A grating interferometer, called the “optical encoder,” is a commonly used tool for precise displacement measurements. In contrast to a laser interferometer, a grating interferometer is insensitive to the air refractive index and can be easily applied to multi-degree-of-freedom measurements, which has made it an extensively researched and widely used device. Classified based on the measuring principle and optical configuration, a grating interferometer experiences three distinct stages of development: homodyne, heterodyne, and spatially separated heterodyne. Compared with the former two, the spatially separated heterodyne grating interferometer could achieve a better resolution with a feature of eliminating periodic nonlinear errors. Meanwhile, numerous structures of grating interferometers with a high optical fold factor, a large measurement range, good usability, and multi-degree-of-freedom measurements have been investigated. The development of incremental displacement measuring grating interferometers achieved in recent years is summarized in detail, and studies on error analysis of a grating interferometer are briefly introduced.

Displacement measuring grating interferometer: a review

Groove shape characteristics of echelle gratings with high diffraction efficiency

The designs of 300 mm ruling engine producing gratings and echelles under interferometric control (CIOMP-2) are presented. A new ruling-tool carriage system and its driving mechanism—which are easy to manufacture—are proposed. A new blank carriage system, controlled by a dual-frequency laser interferometer and a piezoelectric actuator, is designed. The CIOMP-2 ruling engine can now rule grating blanks with dimensions up to 300  mm×300  mm, and mainly rules gratings with grating constants between 10 and 2400  lines/mm. The wavelength range of CIOMP-2 gratings is from ultraviolet to mid-infrared wavelengths. Experiments show that the new ruling-tool carriage system works well and stability of motion is improved with the help of a flexure-hinge structure, and the threefold standard deviation values of the blank carriage positioning errors are less than ∼5  nm. For 600  line/mm gratings (diffraction order m=−1), the scatter intensities and ghosts reach 10−5 of the maximum intensity. The scatter intensities and ghost of gratings ruled with CIOMP-2 are low, and no Rowland ghosts are visible. The gratings ruled by CIOMP-2 have high diffraction efficiency and resolving power. CIOMP-2 can also produce varied-line-space, bend-line, and aberration-reducing gratings and echelles.

300 mm ruling engine producing gratings and echelles under interferometric control in China

Groove error is one of the most important factors affecting grating quality and spectral performance. To reduce groove error, we propose a new ruling-tool carriage system based on aerostatic guideways. We design a new blank carriage system with double piezoelectric actuators. We also propose a completely closed-loop servo-control system with a new optical measurement system that can control the position of the diamond relative to the blank. To evaluate our proposed methods, we produced several gratings, including an echelle grating with 79  grooves/mm, a grating with 768  grooves/mm, and a high-density grating with 6000  grooves/mm. The results show that our methods effectively reduce groove error in ruled gratings.

Correcting groove error in gratings ruled on a 500-mm ruling engine using interferometric control.

The equivalent circuit approach (ECA) is used in this work to analyze and design a previously proposed one-dimensional planar blazed grating of the resonant type. The analysis covers both the classical Littrow configuration, when the direction of the relevant diffracted order coincides with that of the incident wave (Bragg blazing), and when these directions are different (off-Bragg blazing). Once the scattering problem of the grating structure is posed as a discontinuity problem inside an equivalent generalized waveguide (corresponding to the unit cell of the original structure) and studied in terms of its equivalent circuit network, the possibility of transferring all the power of the incident plane wave into one single-diffraction order is seen as a simple impedance matching problem. An associated resonance phenomenon is also found to be implicitly associated with this matching condition. This simplifying and fruitful standpoint makes it possible to set up a systematic design procedure to find the specifications of the planar grating for either Bragg or non-Bragg blazing operation. Dielectric and strong skin-effect ohmic losses are easily implemented in the ECA and its effects in the practical design of structures are discussed.

Planar Resonant Blazed Gratings From a Circuit Model Standpoint

Line curvature error greatly influences the quality of the diffraction wave fronts of machine-ruling gratings. To reduce the line curvature error, we propose a correction method that uses interferometric control. This method uses diffraction wave fronts of symmetrical orders to compute the mean line curvature error of the ruled grating, taking the mean line curvature error as the system line curvature error. To minimize the line curvature error of the grating, a dual-frequency laser interferometer is used as a real-time position feedback for the grating ruling stage, along with using a piezoelectric actuator to adjust the stage positioning to compensate the line curvature error. Our experiments show that the proposed method effectively reduced the peak-to-valley value of the line curvature error, improving the quality of the grating diffraction wave front.

Reducing the line curvature error of mechanically ruled gratings by interferometric control

We provided a method to correct the yaw error of a 500 mm grating blank carriage in real time, as the yaw error will bring down the quality of wavefront. We designed a structure with double piezoelectric devices to correct the yaw error. At the same time, to evaluate the correcting ability of our structure, we proposed a relative optical testing structure to verify the correcting accuracy by experiments. The experiment result showed that our method can accomplish the correction of yaw error in real time effectively, at the same time guaranteeing the grating quality.

Yu Haili

Papers

Groove shape characteristics of echelle gratings with high diffraction efficiency

300 mm ruling engine producing gratings and echelles under interferometric control in China

Correcting groove error in gratings ruled on a 500-mm ruling engine using interferometric control.

Reducing the line curvature error of mechanically ruled gratings by interferometric control

Practical method study on correcting yaw error of 500 mm grating blank carriage in real time