This paper presents a robust and low-cost roll angle measurement system (RAMS) on the basis of two parallel beams in association with two position detectors. The commonly occurring influences of beam drift, beam diameter, and intensity variations, and non-parallelism of dual-beam on the roll angular error measurement of precision linear stages are thoroughly considered and reduced. The effectiveness of the designed system and proposed methods were demonstrated by a series of experiments. It has been verified that the designed system’s measurement accuracy is within ± 1.2 arcsec over a measurement range of 1 m. The designed system is easy to construct both in the laboratory environment and factory field.

A robust laser measurement system (LMS), consisting of a sensor head and a detecting part, for simultaneously measuring five-degree-of-freedom (five-DOF) error motions of linear stages, is proposed and characterized. For the purpose of long-travel measurement, all possible error sources that would affect the measurement accuracy are considered. This LMS not only integrates the merits of error compensations for the laser beam drift, beam spot variation, detector sensitivity variation, and non-parallelism of dual-beam that have been resolved by the author’s group before, but also eliminates the crosstalk errors among five-DOF error motions in this study. The feasibility and effectiveness of the designed LMS and modified measurement model are experimentally verified using a laboratory-built prototype. The experimental results show that the designed LSM has the capability of simultaneously measuring the five-DOF error motions of a linear stage up to one-meter travel with a linear error accuracy in sub-micrometer and an angular error accuracy in sub-arcsecond after compensation.

3D imaging and metrology of complex micro-structures is a critical task for precision manufacturing and inspection. In this paper, an accurate and flexible calibration method for 3D microscopic structured light system with telecentric imaging and Scheimpflug projector is proposed. Firstly, a fringe projection 3D microscopy (FP-3DM) system consisting of a telecentric camera and a Scheimpflug projector is developed, which can take full advantage of the depth of field (DOF) and increase the measurement depth range. Secondly, an accurate and flexible joint calibration method is proposed to calibrate the developed system, which utilizes the established pinhole imaging model and Scheimpflug distortion model to calibrate telecentric imaging, and fully considers the correction and error optimization of the Scheimpflug projection model. Meanwhile, the optimized local homography is calculated to obtain more accurate sub-pixel correspondence between the camera and the projector, and the perspective-n-point (PnP) method make the 3D coordinate estimation of the feature point more accurate. Finally, a prototype and a dedicated calibration program are developed to realize high-resolution and high-precision 3D imaging. The experimental results demonstrate that the re-projection error is less than 1µm, and the 3D repeated measurement error based on feature fitting is less than 4µm, within the calibrated volume of 10(H)mm × 50(W)mm × 40(D)mm.

This paper presents a miniature three-degree-of-freedom laser measurement (3DOFLM) system for displacement feedback and error compensation of a nanopositioning stage. The 3DOFLM system is composed of a miniature Michelson interferometer (MMI) kit, a wavelength corrector kit, and a miniature autocollimator kit. A low-cost laser diode is employed as the laser source. The motion of the stage can cause an optical path difference in the MMI kit so as to produce interference fringes. The interference signals with a phase interval of 90° due to the phase control are detected by four photodetectors. The wavelength corrector kit, based on the grating diffraction principle and the autocollimation principle, provides real-time correction of the laser diode wavelength, which is the length unit of the MMI kit. The miniature autocollimator kit based on the autocollimation principle is employed to measure angular errors and compensate induced Abbe error of the moving table. The developed 3DOFLM system was constructed with dimensions of 80 mm (x) × 90 mm (y) × 20 mm (z) so that it could be embedded into the nanopositioning stage. A series of calibration and comparison experiments were carried out to test the performance of this system.

The geometric error motions of rotary stages greatly affect the accuracy of constructed machines such as machine tools, measuring instruments, and robots. In this paper, an embedded sensor system for real-time measurement of two radial and three angular error motions of a rotary stage is proposed, which makes use of a rotary encoder with multiple scanning heads to measure the rotational angle and two radial error motions and a miniature autocollimator to measure two tilt angular errors of the axis of rotation. The assembly errors of the grid disc of the encoder and the mirror for autocollimator are also evaluated and compensated. The developed measuring device can be fixed inside the rotary stage. In the experiments, radial error motions of two points on the axis (h = 5 mm and 60 mm) were measured and calibrated with LVDTs, and the data showed that the radial error motions of the axis were less than 20 μm, and the calibration residual errors were less than 2 μm. When intermittent external forces were applied to the stage, the change of the stage’s error motion could also be monitored accurately.