The coincidence Doppler spectra for Cu and Si have been calculated with the norm-conserving pseudopotential (NCPP) method as well as with the projector augmented-wave (PAW) method. The spectra obtained with the PAW are in better agreement with the experimental results than the NCPP results. In addition, a reconstruction method of all-electron wavefunctions from norm-conserving pseudo-wavefunctions is shown. Very similar spectra to those calculated with the PAW method have been obtained.