Open Access
Add to BibSonomy
Abstract
Augmented reality (AR) is desperately needed in the Metaverse. The geometrical waveguide receives increased attention in AR technology as achieving high resolution, full-color display, etc. However, the stray light and ghost image problems resulting from the parallelism errors severely deteriorate the imaging quality. According to the light propagation of the waveguide, a measuring system based on the combination of the autocollimator and the testing telescope (CAT) method was proposed to measure the parallelism errors of the partially reflective mirror array (PRMA). The results indicated that this method could measure the parallelism errors precisely with the maximum repeatability of 0.63$^{\prime\prime}$. The method could decouple the coupling of the parallelism errors of the PRMA and the substrate surfaces to imaging quality effectively. The precise parallelism measuring is expected to contribute to mass production and low cost by promoting the waveguide design and fabrication.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
With the rapid development of the Metaverse, augmented reality (AR) technology has a more irreplaceable role in technology-mediated consumer experiences globally [1]. In AR, virtual contents are integrated into the real world seen by the user’s eyes [2]. The optical waveguide attracts considerable attention as the critical element of see-through near-eye displays. It has the potential to be widely applied due to its lightweight, small volume, superior optical performance, and larger field of view with compact optical elements [3–6]. Waveguide technology is mainly classified into the geometrical waveguide and diffractive waveguide by their coupler type [7]. Compared to the diffractive waveguide that suffers from rainbow effects and a higher design barrier, the geometrical waveguide with excellent image quality and no color dispersion is a promising path toward consumer AR glasses currently [8,9].
Major categories of the geometrical waveguide mainly include partially reflective mirror array (PRMA) waveguides and micro-mirror array (MMA) waveguides [10]. The scattering and diffraction effect due to the fine structure of the MMA may reduce the image quality. Hence, the PRMA waveguide as the optical combiner is more common in AR glasses (e.g., Lumus [11]). The PRMA waveguide serves as a pupil expander, which generally consists of an in-coupler, a substrate, and an out-coupler (i.e., the PRMA) [see Fig. 1(a)]. The light rays from the microdisplay are collimated by the collimation optics. Then, the collimated rays are coupled into the waveguide by the in-coupler, restricted in the substrate to propagate via the total internal reflection (TIR), and finally coupled out towards the eyes by the partial reflection of the PRMA that breaks the TIR [see Fig. 1(b)]. The in-coupling and out-coupling processes, as well as TIRs in the substrate, have no effect on the beam collimation [12].
Fig. 1. Schematic diagram of the geometrical waveguide based on the partially reflective mirrors array (PRMA). (a) The light propagation simulation. (b) The ray paths of the in-coupling parallel rays through the waveguide. The paths of stray lights when there is (c) the parallelism error between the two substrate surfaces and (d) the parallelism errors between mirrors of the PRMA. The green rays represent normal lights, and the red rays represent stray lights. The insets in (c) and (d) represent the eye box.
However, a significant problem of the PRMA waveguide is the ghost image resulting from stray lights [13]. Minimizing stray lights caused by the different propagation paths of non-collimated rays commonly requires collimation optics to collimate the light rays from the microdisplay [14]. The reflectance of the PRMA is decreased for reflection at large incident angles and vice versa for small incident angles by the stacking of multilayer coating films, which also suppresses stray lights and promises the uniform of the illuminance [15]. To reduce the stray light, Qiwei Wang et al. developed an in-coupling structure, which could effectively avoid two reflections on the entrance mirror [16]. Dewen Cheng et al. proposed a non-sequential ray tracing algorithm to examine the stray light of the planar waveguide and explored a global searching method to find an optimum design with the least amount of stray lights [17]. The method of beam displacing was developed by Luo Gu et al. to displace the stray light from both expanding directions outside the eye box, which reduced the percentage of the stray light within 0.1% [18]. Nevertheless, these techniques all need complex manufacturing process steps, which caused low yields and high costs.
The manufacturing process of PRMA waveguides generally proceeds as follows. Firstly, several parallel glass plates are cemented together through an anodic bonding process after coating. Secondly, the cemented plates are tilted at a certain angle for position cutting. Thirdly, the waveguide is rotated 90° for the lateral cutting. Finally, the waveguide is edge-polished to form a waveguide without inclined corners. The coating, cementing, and polishing processes all interfere with the angle accuracy of the PRMA waveguide [19]. The parallelism errors of the two substrate surfaces and the PRMA result in the formation of ghost images [see Fig. 1(c) and (d)]. According to the angular resolution of the human eye, the tolerance on the parallelism errors of the two substrate surfaces and the adjacent mirrors of the PRMA are only ±6$^{\prime\prime}$ and ±9$^{\prime\prime}$ to avoid the ghosting image [16]. Therefore, the extreme requirement of machining accuracy is one of the biggest bottlenecks of the PRMA waveguide. The resulting machining error is the leading cause of the stray light at present. High-precision measurement of the parallelism error helps to improve processing technology to meet machining accuracy requirements. Parallelism measurement can help verify which design and manufacturing process can guarantee the machining accuracy of PRMA waveguides, which is expected to contribute to mass production and low cost.
However, to our best knowledge, there are no related works on parallelism measurement for PRMA waveguides currently. The commonly used parallelism measuring methods with high precision mainly include the interference method and the autocollimator method [20]. The interference method mainly measures the parallelism error by analyzing the movement or number of the interference fringes, which are formed by the coherent light beams from two surfaces of the workpiece. The autocollimator method is that an autocollimator perpendicularly shoots two surfaces of the workpiece, and the ray will be back to the autocollimator. The parallelism of the workpiece can be calculated by the distance between the two images formed by the returned ray on the focal plane. However, they both cannot measure the parallelism errors of the PRMA precisely due to the refraction of the substrate surface.
In this paper, we concentrate our research on the parallelism measurement of the PRMA waveguide. The combination of the autocollimator and the testing telescope (CAT) method was proposed for the face parallelism measurement between mirrors of the PRMA on the basis of the method of placing a standard reflector behind (PSRB) [21] used for face parallelism measurement between the two substrate surfaces. This paper is organized as follows. Section 2 introduces the overall design of the parallelism measuring system. The optical modeling of the CAT method is presented in Section 3. Section 4 describes the experimental results of testing the PRMA waveguide. Section 5 concludes this paper.
2. Overall design of the parallelism measuring system
2.1 Configuration of the measuring system
The parallelism measuring system [see Fig. 2(a)] was placed on an optical platform, which was mainly composed of a photoelectric autocollimator, a testing telescope, a standard reflector, a rotary stage, two-dimensional (2-D) goniometer stages, etc. The autocollimator (focal length f = 500 mm) combines the function of a collimator and a testing telescope, which can project an image of a reticle into infinity and noncontact micro-angle measurement with high precision. The pixel size and the resolution of the camera in the autocollimator were 3.45 µm and 4096 × 3000, respectively. The waveguide (five mirrors in the PRMA) was fixed on the goniometer and the rotary stage. The distance between two adjacent mirrors in this PRMA waveguide along the substrate surface was about 3 mm. The substrate surface was adjusted to be perpendicular to the main optical axis (the z-axis) of the autocollimator by the adjustment of the yaw and pitch angles around the x- and y-axis. The focal length of the testing telescope was the same as that of the autocollimator. The telescope objective lens was aligned with the in-coupler surface of the waveguide. The parallel rays were imaged into the rear focal plane of the objective lens in the telescope, which was captured by the camera whose pixel size and resolution were 3.45 µm and 1440 × 1080, respectively. The telescope could measure the relative angles of different parallel beams. The standard reflector was placed behind the waveguide, which also could be adjusted posture. The function of the controller was to supply power, adjust the autocollimator’s brightness, and read the angle of the rotary stage.
Fig. 2. Configuration of the parallelism measuring system. (a) Schematic diagram of the system. The red or green dotted lines indicate the directions that the measured angle difference is positive. (b) Typical crosshair image captured by the camera in the autocollimator. Red Line: the subpixel centerline extraction of the crosshair based on the Steger algorithm. Goniometric principles of (c) the photoelectric autocollimator and (d) the testing telescope.
Without loss of generality, the surface flatness of the waveguide is assumed to be good enough to ignore its influence on the direction of out-coupling rays. Ideally, the upper surface and lower surface of the substrate are parallel to each other, and the mirrors of PRMA are also parallel to each other. Under this condition, each mirror of the out-coupler projects light rays in the same direction. The imaging quality of the waveguide is great without stray lights and ghost images. The out-coupling rays are perpendicular to the substrate surface under the condition that in-coupling rays are vertical to the in-coupler.
The precise parallelism measurement needs to fully consider the environmental factors. For example, to avoid the effect of impurity particles in the air, all measurements should be performed in the cleanroom environment. The other light in the space also influences the measurement accuracy. Due to the small measurement ranges of the autocollimator and the telescope, the other light received by them is so little that the light intensity of formed crosshair images is weak. They can be eliminated by image thresholding. Moreover, the surface quality of the waveguide elements (scratches, etc.) affects the accuracy of parallelism measurement. The waveguide to be measured should be tested before and proved that there are no scratches or other visible surface quality defects.
2.2 Micro-angle measurement
In the photoelectric autocollimator, as shown in Fig. 2(c), the green light source illuminates the reticle through the ground glass and the collecting lens, and a crosshair image is produced. Then the crosshair image is collimated by the objective lens. The outgoing parallel beam is reflected by the reflector and returned to the autocollimator through the lens. Finally, the light beam is refocused on the conjugate focal plane through the beam splitter (BS), where the camera is placed. When the reflector is tilted with a pitch angle α around the x-axis, the reflected beam is deflected through an angle 2α. The image is displaced laterally from O’ in the CCD. The displacement can be expressed as
Generally, the angle α is small enough that Eq. (1) can be approximately written as
Hence, the angle measurement is converted into the displacement measurement according to Eq. (2) by the autocollimation principle [22]. The deflection angle 2α can be measured by d/f. Similarly, we can acquire the angle measuring principle of the testing telescope [see Fig. 2(d)]. The two parallel beams at different angles are collected by the telescope, and the crosshair images captured by the camera are at different positions. The distance of the center of the crosshair images is D. The relative angle β between them can be expressed as Eq. (3):
In the autocollimator and the telescope [see Fig. 2(a)], the measured angle difference is positive when the collected beam rotates around the x-axis or the y-axis in the directions indicated by the red or green dotted lines, respectively.
2.3 Crosshair image processing
To improve the precision of the autocollimator and the telescope, it is necessary to position the center of the crosshair with sub-pixel precision. Centerline extraction of the crosshair was adopted to locate the center point, which made full use of the geometric characteristics of the crosshair [see Fig. 2(b)]. Centerline extraction was achieved based on the Steger algorithm [23]. The algorithm solved the Hessian matrix of the image, whose eigenvector corresponding to the maximum absolute value gave the normal direction of each point. The second-order Taylor expansion of the gray distribution function of each pixel along this normal direction was carried out. The zeros of the first derivative of the polynomial obtained by Taylor expansion were calculated to get the centerline point coordinates of the crosshair. The Steger algorithm has the advantages of high accuracy and robustness to stray lights.
In the crosshair image processing, the preprocessing was firstly performed including median filtering to denoise and image enhancement to enhance the image contrast. Secondly, Otsu method [24] for image thresholding was used to eliminate the effects of stray lights because the gray value of the image formed by stray lights was generally low. Thirdly, the crosshair centerline point coordinates were extracted based on the Steger algorithm. Fourthly, the line analytical expressions of the horizontal and vertical centerlines were obtained by the least-squares fitting of the centerline point coordinates. Finally, the center of the crosshair with sub-pixel precision could be calculated by the two expressions. The micro-angle measurement with high precision can be accomplished by measuring the distance between two crosshair centers.
3. Modeling of parallelism measurement
3.1 Parallelism measurement between the two substrate surfaces based on the PSRB method
The standard reflector was adjusted to be directly aligned with the objective lens of the autocollimator. The crosshair image formed by the reflected parallel beam was captured by the autocollimator. Then the waveguide (refractive index is n) was fixed on the goniometer between the autocollimator and the reflector [see Fig. 3(a)]. The waveguide needed to be adjusted so that the vertical of the substrate surface was approximately parallel to the main optical axis of the autocollimator. When the crosshair image of the substrate surface was formed in the camera, they were approximately parallel because the measuring range of the autocollimator was small. The parallelism error around the x-axis of the substrate surfaces is φx which is set to be positive as shown in Fig. 3(c).
Fig. 3. (a) Schematic diagram of the parallelism measurement between the two substrate surfaces. The ray paths before (b) and after (c) placing the waveguide based on the PSRB method.
It should be noted that the reflected beam must all pass through the waveguide, or the beam not passing will form a ghost image of the crosshair. The crosshair would change the position since the face parallelism error between the two substrate surfaces of the waveguide [see Fig. 3(b) and (c)]. This angle represented by the position change of the crosshair is directly connected with the parallelism error based on the Snell’s law, which can be expressed as [21]:
Hence, the parallelism error φx can be expressed as Eq. (6).
It is explicit that the reflected light beam is all from the standard reflector, which avoids the problems caused by the poor reflectance of the waveguide. The traditional method to measure parallelism is that the reflected beams from two surfaces are refocused on the image plane simultaneously [20]. Compared to that, this method overcomes the difficulty that the overlap of the two crosshairs makes it impossible to locate the center points due to the tiny parallelism error. Moreover, the measurement efficiency is improved.
Another thing to note is that the face parallelism is a space angle. Hence, the measured parallelism errors of the substrate surfaces around the x-axis and y-axis are based on the Cartesian coordinate system, where the z-axis is the main optical axis of the autocollimator. As a result, the errors obtained by the autocollimator vary with the relative posture of the autocollimator and the waveguide, but the resultant space angle is constant.
3.2 Parallelism measurement between mirrors of the PRMA based on the CAT method
According to the above analyses, the parallelism errors of the substrate surfaces and the mirrors of the PRMA result in the ghost image, that is, the out-coupling rays from the different mirrors are in different directions. As shown in Fig. 4(a), the parallelism error around the x-axis between the two substrate surfaces is φx, and the mirrors of PRMA are parallel to each other. The η represents the angle between the out-coupling ray and the vertical of the S2. The angle η1 can be written by Eq. (7) under the condition that the angle between the out-coupling rays and the vertical of the substrate surface is less than 5°.
Fig. 4. The ray paths of the in-coupling parallel rays and the angles between the out-coupling rays and the vertical direction of the waveguide substrate due to (a) the parallelism error between the two substrate surfaces as well as (b) the coupling effect of the parallelism error of the two substrate surfaces and mirrors of the PRMA. The parallelism error θ21x between the M2 and the M1 is set to be positive, then that θ31x between the M3 and the M1 is negative. (c) The ray paths of parallel rays through the waveguide from the autocollimator to the telescope.
Accordingly, the angle difference of out-coupling rays from the adjacent mirrors after one TIR is 2nφx. The ray path is shown in Fig. 4(b) when there are both the parallelism errors of the substrate surfaces and the mirrors. It should be noted that the parallelism errors of the PRMA are all based on the mirror M1. θ21x and θ31x are the parallelism errors around the x-axis between M1 and M2, M3, respectively. Let θ21x be positive, then θ31x is negative. The angles η4 and η5 can be expressed as Eq. (9) and Eq. (10):
Therefore, it is indispensable for the parallelism measurement of mirrors to decouple the two kinds of parallelism errors to the contribution of the angles of the out-coupling rays.
Supposing that there is a collimator with a reticle projecting the parallel rays vertical to the in-coupler, the autocollimator collects the out-coupling parallel rays from the waveguide, which is shown in Fig. 5(a). The parallel rays from each mirror can be individually received in turn by the blocking of a rectangular aperture. In the case of known parallelism error φ, the parallelism errors of the PRMA can be obtained by measuring the angle difference Δηi1. However, the parallelism error φ is a spatial angle, that is, the errors around the x- and y-axis are not available based on the Cartesian coordinate system where the z-axis is the main optical axis of the collimator. Hence, the method cannot eliminate the effect of the parallelism error φ on measuring parallelism errors of PRMA. What’s more, it is obvious that the incident rays on the same mirror may be in different directions, such as the rays on the M4 or the M5 in Fig. 5(a). Consequently, this method is challenging to implement due to these constraints.
Fig. 5. (a) The principles of parallelism measurement between mirrors of the PRMA based on the working principle of the waveguide and (b-f) the CAT method. The rays from the autocollimator illuminate the out-coupler of the waveguide through the rectangular aperture and emerge from the in-coupler base on the principle of reversibility of light. The number differences of the TIR between the M2 to the M5 and the M1 are 1, 2, 2, and 3, respectively.
Based on the light propagation in the PRMA waveguide and the principle of reversibility of light, the CAT method was proposed for the face parallelism measurement between mirrors of the PRMA, which is illustrated in Fig. 5(b)-(f). When the parallel rays from the autocollimator illuminate each mirror of the PRMA individually, the emergent rays from the in-coupler surface are still parallel. Under this condition, the original out-coupler is now the in-coupler. The testing telescope receives the parallel rays from the original in-coupler of the waveguide. The angle difference between the parallel rays from any two mirrors can be obtained by the processing of crosshair images. The angle difference 2φx of light rays after one TIR can be obtained by the PSRB method.
Furthermore, the position of the rectangular aperture can be adjusted to make the emergent rays undergo the same number of TIRs. In this way, the two kinds of parallelism errors to the contribution of the angles of the emergent rays can be decoupled. As shown in Fig. 4(c), the relationship between the parallelism errors of the mirrors and the angle difference measured by the telescope can be expressed as Eq. (11).
4. Results and discussion
4.1 Angle calibrations of the autocollimator and the telescope
As shown in Fig. 6(a), the ELCOMAT3000 (±0.25$^{\prime\prime}$ measuring uncertainty in the range of 2000$^{\prime\prime}$ × 2000$^{\prime\prime}$ at 2.5 m) served as the angle reference to calibrate the autocollimator and the telescope [25]. The double-sided mirror fixed on the 2-D goniometer stage was placed in the middle of the ELCOMAT3000 and the autocollimator. Firstly, adjust the double-sided mirror to make the crosshair image at the center of the image plane. Secondly, adjust the ELCOMAT3000 to align with the mirror to prepare to measure the angle of the mirror. Thirdly, rotate the mirror around the x-axis at the step of about 200$^{\prime\prime}$ from -800$^{\prime\prime}$ to 800$^{\prime\prime}$ and capture the crosshair images. Finally, do the same around the y-axis. The sensitivities S of the autocollimator or the telescope around the x- and y-axis can be expressed as Eq. (13).
where E and L are the angles of the mirror measured by the ELCOMAT3000 and the displacement of the crosshair image center, respectively. The angles of the mirror around the x- and y-axis corresponded to the displacements of the X- and Y-axis of the crosshair image, respectively. As shown in Fig. 6(b), the sensitivities of the autocollimator around the x- and y-axis were 0.71$^{\prime\prime}$/pixel and 0.71$^{\prime\prime}$/pixel, respectively. In the range of ±200$^{\prime\prime}$, the maximum non-linear angle errors of the autocollimator around the x- and y-axis were 0.16$^{\prime\prime}$ and -0.39$^{\prime\prime}$. The objective lenses and the camera pixel sizes in the autocollimator and the telescope are the same. Hence, the sensitivities of the autocollimator and the telescope for the angle difference of collected parallel beams were 1.42$^{\prime\prime}$/pixel around the x- and y-axis. The calibration results indicated that the autocollimator and the telescope could meet the measurement accuracy requirements of the parallelism errors.Fig. 6. The angle calibration of the autocollimator by ELCOMAT 3000. (a) Schematic diagram of the calibration. (b) The calibration results of the autocollimator show that the angle sensitivities around the x- and y-axis are both 0.71$^{\prime\prime}$/pixel.
4.2 Parallelism error between the two substrate surfaces
To promise the imaging quality of the PRMA waveguide and measure the parallelism errors of the mirrors of the PRMA, the parallelism of the two substrate surfaces should be measured with high precision firstly. The parallelism measuring system is shown in Fig. 7(a). The photoelectric autocollimator projected the parallel beam to the standard reflector that should be adjusted to align with the autocollimator and reflect the beam to the autocollimator. The crosshair image formed by the reflected beam was captured by the camera in the autocollimator and processed to locate the center coordinate of the crosshair, which served as the reference. The waveguide [see Fig. 7(b)] to be measured was fixed on the goniometer in the middle of the autocollimator and the reflector. Its posture was controlled to make the parallel beam projected by the autocollimator approximately vertical to its substrate surfaces. Due to the parallelism error between the two surfaces, the direction of the reflected beam was changed, i.e., the crosshair image was moved.
The crosshair images before and after placing the waveguide are shown in Fig. 8(b) and (c). It is known that the refractive index of the waveguide is 1.5163. The parallelism error ${\bar{\varphi }_s}$ of the waveguide was 4.55$^{\prime\prime}$ with a repeatability error of 0.25$^{\prime\prime}$, which was measured ten times repeatedly [see Fig. 8(a)]. The waveguide was re-fixed for each measurement.
Fig. 8. (a) The parallelism errors of the substrate surfaces. The crosshair images before (b) and after (c) placing the waveguide.
4.3 Parallelism errors between mirrors of the PRMA
After measuring the parallelism error between the two substrate surfaces, the system should remain constant. The φx and φy were -4.26 and -1.02, respectively. The standard reflector should be closed to avoid the measurement. The testing telescope was firstly adjusted to receive the parallel rays from the original in-coupler of the waveguide. Its main optical axis should be approximately vertical to the in-coupler. The rectangular aperture of 1 mm parallel and close to the waveguide could be moved slightly along the y-axis. Knowing the geometry of the waveguide and the light propagation path, the position of the aperture could be precisely controlled to make each mirror of the PRMA illuminate individually. In this way, the parallel rays from every mirror could be imaged in the telescope respectively. The exposure time was set to 0.8s because of low brightness due to occlusion by the aperture. The crosshair images formed by every mirror are shown in Fig. 9(a)-(e). The stray light in images may be caused by coating films of the PRMA. The parallelism errors of the PRMA based on the mirror M1 were acquired by the location of the center points according to Eq. (12). The parallelism errors from the M2 to the M5 around the x-axis were 1.36$^{\prime\prime}$, -0.41$^{\prime\prime}$, 5.03$^{\prime\prime}$, -11.41$^{\prime\prime}$, respectively. Those around the y-axis were 5.68$^{\prime\prime}$, 5.92$^{\prime\prime}$, 6.65$^{\prime\prime}$, -2.37$^{\prime\prime}$, respectively. The results of ten repeated experiments indicated that the CAT method had good repeatability with the maximum standard deviation of 0.63$^{\prime\prime}$ [see Fig. 10].
Fig. 9. The typical crosshair images formed by every mirror, and the center point coordinates of each crosshair.
Fig. 10. The parallelism errors of the PRMA between the mirror M2 to M5 and the mirror M1. The maximum standard deviation of ten repeated experiments was 0.63$^{\prime\prime}$.
However, this method is closely related to the imaging quality of each mirror. The defects of the coating films may result in ghost images that adversely affect the positioning accuracy of the center point. The parallelism error between the two substrate surfaces will accumulate as the number of TIR increases, which also has a bad effect on the parallelism measurement between mirrors of the PRMA. Moreover, there are no methods of measuring the PRMA parallelism currently to clarify the limitations of this study in detail. Fortunately, the accumulating error due to the increasing number of TIR may be reduced by the precision improvement of the autocollimator.
For precise parallelism measurement of the PRMA waveguide, the recommended procedure is first to measure the parallelism error of the two substrate surfaces. If this error is less than 6$^{\prime\prime}$, the imaging quality of each mirror is observed. If it is good, continue to measure the parallelism error between each mirror of the PRMA. In this way, the quality of the waveguide can be accurately and efficiently distinguished. Through the angle difference of the parallel beams from each mirror, the design and fabrication of the waveguide can be validated and optimized accurately and efficiently.
The overlapping crosshairs in the image formed by all mirrors of PRMA indicated that the directions of the parallel beams emitted from each mirror are inconsistent, that is, there are parallelism errors between any two mirrors. Therefore, the parallelism and the brightness uniformity could be seen intuitively according to the crosshair images owing to the telescope’s high resolution. Furthermore, through the combination of the autocollimator and the telescope instead of direct observation by the human eye, the imaging quality (e.g., brightness uniformity, ghost image) of different types of waveguides under different perspectives can be evaluated efficiently.
5. Conclusion
In this paper, the CAT method and the measuring system were presented for the parallelism measurement of the PRMA waveguide based on the light propagation in the waveguide. The high sensitivities of the autocollimator and the telescope guaranteed the precision requirements of the parallelism measurement. The experimental results showed that the CAT method was able to accurately measure the parallelism errors of the PRMA with the maximum repeatability of 0.63$^{\prime\prime}$, and effectively decouple the coupling of the two kinds of parallelism errors to imaging quality. The precise parallelism measurement helps improve and develop the waveguide design and fabrication, which is expected for promoting mass production and low cost.
The potential application of the system is to measure the verticality of two-dimensional PRMA waveguides by the combination of the autocollimator and the rotary stage. Meanwhile, it also has broad application prospects in the imaging quality test of the optical waveguide through the calibrations of the colorimeter and the illuminometer. In the future, we will develop a machining quality measurement system for all geometrical waveguides to promote mass production.
Funding
National Key Research and Development Program of China (2021YFC2600503).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. C. Flavián, S. Ibáñez-Sánchez, and C. Orús, “The impact of virtual, augmented and mixed reality technologies on the customer experience,” J. Bus. Res. 100, 547–560 (2019). [CrossRef]
2. T. Zhan, K. Yin, J. Xiong, Z. He, and S. T. Wu, “Augmented Reality and Virtual Reality Displays: Perspectives and Challenges,” iScience 23(8), 101397 (2020). [CrossRef]
3. J. Xiong, E. L. Hsiang, Z. He, T. Zhan, and S. T. Wu, “Augmented reality and virtual reality displays: emerging technologies and future perspectives,” Light: Sci. Appl. 10(1), 216 (2021). [CrossRef]
4. C. T. Draper and P. A. Blanche, “Holographic curved waveguide combiner for HUD/AR with 1-D pupil expansion,” Opt. Express 30(2), 2503–2516 (2022). [CrossRef]
5. X. Shi, Z. Xue, S. Ma, B. Wang, Y. Liu, Y. Wang, and W. Song, “Design of a dual focal-plane near-eye display using diffractive waveguides and multiple lenses,” Appl. Opt. 61(20), 5844 (2022). [CrossRef]
6. Y. Shin, Y. Jiang, Q. Wang, Z. Zhou, G. Qin, and D.-K. Yang, “Flexoelectric-effect-based light waveguide liquid crystal display for transparent display,” Photonics Res. 10(2), 407 (2022). [CrossRef]
7. K. Yin, Z. He, J. Xiong, J. Zou, K. Li, and S.-T. Wu, “Virtual reality and augmented reality displays: advances and future perspectives,” J. Phys. Photonics 3, 022010 (2021). [CrossRef]
8. Y. Zhang and F. Fang, “Development of planar diffractive waveguides in optical see-through head-mounted displays,” Precis. Eng. 60, 482–496 (2019). [CrossRef]
9. D. Cheng, Q. Wang, L. Wei, X. Wang, L. Zhou, Q. Hou, J. Duan, T. Yang, and Y. Wang, “Design method of a wide-angle AR display with a single-layer two-dimensional pupil expansion geometrical waveguide,” Appl. Opt. 61(19), 5813 (2022). [CrossRef]
10. M. Xu and H. Hua, “Geometrical-lightguide-based head-mounted lightfield displays using polymer-dispersed liquid-crystal films,” Opt. Express 28(14), 21165–21181 (2020). [CrossRef]
11. B. C. Kress and I. Chatterjee, “Waveguide combiners for mixed reality headsets: a nanophotonics design perspective,” Nanophotonics 10(1), 41–74 (2020). [CrossRef]
12. M. Xu and H. Hua, “Finite-depth and vari-focal head-mounted displays based on geometrical lightguides,” Opt. Express 28(8), 12121–12137 (2020). [CrossRef]
13. L. Gu, D. Cheng, Q. Wang, Q. Hou, S. Wang, T. Yang, and Y. Wang, “Design of a uniform-illumination two-dimensional waveguide head-up display with thin plate compensator,” Opt. Express 27(9), 12692–12709 (2019). [CrossRef]
14. Q. Wang, D. Cheng, Q. Hou, L. Gu, and Y. Wang, “Design of an ultra-thin, wide-angle, stray-light-free near-eye display with a dual-layer geometrical waveguide,” Opt. Express 28(23), 35376–35394 (2020). [CrossRef]
15. M. Xu and H. Hua, “Methods of optimizing and evaluating geometrical lightguides with microstructure mirrors for augmented reality displays,” Opt. Express 27(4), 5523–5543 (2019). [CrossRef]
16. Q. Wang, D. Cheng, Q. Hou, Y. Hu, and Y. Wang, “Stray light and tolerance analysis of an ultrathin waveguide display,” Appl. Opt. 54(28), 8354–8362 (2015). [CrossRef]
17. D. Cheng, Y. Wang, C. Xu, W. Song, and G. Jin, “Design of an ultra-thin near-eye display with geometrical waveguide and freeform optics,” Opt. Express 22(17), 20705–20719 (2014). [CrossRef]
18. L. Gu, D. Cheng, Q. Wang, Q. Hou, and Y. Wang, “Design of a two-dimensional stray-light-free geometrical waveguide head-up display,” Appl. Opt. 57(31), 9246–9256 (2018). [CrossRef]
19. D. Cheng, Q. Wang, Y. Liu, H. Chen, D. Ni, X. Wang, C. Yao, Q. Hou, W. Hou, G. Luo, and Y. Wang, “Design and manufacture AR head-mounted displays: A review and outlook,” Light: Advanced Manufacturing 2(3), 336 (2021). [CrossRef]
20. J. Zhang, B. Pan, H. Liu, X. Zhu, R. Kang, D. Du, and J. Guo, “Parallelism measurement method for nontransparent flat parts,” Appl. Opt. 61(1), 1 (2022). [CrossRef]
21. Y. Huang, Y. Yang, J. Liang, Z. Miao, M. Zhao, and Y. Zheng, “An optical glass plane angle measuring system with photoelectric autocollimator,” Nanotechnol. Precis. Eng. 2(2), 71–76 (2019). [CrossRef]
22. M. Astrua and M. Pisani, “Improved performance of a refurbished photoelectric autocollimator,” Meas. Sci. Technol. 32(1), 015010 (2021). [CrossRef]
23. C. Steger, “An unbiased detector of curvilinear structures,” IEEE Trans. Pattern Anal. Machine Intell. 20(2), 113–125 (1998). [CrossRef]
24. T. Y. Goh, S. N. Basah, H. Yazid, M. J. Aziz Safar, and F. S. Ahmad Saad, “Performance analysis of image thresholding: Otsu technique,” Measurement 114, 298–307 (2018). [CrossRef]
25. R. Li, M. Zhou, I. Konyakhin, K. Di, Y. Lu, J. Guo, and Y. Liu, “Cube-corner autocollimator with expanded measurement range,” Opt. Express 27(5), 6389–6403 (2019). [CrossRef]
