Enhanced Heterodyne Grating Interferometer for Simultaneously Measuring Tri-Axial Linear Motions

A novel Heterodyne Grating Interferometer (HTGI) with a rotationally symmetric optical configuration is proposed to achieve the simultaneous measurement of tri-axial linear motions with a large <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Z</i>-axis range and a large <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Z</i>-axis rotation tolerance. In this design, the ±1-<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">st</i> order diffracted beams from one incident beam were purposely rotated around the central axis by an angle of 180° to interfere with them from the other incident beam. In this configuration, all beams can shift identical distances along the same direction to maintain interference, when the grating has large <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Z</i>-axis motions and rotations. Experimental testing demonstrates high linearities comparable with commercial capacitive sensors, and sub-nanometric resolutions by identifying 0.25 nm motions via the spectrum analysis for all the tri-axial measurements. Moreover, a greatly extended <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Z</i>-axis range of 7.6 mm and a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Z</i>-axis rotation tolerance of 0.75° were achieved, well demonstrating the superiority of the proposed design.