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Abstract
We report a switchable holographic optical element based on a liquid lens for a see-through display. For the switchable holographic optical element, we recorded two optical components in the holographic film in two steps. A numerical simulation was also done to define the recording and reconstruction conditions. After the recording process, the entire system was changed from 4f optics to Maxwellian optics by changing wavefront of the reference wave using a liquid lens. The diffraction efficiency was 0.46 for a single element recording and around 0.14 for a double element recording. The holographic display and the Maxwellian display were successfully switched without any crosstalk. The field of view and eye box of the holographic display were 1° and 4.36 mm, respectively, and the field of view and the eye box of the Maxwellian display were 3.8° and 23.2 um, respectively. In the proposed system, spatial frequency filtering by the liquid lens and image shape distortion seriously affected the hologram image. However, we successfully verified the feasibility of our proposed switchable holographic optical element using a liquid lens.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Digital holographic display is an effective and a useful technology in various fields [1]. The digital holographic display can provide a nature scene-like object in the air by controlling the phase and amplitude of the light. Hence, the digital holographic display is considered a promising technology for next generation displays [2]. Basically, the amplitude and phase of the light are modulated by a spatial light modulator, such as a transmissive liquid crystal [1], a liquid crystal on silicon (LCOS) [3,4], or a digital mirror device (DMD) [5], etc. Although the digital holographic display has progressed tremendously by advanced semiconductor technology, it still has inevitable obstacles for commercialization, such as a small field of view (FOV), a small exit pupil, DC noise and high order noise, etc, because of the large spatial bandwidth of the spatial light modulator (SLM) [6–12]. Although most of these issues can be solved by decreasing the pixel pitch, unfortunately, current available spatial light modulators are not enough to provide a large hologram for multiple observers. Thus, current holographic display is specified for single user. Thus, most holographic displays use 4f optics with a spatial filter to eliminate DC noise and high-order noise and to compensate for chromatic aberration. However, although 4f optics is a direct solution to create a clear hologram, the 4f optics needs two solid lenses, which makes the device too heavy to use for see-through displays like head-mounted displays and glasses.
A volume holographic grating is utilized as optical elements like lenses or mirrors. They are space-saving, lightweight, wavelength and angle selectivity, transparent and potentially low-cost [13]. Additionally the volume holographic grating does have the advantage of adding freedom to the optical design process, as incidence and exit angle can be chosen independently. In addition, multiplexed volume holographic grating (or multiplexed HOE) reconstructs all multiple wave simultaneously, when reference wave enter into the multiplexed volume holographic grating [14]. In this paper, we found that the changing wavefront of reference wave by liquid lens can select the each recorded holographic optical elements. Thus, entire optical system can be changed by combination the liquid lens and the holographic film. Not only does this increase the freedom of the optical system, it is expected to be effective in terms of weight and cost. Therefore, we mainly focused on demonstrating the feasibility of the switchable holographic optical element.
In our previous research, we put together both a holographic display and a Maxwellian display using a liquid lens [15]. The Maxwellian display, which offers images that are always focused to the retina, provides extended information for the observer [16–18]. In addition, the Maxwellian display increases the availability of see-through displays for people with vision problems such as presbyopia and myopia [19].
In this paper, we described our design of a switchable holographic optical element based on a liquid lens for see-through display. The switchable holographic optical element recording setup and reconstruction setup are described in section 2. Then the optical characteristics of the switchable holographic optical element are given in section 3. Finally, concluding remarks are in section 4.
2. Design and theory of see-through display based on switchable holographic optical elements
2.1 System specification
Our proposed switchable holographic optical element based see-through display configuration was illustrated in Fig. 1. A SLM (Holoeye, LC-2012) was used and the wavelength of the laser source was 633 nm (SIGMAKOKI, 05-LHP-121). A linear polarizer was used to set phase mostly mode for the SLM. A liquid lens (Optotunes, EL-10-30-TC) was combined with a concave lens to adjust the diopter from 0 D to 20 D. The SLM, the liquid lens, and a holographic optical element were put in the same interval with f as shown in Fig. 1. When liquid lens was set to 20D, a concave mirror of 20 D is recorded on the hologrpahic optical element. On the other hand, when the liquid lens was set at 0 D, the reference wave became a plane wave. Then, a concave mirror of a 6.7 D was recorded in the holographic film. After recording, we chose the reconstructed wave by switching the reference wave using liquid lens as shown in Fig. 1(b). Therefore, when the liquid lens was set at 20 D, the entire system became 4f optics. On the other hand, when the liquid lens was set at 0 D, the entire system became the Maxwellian display optics. Our holographic film (Litiholo, C-RT20) had a 99% diffraction efficiency in a monochromatic condition in the best recording condition. Generally, high order diffraction and DC noise should be considered to get holographic see-through display. If the pixel pitch is sufficiently small, the high order diffraction is located outside of the pupil. Assuming that the pupil size (exit pupil) is 7mm, 4.5 um pixel pitch is enough to rid out high order diffraction. Unfortunately, the pixel pitch of our used SLM was insufficient to rid out high order diffraction. Thus, we only considered DC noise in this study. A DC block filter was used to eliminate DC noise [20]. All items used in this study were listed in Table 1. A refractive index modulation of holographic film was not provided by company, hence it was calculated using diffraction efficiency, thickness and wavelength. Detailed will discuss in section 2.2.
Fig. 1 Our proposed switchable holographic optical element based see-through display: (a) switchable holographic optical element recording setup, and (b) reconstruction setup.
Table 1. Specifications of the spatial light modulator, liquid lens, and holographic film.
2.2 Basic theory of holographic optical elements
A holographic film is a kind of photopolymer, which is polymerized by incident of light. Thus, interference pattern between different waves can be recorded in the holographic film as shown in Fig. 2. In the holographic optical elements, an angular selectivity, a wavelength selectivity and a diffraction efficiency are major factor to characterize the performance of the holographic optical element [14]. Among them, the diffraction efficiency is the most important to reconstruct clear object wave. Thus, before experiment, a numerical simulation of the diffraction efficiency was performed to determine the recording condition. Kogelnik’s coupled wave theory was used to simulate the characteristics of the holographic film because of its simplicity [21]. The diffraction efficiency is associated with the wavelength, angle of reference wave and object wave, average refractivity, refractive index modulation, and thickness. However, all items, except the angle between the reference wave and the signal wave, depend on the holographic film characteristics [21,22]. There are ways to improve the refractive index modulation by adjusting the total exposure dosage, the power density of the writing beams, and the ratio of power in the reference and signal beams, etc [23,24]. However, we did not address improvement of the refractive index modulation in this study. Hence, we had to adjust the angle of reference wave and object wave to obtain the optimal diffraction efficiency. Relationship between the diffraction efficiency and the angle between reference wave and object wave was calculated for comparing with measured results.
The diffraction efficiency of the lossless reflection volume holographic grating can be described as
where and denote the coupling variable and Bragg mismatch variable, respectively. When and are equal or is bigger than , the diffraction efficiency converges to 1. Thus, increasing refractive index modulation or increasing film thickness are direct solutions for improving diffraction efficiency. Hence, the angle between reference wave and object wave is the only value for changing as we mentioned before.where d and Δn respectively denote the thickness and the refractive index modulation of the holographic film, and θR and θO are respectively the angle of reference wave and object wave. is Bragg mismatch variable and Γ is the Bragg mismatch coefficient which is related to the angular deviation and wavelength deviation [14]. However, Bragg matched condition was only considered in this study, hence was a constant.Unfortunately, refractive index modulation of holographic film was not provided from company. Therefore, we calculated refractive index modulation by Eq. (4) [14]. In this study, refractive index modulation was 0.03.
The angle of object wave was fixed with 0° as shown in Fig. 2. Thus, the diffraction efficiency was calculated by changing the angle of the reference wave. When the angle of reference wave was increased, the diffraction efficiency was decreased from 0.66 to 0.16 as shown in Fig. 3. In other words, if the reference wave passed through the perpendicular direction of the holographic film, the diffraction efficiency showed maximum diffraction efficiency. However, assuming that a human head was placed in front of the holographic film as shown in Fig. 4, the angle of reference wave of less than 60° was impossible.
Fig. 3 Numerical simulation results of the diffraction efficiency with reference wave angle variation.
Thus, the angle of reference wave (θR) was set at 60°. Then, the diffraction efficiency showed 0.44 in numerical calculation and measured result showed 0.46 that was a similar with calculated one.
2.3 Switchable holographic optical elements based on liquid lens
Usually, multiplexed volume holographic grating is recorded interference pattern between a reference wave and multiple object waves. Then, the reference wave can reconstructs multiple object waves with maximum efficiency [25,41]. The holographic film is a thick photopolymer, kind of dry film with sensitive on visible light [13,14]. Thus, thick photoresist needs a sufficient exposure time or an exposure dosage for polymerization of holographic film. If exposure time and exposure dosage are not enough, the photoresist polymerize only some area as shown in Fig. 5. Some researchers were applied this phenomena in grayscale lithography of MEMS [26].
In this study, two different interference patterns were recorded by controlling exposure time as shown in Fig. 6. Intensity of reference wave and object wave were 0.125 mW/cm2 which was manually controlled with neutral density filter. Exposure energy for fully polymerization was 20 mJ/cm2 as shown in Table 1. Thus, a single object wave was recorded for 80 seconds. In this case, intensity of diffracted light and transmitted light were measured with 0.07 mW and 0.08 mW, respectively. Thus, the diffraction efficiency showed 0.46. The intensity of each waves were measured with laser power meter (SANWA). The diffraction efficiency can be described as
and denote intensity of diffracted light and intensity of transmitted light, respectively. On the other hands, in order to get switchable holographic optical element, each interference patterns between reference wave and object wave were recorded step by step. Firstly, interference pattern between 20 D lens and mirror was recorded for 60 seconds as shown in Fig. 6(a). Then, interference pattern between 0 D lens and 6.7 D lens was recorded for 20 seconds as shown in Fig. 6(b). Total exposure energy of those two processes was 20 mJ/cm2.Although it was not captured with TEM or Microscopy, it is expected that the interference patterns will be recorded in two layers inside the holographic film. Usually, photopolymer begin polymerization from the surface [27,28]. Thus, first interference pattern would be recorded near the surface of the holographic film as shown in Fig. 7(a). Then second interference pattern would be recorded inside the surface of the holographic film as shown in Fig. 7(b). After those process, the holographic film which was recorded two interference patterns would be get as shown in Fig. 7(c). In this case, the holographic film is half the thickness because it is like being separated into two layers. Actually, the diffraction efficiency decreased to 0.14 at 8 um film thickness in numerical calculation. However, measured results of each object waves also showed 0.17 and 0.18, respectively.
Fig. 7 (a) Object wave 1 recording illustration, (b) Object wave 2 recording illustration, and (c) Recorded holographic film with 2 layers.
Object waves change as reference wave changes by the liquid lens as shown in Fig. 8 (Visualization 1). It showed clearly changed object wave without any crosstalk between object waves. Recording condition and diffraction efficiency of our proposed switchable holographic optical elements were listed in the Table 2.
Fig. 8 (a) Reconstructing object wave 1 (Lens) and (b) reconstructing object wave 2 (Mirror) (Visualization 1).
Table 2. Holographic Film recording condition and diffraction efficiency.
Also, the angular selectivity is an important value to avoid crosstalk between object waves because the plane wave has the constituent parts of a spherical wave. Hence, we expected that the crosstalk between objective waves would be caused slightly. Whereas it was not caused in the experimental results as shown in Fig. 13 and 16. Although the angular selectivity was 2.1° which was not a good results in numerical calculation in this study, theoretical reasons were not found out yet. Thus, Relationship between crosstalk and angular selectivity needs a further study.
3. Realization of see-through display based on holographic optical elements
3.1 Realization of see-through display and image shape distortion
Switchable holographic optical elements recording system was assembled on the optical table as shown in Fig. 9(a).
Fig. 9 (a) Recording setup of switchable holographic optical element film and (b) See-Through Display system based on switchable holographic optical elements.
After recording process was done as we mentioned in chapter 2.2, mirrors were removed as shown in Fig. 9(b). Then the focal length of the liquid lens was tuned to switch the reference wave from 20 D to 0 D. As a result, the whole system was changed from 4f optics to the Maxwellian optics as shown in Fig. 6. Usually, the reference wave was off the perpendicular direction of the holographic film [14,41], hence the reconstructed wave made image shape distortion as shown in Fig. 10(b) and 10(e). The distorted hologram can be compensated by adding inverse direction distortion. It can be solve with two options that adding aspherical lens phase to hologram pattern or deformation of original image are. In our case, the hologram was shorten with horizontal direction, therefore, the original image was enlarged horizontal direction.
Fig. 10 (a) and (d) are original images, (b) and (e) are shape distorted hologram images, (c) and (f) are compensated hologram images.
3.2 Hologram generation based on Gerchberg-Saxton iteration algorithm
Generally, there are ways to generate the hologram, such as a point cloud, a triangular patch, and a depth layer [29–31]. Each algorithms has its merits and demerits. For this research, we used a depth-layer hologram, which is widely used. Because the depth layer based hologram can be implemented easier and quicker than the point cloud hologram and the triangular patch holograms [31,32]. In this study, the depth layer-based hologram was processed under sequences.
- 1. 3D object is sliced with several layers.
- 2. Sliced layers pass Gerchberg-Saxton Iteration Algorithm with zero padding to find optimal phase distribution.
- 3. Transfer function (Angular spectrum propagation) is added in complex amplitude of iterated sliced layers.
- 4. Extract phase distribution from the complex amplitude of sliced layers.
The angular spectrum algorithm was used as the transfer function. Because, due to the paraxial approximation of the Fresnel diffraction, using the Fresnel diffraction algorithm causes calculation errors in systems with a high numerical aperture [15,33]. Also, used SLM was set as a phase only modulation. Hence, it needs to retrieval phase distribution by adding a reflection model or the Gerchberg-Saxston Iteration Algorithm (GS algorithm) [34]. GS algorithm is a common method to find out optimal phase distribution for target amplitude distribution and it is widely used in astronomy, biology, display, and so forth. Although GS algorithm gives a precise phase distribution than the other phase retrieval methods [34–36], it takes a lot of time to get proper image quality. However, GS algorithm was done for 100 times in this study. Although it took 5 seconds for each layers, this research focused on the multiplexing both the holographic display and the Maxwellian display, not the real time processing. The hologram generation diagram was illustrated in Fig. 11.
In addition, the liquid lens we used could not cover the entire area of the SLM in our proposed system. When the liquid lens put at the center of the SLM, it worked as low pass filter. Thus, in order to avoid low pass filtering problem, the hologram pattern was generated with 300x300 pixels as shown in Fig. 12(a). Although the hologram showed rough resolution and speckle noise, the hologram became sharper than our previous study as shown in Fig. 12(b) and 12(c) [15], because high frequency component were passed.
Fig. 12 (a) Liquid lens and hologram pattern, (b) Numerical reconstructed hologram of square, and (c) Numerical reconstructed hologram of letter ‘K’.
3D objects for the holographic display were used with square and letter ‘K’ as shown in Fig. 13(a) and 13(d). Each reconstructed hologram placed 50 cm behind the SLM. And the reconstructed hologram was captured by a monochrome CCD camera (Stingray). As you can see in Fig. 13(b) and 13(e), when the camera was focused at 50 cm position, the hologram appeared. The yellow lined boxes in Fig. 13 are magnifications of the captured images. Although the reconstructed hologram showed rough image resolution and large number of speckles because of small number of pixels, the hologram was correctly formed at the intended position.
3.3 Maxwellian display (retinal projection display)
Maxwellian display (or Retinal projection display) is a display technology extremely extending depth of focus (DoF). When small diameter of plane wave enter into the lens of eye, numerical aperture of the plane wave is extremely large. Thus, the DoF becomes large enough to cover changing of eye’s diopter as shown in Fig. 14. For instance, if laser beam enters into the lens of eye, the DoF becomes infinity. Therefore, observer always see clear image as shown in Fig. 15 which was simulated with optical simulation tool (Zemax).
Fig. 15 Simulation results of our designed Maxwellian display, when eye focused at (a) 30 cm, (b) 50 cm, (c) 70 cm and (d) 100cm.
The depth of focus is described as
λ, f and d denote wavelength, focal length and beam diameter, respectively. Actually, the plane wave spreads from the SLM with diffraction angle as shown in Fig. 14. Beam diameter (d) can be determined simple triangular function and it was 1.3 mm. Assuming that length of the pupil was 25 mm, the DoF was 1.7 mm ~1.8 mm. In this case, the Maxwellian images can be seen clearly, when eye focuses on an object from 60cm to infinity.‘KAIST’ letters and bolt used as the Maxwellian images. Then, the camera focused at 50 cm and 1 m and the images were not blurred as you can see in Fig. 16.
3.4 Field of view and exit pupil of proposed see-through display
Field of view (FOV) and exit pupil of the hologram display can be expressed as follows [15,37]:
where p and L denote the pixel pitch of the SLM and the distance between the reconstructed object and the eye. The FOV and the exit pupil of our proposed holographic display were 1° and 4.36 mm, respectively.The FOV and the exit pupil of the Maxwellian display can be expressed as follows [15]:
where f and R are the focal length and the radius of lens. In our proposed system, the recorded lens has a 150 mm focal length and a 10 mm diameter. Thus, the FOV and the exit pupil of our proposed Maxwellian display were 3.8° and 23.2 um, respectively. Thus, large aperture size of the liquid lens are needed to get sufficient FOV and exit pupil [38].The FOV and the exit pupil of our proposed hologram display and Maxwellian display did not sufficiently cover the eye’s movement (the pupil moves +/4mm when the eye gazed at +/−25 deg). However, we expect that it can be solved by applying smaller pixel pitch, larger aperture liquid lens and recording of multiple optical elements [39–42].
4. Conclusion
Holography is a promising technology for various fields, especially in 3D displays. The Maxwellian display is a good candidate for a focus free display. Each type of display has advantages for the observer, but they are difficult to combine in a single system. In addition, optical see-through head-mounted displays are appropriate for use in the current the hologram display and the Maxwellian display. In this context, two different optics were put into one system using the liquid lens from our previous study. However, many lenses are not only heavy and costly, they also have a problem for use in a holographic see-through display because they have a long optical path length. Hence, in this paper, we described our developed switchable holographic optical element film using a liquid lens. We did numerical calculations to optimize the HOE film recording conditions and successfully confirmed switching between recorded signals. The diffraction efficiency was around 0.14 for the signals without any crosstalk. Unfortunately, current proposed see-through display was not enough to meet eye relief condition of conventional near-eye display as shown in Fig. 9. However, our proposed system has a potential to meet near-eye display conditions, if 50 D lens is recorded in the HOE film for the Maxwellian display. In addition, proposed system cannot cover the eye’s movement perfectly (the pupil moves +/4mm when the eye gazed at +/−25 deg), our proposed approach will extend the function of see-through displays and also solve the FOV, the exit pupil, complexity, weight, and cost.
Funding
KAIST (Venture Research Program for Master’s and PhD Students in the College of Engineering).
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