A method for creating an apodization mask is disclosed. According to the method, a grid is created for the pattern. The grid includes a number of elements. Each element is processed to determine whether the element is to be made transmissive based on a predetermined local optical density and a random value. The predetermined local optical density and the random value are associated with the element. The random value is generated on a random basis. Each element is further processed to determine whether the position of the element is to be shifted. The positional shift is determined on a random basis. The grid with the processed elements is then used to make an apodization mask. The apodization mask may be used in an optical instrument, such as, an interferometer.