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Abstract
The paper presents an augmented reality display based on the free-space combiner, consisting of two holographic mirrors: flat and spherical. A feature of such a system is a high-reflection coefficient of mirrors up to 90% for one wavelength and a high transmittance to the lumen up to 67% throughout the rest of the visible spectrum, unlike similar solutions implementing principles of polarization or dichroic beam splitting. The recording scheme and calculation of a separate flat holographic mirror and spherical holographic mirror are described. The proposed augmented reality display can provide multifocality, i.e., reproduction of virtual images at several distances, which demonstrates a certain perspective of this implementation in terms of compensation for the vergence accommodation conflict.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. INTRODUCTION
Recently, significant progress has been made in the field of information visualization technologies through augmented reality (AR) optical systems [1–4], and various optical schemes for presenting virtual information to the user have been developed [5,6]. In practice, the advantages of head-mounted displays (HMDs) have been confirmed in the industrial sector, medicine, education, etc. Systems built on the basis of planar optical waveguides are particularly popular [7–10], because their application makes it possible to reduce the weight and size parameters of the entire system by the entrance pupil expansion to the required size [11,12]. Metasurface-based AR combiners are also promising direction for a HMD [5,13].
However, systems based on holographic and geometric prism waveguides have high optical losses. In the case of holographic waveguides, diffraction gratings are limited by diffraction efficiency. Geometric prism waveguides use polarizers and translucent coatings to minimize the size of the optical system resulting in the need to use a bright LED backlight for DLP or LCoS image sources [14,15]. Despite common development issues such as optical efficiency, heat generation control, and energy consumption, other optical schemes still have potential in AR optical design, such as free-form prisms [16,17], free-space combiners (FSC) [18], and birdbath schemes [19–21].
Birdbath scheme systems have a low cost and are relatively compact with good image quality. These systems have a wide field of view, which is difficult to provide using waveguides. Despite all the advantages, birdbath schemes have poor light transmission (blocking about 75% of environmental light) [22], which cannot be increased. At the same time, there are bright monochrome self-luminous displays that allow us to increase transmission in such systems by using a spectrum-selective coating with a high-reflection coefficient for only one wavelength. This coating can be a dielectric one, in which the maximum reflection coefficient is provided only for a certain angle of incidence or a holographic coating. In holographic combiners, the reflection coefficient can keep the same value for a range of angles, if this is spelled out in the recording scheme. Holographic highly selective combiners are the specific basis of the system described in this paper. This solution is not suitable for every AR task, but it still has certain prospects in manufacturing, aviation, and navigation, where the output of monochrome information is sufficient.
The paper raises questions concerning the development of off-axis holographic components that have not been fully discussed in the literature. The proposed methods take into account the specifics of holographic mirrors as part of the HMD, highlighting the relevance of this work. The research incorporates the computation methodology for holographic mirrors utilized in a FSC, the design of the recording system for holographic mirrors (considering photosensitive material shrinkage), the FSC layout principles that depend on holographic mirror parameters, the assessment of parameters implicated in the image quality, and the FSC testing under multifocal mode.
2. THEORETICAL ANALYSIS
A. Requirements for the Optical Scheme
The FSC analyzed in this work includes two optical elements: a holographic flat mirror (HFM) and a holographic spherical mirror (HSM). The schematic diagram of such a system is shown in Fig. 1(a).
Fig. 1. (a) Schematic diagram of an off-axis FSC (view from the side): green lines, beams reflected by the HFM; blue lines, beams reflected by the HSM. (b) Diagram of the Bragg mirror to explain Eq. (1). (c) Schematic diagram of a co-axis FSC (view from the side): green lines, beams reflected by the HFM; blue lines, beams reflected by the HSM.
The HSM focuses beams going into the user’s eye, and the HFM is necessary for breaking the optical axis at an angle of 45° and minimizing the dimensions of the device. Each mirror is a glass substrate, flat or spherical, covered with a layer of three-dimensional photosensitive material with a phase hologram of the mirror. Both holographic mirrors are recorded in colliding beams by the Denisyuk method and operate in the Bragg diffraction mode [23]:
where ${\rm K} = {2}\pi {\rm /}\Lambda$ represents the constant of the Bragg grating with period $\Lambda$ in the direction of in-phase surfaces shown at Fig. 1(b), $\beta = {2}\pi { /}\lambda$ is the mean propagation constant for radiation with wavelength $\lambda$, $n$ is the refractive index, $\gamma = {0}$ is the inclination angle of in-phase surfaces, and ${\theta _n}$ is the angle of incidence in the medium of the Bragg grating.As shown in Fig. 1(a), the HFM first deflects the rays from the projector towards the spherical mirror with a high-reflection coefficient. Then the radiation is reflected back by the HSM. The HFM transmits the light freely into the user’s eye (exit pupil) with the maximum transmission coefficient. From an optical system design perspective, the spectral-angle selectivity of the HFM should be such that radiation reflected from the HSM enters the user’s eye, rather than being re-reflected from the HFM. Geometrically, this requirement means that at any point on the HFM, the angular deviation between rays reflected and incident by the HFM must exceed the angular selectivity $\Delta \theta$. This ensures a high-reflection coefficient when rays are reflected by the HFM and high-transmission coefficient when rays pass through the HFM in the opposite direction.
In the co-axis scheme, as Fig. 2(c) shows, the axial ray after reflection from the HSM falls at the same point for the second time on the HFM by the same angle. Then, in both cases, the Bragg condition [Eq. (1)] will be satisfied. As a result, there will be a vanishing effect of the central part of the image, and a very low brightness at the image center should be expected. Thus, the axial arrangement of two holographic mirrors is unacceptable for the chosen scheme of the AR display. This necessitates an off-axis arrangement, which means tilting the spherical mirror to an angle exceeding the angular selectivity to disrupt the Bragg condition in the field center. The tilting angle is presented by $\psi$ in Fig. 1(a).
Fig. 2. Ray path in the FSC unfolded relative to the HFM: ${\delta _1}$, ${\delta _2}$, angular deviations from Bragg directions at primary and secondary incidence to the HFM; C, center of the entrance pupil; $\omega$, field of view; ${h_{\rm{in}}}$, ${h_{\rm{out}}}$, half-width of the entrance and exit pupils.
B. Selectivity Constraints
Figure 2 shows an expanded ray diagram of the off-axis FSC with introduced tilt $\psi$ of the HSM relative to the co-axial arrangement at Fig. 1(c). For the analyzing convenience, the ray path is given in the unfolded form relative to the HFM. The green lines show the directions of the rays provided by the object beam during the recording of the HFM. The blue lines are rays propagating to the exit pupil. Here ${\delta _1}$ is the deviation from the HFM Bragg angle for the rays coming from the entrance pupil, and ${\delta _2}$ is a deviation from the HFM Bragg angle after reflection from the spherical mirror. The feature of the FSC scheme based on holographic mirrors consists of tilting the axis of the spherical mirror relative to the axial beam in the field of view by some angle $\psi$. No rays reflected by the HSM should satisfy the Bragg condition when they meet the HFM for the second time, i.e., when passing through the HFM in the direction of the exit pupil. Therefore, the FSC off-axis scheme is based on the elements for co-axial geometry. It is achieved by the joint rotation of the flat and spherical mirrors in the meridional section by the $\psi$ angle, which was chosen for constructive reasons.
All rays from the center C and nearby points of the entrance pupil FSC fall on the HFM under the Bragg condition, experiencing maximum reflection. Field rays far from the pupil center fall on the HFM with a deviation ${\delta _1}$ from the Bragg angle and are attenuated when the deviation gets higher. In contrast, the transmittance should be maximized in the back-ray path, and this transmittance will be ${\delta _2}$.
The selectivity depends on the modulation properties of the recording medium and the parameters of the Bragg grating in the local section of the mirror. For the estimation of HFM selectivity, one can use the coupled wave theory [23]. Moreover, the selectivity calculation will depend on the grating parameters in a particular section of the field.
The period of the volume diffraction grating $\Lambda$ should increase from the center of the mirror to the edge, as Fig. 1(a) shows. The selectivity will differ at the center and at the edge of the field. Both spectral and angular selectivity can be determined by plotting the contour of the dependence of diffraction efficiency $\eta$ on the magnitude of the deviation from the Bragg condition, using the equations
ν represents the modulation parameter, which characterizes the change of medium parameters in the recording area); ${n_1}$ is the refractive index modulation; T is the photosensitive layer thickness; ${c_{\rm inc}} = \cos \theta$, ${c_{\rm dif}} = \cos \theta - \cos \gamma \cdot{\rm K}/\beta$ are the angular coefficients of incident and diffracted waves on the Bragg mirror; $\xi$ is the mismatch parameter, which characterizes the selective properties of the Bragg grating; $\vartheta$ is the dephasing coefficient, which characterizes the permissible deviations from Bragg conditions and allows us to relate angular and spectral selectivity.
To determine the off-axis tilt angle $\psi$, we perform a preliminary numerical evaluation of the HFM selectivity value at the edge of the field. Thick layers of dichromated gelatin (DCG) are used as a material for HFM and HSM recording [24]. The resolution of this material can reach ${10000}\;{{\rm mm}^{- 1}}$, and the refractive index is $n = {1.52}$. According to preliminary exposure tests, the refractive index modulation can reach the order of ${n_1} = {0.01}$, and the layer thickness can vary depending on the application; in our case, T is 25 µm.
If the required angular field is $\omega = [- {20},\;{20}]\;^\circ$, then the maximum angle of incidence in the air on HFM tilted at an angle of 45° should be $\theta = {65}^\circ$. In a medium with refractive index $n = {1.52}$, this angle is ${\theta _n} = {36.6}^\circ$. The reconstruction wavelength applied in the system is $\lambda = {546}\;{\rm nm}$. According to Eq. (1), the period of Bragg mirror inside the medium will be $\Lambda = {224}\;{\rm nm}$; in this case, the required resolution of photosensitive medium should be about ${4470}\;{{\rm mm}^{- 1}}$. By Eqs. (2)–(5) we calculate the dependence of diffraction efficiency within the deviation from the Bragg condition in air $\Delta \theta = [- {3},\;{3}]^\circ$. Figure 3 shows the calculation results for two local gratings of the HFM corresponding with 20° and ${-}{20}^\circ$ FSC fields of view.
Fig. 3. Diffraction efficiency analysis for the reflection Bragg grating made of DCG: (a) angular selectivity plots for field of view edges and (b) spectral selectivity plots for field of view edges.
The selectivity is determined by the full width of the half-maximum $\Delta {\theta _{{\rm HFM} \max}} = {0.972}^\circ$, $\Delta {\theta _{{\rm HFM} \min}} = {0.278}^\circ$, $\Delta {\lambda _{{\rm HFM} \max}} = {35.12}\;{\rm nm}$, and $\Delta {\lambda _{{\rm HFM} \min}} = {9.84}\;{\rm nm}$. In this case, as Fig. 3 shows, at the edge of the field $\omega = {20}^\circ$, the mirror continues to filter radiation within the entire range of deviations under consideration.
In order to accurately meet the requirements in real conditions and with real properties of photosensitive materials, when the parameters may differ from the calculated ones, we will tentatively accept $\psi = {6}^\circ$. This exact value will be realized during the holographic recording.
C. HFM Holographic Recording
According to the HFM arrangement, the central ray of the field of view should correspond to the angle of incidence ${\theta _0} = {45}^\circ + \psi = {51}^\circ$ and be passed by the HFM in the direction of the pupil of the observer’s eye with minimal losses.
Figure 4(a) shows the optical scheme of the HFM recording setup. The HFM is a phase hologram formed by the refractive index modulation obtained by interference of a beam with a spherical wavefront and the same beam reflected from a flat or spherical mirror. The elements were recorded on photographic plates with a recording layer 25 µm thick based on DCG using a solid-state YAG laser with a wavelength of 532 nm.
Fig. 4. (a) Optical scheme of the HFM recording setup. (b) Schematic diagram for determining the parameters of the object beam during HFM recording: C, center of the FSC entrance pupil; P, point radiation source for the object beam; $T$, $O$, $B$, points selected for determining the position of $P$; ${L_1}$, distance from the mirror to the object beam source (pinhole); ${L_2}$, distance from the center of the entrance pupil to the center of the mirror C.
The radiation from the laser expands along the angular aperture using a negative lens (${-}{1.5}\;{\rm dpt}$) until the linear aperture of the ${40} \times$ microlens is filled after reflection by the mirror. After spatial filtering by the microlens and the point aperture (pinhole with a diameter of 10 µm), the formed homocentric subject beam is directed to the recording photosensitive plate for recording the HFM. The axial point $O$ of the recorded HFM on the plate is located at the calculated distance ${L_1}$ from the center $P$ of the homocentric divergent beam being formed at the calculated angle ${\varphi _1}$ of the beam incident on the mirror.
The recording substrate with a photosensitive DCG layer is located horizontally on the installation and is turned downwards by a photosensitive layer in contact with a flat metallized mirror. The flat mirror forms the object beam, which goes in the opposite direction to the incident beam and interferes with it in the volume of the recording layer. This is equivalent to recording the HFM in counter homocentric colliding beams with the formation of interference field antinodes parallel to the plane of the plate during recording. As a result, a holographic flat mirror is recorded.
Figure 4(b) shows a diagram illustrating the calculation of the parameters ${L_1}$ and ${\varphi _1}$, which determine the position of the center $P$ of the object beam in the HFM recording scheme when using radiation with a wavelength of ${\lambda _{1}} = {532}\;{\rm nm}$, which is different from the reconstruction wavelength ${\lambda _2} = {546}\;{\rm nm}$.
Since DCG is hygroscopic, the shrinkage of the K recording layer during post-exposure processing must be taken into account in the calculations. Estimated by the ratio of the thickness of the recording layer before and after the specified photochemical treatment, this parameter is preliminarily assumed to be equal to К $ = {0.96}$ (determined experimentally).
The algorithm for calculating the position of the center of the subject beam P when recording the HFM consists of the following steps.
- (1) Calculating for the selected points $T$, $O$, and $B$ in the main section of the HFM the period $\Lambda$ of the interference structure in the recording layer as in Fig. 4(b); the coordinates of the ${x_i}$ calculated points on the mirror for point $B$ ${x_1} = OB$, for point $O\;{x_2} = {0}$, and for point $T$ ${x_3} = - OT$.
- (2) Calculating for the same points the angles of incidence ${\varphi _1}$ of rays in the subject beam with a wavelength ${\lambda _1}$, providing the same period $\Lambda$ of the interference structure in the recording layer. The position of the center of the object beam P is the intersection point or area of intersection of the rays forming the object beam. The angles of incidence of rays ${\varphi _{2i}}$ are determined by the equation
According to the optical scheme, we assume ${L_2} = {186}\;{\rm mm}$ (Fig. 2). The angles ${\varphi _{{\rm n}2 I}}$ between the refracted rays of the beam incident on the HFM in the recording medium with a refractive index ${\rm n} = {1.52}$ and the plane of the photosensitive plate are equal to
$${\varphi _{{\rm n2}\;i}} = \frac{\pi}{2} - \arcsin \left({\frac{{\arcsin {\varphi _{{\rm n2}\;i}}}}{n}} \right).$$The period ${\Lambda _2}$ of the interference structure in the recording layer ensures the fulfillment of the Bragg condition when the incident beam with a wavelength of ${\lambda _2}$ and by an angle of ${2}{\varphi _{{\rm n}2 I}}$ is reflected from the HFM inside the photosensitive emulsion. It is calculated in accordance with the known diffraction grating equation:
The period ${\Lambda _1}$ of the interference structure in the emulsion when recording at the wavelength ${\lambda _2}$ with the angle ${2}{\varphi _{{\rm n}1 i}}$, taking into account the shrinkage coefficient K, will be calculated as
Considering ${\Lambda _{1}}\; = {\Lambda _2}$ from (8) and (9), we obtain the angles ${\varphi _{{\rm n}1 i}}$ between the object rays refracted in the photosensitive plate and the plane of this plate when recording the HFM:
- (3) Calculating the position of the center of the object beam P as the intersection point or the central point of the intersection area of the rays of the object beam. The sequential application of Eqs. (6)–(11) gave the following values of the angles ${\varphi _{1i}}$ of the object beam when recording the HFM: $\varphi_{11} = 54.6^\circ$, ${\varphi _{12}}\; = {48}^\circ$, and $\varphi_{13} = 39.9^\circ$. The graphical representation using the found values of the angles ${\varphi _{1i}}$, as shown in Fig. 4(b), gave the following values of the parameters determining the position of the object point $P$ when relative to the mirror point on the FSC axis: ${L_1} = {194.4}\;{\rm mm}$ and ${\varphi _1} = {47.9^\circ}$.
D. HSM Holographic Recording
The HSM should be a three-dimensional holographic structure registered in a thick DCG layer deposited on a concave spherical surface. When working as part of the FSC, the HSM provides an effective reflection of a radiation beam with a wavelength of 546 nm at a beam angle of incidence of $\theta = \psi = {6}^\circ$. The holographic layer on the HSM should make minimal losses in the lumen study passing through it.
Figure 5(a) shows an optical scheme of the HSM recording installation, according to the general principles of construction; a similar scheme of the HFM recording installation is shown at Fig. 4(a), with the exception of a concave spherical metallized mirror. The axial point $O$ of the recorded HSM is located at the calculated distance ${L_1}$ from the center P of the homocentric divergent beam being formed at the calculated angle ${\varphi _1}$ of the beam incidence on the HSM.
Fig. 5. (a) Optical scheme of the HSM recording setup. (b) Schematic diagram for determining the parameters of the object beam during HSM recording: C, center of the FSC entrance pupil; P, point radiation source for the object beam; R, spherical mirror radius; $T$, $O$, $B$, points selected for determining the position of P; ${L_1}$, from the mirror to the object beam source (pinhole); ${L_2}$, distance from the center of the entrance pupil to the center of the mirror C.
The presence of a spherical mirror in the composition of this design ensures, after reflection of the radiation has reached the mirror layer, the formation of a homocentric beam converging at a point that is an image of point P. As a result, the scheme provides HSM recording in colliding homocentric beams with the formation of the interference field in the emulsion layer during recording, parallel to the mirror surface at each point.
Figure 5(b) shows a diagram illustrating the calculation of the parameters ${L_1}$ and ${\varphi _1}$, which determine the position of the center P of the object beam of rays in the HSM recording scheme, as shown at Fig. 5(b). The value of ${L_2}$ in the calculations of the geometry of the HSM recording scheme is greater than the values of this parameter for the HFM recording scheme (186.15 mm) by the value of the distance between the HFM and HSM, which is 35 mm. Therefore, here ${L_2} = {221.15}\;{\rm mm}$.
The algorithm for calculating the position of the center of the subject beam P when writing the HSM is similar to the algorithm given above for the HFM. The difference here was that the angles of incidence ${\varphi _{2i}}$ of the rays incident on the HSM from point C, which is the center of the pupil of the entrance to the FSC, from the scheme in Fig. 5(b) were defined as
Calculations with the sequential application of the ratios (12) and (8)–(11) gave the following values of the angles of incidence ${\varphi _{1i}}$ of the beams of the object beam when writing the HSM: ${\varphi _{11}} = {13.35^\circ}$, ${\varphi _{12}} = {6.78^\circ}$, and ${\varphi _{13}} = {3.17^\circ}$, respectively, for points $B$, $O$, and $T$ of the mirror. The graphical representations using the found values of the angles ${\varphi _{1i}}$, as shown in Fig. 5(b), gave the following values of the parameters determining the position of the subject point P when writing the HSM relative to the mirror point on the FSC axis: ${L_1} = {188.3}\;{\rm mm}$ and ${\varphi _1} = {7.29^\circ}$.
3. RESULTS OF THE EXPERIMENT
A. Measurement of Key Parameters
Holographic mirrors were recorded following the previously proposed techniques in a layer of DCG that was deposited on glass substrates. In this instance, the devised methods of calculating and recording holographic mirrors, as well as the feasibility of operating such a system in a multifocal display mode, were only conceptualized. Consequently, optical glass was utilized as substrates but, from the point of view of holographic mirrors operation and the FSC in general, the use of glass as a substrate is not necessary. In contrast, the use of transparent polycarbonate substrates for flat and spherical mirrors (can be obtained by molding) is more preferable for this implementation, since they are less fragile and do not increase the risk of eye damage, as well as lighter compared to optical glass.
It should be noted that DCG is an unstable material for producing holographic mirrors from the point of view of ensuring repeatability of parameters, it has high shrinkage and hygroscopicity. At the same time, there are several advantages, namely high transparency and high diffraction efficiency; therefore, it was used in the research process. Its replacement with photopolymers is preferable, but we have not yet investigated the issue of applying photopolymer materials to curved substrates, while it has been worked out for DCG.
The production of a DCG layer of the required thickness on substrates for flat and spherical mirrors is provided by the molding method. At the first stage, the substrate and cover glass are prepared and cleaned. They should have a temperature of about 34–36 deg. The surface of the cover glass should correspond to the desired shape of the surface of the DCG layer, and its linear geometric dimensions of the glass should be larger than the dimensions of the substrates by 5–10 mm. An anti-adhesive layer (e.g., dimethyldichlorosilane) is applied to the cover glass. Next, a DCG solution (prepared according to a standard formulation) is applied to the cover glass with a small excess, and three spacers are installed along the contour on the cover glass. The spacers provide the required layer thickness but, when choosing them, it should be borne in mind that, when drying, the thickness decreases by about 10 times. After that, it is necessary to put the substrate of the future mirror on top so that its surface touches all the spacers. The substrates are then transferred to a cold table to carry out the cooling process. This process takes 30–40 min at a temperature of 8–10 deg. The cover glass and spacers are removed. This is followed by a drying process under normal conditions during the day.
Figures 6(a) and 6(b) show photographs of the manufactured HFM and HSM.
In the process of testing the manufacturing technology of the HFM and HSM with the measurement of the parameters of the manufactured experimental samples, the dependence of the parameters of the samples on the parameters of the technology at all stages of manufacturing, including the storage conditions of the recording material after its receipt from the manufacturer, was established. The most critical is this dependence for the amount of shrinkage to the recording material (DCG layer) from the moment the hologram is recorded to the sealing with protective glass. This is due to the fact that the deviation of the actual shrinkage from the calculated one leads to non-compliance with the Bragg condition for quasi-monochromatic radiation when radiation is reflected by hologram elements. For example, with the calculated value К$\; = {0.96}$, the obtained К$_{\rm real} = {0.93}$ leads to a shift of the value ${\lambda _{\rm{max}}}$ on the measured spectral curve $\rho = f(\lambda)$ from the calculated 546 to 565 nm. When installing such a mirror in the FSC, a significant attenuation of the image brightness should be expected. In this regard, it is necessary to ensure the stability and reproducibility of the parameters of the technological process, including temperature and humidity during each technological operation.
Figure 7(a) shows the dependence curves of the relative intensity for the HFM and HSM, comparing it to the relative intensity of the white source used in measurements [Fig. 7(b)].
Fig. 7. (a) Dependence curve of the HFM (red line) and HSM (yellow line) relative intensity for the mirror point on the optical axis at the incidence angle of $\theta = {51}^\circ$. (b) Relative intensity of the white source.
The estimation of the width of the spectral selectivity contour for two mirrors was carried out using the Jeti Spectraval 1501 spectroradiometer and a white light source, the radiation of which fell on the mirrors. For an HFM operating as part of an FSC at a beam incidence angle of 51°, the measured value of spectral selectivity from Fig. 7(a) was $\Delta {\lambda _{0.5}} \approx \;{12}\;{\rm nm}$. For the HSM, the measured value of spectral selectivity from Fig. 7(a) is $\Delta {\lambda _{\lambda 0.5}} \approx \;{25}\;{\rm nm}$. The higher selective properties of the HFM compared to the HSM are due to the operation of a flat mirror at higher values of the Bragg angle in the DCG layer.
Non-zero diffraction efficiency can be observed in other areas of the spectrum, particularly in the blue band, as depicted in Fig. 7(a). In constructing the RGB full-color experiment, unwanted crosstalk may lead to chromatic aberrations. In this case, we will have to increase selectivity, making the diffraction band narrower. This problem can be solved by switching to photosensitive media with a larger dynamic range of the refractive index modulation. For example, in the case of the Bayfol HX photopolymer, the dynamic range exceeds ${n_{1}} = {0.03}$ [25].
The transmittance value $t$ was measured using a white light source and a radiation power meter. For the HFM, the value of $\tau$ was 0.83; for the HSM, the value of $\tau$ reaches 0.8. By multiplying these coefficients, we obtain the value of the total FSC transmission coefficient per lumen, namely 0.67. The measurement of the reflection coefficient $\rho$ of the mirrors was carried out in monochromatic light, using an LED radiation source with a dominant wavelength $\lambda = {0.545}\;{\unicode{x00B5}{\rm m}}$ and a radiation power meter. For the HFM, the values of $\rho$ in the maximum reflectivity reach 0.88; for the HSM, the values reach 0.79. Specifically, the total reflection coefficient at the working wavelength for the FSC is 0.7.
The visual resolution of the FSC is determined on the installation, the photo of which is shown in Fig. 8(a).
A green-emitting LED illuminates a diffuser with a test object located directly behind it. The test object is a plate with a set of dashed targets transparent on an opaque background with a different angular distance $\alpha$ between the strokes known for each zone (when working with a lens with a focal length $f = {1600}\;{\rm mm}$). The test object is located in the front focal plane of the FSC. To exclude the influence of the observer’s visual acuity, the image of the test object is viewed behind the exit pupil of the FSC using a visual tube, while the lens of the tube is diaphragmed to a diameter of 8 mm corresponding to the maximum value of the pupil diameter of the eye. The world is visually fixed with extremely distinguishable strokes of all four directions. The visual resolution of ${\alpha _{\rm{FSC}}}$ in the case of distinguishing worlds with an angular distance between strokes is estimated as
When measuring the visual resolution of the FSC by the layout Fig. 7(b), it was found that an element with a minimum angular size between adjacent strokes of this element $\alpha = {2.{58}^{\prime \prime}}$ angular seconds is clearly distinguishable, i.e., the FSC resolution in accordance with (13) will be ${\alpha _{\rm FSC}} = {{70}^{\prime \prime}}$.
B. Multifocal Imagery
To demonstrate the operation of the system, an installation was assembled for displaying images at three different distances. It should be noted that a number of studies are currently being conducted to ensure the multifocality of augmented reality displays in order to reduce the vergence accommodation conflict of the human eye, which causes discomfort to the user working with the augmented reality system, namely, visual fatigue, eye strain, blurred vision, and headache during and even after using the system. The construction of multifocal systems is possible in several ways: temporal [26–28], spatial [29–31], and polarizing [32–35]. The spatial method can be implemented by using two projection optical systems, which increases the dimensions of the structure due to the need for longitudinal separation of the reflecting screens by a significant distance. Systems based on time multiplexing are interesting because they allow the implementation of varifocal displays with a continuous change in focal length, but require ultrafast devices for moving optical components [36]. The polarization method of implementing multifocal displays is based on a change in the optical distance in the system, depending on the state of polarization; the disadvantage of such a system is a limited number of focal planes. Since there are only two orthogonal polarization states, a polarizing multiplexed display can generate only two independent focus depths. In addition, due to the presence of polarizers in the optical system of the device, the brightness of the output image decreases.
In this work, we study the possibility of providing multifocality in systems based on holographic mirrors reflecting the image projected on them from a monochrome display at the wavelength of its radiation and transmitting the rest of the visible light through the use of a varifocal object, which allows adjusting its focal length from 20 mm to infinity, which may provide the opportunity to rebuild the plane of the virtual object forming images by the focal length range or accommodation distances.
To demonstrate the operation of the system, an installation was assembled for displaying images at three different distances. The scheme of the system is shown in Fig. 9. The radiation from the microdisplay hits the varifocal lens, which forms intermediate images. After that, the radiation is reflected from the HFM to the HSM, which transmits an intermediate image and redirects the radiation to the user’s eye through the HFM, which already operates in transmission mode. When the focal length of the lens is changed, the accommodation distance of the virtual images will change.
The installation shown in Fig. 10(a) consists of a layout of FSC systems, which includes two holographic mirrors and varifocal lens, which includes a lens with a variable focal length and a monochrome ($\lambda = {0.532}\;{\unicode{x00B5}{\rm m}}$) Si-OLED display as a radiation source. At a distance of 20 mm, 200 mm, and infinity (represented by a distance of 3 m) from the device, mounting posts with corresponding distance designations were located as Fig. 10(b) shows to check the position of the focusing plane (image reproduction), i.e., the multifocality of the system.
A number of test images that were obtained using the assembled system are presented in Fig. 11. The information is displayed in three different planes by changing the focal length of the varifocal lens. In this study, we used a lens with mechanical movement of optical components, but the use of liquid lenses for this task in the future will allow us to move the focusing plane at high speed. When the image is projected to infinity and the camera focuses to infinity, as Fig. 11(a) shows, the image is clearly visible. At the same time, if you focus the camera at a distance of 200 mm, as Fig. 11(b) shows, the image will be blurred, when focused at a distance of 20 mm. The text is blurred even more, as Fig. 11(c) shows.
Fig. 11. (a) Image at infinity; the camera focuses on infinity. (b) Image at infinity; the camera focuses on a distance of 200 mm. (c) Image is at infinity; the camera focuses at a distance of 20 mm. (d) Image is at a distance of 20 mm; the camera focuses at a distance of 20 mm. (e) Image is at a distance of 200 mm; the camera focuses at a distance of 200 mm.
Since the size of the field of view changes when the focal length changes, for the appropriate comparison of the results obtained, the scale of the output image was additionally changed so that it was commensurate at each distance.
Thus, it is confirmed that the off-axis FSC based on two holographic mirrors can operate in the multifocal display mode. At the same time, it should be noted that the efficiency of transmitting radiation from the display to the eye of the user of such systems is significantly higher (i.e., lower losses in the optical system) than in schemes based on beam splitters due to the use of mirrors, whose reflection coefficients are high (but for one wavelength), and do not depend on the polarization of the radiation and are the same throughout the range of angles of incidence [36].
4. CONCLUSION
This paper describes a method for calculating parameters and a recording scheme for holographic mirrors for the HMD. It is shown that, when using two holographic mirrors, an off-axis implementation of the FSC is required since, with the axial scheme, partial image attenuation occurs in the paraxial area due to the selectivity of the HFM. When using the FSC with holographic mirrors, the following parameters are provided: the total reflectivity of the FSC in the virtual image generation channel is 0.7, and the total transmittance of the FSC is $\tau = {0.67}$, which confirms sufficiently high efficiency of this system, in comparison with similar variants made on the basis of classical beam-splitting or polarization coatings.
At the same time, this configuration is interesting to the developers of AR optical systems because, unlike waveguide-based systems, multifocality can be implemented in it, i.e., the output of augmented reality images at different distances. Experimental studies were conducted on the possibility of image output at distances of 20 mm, 200 mm, and infinity (represented by a distance of 3 m), as a result of which a conclusion was made about the correct operation of the system.
Funding
Bauman Moscow State Technical University (Priority 2030).
Acknowledgment
The authors acknowledge support from Maria Shishova in processing the results of the experiment.
Disclosures
The authors declare no conflicts of interest.
Data availability
No data were generated or analyzed in the presented research.
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