Two-degree-freedom displacement measurement based on a short period grating in symmetric Littrow configuration

• The optical encoder is based on a grating with period as short as 561.8 nm.
• The optical encoder can measure two-dimensional displacement although a one-dimensional grating is applied.
• The tilt angle of the grating is taken into account to decrease the cosine error.
• Good stable results can be obtained due to the small different optical paths of reference light and measuring light.

An optical encoder based on symmetric Littrow configuration is presented. Although the grating is one dimensional, both horizontal and vertical displacement can be measured simultaneously. The angle between grating vector and horizontal movement is taken into account in the measurement results, which not only decreases the requirement of installation but also decreases the cosine error. Thanks to the short grating period of 561.8 nm, a high resolution of 0.137 nm is obtained. The measurement results of optical encoder are compared with that of commercial laser interferometer. The coincident results demonstrate that the encoder should be a useful optical measurement device for detecting two-dimensional movement.