A two-degree-of-freedom (2-DOF) displacement measurement system based on double diffraction gratings is proposed in this paper, which consists of a reflective-type scale grating and a grating read head with a scanning transmission grating. Combining the traditional three-grating interference principle with the Michelson interference principle, the system can measure the displacements of a precision stage along the horizontal direction (X-axis, in the scanning grating plane and vertical to the scanning grating lines) and vertical direction (Z-axis, vertical to the scanning grating plane) simultaneously. The system has the merits of compact structure and uncoupled interference signals in the two axes. By simulating the output signals of the system and comparing them with the experimental results, the validity and feasibility of the system have been verified. The 2-DOF system will be favorable in the displacement measurement of multi-dimensional stages and multi-DOF machines.

In this paper, a two-dimensional (2-D) planar encoder based on two parallel gratings, which includes a scanning grating and scale grating, is presented. The scanning grating is a combined transmission rectangular grating comprised of a 2-D grating located at the center and two one-dimensional (1-D) gratings located at the sides. The grating lines of the two 1-D gratings are perpendicular to each other and parallel with the 2-D grating lines. The scale grating is a 2-D reflective-type rectangular grating placed in parallel with the scanning grating, and there is an angular difference of 45° between the grating lines of the two 2-D gratings. With the special structural design of the scanning grating, the encoder can measure the 2-D displacement in the grating plane simultaneously, and the measured interference signals in the two directions are uncoupled. Moreover, by utilizing the scanning grating to modulate the phase of the interference signals instead of the prisms, the structure of the encoder is compact. Experiments were implemented, and the results demonstrate the validity of the 2-D planar grating encoder.

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