Angle measurement is an essential component of precision measurement and serves as a crucial prerequisite for high-end manufacturing. It guides the implementation of precision manufacturing and assembly. The current angle measurement methods mainly focus on multiple axes, high precision, and large measurement ranges. This article introduces the technology of angle measurement from the perspectives of single-axis and multi-axis measurement schemes. Firstly, the single-axis measurement scheme is primarily achieved through optical methods, such as encoder discs that measure energy changes and interferometric phase changes, as well as mechanical, electromagnetic, and inertial angle measurement methods, among which interferometric methods offer the highest accuracy, with high cost, and encoder discs provide the largest measurement range with an ordinary price. Secondly, in the multi-axis measurement scheme, autocollimation instruments, including plane mirrors, gratings, and self-designed targets, are the main options. Although grating encoders can achieve three degrees of freedom in angle measurement with an ordinary price, they are limited in terms of measurement range and sensitivity compared to self-designed targets. Lastly, artificial intelligence assistance precision measurement is increasingly being embraced due to significant advancements in computer performance, making it more convenient to identify the relationship between measured values and detection values. In conclusion, angle measurement plays a crucial role in precision manufacturing, and the evolving and improving technologies provide the manufacturing industry with greater choices. The purpose of this review is to help readers quickly find more suitable technical solutions according to current application requirements, such as single/multiple axes, accuracy level, measuring range, budget, etc.

Optical interferometry has emerged as a cornerstone technology for high-precision length measurement, offering unparalleled accuracy in various scientific and industrial applications. This review provides a comprehensive overview of the latest advancements in optical interferometry, with a focus on grating and laser interferometries. For grating interferometry, systems configurations ranging from single-degree- to multi-degree-of-freedom are introduced. For laser interferometry, different measurement methods are presented and compared according to their respective characteristics, including homodyne, heterodyne, white light interferometry, etc. With the rise of the optical frequency comb, its unique spectral properties have greatly expanded the length measurement capabilities of laser interferometry, achieving an unprecedented leap in both measurement range and accuracy. With regard to discussion on enhancement of measurement precision, special attention is given to periodic nonlinear errors and phase demodulation methods. This review offers insights into current challenges and potential future directions for improving interferometric measurement systems, and also emphasizes the role of innovative technologies in advancing precision metrology technology.

We investigate a novel two-channel grating encoder that can perform simultaneous measurements of six-degree-of-freedom (DOF) motions of two adjacent sub-components of synthetic-aperture optics such as pulse-compression gratings(PCGs) and telescope-primary mirrors. The grating encoder consists of a reading head and two separate gratings, which are attached to the back of the sub-components, respectively. The reading head is constructed such that there two identical optical probes can share the same optical components. The two probes are guided to hit each of the two gratings and can detect six-DOF motions simultaneously and independently. For each probe, the incident beam propagates through both a three-axes grating interferometry module and a three-axes diffraction integrated autocollimator-module, which detects translational and rotational movement, respectively. By combining the two modules it is possible to perform six-DOF measurement for a single point. The common-path configuration of the two probes enable identical responses to environmental variation, which ensures high accuracy.

Chromatic confocal technology (CCT) is one of the most promising methods for the contactless and accurate measurement of structure profiles. Based on the principles of chromatic dispersion and confocal theory, a dispersion probe is proposed and optimized with several commercial and cheap refractive index lenses. The probe provides 0.3× magnification and a dispersion range of 400 μm with a commercial LED source with an effective bandwidth of ca. 450–623 nm. Since the noise fluctuation can affect the extraction stability of the focal wavelength, a modification to the centroid peak extraction algorithm is proposed in this paper, where several virtual pixels are interpolated among the real pixels of the spectrometer before thresholding. In addition, a series of experiments were carried out to test the system’s displacement measurement performance. The results clearly show that stability is improved by the modified algorithm, and the calibration repeatability is ±0.3 μm in the full measurement range with a linear stage. The standard deviation at the fixed position has an optimal value of 0.009 μm. The section profile of a Fresnel lens is measured by the CCT system to demonstrate its high feasibility and efficiency.

Grating interferometers highly valued for high resolution, straightforward benchmark and insensitivity to environmental disturbances, have become one of the most mainstream methods for ultra-precision positioning. Traditional heterodyne grating interferometers which use a dual-frequency orthogonally polarized laser source suffer nanometer-level periodic nonlinear error due to frequency and polarization mixing, thus becoming incompetent to undertake sub-nanometer measurement. Based on the design of two separated laser beams with a small frequency difference for heterodyne beating, a wavelength-stabilized and quasi-common-path heterodyne grating interferometer is proposed. It incorporates a symmetrical oblique incidence structure where the residual dead path is calibrated and the laser source wavelength is stabilized to the rubidium atomic transition line, diminishing heterodyne phase errors resulted from the optical path difference. This approach not only significantly mitigates periodic nonlinear error to below 0.3 nm, but also enhances measurement resolution, repeatability and interference robustness. The proposed heterodyne grating interferometer is determined for ultra-precision positioning serving for precision machinery manufacturing and scanning beam interference lithography and so forth.

Periodic microscale array structures play an important role in diverse applications involving photonic crystals and diffraction gratings. A polarized holographic lithography system is proposed for patterning high-uniformity microscale two-dimensional crossed-grating structures with periodic tunability. Orthogonal two-axis Lloyd’s mirror interference and polarization modulation produce three sub-beams, enabling the formation of two-dimensional crossed-grating patterns with wavelength-comparable periods by a single exposure. The two-dimensional-pattern period can also be flexibly tuned by adjusting the interferometer spatial positioning. Polarization states of three sub-beams, defining the uniformity of the interference fringes, are modulated at their initial-polarization states based on a strict full polarization tracing model in a three-dimensional space. A polarization modulation model is established considering two conditions of eliminating the unexpected interference and providing the desired identical interference intensities. The proposed system is a promising approach for fabricating high-uniformity two-dimensional crossed gratings with a relatively large grating period range of 500–1500 nm. Moreover, our rapid and stable approach for patterning period-tunable two-dimensional-array microstructures with high uniformity could be applicable to other multibeam interference lithography techniques.