Projection-type see-through near-to-eye display with a passively enlarged eye-box by combining a holographic lens and diffuser

Jiwoon Yeom; Jisoo Hong; Jinsoo Jeong

doi:10.1364/OE.441982

1. Introduction

Holographic optical elements (HOEs) have attracted much attention in research fields of augmented reality (AR) near-to-eye displays (NEDs) by virtue of high transparency and thin film structures [1,2]. The HOEs transform an incoming wave into the pre-defined wavefront by using a refractive index modulation of holographic materials, when it satisfies the Bragg condition of volume gratings. Meanwhile, most natural light from the real-world scene passes through the HOEs without diffraction, since it deviates from the Bragg condition. Based on these characteristics, HOE-based see-through displays have been actively studied for various types of NEDs such as waveguide-based displays [3,4], direct-projection-type (DPT) displays [5–8], light field displays [9,10], and holographic displays [11–13].

In the DPT displays, which could provide the advantage of compact form factor for the NEDs, a displaying source directly projects virtual images on the optical combiner, and the projected images are diffracted into the human eye. The DPT NEDs are typically implemented using HOE lenses (HOELs) and a pico-projector such as a laser beam scanning (LBS) projector, where an off-axis projection configuration is preferred for a small form factor of NEDs as shown in Fig. 1(a). The beam width of each pixel in the projected images is determined by a pupil size of the projector, and it is usually a few millimeters or sub-millimeters like a pencil beam. Since the HOEL-based DPT NEDs have an eye-box proportional to the beam width, they provide an extremely small eye-box such as 1 mm or less in the size. Various studies such as pupil steering techniques, which track the position of the eye and dynamically move the eye-box [7,12–14], have been presented to alleviate this limitation, but they necessarily involve additional and bulky experimental setups with active components operating extremely fast. Alternatively, our proposed method does not involve any temporal multiplexing manners for enlarging the eye-box of the HOEL-based DPT displays.

Fig. 1. Schematics of the HOEL-based DPT displays based on (a) the conventional HOEL designed for the off-axis projection configuration, and (b) the proposed method where the on-axis configuration HOEL and the HOED are combined. The proposed method is capable of providing the enlarged eye-box by widening the beam width of projected pixels using the HOED without losing the advantages of compact form factor due to the off-axis projection configuration.

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Previously reported DPT displays have induced optical aberrations which degrade the image quality [7,13,15–17]. Particularly, such aberrations become severe, as the beam width for each pixel broadens for enlarging the eye-box. For the previous eye-box enlargement method for the HOEL-based DPT displays, complicated compensation methods on the projected images or wavefronts are required for the aberration correction. For example, in Ref. [13], the authors applied the holographic wavefront compensation based on cumbersome calibration methods for the point spread functions of the projected pixels in order to correct the aberrations due to the off-Bragg diffraction. Alternatively, multiple cylindrical lenses [15] or freeform lenses [16] were used instead of a typical glass lens in a recording process of the HOEL to reduce the aberration. However, they require high cost and long fabrication time for the complicated bulk optics, so that the specially designed wavefronts are realized for compensating the aberration of the off-axis HOEL.

In this paper, we propose a passive eye-box enlargement method for a DPT see-through NEDs, which is composed of an HOEL with an on-axis projection configuration and an HOE diffuser (HOED) as shown in Fig. 1(b). The HOED diffuses the projected pixels only in the direction towards the HOEL based on its volume gratings. For the small form factor as the NEDs, the HOED in the proposed method operates with the highly off-axis projection configuration, which is similar to the conventional DPT displays. The diffused lights of the projected pixel are modulated by the HOEL, which is recorded in the on-axis configuration to minimize the aberrations, and provides the virtual images with the enlarged beam width. Since the modulated lights by the HOEL do not satisfy the Bragg condition of the HOED, the virtual images after being diffracted at the HOEL could be observed at the eye-box position.

This paper is organized as follow. In Section 2.1, a thorough analysis on imaging characteristics of the HOEL according to the projection configuration is provided, and simulation results using OpticStudio are presented for validating the analysis. In Section 2.2, the detailed principles and characteristics of the proposed method composed of the HOED and the on-axis HOEL are presented. In Section 3, we present fabrication results for the on-axis HOEL and the HOED, and the measured data for their diffraction properties. Additionally, a proof-of-concept system for displaying experiments is realized with adopting an LBS projector, and the experimental results verify the principles of the proposed method.

2. Principle

2.1 Imaging characteristics of HOEL-based DPT displays

In this section, we analyze the imaging characteristics of the HOEL according to the projection geometry from the off-axis to the on-axis configurations, so that we optimize the projection configuration of the HOEL for enlarging the eye-box. Figure 2(a) shows a diagram for the analysis, where a two-dimensional (2D) coordinate system is used for simplicity in the analysis. The HOEL model in Fig. 2(a) offers the possibility to analyze the diffraction characteristics in both the on-axis and off-axis projection configuration, so that we derive a generalized and comprehensive model for the HOEL. Suppose a center of the projector located at F₂[f₂sinθ_i, f₂cosθ_i] projects the images on the HOEL that lies at z=0 plane. At each position in the HOEL, an incident light is diffracted and focused at a focal point of the HOEL represented as F₁[0, f₁] in Fig. 2(a). The HOEL is assumed to be recorded by the interference between two spherical waves, whose focal points correspond to a projection center (F₂) and the center of the eye-box (F₁). Note that when a projection angle θ_i is zero, the HOEL operates in the on-axis projection configuration. Otherwise, it operates in the off-axis projection configuration. Additionally, if we assume the projection center is far enough from the HOEL (i.e. infinite f₂), the HOEL model in Fig. 2(a) corresponds to the collimated projection configuration as used in the various studies [7,8,12].

Fig. 2. Schematics of the HOEL-based DPT display for analyzing the imaging characteristics according to the projection configuration: (a) the analysis parameters, (b) a wavevector space diagram corresponding to the sub-region Q at the HOEL, and (c) a schematic diagram to examine the footprint of the diffracted rays at the HOEL for the parallel ray bundles with given field angle φ (the eye-box plane is sampled by n number of sub-regions for each field angle).

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The aberrations of the off-axis configuration HOEL in Fig. 2(a) become severe, as the projected ray bundles for each pixel do not have the narrow beam width. Consequently, it is hard to achieve the affordable eye-box size based on the off-axis configuration. In order to find the imaging characteristics of the DPT displays with enlarging the eye-box, now we suppose ray bundles starting from the eye-box plane and heading for the projection source direction through the HOEL. It is similar to the conventional strategy of the lens design for the NEDs, where the pupil surface (eye-box plane in the NED systems) is assumed to emit parallel ray bundles and the lenses are optimized for the ray bundles with the same field angle to make the smallest focus spot at the image plane (display plane in the NED system).

For a given field angle φ, parallel ray bundles with the width of w_EB propagate into the HOEL. As in Fig. 2(a), suppose a single ray in the ray bundles which starts from the position P[ξ, f₁] arrives at Q[q, 0] on the HOEL, where x component q is represented as Eq. (1)

(1)$$q = {f_1}\tan \varphi + \xi .$$

Even though the volume gratings of the HOEL have aperiodic structures with varying grating vectors according to the position, a local grating in a sub-region could be modeled as a homogenous grating [18,19]. Such a localized grating approximation is valid as the spherical waves used in the recording process of the HOEL vary slowly within each sub-region of the holographic material. As shown in Figs. 2(a) and 2(b), a volume grating at the sub-region Q is approximated into a homogenous grating formed by two wavevector k₁ and k₂. Note that k₁ and k₂ can be thought as the phase-conjugations of the wavevectors of the signal and reference waves in the typical recording process of the HOEL. We denote k₁ and k₂ as Eqs. (2) and (3).

(2)$${{\boldsymbol k}_1} = \frac{{2\pi {n_r}}}{\lambda }\frac{{{f_1}}}{{\sqrt {{q^2} + {f_1}^2} }}\left[ {\frac{q}{{{f_1}}}, - 1} \right],$$

(3)$${{\boldsymbol k}_2} = \frac{{2\pi {n_r}}}{\lambda }\frac{{{f_2}}}{{\sqrt {{{({{f_2}\sin {\theta_i} - q} )}^2} + {{({{f_2}\cos {\theta_i}} )}^2}} }}\left[ {\sin {\theta_i} - \frac{q}{{{f_2}}},\cos {\theta_i}} \right],$$

where λ and n_r represent the recording wavelength and the refractive index of holographic material. We denote a grating vector at the sub-region Q as K_g=[K_g,x, K_g,z], which is derived by Eq. (4).

(4)$${{\boldsymbol K}_{\boldsymbol g}} = {{\boldsymbol k}_2} - {{\boldsymbol k}_1}.$$

Combining Eqs. (2)–(4), K_g,x and K_g,z are expressed as Eqs. (5) and (6).

(5)$${K_{g,x}} = \frac{{2\pi {n_r}}}{\lambda }\left( {\frac{{{f_2}\sin {\theta_i} - q}}{{\sqrt {{{({{f_2}\sin {\theta_i} - q} )}^2} + {{({{f_2}\cos {\theta_i}} )}^2}} }} - \frac{q}{{\sqrt {{q^2} + {f_1}^2} }}} \right),$$

(6)$${K_{g,z}} = \frac{{2\pi {n_r}}}{\lambda }\left( {\frac{{{f_2}\cos {\theta_i}}}{{\sqrt {{{({{f_2}\sin {\theta_i} - q} )}^2} + {{({{f_2}\cos {\theta_i}} )}^2}} }} + \frac{{{f_1}}}{{\sqrt {q + {f_1}^2} }}} \right).$$

As in Fig. 2(a), we denote k_p as a wavevector of the probe wave starting from the position of [ξ, f₁] and arriving at the HOE surface with the angle of incidence (AOI) of φ at the sub-region Q. Then k_p is expressed as Eq. (7):

(7)$${{\boldsymbol k}_{\boldsymbol p}} = \frac{{2\pi {n_r}}}{\lambda }\frac{1}{{\sqrt {{{({q - \xi } )}^2} + {f_1}^2} }}[{q - \xi , - {f_1}} ]= [{{k_{p,x}},{k_{p,z}}} ].$$

Since k_p deviates from k₁, a diffraction occurs in the off-Bragg regime and we take into account the Bragg mismatch [16]. In this case, x component (transverse direction) of the diffraction wavevector is the summation of K_g,x and k_p,x. In the longitudinal direction, due to the finite thickness of the holographic medium, the z component of the diffraction wavevector is determined by the energy conservation as in Fig. 2(b). The diffraction wavevector (k_d) is calculated as Eqs. (8) and (9):

(8)$${k_{d,x}} = \frac{{2\pi {n_r}}}{\lambda }\left( {\frac{{{f_2}\sin {\theta_i} - q}}{{\sqrt {{{({{f_2}\sin {\theta_i} - q} )}^2} + {{({{f_2}\cos {\theta_i}} )}^2}} }} - \frac{q}{{\sqrt {{q^2} + {f_1}^2} }} + \frac{{q - \xi }}{{\sqrt {{{({q - \xi } )}^2} + {f_1}^2} }}} \right),$$

(9)$${k_{d,z}} = \sqrt {{{\left( {\frac{{2\pi {n_r}}}{\lambda }} \right)}^2} - {k_{d,x}}^2} ,$$

where k_d,x and k_d,z represent the x and z components of the diffraction wavevector k_d. From Eqs. (8) and (9), even though the parallel ray bundles have the same field angle φ, the diffracted rays head for the different directions according to the starting position ξ.

The optimal distance for the image surface should be derived, where we obtain the minimum focus spot for the field angle φ. Along the projection axis with the incline angle of θ_i, we place virtual screens with various distances from the center of the HOEL to examine the footprint of the diffracted wavefront. If we denote a distance between the virtual screen and the HOEL as l, the footprint of the diffracted ray R[x_r, z_r] could be expressed using Eq. (10):

(10)$$\left\{ {\begin{array}{l} {{x_r} = l\sec {\theta_i} + \frac{{{k_{d,z}}}}{{{k_{d,x}}}}q}\\ {{z_r} = \frac{{{k_{d,z}}}}{{{k_{d,x}}}}({{x_r} - q} )} \end{array}} \right.,$$

where x_r and z_r is the x and z coordinates of the intersection point of virtual screen with the distance of l and the diffracted rays from the ξ with the field angle of φ, respectively.

In Fig. 2(c), if we assume the diffracted wavefront being sampled by n numbers of sub-regions for the eye-box plane, the footprint for the given field angle of φ have n numbers of intersection points R_j (j=1, 2, …, n). The optimal distance for the smallest focus spot of the parallel rays with the field angle φ is expressed as Eq. (11), which minimizes the standard deviation of sets of x_r.

(11)$${\sigma _{l,\varphi }} = \sqrt {\frac{{{{\sum\limits_{j = 1}^n {\left( {{x_{r,j - }}\sum\limits_{j = 1}^n {{x_{r,j}}} } \right)} }^2}}}{n}} ,$$

where σ_l,φ is the standard deviation of x_r with the given l and φ, and x_r,j is the sampled x coordinates of the intersection points R_j. By adding the minimum values of σ_l,φ over every field angles, we define the cost function for design parameters θ_i and f₂ as in Eq. (12):

(12)$${\varepsilon _{{\theta _i},{f_2}}} = \sum\limits_{k = 1}^m {\min ({\sigma _{l,{\varphi _k}}})} ,$$

where φ_k (k=1,2, …, m) represents the sampled field angle with the sampling number of m. Note that the cost function of Eq. (12) is the function of the projection angle (θ_i) and the focal length of the reference wave (f₂). It is related to the focus quality of each spot for the given field angle. Since the small spot size leads to the small value for the cost function, Eq. (12) evaluates the image quality of DPT displays based on the HOEL with the eye-box size of w_EB.

Figure 3 simulates the variation of Eq. (12) according to the various θ_i and f₂. In the simulation, we assume the simulation parameters as follows: φ within the range of ±20 °, ξ within the range of ±2.5 mm, and f₁ = 20 mm. As shown in Fig. 3, the cost function of Eq. (12) decreases according to the increase of f₂ and decrease of θ_i. It means that the HOEL-based DPT displays with the enlarged eye-box shows the minimum aberration or the best image quality, when they are designed with the on-axis (θ_i: zero) and parallel reference waves (f₂: infinity) in the recording process.

Fig. 3. Simulation results for the cost function ε according to the projection configurations of the reference waves by using the proposed analysis model of the HOEL.

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For further validation of the aforementioned analysis, we investigated in detail the spot sizes of the HOEL with the on-axis configuration, whose reference wave is normally incident plane wave, compared to the off-axis one. We conducted the ray tracing simulations using the volume hologram models in Zemax OpticStudio as proposed in [20,21]. The volume hologram models are implemented based on Welford’s equation [22] and coupled wave theory [23], and is capable of evaluating the propagation direction of diffracted light even in the off-Bragg condition. As shown in Figs. 4(a) and 4(b), we assumed two different configurations for the DPT displays, when the reference wave is assumed to project on the HOEL with the off-axis (CASE I) and on-axis configuration (CASE II), respectively. In both cases, the eye-relief distance from the HOEL is selected to a same value with considering the practical applications for the NEDs. Other simulation parameters are listed in Table 1. Additionally, we marked the design parameters used in the OpticStudio simulations in Fig. 3.

Fig. 4. Comparison between the on-axis and the off-axis HOEL for the enlarged beam width: the simulation configurations of the HOEL with the (a) off-axis, (b) on-axis reference wave in OpticStudio, and (c) a comparison of the spot radius between the off- and on-axis projection geometry according to the pupil (eye-box) size.

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Table 1. Specifications of simulated systems in OpticStudio

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Figure 4(c) evaluates the variations of the spot sizes at the image surfaces for the case of φ=0 ° (center field), 5 °, 10 °, and 20 ° (rightmost field) according to the pupil size at the eye-box. In Fig. 4(c), blue dotted lines and red solid lines denote CASE I (off-axis projection configuration) and CASE II (on-axis configuration), respectively. We inputted the parallel ray bundles starting from the eye-box with the different size, and simulated the root mean square (RMS) spot radius at the image surface. In both cases, the spot radius of the inputted field increases as the pupil size at the eye-box plane increases. However, the spot radius of off-axis configuration is much larger than that of on-axis configuration, even though we assume the same observation condition. For example, the RMS spot radius of on-axis configuration with the eye-box of 5.0 mm was approximately 38 μm, which was smaller than that of off-axis configuration with the eye-box of 0.1 mm (120.3 μm). From the results of Figs. 3 and 4(c), we find that the HOEL-based DPT displays provide more benefits in the image quality, particularly when the reference wave is designed to be normally incident plane waves.

2.2 Principles of proposed method

Even though the on-axis HOEL projection configuration provides better image quality compared to the off-axis configuration, it is hard to satisfy the on-axis projection geometry for ergonomically designed see-through NEDs. In this section, we adopt an HOED for enhancing the beam width of each pixel, and satisfy the on-axis projection geometry for the HOEL without losing the merits of see-through properties. The HOED is a volume hologram to perform the functions of the optical diffuser for the projected light, when the projection direction and wavelength satisfy the Bragg condition [24–26].

Figure 5(a) shows a schematic of the proposed method, which is composed of an on-axis HOEL and an HOED with a gap of g. Each pixel projected from the projector is diffused at the HOED by the Bragg diffraction, and emits light rays with an emission angle of φ_D. The reflection-type HOEL with the on-axis configuration performs the focusing power for the diffused light from the HOED, and makes the virtual images of the projected one. The diffusing angle and the optical path length corresponding to the gap (g) determine the width of eye-box as shown in Fig. 5(a). Additionally, both the HOEL and the HOED have high transparency by the virtue of selectivity arising from their volume gratings, so that their combined structure still permits the see-through properties for most natural light from the real-world.

Fig. 5. The imaging principles of the proposed method: (a) a schematic diagram with the design parameters of the proposed method, which is composed of the HOEL and the HOED, and (b) the simulation results of the eye-box size according to the diffusing angle (φ_D) of the HOED and the gap parameter (g) between the HOEL and the HOED.

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The on-axis HOEL makes the virtual images of the diffused light by the HOED at a distant plane that corresponds to the accommodation range of the observer. We denote l_v as the virtual image location formed by the diffused images at the HOED and the optical power of the HOEL, and it is expressed as in Eq. (13) [27]:

(13)$${l_v} = {\left( {\frac{1}{{{f_1}}} - \frac{1}{g}} \right)^{ - 1}},$$

where f₁ is the focal length of the on-axis HOEL as defined in Fig. 2(a). Note that the virtual image location l_v is typically a negative number for the NEDs. The size of the eye-box (w_EB) is expressed as Eq. (14):

(14)$${w_{EB}} = \left( {1 - \frac{d}{{|{l_v}|}}\left( {\frac{{|{l_v}|}}{g} - 1} \right)} \right){w_p} + \left( {1 + \frac{d}{{|{l_v}|}}} \right) \cdot 2g \cdot \tan \left( {\frac{{{\varphi_D}}}{2}} \right),$$

where w_p represents the width of projected images at the HOED, and d represents a distance between the HOEL and the eye-box plane as in Fig. 5(a). The diffusing angle (φ_D) should satisfy below condition to ensure the positive values for the eye-box size:

(15)$${\varphi _D} \ge 2{\tan ^{ - 1}}\left( {\frac{{{w_P}}}{{2g}}\left( {\frac{d}{{g(1 + d/|{l_v}|)}} - 1} \right)} \right).$$

According to Eq. (14), as the diffusing angle becomes larger, the size of eye-box broadens. However, the large diffusing angle may cause the transparency of the HOED to deteriorate. The volume gratings in the HOED with the diffusing angle of φ_D requires the interferences among a reference wavevector and numerous signal wavevectors heading for the various propagation directions within φ_D. The multiple gratings formed in the HOED weaken the selective functionality of the HOED. Consequently, the see-through properties of the HOED decrease as the diffusing angle becomes large. There is a trade-off relationship between the transparency and the eye-box size in the proposed system.

Figure 5(b) shows the analysis on the size of eye-box according to the values of the gap (g) and the diffusing angle (φ_D). With considering the typical design parameters of NEDs, the simulation parameters were selected as follows: f₁=20 mm, d=25 mm, w_P=20 mm. As in the simulation results, the eye-box was not formed correctly for the small diffusing angles, since they did not satisfy Eq. (15). The size of eye-box increases according to the diffusing angle of the HOED as expected. Additionally, for the same value of diffusing angle, the eye-box size decreases as the gap increases due to the distant formation of virtual images. Since the eye-box is desirable to cover the pupil size of the human eye, it is recommended to be larger than 4 mm in typical NED applications.

On the other hand, if the HOEL is not designed for the on-axis projection configuration, the diffused light at the projected images significantly deteriorates the image quality of the observed images. For the conventional HOEL with the off-axis configuration, Fig. 6 presents the effects of the diffusing angles on the observed image quality. In Fig. 6(a), the specifications of the off-axis HOEL was assumed to be identical to the CASE I of Fig. 4. If we do not adopt the diffusing screen for the projected images, the observed images were clearly provided only within the limited size of eye-box. Meanwhile, as shown in Fig. 6(b), the observed images showed the blurring according to the increase of the diffusing angle for the projected images, even in the small diffusing angle (φ_D < 5 °). From the simulation results, the off-axis HOEL is not appropriate for being used in the proposed method instead of on-axis HOEL.

Fig. 6. The imaging simulations of off-axis HOEL with adopting the diffusive projected images: (a) a schematic diagram with diffuser screen for the projected images, and (b) the simulation results of the observed images at the eye-box position according to the diffusing angle (φ_D) of the projected pixels.

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3. Experiments

3.1 Fabrication of an HOEL and an HOED

For the experimental verification of the proposed method, we fabricated an HOEL and an HOED using photopolymers. The C-RT20 photopolymers of Liti Holographics, Inc. were laminated on the glass substrates, and were fixed by using the ultraviolet (UV) light after the recording process. Figures 7(a) and 7(b) show pictures of experimental setups for recoding the HOED (in a transmission-type geometry) and the HOEL (in a reflection-type geometry), respectively. In both cases, we used the 660 nm laser (Cobolt Flamenco). In a signal beam path of Fig. 7(a), a wavefront passing after a diffuser was imaged onto the photopolymer plane through an imaging lens with a focal length of 100 mm. We used a ground glass diffuser with the specification of 120 grit (Edmund Optics 83-386) as the diffuser in the signal beam path. A reference wave, passing after an aspheric lens with a focal length of 40 mm, was obliquely incident on the photopolymer with the AOI (θ_i) of 60 °. The diverging angle and the AOI of the reference wave after the aspheric lens should match a projection angle in the displaying experiments. In the recording setup of the HOEL in Fig. 7(b), two beams heading for the opposite directions were interfered at the photopolymer plane, where one was a plane wave and the other one was a spherical wave. The diverging angle of the signal wave, and the distance between the photopolymer and the focal point determined the viewing angle of the virtual images in the proposed method. In the signal beam path, an aspheric lens with a focal length of 30 mm (Edmund Optics 67-255) was used, and the distance between the photopolymer and the focal point of the aspheric lens was 20 mm. The exposure energy of the signal beam for recording the HOED and HOEL was 29.4 mJ/cm² and 27 mJ/cm², respectively.

Fig. 7. Experimental setups and results for recording the HOEs: (a) a picture of experimental setup for recording the HOED with the off-axis configuration (transmission-type), (b) the HOEL with the on-axis configuration (reflection-type), and (c) the fabricated prototypes of the HOEL and the HOED with verifying their see-through properties.

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Figure 7(c) shows fabrication results of the HOEL and the HOED. Both HOEs showed high transparency, where we could view the background scene clearly. The averaged transmittance of the HOEL and the HOED was measured as 84.9% and 62.2%, respectively, compared to a glass substrates in the visible spectrum (from 400 nm to 700 nm). As discussed in Section 2.2, the transmittance of the HOED was lower than the HOEL, since numerous volume gratings were multiplexed in the photopolymer for the diffusive optical properties. We measured the spectral transmittance of the fabricated HOEs using a spectrometer (Flame-S-UV-VIS of Ocean Optics Inc.), when the probe wave was normally incident on the samples.

The diffraction efficiency of the HOEL decreases compared to the periodic and homogenous volume grating due to the aperiodic gratings with varying grating vectors according to the local positions in the photopolymer. For measuring the diffraction efficiency of the HOEL, we added a beam-splitter (BS) in front of the HOEL to separate the directions of the diffracted wavefront from the incident probe wave. Otherwise, if one placed the optical power meter in front of the HOEL to measure the diffracted beam, it occluded the probe wave itself. Alternatively, we estimated the intensity of the diffracted wave from the HOEL by using the reflectivity of the BS and the intensity after reflection by the BS. We measured the diffraction efficiency at three local points in the HOEL, and the averaged diffraction efficiency was measured to be 60.1% for the 660 nm laser.

We analyzed the diffraction properties of the fabricated HOED in the view of the angular selectivity and the diffusing angles. Figure 8(a) shows the experimental setup for measuring the angular selectivity of the HOED, and the measured selectivity near θ_i (60 °) is presented in Fig. 8(b). Since the intensity of the diffracted beam was hard to be measured directly due to the large diffusing angle, we examined the variation of transmitted beams according to the angular deviation alternatively. At each angular deviation, we measured two intensities of transmitted beams passing after the HOED and glass substrate, respectively, and calculated the transmittance of the 660 nm wavelength by using the difference between them. We assumed that the diffraction efficiency of the HOED was proportional to the value which subtracts transmittance (%) from 100%. This assumption is useful to intuitively understand the behavior of the diffracted wave from the HOEs with neglecting the absorption and loss of the photopolymer [9]. Figure 8(b) presents the normalized efficiency according to the angular deviation of the probe beam, and the measured angular selectivity was approximately 8.7 ° in the full width at half maximum (FWHM). In other words, the fabricated HOED reacted hardly to the probe wave with exceeding the angular deviation of 8.7 °. Since the incidence angle of the diffracted light at the HOEL sufficiently exceeds the angular selectivity of the HOED, the virtual images created by the HOEL are viewable without diffusing at the surface of the HOED.

Fig. 8. The diffraction characteristics of the fabricated HOED: (a) the experimental setup and (b) the results for measuring the angular selectivity of the HOED, and (c) the experiments for measuring the diffusing angle of the HOED.

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Figure 8(c) presents a measurement setup and results for the diffusing angle of the HOED. The trajectory of the diffracted light from the HOED created the footprint image on the printed protractor pattern. The diffusing angle was measured by the angular range within the trajectory. As shown in Fig. 8(c), the fabricated HOED had the diffusing angle (φ_D) over 20 °.

3.2 Displaying experiments

We built a proof-of-concept system for the proposed method with adopting an LBS projector (AnyBeam, Taiwan) as shown in Fig. 9(a). The LBS projector projected virtual images in the red color, where each pixel was formed by the narrow beam width smaller than 1 mm due to the small exit pupil of the projector. The projected pixels were firstly diffused at the HOED, and propagated into the HOEL. The on-axis HOEL transformed the propagation direction of the incident rays, and the diffracted rays were able to pass through the HOED due to the angular selectivity of the volume gratings as measured in Fig. 8(b). The gap between the HOED and the on-axis HOEL was approximately 19 mm. In order to measure the total optical efficiency of the prototype in Fig. 9(a), we projected a red colored image without any pattern and measured the intensities of the projected light (in front of the LBS projector) and the diffracted light (at the eye-box position). The measured total efficiency for the prototype was approximately 23.1%.

Fig. 9. Experimental setup for the displaying experiments: (a) displaying setup using the LBS projector and fabricated prototype, (b) a preliminary displaying experimental results using the resolution target images, (c) the captured images through the prototype at the different viewpoint within the eye-box (Visualization 1), and (d) the projected original picture.

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In Fig. 9(b), a preliminary result of the displaying experiment using the resolution target images is presented. Additionally, Fig. 9(c) shows the captured images through the prototype system with the different observation positions within the eye-box, and their original picture to be projected is provided in Fig. 9(d). We placed a camera at the eye-box plane to capture the observed see-through images. A printed background image, the scene of the road and the sky, was placed at the opposite side of the camera for verifying the see-through imaging properties of the proposed method. The observed images of Figs. 9(b) and 9(c) show the virtual images clearly overlaid on the background images. Even though the camera position changed along the horizontal directions at the eye-box plane, the projected images were still viewable as shown in Figs. 9(c) and Visualization 1. The disparity between the virtual images and background image was presented in Fig. 9(c) according to the observation positions within the eye-box.

As the comparison between the proposed method and the conventional off-axis HOEL, we also conducted a displaying experiment using the off-axis HOEL. The off-axis HOEL was fabricated by the interference pattern between two spherical waves. The reference wave was obliquely incident, and the signal wave was normally incident on the photopolymer in the recording process. Figure 10(a) shows experimental setups for the off-axis HOEL, where the projected images from the LBS projector converged into focal point of the HOEL. The camera was positioned at the focal point of the HOEL, and captured the virtual images overlaid on the background image (the virtual and background images were identical to those in Fig. 9). Since the off-axis HOEL had the small eye-box, the observed virtual images disappeared according to the slight movement in the eye-box plane. In contrast to the proposed method, when the camera moved by only 1.0 mm in the lateral direction in the eye-box plane, the half of the virtual images were hard to be viewable as shown in Fig. 10(b).

Fig. 10. Experimental results for the conventional off-axis HOEL as the comparison: (a) the displaying setup using the LBS projector and off-axis HOEL, and (b) the camera captured images through the off-axis HOEL with different camera positions in the eye-box plane. We moved the camera by 1.0 mm in the left and right directions using the linear stage.

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For further investigation of the effect of the proposed method in the view of eye-box size, we compared the reconstructed eye-box of the proposed method with that of the conventional off-axis HOEL. We placed a screen with the grid patterns of 1 mm pitch size at the eye-box plane to examine the size of the eye-box, and projected the full-red images on the HOEs. As shown in Fig. 11(a), the proposed method presented approximately 5.5 mm of eye-box width. Meanwhile, the conventional HOEL-based DPT display with the off-axis projection configuration (without the HOED) presented the eye-box with about 1 mm in the width as in Fig. 11(b), which corresponded to the size of the focal point of the HOEL.

Fig. 11. Experimental results for verification of eye-box: (a) the eye-box images at the screen of the proposed method, and (b) the conventional off-axis HOEL-based NED system. The pitch of the grid pattern used as the screen was 1 mm for the dotted lines and 5 mm for the solid lines.

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4. Conclusion

In this paper, we proposed the DPT see-through display by combining the on-axis HOEL and the HOED, which provided the enlarged eye-box without any temporal multiplexing methods. We conducted the thorough analysis for the imaging characteristics of the HOEL according to the projection configurations, and the HOEL-based DPT displays with the on-axis configuration were proved to provide more benefits in the image quality. The ray tracing simulations using the volume hologram models in OpticStudio validated our analysis. As the experimental verifications, we realized the combined structure of the HOEL and the HOED, whose transparency was 84.9% and 62.2%, respectively. By using the HOED with the diffusing angle over 20 ° and the angular selectivity of 8.7 °, the prototype successfully presented the clear see-through AR images. The implemented proof-of-concept system with the LBS projector provided the eye-box with the lateral size of 5.5 mm, which covered the typical pupil size of the human eye, while the conventional off-axis HOEL only presented the tiny eye-box (∼1 mm).

Even though the HOELs are given much attention for the AR NED technologies by virtue of the high transparency and thin film structures, the spectral dispersion and the spectral selectivity restrict the usage of various types of displaying source. For example, the HOEL may lead to the spectral dispersion of the displayed images with the conventional micro-display panels (such as organic light-emitting diode displays), and show low optical efficiency due to the high spectral selectivity for the broad-band light source. Hence, the combination of the LBS projector and the HOEL is a promising solution for the NEDs with satisfying the high brightness, the small form factor, and the low spectral dispersion. The proposed method could solve the typical problem in these HOEL-based DPT displays, the limited eye-box size, by using the HOED and the on-axis HOEL. We believe that the proposed method is promising to practical implementations of HOEL-based DPT displays with the large eye-box through the compact and light-weight structures.

Funding

Institute of Information & Communications Technology Planning & Evaluation (IITP) grant funded by the Korea government (MSIT) (No. 2020-0-00929, No. 2021-0-00750).

Acknowledgments

This work was supported by Institute of Information & communications Technology Planning & Evaluation (IITP) grant funded by the Korea government (MSIT); (No. 2021-0-00750, Development of HOE technology to provide 4 diopter range focus cue for AR/MR, 50%) and (No. 2020-0-00929, Development of authoring tool for digital HOE hologram generation using optical simulation, 50%).

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.

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Items		Specifications
Recording conditions for the HOEL	Lateral dimension	20 mm × 20 mm
	Thickness	20 μm
	Wavelength	660 nm
Design parameters of the HOEL	f₁	20 mm
	f₂	[CASE I] 40 mm, [CASE II] Infinity
	θ_i	[CASE I] 60 °, [CASE II] 0 °

Projection-type see-through near-to-eye display with a passively enlarged eye-box by combining a holographic lens and diffuser

Abstract

1. Introduction

2. Principle

2.1 Imaging characteristics of HOEL-based DPT displays

2.2 Principles of proposed method

3. Experiments

3.1 Fabrication of an HOEL and an HOED

3.2 Displaying experiments

4. Conclusion

Funding

Acknowledgments

Disclosures

Data availability

References

Supplementary Material (1)

Data availability

Cited By

Figures (11)

Tables (1)

Equations (15)

Optics Express