A laser homodyne straightness interferometer with simultaneous measurement of six degrees of freedom motion errors is proposed for precision linear stage metrology. In this interferometer, the vertical straightness error and its position are measured by interference fringe counting, the yaw and pitch errors are obtained by measuring the spacing changes of interference fringe and the horizontal straightness and roll errors are determined by laser collimation. The merit of this interferometer is that four degrees of freedom motion errors are obtained by using laser interferometry with high accuracy. The optical configuration of the proposed interferometer is designed. The principle of the simultaneous measurement of six degrees of freedom errors including yaw, pitch, roll, two straightness errors and straightness error's position of measured linear stage is depicted in detail, and the compensation of crosstalk effects on straightness error and its position measurements is presented. At last, an experimental setup is constructed and several experiments are performed to demonstrate the feasibility of the proposed interferometer and the compensation method.

Laser homodyne straightness interferometer with simultaneous measurement of six degrees of freedom motion errors for precision linear stage metrology.

This paper proposes a system utilizing a Renishaw XL80 positioning error measuring interferometer and sensitivity analysis design to measure six-degree-of-freedom (6 DOF) geometric errors of a machine tool’s linear guide. Each error is characterized by high independence with significantly reduced crosstalk, and error calculations are extremely fast and accurate. Initially, the real light path was simulated using Zemax. Then, Matlab’s skew ray tracing method was used to perform mathematical modeling and ray matching. Each error’s sensitivity to the sensor was then analyzed, and curve fitting was used to simplify and speed up the mathematical model computations. Finally, Solidworks was used to design the set of system modules, bringing the proposed system closer to a product. This system measured actual 6 DOF geometric errors of a machine tool’s linear guide, and a comparison is made with the Renishaw XL-80 interferometer measurements. The resulting pitch, yaw, horizontal straightness, and vertical straightness error deviation ranges are ±0.5 arcsec, ±3.6 arcsec, ±2.1 μm, and ±2.3 μm, respectively. The maximum repeatability deviations for the measured guide’s pitch, yaw, roll, horizontal straightness, vertical straightness, and positioning errors are 0.4 arcsec, 0.2 arcsec, 4.2 arcsec, 1.5 μm, 0.3 μm, and 3 μm, respectively.

Design of a Measurement System for Six-Degree-of-Freedom Geometric Errors of a Linear Guide of a Machine Tool

A measurement system to simultaneously measure six degree-of-freedom (6DOF) geometric errors is proposed. The measurement method is based on a combination of mono-frequency laser interferometry and laser fiber collimation. A simpler and more integrated optical configuration is designed. To compensate for the measurement errors introduced by error crosstalk, element fabrication error, laser beam drift, and nonparallelism of two measurement beam, a unified measurement model, which can improve the measurement accuracy, is deduced and established using the ray-tracing method. A numerical simulation using the optical design software Zemax is conducted, and the results verify the correctness of the model. Several experiments are performed to demonstrate the feasibility and effectiveness of the proposed system and measurement model.

Measurement system and model for simultaneously measuring 6DOF geometric errors.

In this paper, a compact four-degree-of-freedom (4-DOF) measurement system is presented. With a special optical configuration, the pitch error, yaw error, and two straightness errors of the moving target are able to be detected by only a single laser beam from a collimated laser diode. A 2D hybrid mirror angle steering mount is designed to perform the large angle turning for the axis alignment and very fine angle tuning by PZT actuators for real-time beam drift compensation. A series of calibration and comparison experiments have been carried out to verify the performance of the proposed system. The developed active compensation system could effectively suppress the beam’s angular drift to within ± 0.01 arc-sec in both of yaw and pitch directions. The developed 4-DOF measuring system is compact, low cost, and suitable for long distance geometric error measurement of linear stages.

Low cost, compact 4-DOF measurement system with active compensation of beam angular drift error.

A compact, fiber-coupled, six degree-of-freedom measurement system which enables fast, accurate calibration, and error mapping of precision linear stages is presented. The novel design has the advantages of simplicity, compactness, and relatively low cost. This proposed sensor can simultaneously measure displacement, two straightness errors, and changes in pitch, yaw, and roll using a single optical beam traveling between the measurement system and a small target. The optical configuration of the system and the working principle for all degrees-of-freedom are presented along with the influence and compensation of crosstalk motions in roll and straightness measurements. Several comparison experiments are conducted to investigate the feasibility and performance of the proposed system in each degree-of-freedom independently. Comparison experiments to a commercial interferometer demonstrate error standard deviations of 0.33 μm in straightness, 0.14 μrad in pitch, 0.44 μradin yaw, and 45.8 μrad in roll.

Development of a compact, fiber-coupled, six degree-of-freedom measurement system for precision linear stage metrology

We present a robust optical-roll sensor with a high-dynamic range and high-throughput capabilities. The working principle relies on tracking the amplitude of an optical square wave-encoded light source. After encoding a square wave onto a polarization reference, quadrature demodulation of the polarized light allows us to cancel common-mode noise. Benefits of this sensor include its simplicity, low cost, high-throughput, insensitivity to source amplitude fluctuations, and no inherent drift. In this Letter, we present the working principle and experimentally validate a 43° usable working range with 0.002° resolution. This sensor has the highest reported dynamic range for optical roll sensing.

Robust high-dynamic-range optical roll sensing.

Heterodyne interferometry is a widely accepted methodology with high resolution in many metrology applications. As a functionality enhancement, differential wavefront sensing (DWS) enables simultaneous measurement of displacement, pitch, and yaw using a displacement interferometry system and a single beam incident on a plane mirror target. The angular change is measured using a weighted phase average between symmetrically adjacent quadrant photodiode pairs. In this paper, we present an analytical model to predict the scaling of differential phase signals based on fundamental Gaussian beams. Several numerical models are presented to discuss the effects of physical beam parameters, detector size, system alignment errors, and beam wavefront aberrations on the DWS technique. The results of our modeling predict rotational scaling factors and a usable linear range. Furthermore, experimental results show the analytically predicted scaling factor is in good agreement with empirical calibration. Our three degree-of-freedom interferometer can achieve a resolution of 0.4 nm in displacement and 0.2 μrad in pitch and yaw simultaneously.

https://iopscience.iop.org/article/10.1088/0957-0233/26/12/125203/pdf

Beam geometry, alignment, and wavefront aberration effects on interferometric differential wavefront sensing

A refractometer system using four modified Wu-type heterodyne interferometers with a variable length vacuum cell is presented. The proposed system has two working modes: (1) a moving mode for measuring the absolute air refractive index at the start of a measurement and (2) a static mode for monitoring the air refractive index fluctuation with the same bandwidth as a traditional displacement interferometer. The system requires no gas filling or pumping during the measurement and can be used for real-time refractive index compensation. Comparison experiments with empirical equations are conducted to investigate the feasibility and performance of the proposed system. The standard deviation of the measurement difference between the proposed system and empirical equation is 2.8 parts in 10 7 , which is close to the uncertainty of our refractive index reference based on the accuracy of the environmental sensors. The relative refractive index tracking is a few parts in 10 8 with a bandwidth of 10 Hz, but high bandwidths are readily achievable.

Xiangzhi Yu

Papers

Development of a compact, fiber-coupled, six degree-of-freedom measurement system for precision linear stage metrology

Robust high-dynamic-range optical roll sensing.

Beam geometry, alignment, and wavefront aberration effects on interferometric differential wavefront sensing

Absolute air refractive index measurement and tracking based on variable length vacuum cell

Straightness measurement based on knife-edge sensing