1. Introduction

In the past decade, augmented reality (AR) near-eye display has rapidly been developing as one of the most promising next-generation display technique, which manipulates virtual images and real word [1–3]. To obtain better interaction experience, it is very vital to facilitate the development of optical combiner in AR devices [4–6]. Several types of optical combiner have been proposed, such as beam splitters (BS), prisms and waveguides [7,8]. Pancharatnam–Berry phase lens (PBL), as a planar diffractive optical element, has been widely applied as an important part of optical combiner in AR system [9–11], due to their excellent properties such as high diffractive efficiency, high transmittance, small form factor and polarization selectivity, which provides another degree of freedom to modulate incident light [12–14]. However, the chromatic aberration (CA) of PBLs caused by wavelength-dependent focal length will lead to color breakup at the periphery of images which seriously degrades image quality [15,16]. It is highly desirable to reduce the chromatic aberration of PBLs in AR system in order to enhance the imaging performance.

To achieve chromatic aberration correction (CAC) of PBLs in AR near-eye display, two main methods: digital and optical approaches have been reported [17]. The digital approach can effectively alleviate the chromatic aberration by utilizing theoretical calculation to present input images at different depth depending on R/G/B color [8,18]. However, the digital CAC suffers from processing time and power consumption in AR devices requiring high resolution and frame rate, which degrades system performance of AR near-eye display. In other aspect, due to the continuous phase modulation, the optical methods are also widely used to reduce the CA of PBLs. A system consisting of three identical PBLs with two half-wave plates (HWP) in between was proposed to reduce CA [19]. Kimball et. al. proposed a broadband waveplate (DW) lens composed of two liquid crystal (LC) polymer layers with opposite chirality [20]. Certain angle between optical axis of two LC polymer layer depending on the concentration of chiral dopants leads to broadband. However, theoretical model is required of twist angle between LC polymer layers and concentration of chiral dopant is hard to control. Lee et. al. demonstrated a method to reduce the chromatic aberration of Pancharatnam-Berry phase lens-image combiner (PBLIC) which contains two PBLs by adopting three transparent lens diffuser holographic optical elements (LDHOEs) [5]. LDHOE are volume grating essentially for specific wavelength at proper incident angle. The achromatic images of the system are depicted. However, recording and reconstruction setup are both required to fabricate LDHOE. Wu et. al. reported an optical method to reduce CA of PBLs via combining an ultra-band PBL and a Fresnel lens with opposite chromatic dispersions [21], but this system is also complex. Therefore, simple optical method to reduce the CA of PBL is still highly desirable in AR near-eye display.

In this paper, a simple strategy of chromatic aberration correction in bi-focal AR near-eye display based on multi-layer PBL has been demonstrated and verified by experimental results. The multi-layer PBL, as a part of optical combiner, is fabricated by three liquid crystal polymer phase lenses with central wavelength in red, green, and blue, respectively. The multi-layer PBL can effectively reduce the CA in both convex and concave mode of bi-focal AR system, where the color breakup of virtual images captured in bi-focal AR display is significantly alleviated. The principle is that the chromatic dispersion of single PBL will be reduced by dispersion phase compensation of multi-layer PBL. The AR images captured in AR system with multi-layer PBL are captured and digital value is analyzed to verify reduction of chromatic aberration. The proposed broadband multi-layer PBL can benefit augmented reality displays and find widespread application in the near-eye displays.

2. System design

The polarization holography setup based on modified Sagnac interferometer for PBLs fabrication is shown in Fig. 1(a). A linearly polarized (LP) laser beam (Ar⁺ laser at 488 nm) was filtered and collimated by combination of lens (L₁), pinhole (PH), and another lens (L₂). A polarizing beam splitter (PBS) was used to separate the laser beam into s and p waves while a HWP was applied to obtain equal intensity for s and p waves. The separated two beams after PBS (in blue and yellow color) passed through the mirror (M₁) and another mirror (M₂) in opposite order and output from the same side of PBS. A convex lens (L₃) between M₁ and M₂ was used to generate parabolic phase of polarization field [22]. The distance between L₃ and M₁ and the distance between sample and QWP determine the focal length of sample. The s and p waves were transferred to left-handed circularly polarized light (LCP) and right-handed circularly polarized light (RCP) after passing through a quarter-wave plate (QWP). The direction of polarization field created by the interference of RCP and LCP light is periodically rotating on parabolic phase of L₃. As a result, the lens pattern can be written on the photo-alignment layer. A glass substrate with thickness of 0.7 mm was firstly cleaned with deionized (DI) water, ethyl alcohol, acetone, isopropyl alcohol in sequence. Secondly, 0.5 wt.% solution of azobenzene sulfonic dye (SD-1) in N, N- dimethylformamide (DMF) was spin-coated on the glass substrate as the photo-alignment layer. The direction of SD-1 molecules aligned perpendicular to the polarization field [23]. Finally, the sample coated with SD-1 was exposed by a 488 nm Ar⁺ laser under interferometer, as shown in Fig. 1(a). In the experiment, the parabolic phase pattern of lens was encoded on the SD-1 coated sample with power density of 30 mw/cm². The structure of passive mode PBL is demonstrated in Fig. 1(b), where the directors of nematic LC molecules (as a rod) are oriented in a parabolic pattern aligned with SD-1 molecules. After exposure, LC polymer layers were spin-coated on SD-1 and a transparent PBL with diameter of 18 mm appears on the substrates. The actual picture of single PBL and three stacked PBLs are shown in insets figure i and ii of Fig. 1(b), respectively. The thickness of LC polymer layer is required to satisfy the half-wave retardation condition (Δnd=λ/2) at targeted wavelength (633 nm, 532 nm, or 457 nm) to obtain high diffractive efficiency, according to [7]:

 

Fig. 1. (a) Schematic illustration of optical setup for fabrication of PBL. L₁: convex lens 1; L₂: convex lens 2; L₃: convex lens 3; PH: pinhole; HWP: half-wave plate; PBS: polarizing beam splitter; M₁: mirror 1; M₂: mirror 2; QWP: quarter-wave plate. (b) The structure of PBL with radially orientation of LC molecules. Insets i and ii are picture of single PBL and stacked PBLs. (c) Working principle of PBL as convex lens (concave lens) for RCP (LCP), when light incidents from glass substrate to LC polymer. (d) Working principle of PBL as convex lens (convex lens) for LCP (RCP), when light incidents from LC polymer to glass substrate.

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The working principle of PBL is essentially similar to half-wave plate [13]. When the RCP (LCP) light incidents on PBL, the handedness of the light was flipped into LCP (RCP) light. When the wavelength of incident light and thickness of LC polymer match the half-wave retardation condition of PBL based on Eq. (1), the first-order diffractive efficiency can reach up to 100%. When the LP laser light incidents from the glass substrate side (polymer side) of the sample, the single PBL sample converges the RCP (LCP) light and diverges the LCP (RCP) light at the same time, as shown in Fig. 1(c) (Fig. 1(d)), leading to convex mode and concave mode with shrunken and enlarged images, respectively.

The longitudinal chromatic aberration (LCA) of single PBL results from the dependence of optical power on wavelength (λ_R/K_R=λ_G/K_G=λ_B/K_B) [7], where K_R, K_G and K_B is optical power at red, green and blue, and λ_R, λ_G, and λ_B is the wavelength of light at red, green, and blue, respectively. The focal length f = 1/K. When RCP white light (including red, green and blue colors) incidents on a single PBL as convex mode, different focal length from different optical power for different colors will be generated, leading to the LCA thus the visual fatigue in display, as shown in Fig. 2(a). Herein, the blue light possesses longer focal length than the red light. When LCP white light (including red, green and blue colors) incidents on a single PBL as concave mode, different focal length from different optical power for different colors will be generated, leading to the LCA as well, as shown in Fig. 2(b). Therefore, for an optical system, the LCA can be indicated by the optical power difference (ΔK) between red and blue wavelengths as ΔK = K_R – K_B [13]. In our experiment, a PBL working at 532 nm (green color) with focal length of 33 cm is selected as the single G-PBL. The focal length f for this G-PBL is 25 cm and 37 cm for wavelength of 671 nm (red color) and 457 nm (blue color), respectively, resulting in corresponding optical power K_R of 4 m^-1 and K_B of 2.70 m^-1, respectively. Thus, the ΔK of the single G-PBL is 1.3 m^-1.

 

Fig. 2. Focal length of single PBL depends on wavelength of incident light. When RCP light (a) or LCP light (b) (including red, green and blue light) incidents single PBL, single PBL work in convex mode or concave mode. Focal length of single PBL increase with decrease of wavelength of incident light. When RCP light (including red, green and blue light) incidents RGB-PBLs, the focal length of red, green and blue light can be closed up. When the RCP (LCP) light incidents RGB-PBLs, RGB-PBLs work as convex mode (c) and concave mode (d), respectively.

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To reduce the LCA of single PBL, a RGB-PBLs system consisting of R-PBL, G-PBL and B-PBL with central wavelength of red (633 nm), green (532 nm), and blue (457 nm), respectively, is proposed. The diffractive efficiency of R/G/B PBL can achieve 100% at 633 nm, 532 nm and 457 nm as long as LC polymer thickness of R/G/B PBL matches half-wave retardation condition based on Eq. (1). The working principal of RGB-PBLs is to combine the optical phase of three PBLs with different central wavelength [24] to reduce the LCA. The phase retardations of each R/G/B-PBL only match half-wave retardation condition at specific R/G/B color respectively while the phase retardations mismatch half-wave retardation condition incompletely at wavelength deviating from central wavelength. The phase retardations of RGB-PBLs at R/G/B color is complementary. As a result, the bandwidth of proposed system is broadened and reduce CA effectively. To combine the phase pattern of R/G/B-PBL to achieve achromatic PBLs, the ray projection height and angle-tracing method is utilized to verify the achromatic effect of RGB-PBLs system. The effective focal length of a three-lens system can be derived from Ref. [25] as:

In our experiment, for incident light at 671 nm, $f_1^{\prime}$, $f_2^{\prime}$, and $f_3^{\prime}$ is measured to be 121 cm, 120 cm and 122 cm, respectively, resulting in the calculated effective focal length at 671 nm is $f_{\textrm{671 - eff}}^{\prime}$ =40.4 cm. For incident light at 532 nm, $f_1^{\prime}$, $f_2^{\prime}$, and $f_3^{\prime}$ is 112 cm, 114 cm and 115 cm, respectively, and the calculated effective focal length at 532 nm is $f_{\textrm{532 - eff}}^{\prime}$ =37.9 cm. For incident light at 457 nm, $f_1^{\prime}$, $f_2^{\prime}$, and $f_3^{\prime}$ is 101 cm, 102 cm and 103 cm, respectively, and the calculated effective focal length at 457 nm is $f_{\textrm{457 - eff}}^{\prime}$ =34.1 cm. Therefore, in the RGB-PBLs system, K₆₇₁ =2.48 m^-1 and K₄₅₇ =2.93 m^-1, the calculated ΔK is 0.45 m^-1. Comparing to the value of ΔK = 1.3 m^-1 in single G-PBL, the RGB-PBLs system significantly reduces the ΔK to 0.45 m^-1 with reduction of 65.4%, which finally decreases the LCA and improve the quality of image. Figure 2(c)–2(d) depicts the schematic illustration for RCP and LCP incident for our proposed RGB-PBLs optical system, respectively.

 

Fig. 3. (a) Schematic illustration of CAC AR system using proposed RGB-PBLs (BS: beam splitter; QWP: quarter-wave plate; LP: linear polarizer; CWL: collimated white light). (b) Real experimental setup of CAC AR system. The light path of CWL is presented by yellow arrow. Distances from mirror, RGB-PBLs, Plane 1 (yellow dragon), Plane 2 (brown cattle) and objective lens of camera to BS are marked.

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Figure 3(a) depicts a CAC AR system using proposed RGB-PBLs to reduce the chromatic aberration in bi-focal planes display. As the passive mode of RGB-PBLs was applied in this AR system, bi-focal planes would be generated as marked to be plane 1 and plane 2, respectively. Letters of ‘SUSTech’ were printed on a paper and illuminated by collimated white light (CWL). Then, the incident white light was reflected by mirror, modulated into RCP or LCP light by passing through a linearly polarizer (LP) and quarter-wave plane (QWP) in sequence, and then incidents into the RGB-PBLs. After the RGB-PBLs, a beam splitter (BS) was used as the optical combiner in this AR system which possessed transmittance ratio of nearly 50%. A camera (Nikon D7100) is applied to simulate single eye of human and capture the image of ‘SUSTech’ floating in real world. The images were finally projected into the real world by the BS. When the incident light is RCP (LCP) light, RGB-PBLs works in convex (concave) mode and the image was displayed at Plane 1 (Plane 2), leading to a bi-focal plane display depending on the circular polarization of incident light. The real experimental setup of RGB-PBLs AR system is demonstrated in Fig. 3(b), where the light path of incident CWL is presented by yellow arrows. The distances from mirror, RGB-PBLs, Plane 1 (yellow dragon), Plane 2 (brown cattle) and objective lens of camera to BS is 10 cm, 6.5 cm, 16 cm, 31 cm and 9 cm, respectively.

3. Results and discussions

In our experiment, the first-order diffractive efficiency of single R/G/B PBL was measured firstly. Figure 4 shows the photo images of laser beams (633 nm, 532 nm, and 457 nm) captured at focal planes. Figure 4(a)–4(c) show the photo image of collimated laser beams with 8 mm diameter passing through no lens at wavelength of 633 nm, 532 nm, and 457 nm, respectively. When the incident light is RCP light, the PBL works as a convex lens, the obtained photo images (small point) at the focal length are shown in Fig. 4 (d)-(f), respectively, where the incident light converges into a spot with small diameter. By contrast, the PBL works as a concave lens when the incident light is LCP light. The photo images (large point) at focal planes are demonstrated in Fig. 4(g)–4(i) with 15 mm diameter. The diffractive efficiency of fabricated R/G/B PBL is measured be larger than 92% and the zero-order leakage is hardly to be observed.

 

Fig. 4. Photo images of collimated laser beam passing through no lens at wavelength of (a) 633 nm, (b) 532 nm, and (c) 457 nm, respectively. Photo image at the focal length of PBL when the incident light is RCP light at (d) 633 nm, (e) 532 nm, and (f) 457 nm, respectively. Photo images at the focal length of PBL when the incident light is LCP light at (g) 633 nm, (h) 532 nm, and (i) 457 nm, respectively.

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The transmittance of R-PBL, G-PBL, B-PBL and RGB-PBLs is shown in Fig. 5. The transmittance of R-PBL, G-PBL and B-PBL are over 94% from 450 nm to 700 nm, and the transmittance of RGB-PBLs reduces to 75% due to increase loss from added optical elements.

 

Fig. 5. Transmittance of R-PBL (red line), G-PBL (green line), B-PBL (blue line) and RGB-PBLs (black line) over range of 450 nm -700 nm.

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As mentioned above, the CAC AR system using proposed RGB-PBLs can largely reduce the chromatic aberration in bi-focal planes display. Figure 6(a)–6(b) demonstrate the measured photo images of ‘SUSTech’ at convex mode (corresponding to plane 1 in Fig. 3) when the G-PBL (RGB-PBLs) is used in the bi-focal planes display. Figure 6(e)–6(f) demonstrate the measured photo images of ‘SUSTech’ at concave mode (corresponding to plane 2 in Fig. 3) when the G-PBL (RGB-PBLs) is used in the bi-focal planes display. It can be seen that, in Fig. 6(a), the color breakup at the edge of letters is obvious. In contrast, the color breakup of letters is lagrely reduced in Fig. 6(b), indicating an excellent reduction of vergence-accommodation conflict while using the RGB-PBLs for chromatic aberration correction. The comparison is also supported by analyzing the digital value of letter ‘T’ in ‘SUSTech’. In Fig. 6(c), 6(d), 6(g), and 6(h), the digital value of letter ‘T’ is calculated by MATLAB at different pixels, corresponding to that in Fig. 6(a), 6(b), 6(e), and 6(f), respectively. The intersection of white and black at top edge of the letter ‘T’ is selected to be analyzed. The R/G/B line represents the digital value at each pixel. The closer the three lines are, the color breakup is less obvious. In convex mode, in Fig. 6(c), it is shown that the R/G/B lines from 30 px to 50 px are separated largely which means the color breakup is severe. By contrast, in Fig. 6(d), the R/G/B lines from 20 px to 40 px are closer which means the color breakup is inconspicuous. In concave mode, it can be seen that the color breakup at the edge of ‘SUSTech’ in Fig. 6(e) (G-PBL applied) has been largely diminished in Fig. 6(f) (RGB-PBLs). The R/G/B lines from 40 px to 60 px in Fig. 6(g) are separated largely. In contrast, the R/G/B lines from 40 px to 60 px are closer in Fig. 6(h), comparing to that of Fig. 6(g). Therefore, the experimental results show that the chromatic aberration in our bi-focal AR system can be effectively reduced while using fabricated RGB-PBLs system comparing to the single G-PBL.

 

Fig. 6. Photo images of ‘SUSTech’ at convex mode in the bi-focal planes display when using the (a) G-PBL, (b) RGB-PBLs. The digital value of letter ‘T’ at different pixels at convex mode in case of (c) G-PBL and (d) RGB-PBLs. Photo images of ‘SUSTech’ at concave mode in the bi-focal planes display when using the (e) G-PBL, (f) RGB-PBLs. The digital value of letter ‘T’ at different pixels at convex mode in case of (g) G-PBL and (h) RGB-PBLs.

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To demonstrate the convex and concave mode of the bi-focal CAC AR system using proposed RGB-PBLs more clearly, a dragon toy and a cattle toy is located at the focal length of image in convex mode (plane 1) and concave mode (plane 2), respectively. Figure 7(a) and 7(b) demonstrate the photo images of shrunken ‘SUSTech’ in convex mode (by RCP) and enlarged ‘SUSTech’ in concave mode (LCP), respectively, where the dragon toy and cow toy can be clearly observed. The distance of plane 1 and plane 2 is 24.5 cm and 40 cm far from the objective lens of camera, respectively. The distance between the two focal planes in real world is about 15.5 cm. It can be seen that the proposed bi-focal AR system can realize the bi-focal display with less color breakup.

 

Fig. 7. Photo image from bi-focal CAC AR system using proposed RGB-PBLs. (a) shrunken ‘SUSTech’ in convex mode (by RCP) and (b) enlarged ‘SUSTech’ in concave mode (LCP).

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4. Conclusion

In summary, we demonstrate a simple strategy of chromatic aberration correction in bi-focal AR near-eye display based on multi-layer PBL with experimental results. The multi-layer PBL, as a part of optical combiner, is fabricated by three liquid crystal polymer phase lenses with central wavelength in red, green, and blue, respectively. The multi-layer PBL can effectively reduce the CA in both convex and concave mode of bi-focal AR system, where the color breakup of virtual images captured in bi-focal AR display is significantly alleviated. Comparing to the value of ΔK = 1.3 m^-1 in single G-PBL, the RGB-PBLs system significantly reduces the ΔK to 0.45 m^-1 with reduction of 65.4%, which finally decreases the LCA and improve the quality of image. The proposed broadband multi-layer PBL can benefit augmented reality displays and find widespread application in the near-eye displays.