Design and testing of a two-axis surface encoder with a single Littrow configuration of a first-order diffraction beam

A simple but effective optical design is proposed to expand the measurement range of a surface encoder in the out-of-plane Z-direction, which had been much shorter than that in the in-plane X-direction. A zeroth-order and a first-order diffraction beams generated at a transparent grating are projected onto a parallelly aligned scale grating. The reflected zeroth-order beam from the scale grating interferes with a beam from a reference plane mirror for the Z-directional measurement over an expanded range of 13 mm. A single Littrow configuration is established for the first-order diffraction beam to travel to and from the scale grating on the same path so that it can interfere with the reflected zeroth-order beam for the X-directional measurement regardless of the Z-position of the scale grating. A prototype sensor is constructed for demonstrating the effectiveness of the proposed optical design for expansion of Z-range. Uncertainty analysis on the measurement results is also conducted.