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Abstract
Pancake virtual reality head-mounted displays (VR-HMDs) have attracted the attention of researchers in both academia and industry because of the compact size and light weight. However, owing to the use of optical path folding, there exist various stray lights in the optical system, which seriously degrades user experience. In this study, we analyze the causes and effects of multiple types of stray light systematically and design a VR-HMD with low stray light, large exit pupil diameter (EPD), compact form and light weight. Subsequently, several effective stray light suppression solutions are proposed and implemented. Finally, a prototype of a compact pancake VR-HMD system is successfully demonstrated. The prototype has stray light of less than 2.3%, a diagonal field of view (FOV) of 96° and an EPD of 10 mm at an 11 mm eye relief (ERF).
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Head-mounted displays (HMDs) can be divided into virtual reality (VR) HMDs and augmented reality (AR) HMDs according to whether the user can see the real world [1–3]. Features like a wide field of view (FOV), a large pupil size and a compact form factor are common pursuits for AR-HMDs and VR-HMDs, but it is usually challenging to achieve these properties simultaneously [4–6]. VR-HMDs provides an isolation from external environment and a deep sense of immersion to the user. Therefore, they have been widely used in entertainment [7,8], education [9,10], training, and other fields [11,12].
However, traditional VR-HMDs adopting smooth aspherical optics [13,14] and Fresnel optics [15,16] are bulky, with a small exit pupil diameter (EPD) and low imaging performance. As the demand of users for higher product experience increases, the abovementioned traditional VR-HMDs can no longer meet the requirements. Pancake optics [17,18] is an emerging VR optical architecture adopting optical path folding to multiplex optical surfaces, which can not only reduce the overall length (OAL) of the system, but also reduce the pressure of optical power on each surface and thus improve the system imaging quality.
The pancake optical system was first proposed by LaRussa for immersive flight simulators [19]. Later in paper published in 1978, LaRussa proposed a holographic pancake system composed of a planar beam splitter, two polarizers, quarter-wave plate (QWP), and a holographic mirror, achieving a FOV of 84° [20]. In subsequent studies, Lacroix changed the planar beam splitter in the initial design to a 3 M reflective polarizer to further suppress the straight-through of stray light and improve the contrast of the virtual image [21].
Wong et al. discussed multiple configurations of pancake systems and polarization control with birefringent reflective polarizers, and then they explored additional benefits of using pancake optics for virtual reality systems [22]. Geng et al. analyzed smooth refractive optics, Fresnel lenses, and pancake lenses, compared their indicators such as pupil swim, size, weight and stray light, and pointed out that the pancake system had a lot of potential if the contrast/stray light problems can be solved [23]. Cholesteric liquid crystal (CLC) polarization optics can be used in thin pancake system with a broadband circular polarizer placed behind the CLC lens to absorb stray light [17].
There are at least two beam-splitting surfaces in the pancake optical system to achieve optical path folding. Various pancake forms have been proposed and compared in our previous study. A preferred schematic diagram of a pancake system with three lenses is shown in Fig. 1. The light emitted from the display is refracted on surface S6 and enters the optical system. After passing through Lens 2, it reaches the second surface S2 of Lens 1, and then gets reflected by the beam splitter 1. After passing through Lens 2 again, it reaches S6 of Lens 3, and gets reflected by the beam splitter 2. Subsequently, the light passes through Lens 2 for the third time, reaches S2 of Lens 1, and passes through this time. Finally, the light passing through the first surface S1 enters human eyes. The light is transmitted thrice between two beam-splitting surfaces S2, S6, which greatly shortens the overall length of optical system. However, if both beam-splitting surfaces use a traditional half mirror, there will be a strong stray light that passes through the two beam-splitting surfaces directly and reaches the human eye.
Assuming that both the beam-splitting surfaces are half mirrors and there is no energy loss in all lenses, the optical efficiencies of normally magnified virtual image and stray lights and their contrast ratios are calculated as follows:
When S2 and S6 are half mirrors, T2 = R2 = T6 = R6 = 50%, then the stray light ratio can be calculated as
If both the beam-splitting surfaces are half mirrors, the brightness of straight-through stray light is four times that of the normal virtual image, and the position of the stray light is close to the normal virtual image, which seriously affects the user experience and makes the optical system unusable.It is therefore necessary to introduce polarizing optics to prevent stray light from entering the user’s eye. However, due to the imperfect performance of polarizing optical elements and the residual surface reflections on lens surfaces, there will still be various types of stray lights. In the following sections, we will firstly introduce the general working principle of polarizing optics in the pancake system. Then we will systematically analyze the paths of stray light in pancake system and provide a series of stray light suppression methods.
2. Pancake optical principle
As mentioned above, the introduction of polarizing optics into the optical system can theoretically eliminate straight-through stray light. As plotted in Fig. 2, on surface S2 of Lens 1, a polarization beam splitter (PBS, also called reflective polarizer) is adopted to replace the general beam splitter, which reflects s-polarized light and transmits p-polarized light. Therefore, the light is fully reflected when it reaches the S2 surface for the first time and is fully transmitted for the second time.
As shown in Fig. 2, the circularly polarized light emitted from display (assuming left circularly polarized (LCP) display) passes through a half mirror and enters the optical system. When passing through Lens 2 and Lens 3, it remains left circularly polarized (LCP). Then, it is converted to s-polarized light by the quarter wave plate (QWP). The PBS reflects the s-polarized light at S2 and preserves the polarization state. After passing through the QWP again, the light becomes LCP and is reflected by the half mirror when it reaches S6. The light now becomes right circularly polarized (RCP). The RCP light passes through the QWP and becomes p-polarized light. It passes though the PBS and eventually reaches the exit pupil. Ideally, the efficiency of this polarized pancake system is 25%, which is, however, hard to reach due to the imperfection in light polarization and polarizing optics. As a result, a small portion of directly transmitted stray light still exists.
The transmittance and reflectance of polarized light on PBS vary with the change of incident angle and wavelength. In order to calculate the portion of stray light, we take the average value of the transmittance and reflectance of on-axis light over spectrum as an approximation. According to the data of PBS in Ref. [24], the average reflectance of s-polarized light Rs is 98.3% and the average transmittance Ts is 0.0085% in the spectral range of 450-650 nm. The average transmittance of p-polarized light Tp is 96.2% and the average reflectance Rp is 0.11%. According to Eq. (1), the ratio of stray light to normal image can be calculated as:
In this study, we adopt the design from a previous study [18], which used a 2.1-inch display with a resolution of 1600 × 1600 and a pixel size of 24 µm for a design with an EPD of 10 mm. Additionally, the design can achieve a -1∼-7D diopter adjustment, with -1D corresponding to virtual image distance (VID) of 1 m as the main diopter. In the optical system, Lens 1 and Lens 2 are plastic lenses and Lens 3 is a glass lens to reach a good balance between lightness and optical performance. The total length of the system is less than 20 mm, with an FOV of 96°, an effective focal length (EFL) of 22.9 mm, an ERF of 11 mm and a weight of less than 20 g. The system specifications are shown in Table 1.
Table 1. Specifications of the pancake optical system
3. Pancake stray light path analysis and calculation
Besides the straight-through stray light shown in Fig. 3(a), there are also other possible paths of stray light in the optical system, as shown in Fig. 3. There exist various residual reflections on lens surfaces due to the limitation of the coating process, which does not affect the imaging quality much in general optical systems. However, owing to the relatively low optical efficiency of the pancake VR-HMDs, the residual reflections on these surfaces cause nonnegligible stray lights. The ratios of various stray lights are shown in Table 2. For convenience, we will thereafter directly use the letter in parentheses to represent the corresponding stray light plotted in Fig. 3.
Fig. 3. Optical paths of stray light in the pancake optical system: (a) straight-through stray light; (b) stray light caused by the cover glass of the display; (c) reflection between the half mirror S6 and the cover glass of the display; (d) residual reflection on S5 of Lens 2; (e) residual reflection on S4 of Lens 2; (f) residual reflection on S3 of Lens 2; (g) residual reflection on the surface of the QWP, which is attached to S2 of Lens 1, (h) residual reflection on the front surface of the QWP and one more reflection on S6, (i) secondary reflection between the PBS and half mirror, (j) stray light due to light reflection by the display surface and directly passing through the module.
Table 2. Calculation of the portion of stray lights
There is approximately 2% residual reflection on the front surface of the display, which leads to two types of observable stray light. Stray lights in Fig. 3(b) and (c) are both caused by the reflections of display. For stray light (b), when the light passes through the half mirror S6 for the second time, it is reflected on the front surface of display and then passes through the half mirror again. The portion of this type of stray light is approximately 1.04%. For stray light (c), the light from the display reaches the half mirror. Half of the light is reflected back to the display, and then reflected on the front surface of display again. The portion of stray light (c) is also about 1.04%.
Stray light in Fig. 3(d) is caused by light reflected on S5 before it reaches the half mirror for the second time. Lens 3 is made of glass. The residual reflection on S5 (approximately 0.3%) is lower than that on the plastic lens surface. This type of stray light will form a ghost image with nearly the same size as the normal image because Lens 3 is almost a meniscus lens of equal thickness. The portion of this type of stray light is approximately 0.63%.
The residual reflection of anti-reflection coated plastic lens surface is approximately 0.7%, which is higher than that of the glass lens. Light reflections on the front and rear surfaces of Lens 2 lead to 1.49% of stray light of Fig. 3(e) and 1.51% of stray light in Fig. 3(f).
Stray light in Fig. 3(g) and (h) are caused by the residual surface reflection of QWP attached on Lens 1. The residual reflection of QWP is approximately 0.7% (approximately 2% residual reflection before anti-reflection coating).
For stray light in Fig. 3(g), the light after reflected on the PBS is reflected on the inner surface of QWP (assuming the inner surface reflection is still 0.7%), and then passes through the PBS. The thickness of QWP is so thin that it is negligible. Therefore, the light paths of stray light (a) and (g) are almost coincident and their ghost image performance including magnification and position is same. The portion of this type of stray light is approximately 1.53%, which is the most serious stray light.
The LCP light emitted from display becomes RCP light after reflection on the QWP, then it is reflected at S6 and becomes LCP light again. Another round of reflection between the PBS and the half mirror S6 is necessary for the exit of light because LCP light cannot pass through S2. The portion of stray light in Fig. 3(h) is 0.35%. Owing to one more reflection than the normal optical path, the stray light forms a shorter EFL and its image is larger than the normal image.
Stray lights in Fig. 3 (i) and (j) are also due to reflection on the QWP or display surfaces. The root cause of these stray lights is consistent with (a), which is the undesirable polarization state of the light. Other types of stray lights may also be generated by reflecting on other surfaces including structure sidewalls; however, they are not included in Fig. 3 because the effects of these stray lights can be negligible. The portions of stray light in Fig. 3(a), (i), and (j), as shown in Table 2, are relatively small because the calculations assume that the light polarization state is ideal, and only the leakage of S-polarized light on the PBS is considered. In reality, the portions of such stray lights are much higher than the theoretically calculated value in Table 2. There are multiple reasons for the undesirable polarization state, such as low degree of polarization of light exiting from the display, imperfect performance of polarizing optical elements, QWP phase delay error, residual stress in lenses, etc. All of these lead to changes in the polarization state and therefore stray lights. Such stray lights are difficult to analyze quantitatively owing to the large number of uncertainties.
4. Stray light simulation and suppression
4.1 Stray light path analysis
In this study, LightTools [25] software was used to simulate the system. We imported the optical system structure file into LightTools and set the wavelength, material, optical properties of each surface to simulate the optical path of the real system. An ideal lens at the location of the pupil was placed to simulate the human eye. The receiver at the focal plane of the ideal lens was added to observe the system imaging performance.
Among the stray lights mentioned above, the ghost images of stray lights in Fig. 3(b), (c) and (d), almost overlap with the original image and are hard to distinguish. Therefore, we purposefully introduced decenter and tilt errors, which do exist in actual fabrication process. We also adjusted the position of the perfect lens in the eyebox to simulate the human eye at different observation positions. We finally obtained seven kinds of stray light path simulations to demonstrate the relationship between stray light and normal image, as shown in Fig. 4.
It should be noted that the results in Fig. 4 mainly serve to illustrate the shape and position of stray light images. The brightness of image may not be precise because we need to adjust certain parameters in the non-sequential ray tracing to obtain an acceptable image. For more accurate stray-light intensity values, one should refer to Table 2.
The light paths of stray light in Fig. 3(a) and (g) are almost coincident, we combine these two type of stray lights together during the simulation process and the stray light intensity is the sum of the two, which will theoretically reach 1.55%. The stray light superimposed by stray light (a) and (g) is the most serious of all the above.
The top three stray lights in Fig. 3(e), (f) and (g) can be further suppressed by improving the residual reflection of QWP and Lens 2. In addition, if the QWP is attached to the Lens 2 or Lens 3, the stray light (g) can be completely eliminated.
The actual portion of the stray light in Fig. 3(a), (i) and (j) caused by a nonideal polarization state is relatively high. We considered the following aspects to reduce the ratio of such types of stray light: (1) introducing a set of polarizing optical elements to improve the polarization of the light emitted from the display; (2) improving the telecentricity in the image space during design, and using a display with a smaller divergence angle to minimize the incident angle of light on the PBS; (3) improving the quality of QWP and polarizer; (4) optimizing the injection molding process to reduce the birefringence of the resin lens; (5) attentively controlling the relative angle of the polarizing optical element and QWP during film lamination and assembling.
Stray lights in Fig. 3(b) and (c) are generated by the surface reflection of display. Therefore, reducing the display surface reflection can suppress these types of stray light. Additionally, the introduction of another set of polarizing optical elements can eliminate such stray light while increasing the polarization of the light from the display, resulting in a higher contrast of the overall optical system, as described in Section 4.2.
Stray lights in Fig. 3(d), (e), (f) and (g) need to be optimized using a better anti-reflection coating technology to reduce the residual reflections on optical surfaces. For stray light (g), because the QWP is a flat film, a high-quality anti-reflection film can also be laminated on it to reduce the residual reflection on its surface.
4.2 Straight-through stray light suppression method during design
To explore and eliminate the straight-through stray light as shown in Fig. 5 with maximum brightness in the optical path, we explored the relationship between the optical power and the VID of the optical system that propagates the straight-through stray light in Fig. 5 and proposed a method to suppress it in the optical design stage. We assume that all lenses in the system are thin lenses, so the total optical power of the system is
A stray light suppression film (SLSF) can be placed between Lens 3 and the display to suppress stray lights. The SLSF consists of two layers of the anti-reflection film, two layers of the QWP and a polarizer, whose structure is shown in Fig. 6. The anti-reflection films are used to reduce the reflection of the QWP surface without changing the light polarization state.
The working principle of SLSF is shown in Fig. 7. Ray 1 of the LCP light from the display passes through the anti-reflection film and QWP and is turned to s-polarized light, which can be transmitted through the polarizer. Then ray 1 passes through the QWP and Anti-reflection film for the second time and is converted to RCP light by the reflection on the half mirror. Afterwards, the RCP light ray 1 propagates through the anti-reflection film and QWP once again, and then it is converted to p-polarized light and absorbed by the polarizer. Apart from improving the polarization state of display light, other non-polarized lights in the system can also be suppressed. For example, a non-polarized light ray 2 in Fig. 7 is turned into s-polarized light after passing the polarizer. After passing the QWP, the s-polarized light is turned into LCP light. It is then reflected by the front surface of display and becomes RCP light. Afterwards, the RCP light propagates through the anti-reflection film and QWP again and becomes p-polarized light, which is absorbed by the polarizer.
In this study, we adopt a glass-plastic hybrid form pancake design. If the PBS is located on the surface S1, then the birefringence of all three lenses needs to be very small. The material choice will be more restricted in the design process. Additionally, the PBS film will be more easily damaged by frequent wiping during use. Therefore, we place the PBS on S2 of the first lens. Because the light does not pass Lens 1 in the optical path folding, except for the final exiting after S2, the birefringence of Lens 1 does not have an impact on the stray light and needs not to be controlled, which is advantageous in the design and fabrication process. Lens 3 is made of glass material. Its birefringence can be eliminated through high-temperature annealing. However, the plastic Lens 2 will produce more obvious birefringence during the injection molding process, and the elimination of birefringence has higher requirements.
The birefringence of plastic lens is related to material selection, lens shape, mold design, lens injection molding process, and annealing process. The birefringence leads to changes in the polarization state of light, resulting in serious stray light problems in pancake system. Here, we use phase retardation (PR) to quantize the birefringence.
4.3 Birefringence elimination method
To control the birefringence of plastic lens, it is necessary to constrain the ratio of the lens center and edge thickness in the design process, while controlling the first and second derivatives of the lens curvature to ensure the smoothness. During the mold design process, the birefringence of lens is related to the position, size, and shape of gate as well as the cooling system of mold. In the injection molding process, injection parameters, such as injection speed, pressure, temperature, and pressure holding time, all affect the birefringence. Mode flow analysis is very helpful for the evaluation of birefringence. Owing to the birefringence of optical resin material and the uneven thickness of the lens, it is difficult to meet the requirement of invisible birefringence directly in the injection molding process. Therefore, the annealing process is needed to further eliminate the birefringence.
Figure 8 shows a flow chart of the manufacturing process of an ultra-low birefringence optical element. The process can be divided into six steps. (1) mold design and mold flow analysis: making sure that the position, size, and shape of the gate are reasonable and the cooling system is uniform [26]; (2) mold core machining: using the single-point diamond turning technology to ensure mold core accuracy [27,28]; (3) lens fabrication: utilizing high-precision injection molding equipment and setting reasonable injection parameters to reduce the birefringence of the lens [29]; (4) lens annealing: eliminating the birefringence of the lens through an annealing process of several hours using temperature-controlled equipment; (5) residual birefringence measurement: ensuring that the residual PR is small enough and invisible to the human eye; (6) surface accuracy measurement: ensuring that the surface precision of lens meets the design tolerance requirement. Additionally, injection molding optimization and even compensation machining of the mold core will be also required.
The PR values and distribution are related to the shape of the lens; therefore, mold design and injection molding optimization. Some exemplary measures to reduce lens birefringence are: (1) increasing the size of injection gate; (2) reducing the injection pressure and speed; and (3) increasing the cooling time in the injection process.
4. Prototype and Experimental Results
A prototype of pancake VR-HMD was designed and developed as shown in Fig. 9(a). The overall thickness of prototype is less than 20 mm, approximately one-third that of a traditional VR optics system, with a significantly better optical performance. To meet the requirements of users with myopia, an optomechanical design with diopter adjustment was used, as shown in the internal structure plotted in Fig. 9(b).
We measured the brightness of the virtual display with a calibrated imaging luminance meter, and the average brightness of the small square and the maximum brightness of the stray light are used for the calculation as the stray light may partially overlap with the normal image. To measure the stray light, we use a high-contrast picture with nine white squares, as depicted in Fig. 10(a). A camera is placed at the exit pupil to capture the virtual image and the brightness of normal virtual image can be calculated. The calculation of stray light brightness, however, is a little more complex. First, we detect the boundary of the nine squares with our self-developed algorithm. Then, we fill the nine squares with black contents. The remaining image is regarded as stray light and its brightness can be calculated. The stray light ratio is calculated as follows. For each square, we calculate the corresponding stray light ratio by dividing the maximum stray light brightness by average normal virtual image brightness. The final stray light ratio is chosen as the largest value of nine results.
Fig. 10. Stray light suppression. (a) The original image on the display; (b) stray light performance of the virtual image that significantly affects the user experience; (c) the optical performance when the stray light was suppressed to 5.2%; (d) relatively ideal optical effect when the stray light was suppressed to 2.3%.
We first measured an early prototype without anti-reflection film on QWP, nor the birefringence optimization. The residual reflection of QWP without anti-reflection coating can reach 4% and the stray light ratio would exceed 10% if different types of stray light are superimposed at the same time, which seriously affects the optical performance, as shown in Fig. 10(b). Reducing the residual reflections on optical surface (especially the QWP) and birefringence of the lenses, the stray light is effectively suppressed to around 5%, as shown in Fig. 10(c). This result is already better than some commercial products on the market (eg. HUAWEI VR Glass: 6%-8%, according to our testing method).
The introduction of SLSF can further suppress stray light. However, owing to the unsatisfactory polarizing elements (including polarizer, QWP, and PBS), the stray light cannot be completely eliminated. Finally, we suppress the stray light to 2.3%, as shown in Fig. 10(d). This result is significantly better than most of current commercial products. Although the stray light of our system is still visible to the human eye, it basically does not affect the user experience. It is worth mentioning that pancake VR-HMDs has a better optical performance than the traditional VR system using Fresnel lens.
We selected a high-contrast picture of a resolution target for stray light testing as shown in Fig. 11(a). The captured image showed no perceivable stray light, as shown in Fig. 11(b). A colorful picture, as shown in Fig. 11(c), was also used to demonstrate the overall performance and a satisfactory display performance was also achieved, as shown in Fig. 11(d).
Fig. 11. Experimental demonstration. (a) High-contrast picture with distortion correction on the display, (b) good performance of stray light under a high-contrast picture captured with a camera, (c) a colorful picture with distortion correction on the display, and (d) high-immersion and color-reproduction VR display performance.
5. Conclusion
In this study, a compact VR-HMD system with ultra-thin form, large EPD, wide FOV, and low stray light has been developed. The OAL of the system is below 20 mm with a diagonal FOV of 96° and an EPD of 10 mm at 11 mm ERF. The stray light of the system has been suppressed to 2.3%. The causes of stray light in this type of optical system are analyzed in detail. Subsequently, various effective measures for suppressing the stray light are proposed. The prototype of a compact pancake VR-HMD system with a low stray light has been successfully developed and the experimental results demonstrate a good performance. We believe this work will offer important guidance on future design of pancake display systems for stray light suppression.
Funding
Beijing Science and Technology Planning Project (G-2022-04, Z221100006722011); Young Elite Scientist Sponsorship Program by CAST (2019QNRC001); Beijing Municipal Natural Science Foundation (1222026); National Key Research and Development Program of China (2021YFB2802100).
Acknowledgments
We would like to thank Synopsys for providing the education license of CODE V and LightTools.
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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.
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