Open AccessArticle

Improved Autocollimator for Roll Angle Measurement with an Enlarged Measuring Range

Yan Guo

Yu Zhang

Jiali Ji

Qing Yan

Huige Di

Li Wang

and

Dengxin Hua

School of Mechanical and Precision Instrument Engineering, Xi’an University of Technology, Xi’an 710048, China

Author to whom correspondence should be addressed.

Appl. Sci. 2025, 15(5), 2256; https://doi.org/10.3390/app15052256

Submission received: 27 January 2025 / Revised: 16 February 2025 / Accepted: 17 February 2025 / Published: 20 February 2025

(This article belongs to the Special Issue Advances in Optical Instrument and Measurement Technology)

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Abstract

An autocollimator is a goniometer established according to the principle of autocollimation, but it is ineffective for measuring the roll angle. This paper proposes an improved autocollimator available for large-range roll angle measurement, which maintains the optical structure of the classic one while incorporating a wedge prism (WP) working in transmissive mode as a roll angle sensing element to dissociate the collimated beam into two beams. According to the moving paths of the two light spots focused on the photodetector, the roll angle of the WP can be solved. The measuring method is expounded, and the calibration results reveal that the improved autocollimator has an accuracy of ±13.55 arcsec over a range of 360°, confirming its feasibility for roll angle measurement where a large measuring range is required.

Keywords:

autocollimator; roll angle measurement; measuring range; wedge prism

1. Introduction

An angle is a basic physical quantity, and many other parameters can be converted to angles; thus, angle measurement is of great significance in the fields of aerospace, optical processing, equipment manufacturing, etc. [1,2]. Compared with laser interferometer [3,4,5], polarization detection [6,7], and internal reflection methods [8,9], the autocollimator is more frequently employed owing to the advantages of a simple architecture and high accuracy [10,11,12]. Over the years, the performance of the autocollimator has been greatly enhanced with the continuous development of component materials and fabrication technologies. However, its fundamental structure and measuring principle have not changed [13]. The autocollimator perceives the deflection of the reflected beam, but can only give the pitch angle and yaw angle of a planar mirror rather than the roll angle around the optic axis.

To address this issue, many scholars have carried out relevant studies. Dagne et al. [14] aligned a laterally placed autocollimator with a planar mirror that could translate along a guideway. Thus, the roll angle of this mirror around the guideway was equivalent to the pitch angle for the autocollimator, and its measurement error was within ±0.9 arcsec. Ren et al. [15] built an autocollimation system that utilized a grating instead of a planar mirror to generate two diffracted beams. The roll angle of the grating could be computed through the beam spot displacements on two position-sensitive detectors, and a measuring accuracy of ±0.2 arcsec over a range of 250 arcsec was achieved. Gao et al. [16] proposed a dual-collimator method where one emitted a light beam with a dot-array pattern, while the other admitted this beam. The roll angle of the admitting collimator was solved in terms of dot distribution parameters, and the measurement error was better than ±1 arcsec within ±150 arcsec. Hoang et al. [17] designed a pyramidal prism which was equivalent to a pair of right-angle prisms and could produce two reflected beams. Then, a goniometric algorithm allowed roll angle calculation based on the beam spot positions, but the calculation error was significantly affected by collimation angles. Li et al. [18] devised a cylindrical corner cube prism to form a cross-line image on a CMOS camera. By detecting the image obliquity, the roll angle of the prism was determined, and a measuring accuracy of ±6.1 arcsec over a range of ±20° was realized. Zhai et al. [19] adopted a right-angle prism (RAP) as a reflector of a goniometric system to create two reflected beams. The roll angle of the RAP could be acquired by dividing the difference in the vertical displacements of the two beam spots by the spacing between both beams. The measurement error ranged from −1.5 to 2.2 arcsec within ±100 arcsec. Yin et al. [20] incorporated the moiré technique into an autocollimation system to generate a group of fringes. Subsequently, they worked out the roll angle of a RAP based on the variation in fringe width, and attained a root-mean-square error of 5 arcsec within 1000 arcsec. Wang et al. [21] proposed an autocollimator that used an optical wedge working in reflective mode rather than a planar mirror. The roll angle of the optical wedge was solved according to the y-directional displacement of the light spot reflected from its rear face, and the measurement error did not exceed ±35 arcsec within ±2°. Guo et al. [22] presented an autocollimation system using a cooperated reflector. A collimated beam carrying a crosshair image was projected onto the reflector and then returned. The roll angle of the reflector was determined by sensing the rotation angle of the crosshair image. Although the above autocollimation methods materialize the roll angle measurement, there are still some deficiencies. First, their measuring range is relatively small (maximum of only ±20°) and some of them may be susceptible to crosstalk effects, which will limit the application occasions. Second, they are likely to require customized optics and complicated data-processing algorithms, bringing high cost and slow measurement.

This paper proposes an improved autocollimator for measuring the roll angle, which can cover the whole range of 360°. Moreover, it is immune to the crosstalk effect, does not require specially made optics, and has a simple data-processing algorithm because it receives only two circular light spots. The improved autocollimator maintains the optical structure of the classic one; the difference is that a wedge prism (WP) working in transmissive mode is incorporated as a roll angle sensing element to dissociate the collimated beam into two beams. By analyzing the moving paths of the two light spots on the photodetector, the roll angle of the WP can be acquired. In addition, an experimental prototype is established and its feasibility is verified. The other sections of this paper are structured as below. Section 2 outlines the measuring method. Section 3 presents the experiments and results. Finally, Section 4 recaps this paper and discusses possible improvement measures.

2. Methods

2.1. Optical Configuration

Figure 1 depicts a schematic of an improved autocollimator for roll angle measurements. A light beam from a light-emitting diode (LED) illuminates an aperture stop (AS). After passing through a beam splitter (BS) and an objective lens (OL), it becomes a collimated beam. When this beam hits the front (deposited with a beam-splitting film) of the WP, it is dissociated into two beams. One beam directly returns, while the other beam successively passes through the WP’s front and back, bounces from a planar mirror (PM), and reverses through the WP’s back and front. Finally, both beams converge on a photodetector (CMOS) and form two light spots, which will be sent to a computer to extract their coordinates by means of an image-processing program.

2.2. Measurement of Roll Angle

The classic autocollimator does not work for measuring the roll angle, since the light spot on the photodetector does not move as the PM rolls. To overcome this difficulty, the WP is inserted in front of the PM and rolls with a target to be measured, but the PM remains stationary. Figure 2a illustrates the roll angle measuring principle. A light beam can be represented by a directing vector following its propagation direction and with a length equal to the refractive index of the medium in which this beam propagates, whereas a reflecting or refracting surface can be represented by its normal vector pointing from the incident medium to the interface, with a length of 1. In this way, the vector form of the reflection and refraction laws can be applied to calculate the directions of reflected and refracted beams. Before the WP rolls, as the collimated beam passes through the WP’s front and back, the PM, and the WP’s back and front in sequence, the normal vectors of each refracting and reflecting surface can be expressed as

\{\begin{cases} N_{1} = {[0 0 - 1]}^{T}, \\ N_{2} = {[- θ 0 - 1]}^{T}, \\ N_{3} = {[0 0 - 1]}^{T}, \\ N_{4} = {[θ 0 1]}^{T}, \\ N_{5} = {[0 0 1]}^{T}, \end{cases}

(1)

where θ signifies the wedge angle of the WP and takes a small value. The collimated beam with directing vector

A_{0} = {[\begin{matrix} 0 & 0 & - 1 \end{matrix}]}^{T}

propagates against the z-axis to the WP and is split into two beams by its front. According to the reflection law [23], the directing vector of the reflected beam is calculated as

A_{1} = A_{0} - 2 (A_{0} \cdot N_{1}) N_{1} = {[0 0 1]}^{T} .

(2)

Then, this beam converges on the origin of the CMOS and forms light spot 1, as marked with a red ring in Figure 2b. For the transmitted beam, according to the refraction law [23], its directing vector is calculated as

A_{2} = A_{0} + (\sqrt{n^{2} - 1 + {(A_{0} \cdot N_{1})}^{2}} - A_{0} \cdot N_{1}) N_{1} = {[0 0 - n]}^{T},

(3)

where n signifies the refractive index of the WP. Subsequently, this beam is refracted by the WP’s back, reflected by the PM, and refracted again by the WP’s back and front. The directing vectors of these refracted and reflected beams involved in the above process are calculated as

\{\begin{cases} A_{3} = A_{2} + (\sqrt{1 - n^{2} + {(A_{2} \cdot N_{2})}^{2}} - A_{2} \cdot N_{2}) N_{2} = {[θ (n - 1) 0 - 1]}^{T}, \\ A_{4} = A_{3} - 2 (A_{3} \cdot N_{3}) N_{3} = {[θ (n - 1) 0 1]}^{T}, \\ A_{5} = A_{4} + (\sqrt{n^{2} - 1 + {(A_{4} \cdot N_{4})}^{2}} - A_{4} \cdot N_{4}) N_{4} = {[2 θ (n - 1) 0 n]}^{T}, \\ A_{6} = A_{5} + (\sqrt{1 - n^{2} + {(A_{5} \cdot N_{5})}^{2}} - A_{5} \cdot N_{5}) N_{5} = {[2 θ (n - 1) 0 1]}^{T} . \end{cases}

(4)

Ultimately, the beam refracted by the WP’s front also focuses on the CMOS and forms light spot 2, as marked with the green ring in Figure 2b. When the WP rolls by an angle γ, the rotation matrix [24] is written as

R = [\begin{matrix} \cos γ & - \sin γ & 0 \\ \sin γ & \cos γ & 0 \\ 0 & 0 & 1 \end{matrix}] .

(5)

Correspondingly, the normal vectors of each refracting and reflecting surface become

\{\begin{cases} {N_{1}}^{'} = R N_{1} = {[0 0 - 1]}^{T}, \\ {N_{2}}^{'} = R N_{2} = {[- θ \cos γ - θ \sin γ - 1]}^{T}, \\ {N_{3}}^{'} = N_{3} = {[0 0 - 1]}^{T}, \\ {N_{4}}^{'} = R N_{4} = {[θ \cos γ θ \sin γ 1]}^{T}, \\ {N_{5}}^{'} = R N_{5} = {[0 0 1]}^{T} . \end{cases}

(6)

Following the previous analytical method, the directing vector of the beam reflected by the WP’s front is calculated as

{A_{1}}^{'} = {[0 0 1]}^{T} .

(7)

Meanwhile, the directing vector of the beam experiencing refractions by the WP’s front and back, reflection by the PM, and repetitive refractions by the WP’s back and front is calculated as

{A_{6}}^{'} = {[2 θ (n - 1) \cos γ 2 θ (n - 1) \sin γ 1]}^{T} .

(8)

When comparing the directing vectors A₁, A₆, A₁′, and A₆′, that is, Equations (2), (4), (7) and (8), it can be observed that before and after the WP rolls, light spot 1 stays at the origin of the CMOS, while light spot 2 rotates around the origin, whose moving path can be expressed as the parameter equation system of the circle:

\{\begin{matrix} x = L \times \cos γ, \\ y = L \times \sin γ, \end{matrix}

(9)

where L = f × 2θ(n − 1) signifies the rotation radius of light spot 2; and f signifies the focal distance of the OL. As shown in Figure 2b, if the WP rolls by an angle γ, light spot 2 will rotate around the origin by the same angle. Thus, it is recapitulated that the roll angle of the WP is equivalent to the rotation angle of the straight line determined by the origin and light spot 2. As long as the CMOS detects the coordinates of light spot 2, the roll angle of the WP can be calculated.

2.3. Crosstalk Effect

During the actual measurement of roll angle γ, the measured target may also generate pitch and yaw angles, and thus the potential crosstalk of these two angles on the roll angle measurement should be broken down. Assuming that the measured target, to which the WP is attached, produces three-dimensional angles, the rotation matrix [24] is rewritten as

R^{'} = [\begin{matrix} 1 & 0 & 0 \\ 0 & \cos α & - \sin α \\ 0 & \sin α & \cos α \end{matrix}] [\begin{matrix} \cos β & 0 & \sin β \\ 0 & 1 & 0 \\ - \sin β & 0 & \cos β \end{matrix}] [\begin{matrix} \cos γ & - \sin γ & 0 \\ \sin γ & \cos γ & 0 \\ 0 & 0 & 1 \end{matrix}],

(10)

where α and β signify the pitch and yaw angles, respectively, which usually take small values. Correspondingly, the normal vectors of each refracting and reflecting surface become

\{\begin{cases} {N_{1}}^{″} = R^{'} N_{1} = {[- β α - 1]}^{T}, \\ {N_{2}}^{″} = R^{'} N_{2} = {[- θ \cos γ - β - θ \sin γ + α - 1]}^{T}, \\ {N_{3}}^{″} = N_{3} = {[0 0 - 1]}^{T}, \\ {N_{4}}^{″} = R^{'} N_{4} = {[θ \cos γ + β θ \sin γ - α 1]}^{T}, \\ {N_{5}}^{″} = R^{'} N_{5} = {[β - α 1]}^{T} . \end{cases}

(11)

Based on the previous analytical method, the directing vector of the beam reflected by the WP’s front changes to

{A_{1}}^{″} = {[2 β - 2 α 1]}^{T} .

(12)

Meanwhile, the directing vector of the beam undergoing refractions by the WP’s front and back, reflection by the PM, and repetitive refractions by the WP’s back and front changes to

{A_{6}}^{″} = {[2 θ (n - 1) \cos γ 2 θ (n - 1) \sin γ 1]}^{T} .

(13)

When comparing Equations (7), (8), (12), and (13), it can be observed that light spot 1 displaces owing to the pitch and yaw angles, but we still regard its initial position (the origin of the CMOS) as the rotation center, around which light spot 2 rotates, and its moving path is the same as that without crosstalk. Thus, it can be deduced that the roll angle measurement will not be affected by the crosstalk effect.

3. Experimental Results

3.1. Experimental Facility

To evaluate the performance of the improved autocollimator, an experimental prototype was constructed, as shown in Figure 3. The LED (Daheng Optics, Type GCI-060401, Beijing, China) possessed a 620 ± 10 nm wavelength and 3 W output power, respectively. The diameter of the central hole of the AS was 2 mm. The BS possessed a 0.5 split ratio. The diameter and focal distance of the OL were 50.8 mm and 300 mm, respectively. The CMOS (Daheng Imaging, Type ME2P-2621-15U3M, Beijing, China) possessed a 2.5 μm pixel dimension and 5120 × 5120 pixels, respectively. The WP was made of N-BK7 glass with a refractive index of 1.517 and a wedge angle of 1° such that the angle of the beam with directing vector A₆ was less than 1.034° with respect to the optic axis. The mean transmissivity of the beam-splitting film deposited on the front of the WP was 62.3%, which made the light intensity of light spots 1 and 2 roughly equal and thus suppressed the adverse effect resulting from an inconsistent light intensity. The two light spots received by the CMOS were diverted to a computer for preprocessing (denoising and thresholding). Then, a gray centroid algorithm was employed to extract the light spot coordinates, which were used for calculating the roll angle.

3.2. Tests of Stability and Repeatability

Stability is the capability of a measuring instrument to keep its metrological characteristics constant over time and is also the prerequisite for the instrument to measure accurately. It is largely affected by electrical noise and the peripheral environment and should be examined immediately after the instrument is constructed. The stability of the improved autocollimator was tested on an optical stage in a laboratory. The indoor temperature was kept at about 25 °C and there was no lighting. The WP was installed on a three-dimensional rotary table. We adjusted the rotary table such that light spot 1 was located at the origin of the CMOS, and the straight line determined by light spots 1 and 2 was at an angle of about −92.7° to the x-axis. After preheating for 30 min, the improved autocollimator took photos at a frame rate of 0.5 fps during a 10 min period. Figure 4 maps the stability curve of the WP’s roll angle. The peak-to-valley value of the curve was 3.62 arcsec and the standard deviation was 0.73 arcsec, indicating that the improved autocollimator tended to run stably.

To investigate the measurement repeatability of the improved autocollimator, several independent measurements were performed. While the autocollimator was running stably, a piece of cardboard was placed ahead of it and withdrawn a few seconds later. Then, a measured value was logged. This process was executed ten times, and the measured values (after subtracting the initial measured value) are shown in Table 1. The standard deviation of the measured values calculated using the Bessel formula was 1.72 arcsec, which was considered the repeatability error.

3.3. Calibration and Resolution Test

A standard autocollimator (Shanghai MicroCre Light-machine, Type YRMAT-2010B, Shanghai, China) and a polyhedral mirror were employed as the benchmarks to calibrate the improved autocollimator. The standard autocollimator possessed a 0.1 arcsec resolution and ±0.5 arcsec accuracy. The polyhedral mirror had 24 faces in total, and the angle between the normals of two adjacent faces was 15°. Figure 5a illustrates the calibration experiment. The WP and polyhedral mirror were installed on a rotary table for rolling. The improved autocollimator was aligned to the WP, while the standard autocollimator on the side was aligned perpendicularly to one face of the polyhedral mirror. The rotary table rolled at 30° intervals and was measured simultaneously by both autocollimators. Figure 5b maps the results of the calibration experiment. The measurement errors acquired by comparing the measured values given by the improved autocollimator with the reference values given by the standard autocollimator did not exceed ±13.55 arcsec, with a standard deviation of 8.88 arcsec, over a range of 360°. These measurement errors were mainly caused by random and systematic errors. The former arose from electrical noise in the CMOS, fluctuations in environmental parameters such as humidity and temperature, mechanical vibrations, and stray light. The latter originated from the WP’s optical parallelism deviation owing to manufacturing flaws, as well as deformation and misorientation owing to improper installation. The measured values of the improved autocollimator were linearly fitted, and a linearity of 0.9993 was obtained.

Moreover, the roll angle resolution was tested utilizing the same experimental kit. The standard autocollimator monitored the roll angle increment of a certain face of the polyhedral mirror, while the improved autocollimator synchronously detected the roll angle of the WP, and its measurement results are drawn in Figure 6. As can be seen, the improved autocollimator could recognize the increment of 10 arcsec, and thus the roll angle resolution was better than 10 arcsec.

3.4. Applications of Improved Autocollimator

This subsection provides two applications of the improved autocollimator. In the equipment manufacturing industry, the roll angle of a linear stage results from the shape error of the guide-rail, which will adversely affect its positioning accuracy. As an application, the improved autocollimator was used to measure the roll angle of the linear stage to facilitate the shape modification of the guide-rail. Figure 7a illustrates the experimental setup. The WP was fixed to a linear stage that could move along a guide-rail, and the improved autocollimator measured the roll angle of the linear stage. An electronic level (Qingdao Qianshao, Type WL9, Qingdao, China) possessing ±(1 + 0.02 × reading) accuracy was also placed on the linear stage to synchronize the roll angle measurement for comparison. The linear stage was moved by hand from near to far with an increment of approximately 50 mm and a travel of 400 mm. Figure 7b maps the measurement curves of both instruments. The deviations between the two curves ranged from −8.63 to 16.92 arcsec. The main reasons for the deviations may be that the WP and electronic level were in different positions on the linear stage, and the electronic level was marginally misdirected. Nonetheless, the tendencies of the two measurement curves were greatly consistent, which exemplified that the improved autocollimator was suitable for this practical, concrete task.

In the optical industry, the wedge angle of an optical wedge is a critical parameter that determines the direction of the refracted beam. As a second application, the improved autocollimator can be used to measure the wedge angle of an optical wedge specimen to perfect its processing. Specifically, the currently used WP can be replaced by the specimen. Then, the specimen is rolled by 360°, and a circular moving path of light spot 2 around light spot 1, as well as the rotation radius L, can be detected on the CMOS. Consequently, the wedge angle of the specimen is calculated to be L/[2f × (n − 1)].

4. Discussion and Conclusions

This paper proposes an improved autocollimator for roll angle measurement, which can cover the whole range of 360° and maintains the optical structure of the classic autocollimator while incorporating a WP working in transmissive mode as a roll angle sensing element to dissociate the collimated beam into two beams. The roll angle of the WP can be solved through the moving paths of the two light spots on the CMOS. Furthermore, an experimental prototype was constructed, whose performance was estimated. The experimental results reveal that the improved autocollimator has a stability of 3.62 arcsec within 10 min, a repeatability error of 1.72 arcsec, an accuracy of ±13.55 arcsec over a range of 360°, and a resolution of better than 10 arcsec. It can be used for roll angle measurement where a large measuring range is required, such as measuring the roll angle of a simulated aircraft in a wind tunnel, calibrating the rotation accuracy of a rolling table, shaft, or mechanical arm, and guiding the assembly of structural parts including the alignment of the joints of two pipelines.

Despite the positive advances of the improved autocollimator, further research is needed. Firstly, the measurement error owing to random and systematic errors needs to be reduced, which can be performed by digital filtering, error modeling, and compensation. Secondly, the roll angle resolution needs to be improved. According to the geometric relationship shown in Figure 2b, there are two remedies. One is to prolong the rotation radius of light spot 2, which can be achieved by increasing the focal distance of the OL and the wedge angle and refractive index of the WP. Another is to enhance the displacement resolution of light spot 2, which can be realized by optimizing the image-processing algorithm, as well as the shape and size of the AS. Thirdly, the experimental prototype needs to be industrialized, which can be accomplished by using smaller optical components and designing dedicated opto-mechanical structures. Error reduction, resolution improvement, and industrialization will be the focuses of our next steps.

Author Contributions

Conceptualization, Y.G.; data curation, Y.Z. and J.J.; formal analysis, Y.G. and Y.Z.; funding acquisition, Y.G.; investigation, Y.Z. and J.J.; methodology, Y.G. and Y.Z.; project administration, Q.Y., H.D., L.W., and D.H.; resources, Q.Y., H.D., L.W., and D.H.; software, Y.Z.; supervision, D.H.; validation, Y.Z.; visualization, Y.Z.; writing—original draft, Y.Z.; writing—review and editing, Y.G. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the Natural Science Basic Research Program of Shaanxi Province (2024JC-YBQN-0705) and the Shaanxi Province Postdoctoral Science Foundation (2023BSHEDZZ251).

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The original contributions presented in this study are included in the article; further inquiries can be directed to the authors.

Acknowledgments

We thank Zhichao Dong for his support in processing the wedge prism (WP).

Conflicts of Interest

The authors declare no conflicts of interest.

References

Kumar, A.S.A.; George, B.; Mukhopadhyay, S.C. Technologies and applications of angle sensors: A review. IEEE Sens. J. 2021, 21, 7195–7206. [Google Scholar] [CrossRef]
Shimizu, Y.; Matsukuma, H.; Gao, W. Optical sensors for multi-axis angle and displacement measurement using grating reflectors. Sensors 2020, 19, 5289. [Google Scholar] [CrossRef]
Lin, C.; Zhou, S.; Shi, L.; Yang, Y.; Wu, G. Two-dimensional angle measurement with sub-arcsecond precision and MHz update rate using heterodyne interferometry with optical frequency comb. Opt. Lett. 2024, 49, 526–529. [Google Scholar] [CrossRef] [PubMed]
Liang, X.; Lin, J.; Yang, L.; Wu, T.; Liu, Y.; Zhu, J. Simultaneous measurement of absolute distance and angle based on dispersive interferometry. IEEE Photonics Technol. Lett. 2020, 32, 449–452. [Google Scholar] [CrossRef]
Kumar, Y.P.; Chatterjee, S.; Negi, S. Small roll angle measurement using lateral shearing cyclic path polarization interferometry. Appl. Opt. 2016, 55, 979–983. [Google Scholar] [CrossRef]
Plosker, E.; Bykhovsky, D.; Arnon, S. Evaluation of the estimation accuracy of polarization-based roll angle measurement. Appl. Opt. 2013, 52, 5158–5164. [Google Scholar] [CrossRef]
Plosker, E.; Arnon, S. Statistics of remote roll angle measurement. Appl. Opt. 2014, 53, 2437–2440. [Google Scholar] [CrossRef]
Kim, I.I.; Lie, Y.; Park, J.S. Aperture total internal reflection (A-TIR) for contact angle measurement. Opt. Express 2021, 29, 41685–41702. [Google Scholar] [CrossRef]
Zhang, A.; Huang, P. Total internal reflection for precision small-angle measurement. Appl. Opt. 2001, 40, 1617–1622. [Google Scholar] [CrossRef] [PubMed]
Larichev, R.A.; Filatov, Y.V. A model of angle measurement using an autocollimator and optical polygon. Photonics 2023, 10, 1359. [Google Scholar] [CrossRef]
Li, R.; Konyakhin, I.; Zhang, Q.; Cui, W.; Wen, D.; Zou, X.; Guo, J.; Liu, Y. Error compensation for long-distance measurements with a photoelectric autocollimator. Opt. Eng. 2019, 58, 104112. [Google Scholar] [CrossRef]
Zhukov, Y.P.; Loychii, I.L.; Pestov, Y.L.; Sergeev, V.A.; Stradov, B.G. Compact two-coordinate digits autocollimator. J. Opt. Technol. 2019, 86, 476–479. [Google Scholar] [CrossRef]
Guo, Y.; Cheng, H.; Wen, Y.; Feng, Y. Three-degree-of-freedom autocollimator based on a combined target reflector. Appl. Opt. 2020, 59, 2262–2269. [Google Scholar] [CrossRef] [PubMed]
Dagne, H.; Lou, Z.; Zhang, J.; Zhou, J. Roll angle error measurement of linear guideways using mini autocollimators. In Proceedings of the 2024 10th International Conference on Mechatronics and Robotics Engineering, Milan, Italy, 27–29 February 2024; pp. 220–227. [Google Scholar]
Ren, W.; Cui, J.; Tan, J. Precision roll angle measurement system based on autocollimation. Appl. Opt. 2022, 61, 3811–3818. [Google Scholar] [CrossRef] [PubMed]
Gao, Y.; Wang, X.; Huang, Z.; Zhan, D.; Hu, C. High-precision rolling angle measurement for a three-dimensional collimator. Appl. Opt. 2014, 53, 6629–6634. [Google Scholar] [CrossRef] [PubMed]
Hoang, P.V.; Konyakhin, I.A. Autocollimation sensor for measuring the angular deformations with the pyramidal prismatic reflector. Proc. SPIE 2017, 10231, 263–269. [Google Scholar]
Li, R.; Xie, L.; Zhen, Y.; Xiao, H.; Wang, W.; Guo, J.; Konyakhin, I.; Nikitin, M.; Yu, X. Roll angle autocollimator measurement method based on a cylindrical cube-corner reflector with a high resolution and large range. Opt. Express 2022, 30, 7147–7161. [Google Scholar] [CrossRef] [PubMed]
Zhai, Y.; Feng, Q.; Zhang, B. A simple roll measurement method based on a rectangular-prism. Opt. Laser Technol. 2012, 44, 839–843. [Google Scholar] [CrossRef]
Yin, Y.; Cai, S.; Qiao, Y. Design, fabrication, and verification of a three-dimensional autocollimator. Appl. Opt. 2016, 55, 9986–9991. [Google Scholar] [CrossRef] [PubMed]
Wang, J.; Bai, Y.; Zhao, W.; Xie, N.; Zhang, L. Three-axis angle measurement method based on an optical wedge. Appl. Opt. 2024, 63, 1125–1134. [Google Scholar] [CrossRef] [PubMed]
Guo, Y.; Cheng, H.; Liu, G. Three-degree-of-freedom autocollimation angle measurement method based on crosshair displacement and rotation. Rev. Sci. Instrum. 2023, 94, 015108. [Google Scholar] [CrossRef]
Yu, D.; Tan, H. Engineering Optics, 4th ed.; China Machine Press: Beijing, China, 2024; pp. 4–5. [Google Scholar]
Wang, C.; Zhou, X.; Fei, Z.; Gao, X.; Jin, R. A three dimensional point cloud registration method based on rotation matrix eigenvalue. Proc. SPIE 2017, 10410, 276–281. [Google Scholar]

Figure 1. Schematic of improved autocollimator for roll angle measurements.

Figure 2. Roll angle measurement: (a) principle and (b) light spots on CMOS before and after WP’s rolling.

Figure 3. Photograph of improved autocollimator for large-range roll angle measurement.

Figure 4. Results of stability test.

Figure 5. Calibration experiment: (a) setup and (b) results.

Figure 6. Results of resolution test.

Figure 7. Actual test of linear stage: (a) experimental setup and (b) results.

Table 1. Results of repeatability test.

Order	1	2	3	4	5	6	7	8	9	10
Measured value (arcsec)	−2.55	0.34	−2.83	−4.73	−1.67	−5.5	−1.19	−2.16	−3.76	−3.44

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Guo, Y.; Zhang, Y.; Ji, J.; Yan, Q.; Di, H.; Wang, L.; Hua, D. Improved Autocollimator for Roll Angle Measurement with an Enlarged Measuring Range. Appl. Sci. 2025, 15, 2256. https://doi.org/10.3390/app15052256

AMA Style

Guo Y, Zhang Y, Ji J, Yan Q, Di H, Wang L, Hua D. Improved Autocollimator for Roll Angle Measurement with an Enlarged Measuring Range. Applied Sciences. 2025; 15(5):2256. https://doi.org/10.3390/app15052256

Chicago/Turabian Style

Guo, Yan, Yu Zhang, Jiali Ji, Qing Yan, Huige Di, Li Wang, and Dengxin Hua. 2025. "Improved Autocollimator for Roll Angle Measurement with an Enlarged Measuring Range" Applied Sciences 15, no. 5: 2256. https://doi.org/10.3390/app15052256

APA Style

Guo, Y., Zhang, Y., Ji, J., Yan, Q., Di, H., Wang, L., & Hua, D. (2025). Improved Autocollimator for Roll Angle Measurement with an Enlarged Measuring Range. Applied Sciences, 15(5), 2256. https://doi.org/10.3390/app15052256

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