Utility Functions

xrayphysics.xrayPhysics.effectiveZ(self, chemicalFormula, min_energy=10.0, max_energy=100.0, arealDensity=0.0)

Calculate the effective atomic number of a material

Parameters:

  • chemicalFormula (string) – atomic number, chemical formula, mixture of compounds with mass fractions, or member of the material library

  • min_energy (scalar) – the minimum of the energy in which to perform the calculation

  • max_energy (scalar) – the maximum of the energy in which to perform the calculation

  • arealDensity (scalar) – the areal density (g/cm^2) to use for the calculation

Returns:

The effective atomic number

xrayphysics.xrayPhysics.effectiveLAC(self, Z, density, thickness, spectralResponse, gammas)

Calculates the effective Linear Attenuation Coefficient (LAC) of a polychromatic x-ray beam through of a material of specified thickness

The model is given by

\[\begin{split}\begin{eqnarray*} \mu_{eff}(L) &:=& \frac{-\log\left(\int \widehat{s}(\gamma) e^{-\mu(\gamma)L} \, d\gamma\right)}{L} \\ \widehat{s}(\gamma) &:=& \frac{s(\gamma)}{\int s(\gamma') \, d\gamma'} \end{eqnarray*}\end{split}\]

where \(\mu\) is the LAC of the material, \(\gamma\) is the x-ray energy (keV), \(L\) is the material thickness, and \(s\) is the x-ray spectra. The limit of \(L \rightarrow 0\) is given by

\[\begin{eqnarray*} \mu_{eff}(0) &:=& \int \widehat{s}(\gamma) \mu(\gamma) \, d\gamma \end{eqnarray*}\]
Parameters:

  • Z (scalar or string) – atomic number, chemical formula, mixture of compounds with mass fractions, or member of the material library

  • density (scalar) – mass density (g/cm^3) of the material

  • thickness (scalar) – the thickness (cm) of the material

  • spectralResponse (numpy array) – spectra model

  • gammas (numpy array) – energies at which the spectra model is defined

Returns:

The effective Linear Attenuation Coefficient (LAC, (length units)^-1)

xrayphysics.xrayPhysics.effectiveEnergy(self, Z, density, thickness, spectralResponse, gammas)

Calculate the effective energy of a polychromatic beam passing through a material of a given thickness

The model is given by

\[\begin{eqnarray*} \mu(\gamma_{eff}) &:=& \mu_{eff}(L) \end{eqnarray*}\]

i.e., the effective energy is the energy at which the LAC of the material at this energy is equal to the effective LAC of the material. See the description of the effectiveLAC function

Parameters:

  • Z (scalar or string) – atomic number, chemical formula, mixture of compounds with mass fractions, or member of the material library

  • density (scalar) – mass density (g/cm^3) of the material

  • thickness (scalar) – the thickness (cm) of the material

  • spectralResponse (numpy array) – spectra model

  • gammas (numpy array) – energies at which the spectra model is defined

Returns:

The monochromatic energy (keV) that would provide the same attenuation as the given polychromatic spectra

xrayphysics.xrayPhysics.transmission(self, Z, density, thickness, spectralResponse, gammas)

Calculate the transmission through a given material

This model is given by

\[\begin{eqnarray*} \frac{\int s(\gamma) e^{-\mu(\gamma)L} \, d\gamma}{\int s(\gamma') \, d\gamma'} \end{eqnarray*}\]

where \(\mu\) is the LAC of the material, \(\gamma\) is the x-ray energy (keV), \(L\) is the material thickness, and \(s\) is the x-ray spectra.

Parameters:

  • Z (scalar or string) – atomic number, chemical formula, mixture of compounds with mass fractions, or member of the material library

  • density (scalar) – mass density (g/cm^3) of the material

  • thickness (scalar) – the thickness (cm) of the material

  • spectralResponse (numpy array) – spectra model

  • gammas (numpy array) – energies at which the spectra model is defined

Returns:

The transmission (unitless) through the given filter