Overlay control is of vital importance to good device performances in semiconductor manufacturing. In this work, the differential Mueller matrix calculus is introduced to investigate the Mueller matrices of double-patterned gratings with overlay displacements, which helps to reveal six elementary optical properties hidden in the Mueller matrices. We find and demonstrate that, among these six elementary optical properties, the linear birefringence and dichroism, LB' and LD', along the ± 45° axes show a linear response to the overlay displacement and are zero when the overlay displacement is absent at any conical mounting. Although the elements from the two 2 × 2 off-diagonal blocks of the Mueller matrix have a similar property to LB' and LD', as reported in the literature, we demonstrate that it is only valid at a special conical mounting with the plane of incidence parallel to grating lines. The better property of LB' and LD' than the Mueller matrix elements of the off-diagonal blocks in the presence of overlay displacement verifies them to be a more robust indicator for the diffraction-based overlay metrology.