Peak Shape: Thompson-Cox-Hastings pseudo Voigt

 

 

                                                                               

 

The pseudo-Voigt function is an approximation to the Voigt function defined as the convolution of a Lorentzian and a Gaussian:

 

                                                    

 

where  and  have different FWHM (  and , respectively). The  function is an approximation that substitutes the two shape parameters  and  by the pair .

 

 

 

       

 

                               

 

 

 

The inversion of the above two expressions leads to the relations:

 

 

 

                                                    

 

                                            

 

The FWHM of the Gaussian  and Lorentzian  components is calculated as: