High-order diffraction gratings with an isosceles triangle profile for a nano-precision linear optical encoder

High-order diffraction is preferred to nanoscale displacement measurement by linear optical encoder. The diffraction efficiency at high orders, however, is limited. In this Letter, a high-order diffraction grating with an isosceles triangle profile in cross-section is proposed, and it could achieve over 40% in the diffraction efficiency of the ±4th order. Fabricated by anisotropic etching of Si (100) and followed by replication, the grating period is 4.82 μm and the symmetrical side angle for diffraction is 46.1°. Experiments indicate that, by the interference of ±4th order (optical subdivision is 8 times), the positioning accuracy in 1 mm travel length is 37.1 nm, the repeatability is 3.7 nm, and the stability is 3.6 nm @ 60 s, which are measured by the standard deviation (<i>σ</i>).