A planar encoder using conjugate optics is proposed for sensing the 2-D displacement of a 2-D grating. A Doppler frequency shift of diffracted light is generated when the grating moves. The optical conjugate path can compensate for the error arising from the relative tilt between the optical head and the scale (head-to-scale tilt). Additionally, the optical head is easily integrated, having high tolerance in component-to-component placement. The 2-D displacement system with the 2-D grating, which has period of 1.6 µm in both the X and Y directions, provides a signal period of 0.4 µm by using a double-diffraction configuration. This system and associated electronics provide interpolation with a factor of 400, corresponding to a measurement resolution of 1 nm.