `_ .. [2] D.F.R. Mildner, J.M. Carpenter, and C.A. Pelizzari *Generalized Attenuation Correction Factor for Scattering from Cylindrical Targets* Review of Scientific Instruments **45.4** (1974): 572. doi: `10.1063/1.1686687 `_ .. [3] D.F.R. Mildner and J.M.Carpenter *Improvements to the Chebyshev Expansion of Attenuation Correction Factors for Cylindrical Samples.* J Appl Crystallogr **23.5** (1990): 378–386 doi: `10.1107/S0021889890005258 `_ .. categories:: .. sourcelink::