Diffractive optical element (DOE) is used to convert inputting optical field to the outputting one on image plane with desired intensity distribution. Since DOE design is a numerical process, the definition of performance parameter of approach distance (PPAD) under continuous condition is given and methods of calculation from discrete samples are argued. Correspondingly, discrete performance parameter of approach distance (DPPAD) is defined to evaluate designed results during designing process under discrete condition. According to the PPAD calculation equation under continuous condition and DPPAD under discrete condition, a general DOE designed result shows that sometimes there are tremendous differences between PPAD value and DPPAD. By analyzing the errors of DPPAD, it is pointed out that to design a faithful DOE result, the sampling interval between 2 neighbor points on outputting plane must has extra limitation despite of sampling theory. Otherwise, the designed result just looks good but it is a bad one in fact, and the DPPAD will not be consistent with PPAD. In the end, an example of faithful designed DOE is given.