We propose a paraxial solution for pixel shift selectivity, which can simulate the pixel shift selectivity in two dimensions and in wide range easily. Thus, the effect of different reference patterns can be calculated in detail. From the simulation result, we conclude that the pixel shift selectivity get worse for amplitude modulation reference patterns. Making no modulation is the best reference pattern for pixel shift selectivity, however the point spread function will be worst in this case. To get an optimum system in both pixel shift selectivity and point spread function, the reference pattern with phase modulation will be the best choice.