Difference between a standard HAM and a double-grating HAM. The first element of the double grating is the standard HAM pattern with an added polarization grating pattern (i.e., the phase ramp) with 70 periods across the full pupil. The second grating is not shown. The resulting PSFs show that the polarization leakage is directed from the center into two off-axis PSFs. Both elements have 2% leakage, and we assume a linear polarization fraction of 10%. Closure phase offsets due to polarization leakage are greatly reduced with the double-grating method.