Space bandwidth product enhancement of holographic display using high-order diffraction guided by holographic optical element

Gang Li; Jinsoo Jeong; Dukho Lee; Jiwoon Yeom; Changwon Jang; Seungjae Lee; Byoungho Lee

doi:10.1364/OE.23.033170

1. Introduction

Holographic display is regarded as the ultimate way to provide 3D depth cues for human, since it enables us to reconstruct complex wavefronts of light scattered from 3D objects [1]. To date, the quality of analog hologram reaches quite a high level [2, 3]. Electronic hologram, however, still suffers from a lot of obstacles such as narrow viewing angle, small viewing window (i.e. observable image size), and full color expression. In order to implement high quality video holograms, display devices such as spatial light modulator (SLM), should satisfy very fine pixel pitch and a large number of pixels for providing a sufficient wide viewing angle and a large size viewing window. Space bandwidth product (SBP) is an appropriate metric to evaluate the quality of holographic display. The SBP of a holographic display is defined as the product of the physical dimension and the corresponding 2D bandwidth of the display, which can be regarded as the total pixel count of the device. There are two issues directly related with the SBP level: qualities improvement of the viewing angle and the viewing window. When the SBP is constant, there is a relation of trade-off between the viewing angle and the size of viewing window.

Several studies were carried out for obtaining a high SBP to alleviate the issues about viewing angle and viewing window in the holographic display [4–11]. The common way to achieve the high SBP is using plural SLMs in a system. A typical method that tiles multiple SLMs without gap between the adjacent ones, is arranging them at both sides of a sufficient large beam splitter with regular intervals [4, 5]. Fukaya et al. demonstrated a viewing angle enlarged holographic display by tiling three SLMs in Fourier hologram configuration. Later the system was improved by tiling five higher resolution SLMs. Kozacki et al. proposed a wide viewing angle holographic display system using numerous SLMs in a curved structure [6] which does not need a large size Fourier transforming optics to cover all the SLMs. Hahn et al. also proposed a holographic stereogram system using curved array of a number of SLMs [7]. In this method, in order to remove the gaps resulted from pupils of the transfer lenses, three sub-regions of an SLM were rearranged to be positioned in contact with each other diagonally. Actually, the SBP of a single SLM was not increased because the pixel count in the vertical direction was sacrificed. Other methods for enlarging the viewing angle of the holographic display, which focused on naked eye observation, were proposed [8, 9]. Yaras et al. implemented one of the systems by tiling 9 SLMs; Kozacki et al. demonstrated another one by using additional SLMs placed in a specified image space. When a large size object is reconstructed in a small size viewing window, only a certain part of the object can be observed at a view point. Several methods that arrange multiple 4K × 2K-pixels SLMs in a planar structure to increase the size of viewing window were reported [10, 11]. For all the methods mentioned above, the inevitable problem is need of a large number of SLMs. In fact, considering cost, volume and alignment of the system, using a lot of SLMs to achieve a high level SBP is difficult to be an ultimate solution. Thus, how to increase the SBP for a single SLM is one of the most important issues in this field.

Using high-order diffraction terms of an SLM can be an alternative. High-order diffraction inherently occurs in the holographic display because of the periodic pixelate structure of the SLM. Generally, the high-order terms are regarded as noise to be filtered in most cases. All of them keep the same resolution and information, but have different propagation directions and intensities. Therefore, if the frames of them can be divided by temporal-multiplexing manner, meanwhile the propagation directions and intensities can be appropriately adjusted, the high-orders of a single SLM are able to function as if several SLMs are arranged in the necessary structure. Mishina et al. reported utilization of the high-order diffraction in the holographic display [12]. In the system, they used first and zeroth orders of the reconstructed beams from the hologram with aliasing. Each order image was reconstructed by a certain part of the SLM, thus the entire SBP was not increased.

In this paper, the SBP improvement of a single SLM in the holographic display is proposed by using high-order diffraction of it. The principle of the proposed method is illustrated in Fig. 1. The adopted order images are arranged with the same intensity and propagation direction using guiding optics and temporal-multiplexing system, so that a several-fold increase in SBP of a single SLM is achieved. The guiding optics system consists of holographic optical element (HOE) and a set of relay lenses. One of the important optical characteristics of the HOE is the controllable diffraction efficiency which can be adjusted by controlling the exposure energy in the recording process. For this reason, the HOE which can function as both attenuator and mirror enables us to adjust both the intensity and propagation direction of the reconstructed beams [13–17]. Thus, the guiding optics system can be simplified by utilizing the features of HOE. Meanwhile, the relay lens system is used for obtaining a seamless arrangement of the guided different order images. Section 2 discusses several vital conditions that should be satisfied for using the HOE in the proposed system, and then the recording and reconstruction processes of the HOE are described. Section 3 shows a simple computer generated hologram (CGH) algorithm to compensate wavefront distortion caused by use of the HOE. Finally, the experimental results are demonstrated for verifying the proposed method.

Fig. 1 Schematic diagram of proposed method.

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2. HOE design for guiding high-order diffraction terms of an SLM

The high-order diffraction terms of an SLM carry the same information but have different propagation directions and intensities. Thus, the guiding optics should be able to adjust both direction and intensity for them. Therefore, HOE whose diffraction angle and efficiency can be conveniently adjusted at the same time, is adopted as the guiding optics. First of all, the optical characteristics of the HOE that should satisfy the design conditions are explained.

2.1 Condition for using HOE to guide high-order diffraction terms of an SLM

The waves modulated by a single order of an SLM have various directional components within the diffraction angle range ∆𝜑 = [-𝜑/2, + 𝜑/2], where 𝜑 is the diffraction angle of the SLM. Thus, Bragg-mismatching occurs when we use the waves from the SLM as the probe wave of HOE in the reconstruction process. Therefore, angular variation of the reconstructed wave and the diffraction efficiency distribution according to the angular deviation of the probe wave are analyzed. There are two different ways to record HOE, i.e., reflection and transmission types. In this paper, the reflection type is adopted, and the schematic diagram for the HOE is shown in Fig. 2. Here u and v axes denote the thickness and the transverse directions of the recording material; wave vectors k_s, k_r, and k_p, corresponding to the signal, reference, and probe waves are regarded as plane waves with the same magnitude.

Fig. 2 Schematic diagram of reflection type HOE.

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First, the angular variation caused by angular deviation of the probe wave is discussed. As shown in Fig. 2, the recorded grating vector k_g is given by Eq. (1).

k_{g} = \hat{u} [| k_{s} | \sin (θ_{s \cdot i n}) - | k_{r} | \sin (θ_{r \cdot i n})] + \hat{v} [| k_{s} | \cos (θ_{s \cdot i n}) + | k_{r} | \cos (θ_{r \cdot i n})],

where k_s and k_r are the wave vectors of signal and reference waves inside the medium. The outside signal and reference waves are incident to the medium with the angles 𝜃_s and 𝜃_r, respectively; 𝜃_s·in and 𝜃_r·in are the angles of those waves after being refracted in the medium, which can be calculated by Snell’s law: 𝜃_r·in = sin⁻¹[sin(𝜃_r)/ρ] and 𝜃_s·in = sin⁻¹[sin(𝜃_s)/ρ], where ρ is the refractive index of the recording material. Since shrinkage effect occurs after HOE curing process, the recorded grating vector k_g is changed to k′_g, which is given by Eq. (2),

{k^{'}}_{g} = \hat{u} {\frac{1}{1 + α_{u}} [| k_{s} | \sin (θ_{s \cdot i n}) - | k_{r} | \sin (θ_{r \cdot i n})]} + \hat{v} {\frac{1}{1 + α_{v}} [| k_{s} | \cos (θ_{s \cdot i n}) + | k_{s} | \cos (θ_{r \cdot i n})]},

where 𝛼_u and 𝛼_v are the shrinkage factors of the material along u and v axes, respectively. In the reconstruction process, if a probe wave is incident to the medium, the components of reconstructed wave vector in the u axis can be written as k_c·u = k_p·u + k′_g·u, where k_p is the wave vector of the probe wave. In general, the shrinkage effect occurring along v axis is dominant. Thus, the angle of the reconstructed wave outside the medium can be expressed as

θ_{c} = \sin^{- 1} {\sin (θ_{p}) + \sin (θ_{s}) - \sin (θ_{r})},

where 𝜃_p is the angle of the probe wave outside the medium. If the angle of the reconstructed wave linearly changes according to the angular deviation of the probe wave within the range ∆𝜑, it is legitimate to calculate the guided information by a linear transform from the original hologram.

Second, the diffraction efficiency distribution according to the angular deviation of the probe wave can be calculated using Kogelinik’s theory [18]. The angular selectivity of the reflection type HOE is given by

η = {1 + \frac{1 - ξ^{2} / ν^{2}}{[\sin h^{2} {(ν^{2} - ξ^{2})}^{1 / 2}]}}^{- 1},

where the parameters ξ and ν can be calculated as

\begin{array}{l} ν = \frac{i π Δ d Δ n}{λ {[\cos (θ_{g} - θ_{p}) \cos (θ_{g} + θ_{p})]}^{1 / 2}}, \\ ξ = \frac{π Δ d Δ θ \sin θ_{p}}{Λ \cos (θ_{g} - θ_{p}) - (λ \cos θ_{g}) / ρ}, \end{array}

where 𝜆 is wavelength of the light source, ∆d is the thickness of the material, 𝜃_g = (𝜃_s·in-𝜃_r·in)/2 is slanted angle of the grating, and ∆n is the coefficient of refractive index modulation. In the angular selectivity curve calculated by Eq. (4), the angle range containing high diffraction efficiency should be larger than ∆𝜑, so that it is able to provide a uniform intensity in a single order component of an SLM guided by the HOE.

2.2 HOE recording and reconstruction process

Figure 3 illustrates k-space diagram for explaining the HOE recording process. Because of the shrinkage effect, changed grating vector k′_g induces phase-mismatching when a probe wave, which is identical to the reference wave in the recording process, is illuminated to the HOE. In order to get Bragg-matching condition, ∆K which expresses the amount of the phase-mismatching should be zero. In the actual display process of the proposed method, the vectors of probe wave (k_p) and reconstructed wave (k_c) have been specified, k′_g should therefore be the targeted grating vector for providing the Bragg-matching condition as shown in Fig. 3. In order to obtain the k′_g, the reference wave (k_r) and the signal wave (k_s) with the corresponding compensated angles are used in the recording process. The angles of the signal and the reference waves are derived from [19].

\begin{array}{l} θ_{s} = \sin^{- 1} {ρ \sin {\cos^{- 1} [(1 + α_{ρ}) \sin (Ψ_{+}) \cdot Γ] + \tan^{- 1} [\frac{1 + α_{u}}{1 + α_{v}} \tan (Ψ_{-})]}}, \\ θ_{r} = \sin^{- 1} {ρ \sin {\cos^{- 1} [(1 + α_{ρ}) \sin (Ψ_{+}) \cdot Γ] - \tan^{- 1} [\frac{1 + α_{u}}{1 + α_{v}} \tan (Ψ_{-})]}}, \end{array}

where 𝛼_𝜌 is the shrinkage factor of the material refractive index; Ѱ₊, Ѱ _-, and Г are given by

Fig. 3 Wave vector space diagram of reflection type HOE.

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\begin{array}{l} Ψ_{+} = [\cos^{- 1} (\frac{\sin θ_{p}}{(1 + α_{ρ}) ρ}) + \cos^{- 1} (\frac{\sin θ_{c}}{(1 + α_{ρ}) ρ})] / 2, \\ Ψ_{-} = [\cos^{- 1} (\frac{\sin θ_{p}}{(1 + α_{ρ}) ρ}) - \cos^{- 1} (\frac{\sin θ_{c}}{(1 + α_{ρ}) ρ})] / 2, \\ Γ = \sqrt{\frac{{(1 + α_{v})}^{2} + {(1 + α_{u})}^{2} \tan^{2} (Ψ_{-})}{1 + \tan^{2} (Ψ_{-})}} . \end{array}

As shown in Fig. 4, HOE₁, HOE₂, and HOE₃ are designed for guiding −1st, 0th, and + 1st order parts of the SLM, respectively. Mirror 1 (M₁) and mirror 2 (M₂) enable us to produce reference and signal waves by appropriately adjusting the positions and angles. The reference waves with the angles 𝜃_r₁, 𝜃_r₂, 𝜃_r₃, and signal waves with the angles 𝜃_s₁, 𝜃_s₂, 𝜃_s₃ are used for recording HOE₁, HOE₂, HOE₃, respectively. One of the key advantages of HOE is the adjustable diffraction efficiency which follows the exposure energy used in the recording process. Hence, in order to keep the uniform intensity of the guided different order terms, the exposure energy for recording each HOE should be controlled according to the energy ratio between different order diffraction terms of the SLM. Thus, the properties such as the propagation directions and intensity distribution of high-order diffraction of the SLM are discussed.

Fig. 4 Schematic of HOE (a) recording and (b) reconstruction processes.

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The SLM with periodic pixelated structure can be regarded as a set of square gratings. In a single period, the formula for one dimensional amplitude transmittance function of the SLM is given by Eq. (8)

t (x) = {\begin{cases} 1,_{} {_{}}_{}_{} | x | < a / 2 \\ 0,_{} {_{}}_{}_{} a / 2 < | x | < p / 2, \end{cases}

where a is size of the pixel aperture and p is pixel pitch of the SLM. The square grating can be regarded as superposition of a series of sinusoidal gratings with different spatial frequencies. Let us denote f₁ = 1/p as the fundamental frequency which provides the basic shape of the square grating. Then, coefficient of the Fourier series which determines energy of the diffraction term is given by

\begin{array}{l} T_{n} = \frac{1}{p} \int_{- p / 2}^{p / 2} t (x) \cdot \exp (- j 2 π f_{n} x) d x \\ {_{}}_{}_{} = \frac{a \sin (π f_{n} a)}{p π f_{n} a}, \end{array}

where f_n denotes the frequency of n-th wave, which is an integer multiple of the fundamental frequency. When a plane wave is incident to a single sinusoidal amplitude grating having the spatial frequency f_n, two diffraction terms whose diffraction angles are ± 𝛽_n = sin⁻¹( ± 𝜆f_n) are generated, respectively. It means that high-order diffraction beams of an SLM are the diffraction terms of the Fourier series carrying different spatial frequencies. The intensities of them are also determined by the spatial frequencies and coefficients of the Fourier series expansions. Besides the diffraction on an individual pixel, the phase difference which is induced by the interference among N pixels should also be considered. According to Eq. (9), the intensity distribution of the high-order diffraction beams can be calculated by

I_{n} = {\frac{\sin [π a \sin (| \pm β_{n} |) / λ]}{π a \sin (| \pm β_{n} |) / λ}}^{2} {\frac{\sin [N π p \sin (| \pm β_{n} |) / λ]}{N \sin [π p \sin (| \pm β_{n} |) / λ]}}^{2} .

In this paper, the exposure energy for recording the HOE₁ and the HOE₃ reaches saturation level, and less dosage which depends on the energy ratio between the adopted order terms, is used for recording the HOE₂.

In the reconstruction process, the direction of the reconstructed waves are the same. In this case, the size of the reconstructed beam is determined by the projection angles of the probe wave to the HOE. In order to obtain a uniform size of the three order diffraction images, the three HOEs should be tilted according to the propagation directions of the three images. If 𝜃_p₂ is given, tilting angles of the HOE₁ and the HOE₃ shown in Fig. 4 can be calculated as

\begin{array}{l} ϕ_{1} = \tan^{- 1} (\frac{\sin (θ_{p}_{2} + β_{1}) - \cos θ_{p 2}}{\cos (θ_{p}_{2} + β_{1})}), \\ ϕ_{3} = \tan^{- 1} (\frac{\cos θ_{p 2} - \sin (θ_{p 2} - β_{1})}{\cos (θ_{p}_{2} - β_{1})}) . \end{array}

For convenience of the alignment in the display process, HOE₂ is set to be parallel with x axis and 𝜃_p₂ is specified as 45°. Thus, d_x and d_z shown in Fig. 4(b), which denote the distance of the adjacent HOE center points along x and z axes, are equal to each other. The distance between the centers of the SLM and the HOE₂ is given by d = (d_x/cos𝜃_p)/tan𝛽₁, thus the positions of the HOEs for the reconstruction process can be determined.

Note that the three different order images are observed at different depth planes because of the path length difference d_z. Therefore, a set of relay lenses having different focal lengths are required for imaging them at the same depth plane and with the same magnification. Overall, the three order diffraction images of the SLM can be guided to the same direction with the same interval and intensity.

3. CGH algorithm for compensating wavefront distortion caused by use of HOE

In the point source method, different points in 3D space can be reconstructed (i.e. focused) by superposing the Fresnel zone plates (FZP) that contain different focal lengths and center positions [20, 21]. In the proposed system, the profile of the FZP is distorted after being guided by the HOE since area of the projected beam on the HOE is altered. Therefore, it causes curvatures difference of the FZP between the horizontal and vertical directions. As shown in Fig. 5, the abnormal FZP induces astigmatism aberration, which means the focal lengths along the horizontal and the vertical directions are different, thus targeted spot cannot be reconstructed at the original focal point.

Fig. 5 Astigmatism aberration caused by distorted FZP.

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In the point source CGH method, if all points can be exactly focused at the specified positions, it enables us to reconstruct the 3D object without distortion. In the proposed method, a simple algorithm for rectifying the astigmatism aberration of the FZP is proposed, which is given by Eq. (12). This computation is performed repeatedly until the FZPs of all object points are compensated.

U (x, y) = \frac{A_{o} \exp [i \frac{2 π}{λ} \sqrt{{[(x - x_{o}) / \cos θ_{p}]}^{2} + {(y - y_{o})}^{2} + {(z - z_{o})}^{2}}]}{\sqrt{{[(x - x_{o}) / \cos θ_{p}]}^{2} + {(y - y_{o})}^{2} + {(z - z_{o})}^{2}}},

where A_o and (x_o, y_o, z_o) are the intensity and Cartesian coordinates of an object point. As shown in Eq. (12), the compensation factor is merely related to the angle of probe wave. The proposed algorithm enables us to achieve a hologram that reconstructs the 3D object without the distortion mentioned above, when the HOE is used to guide waves come from the SLM.

4. Experiments

4.1 Optical characteristics measurements of the HOE recording material

In order to verify the feasibility of using the HOE as the guiding optics for the proposed system, several optical characteristics of the photopolymer, which is the HOE recording material used in this paper, are measured. Figure 6 shows the simulations and corresponding experimental results: angular variation of the reconstructed wave and the corresponding diffraction efficiency according to the angular deviation of the probe wave. In the experiments, a DPSS laser with the wavelength 660 nm is used as the light source; Epson L3C07U-85G13 full-HD (1920 × 1080) LCD panel with 8.5 μm pixel pitch is used as the SLM, thus the diffraction angle is 𝜑 = 4.45°. As shown in Fig. 6(a), a precise motorized rotation stage is used for rotating the HOE in the range [-10°, + 10°]. In this experiment, the HOE is recorded under the condition of 𝜃_r = 50.14° and 𝜃_s = 3.47°. The positions of the center spots of the reconstructed beams according to the angular deviation of the probe wave are measured. Meanwhile, the power of the diffracted (P_D) and transmitted (P_T) beams at the corresponding positions are detected to calculate the diffraction efficiency which is defined as [15–17]

Fig. 6 Feasibility measurements of using HOE as guiding optics for the holographic display: (a) Experimental setup. (b) Angular variation of reconstructed wave and (c) diffraction efficiency according to the angle deviation of probe wave.

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η = \frac{P_{D}}{P_{D} + P_{T}} .

The corresponding simulations are carried out using Eqs. (3) and (4). The parameters of the recording material used in the simulation are ∆d = 16.8 μm, and ∆n = 0.04. Figure 6(a) is the experiment setup. Figure 6(b) demonstrates the angular variation of the reconstructed wave is linear in the range ∆𝜑 = [-2.2°, + 2.2°], and Fig. 6(c) shows the diffraction efficiencies are indeed over 95% in the range. According to the results, it has been confirmed that the conditions mentioned in Section 2.1 are satisfactory. Therefore, it is legitimate to use HOE as the guiding optics in the proposed holographic display system.

Diffraction efficiency of photopolymer according to exposure energy are also measured experimentally, and Fig. 7 shows the dosage curve. In the experiment, the diffraction efficiency is saturated when the dosage is over 10 mJ/cm² [22]. According to Eq. (10) and the SLM specifications, the energy ratio between the ± 1st and 0th order diffraction beams are calculated as 0.37:1. As shown in Fig. 7, the diffraction efficiency of the HOE₁ and HOE₃ are marked in red circle; and the blue one is for HOE₂. The exposure energies for recording HOE₁ and HOE₃ reach the saturation level, so that they are able to provide a uniform diffraction efficiency.

Fig. 7 Diffraction efficiency according to exposure energy.

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4.2 HOE recording and reconstruction

In order to get Bragg-matching condition for the design parameters of the reconstruction process, the angles of the reference and signal waves are compensated by using Eq. (6). In the actual HOE recording experiment, the compensated angles of reference and signal waves are as follows: 𝜃_r₁ = 49.99°, 𝜃_r₂ = 50.14°, 𝜃_r₃ = 49.99°, and 𝜃_s₁ = 3.48°, 𝜃_s₂ = 3.47°, 𝜃_s₃ = 3.48°. According to Eq. (11), the tilting angle of the HOE₁ and HOE₃ are 𝜙₁ = 4.6° and 𝜙₃ = 4.3°, respectively.

In the reconstruction process, the intervals of the adjacent HOEs, in x and z axes are both d_x = 25.4 mm, thus the distance from the center of SLM to that of the HOE₂ is 461.5 mm, and 𝜃_p₁, 𝜃_p₂, and 𝜃_p₃, are all 45°. The horizontal size of the SLM is 16.32 mm, then the image sizes after being guided by the corresponding HOEs are all w′ = 23.08 mm. Figure 8 shows the guided three adopted order images of the SLM using the designed HOEs. According to the experiments, it verifies that the HOE is possible to guide the different order diffraction beams of the SLM to an identical direction (i.e. z axis) with a uniform intensity.

Fig. 8 Guided three order terms of the SLM by the HOEs.

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4.3 Experiments for confriming the CGH compensation algorithm

An experiment is carried out for investigating the distortion of the reconstructed hologram. A normal FZP propagate to the HOE by 𝜃_p = 45°. A screen is placed on an optical rail for adjusting the position along z axis. Figure 9 shows the experimental configuration, setup and the captured reconstruction images at different depths.

Fig. 9 Measurement of FZP distortion. (a) Configuration and (b) the experimental setup. (c) The captured reconstruction images.

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Figure 9(c) shows that the reconstructed image is merely focused in the vertical direction at the depth plane z₁ which is the original focal plane of the FZP. Since the FZP is stretched in the horizontal direction by use of the HOE, the focal length along the vertical direction maintains unchanged. As shown in Fig. 9(c), the wavefronts are diverging spherical wave along the vertical direction and converging spherical wave along the horizontal direction within the depth range from z₁ to z₃. It means that the focal length of the FZP in the horizontal direction is extended. Using the algorithm shown in Eq. (12), the FZP can be compensated in the horizontal direction, so that a target spot can be focused at the correct depth plane. Figure 10 shows the experimental results for verifying the compensation algorithm.

Fig. 10 Comparison of the reconstructed holograms: (a) without using the compensation algorithm and (b) using the compensation algorithm.

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4.4 Holographic display using three different order diffraction images with temporal-multiplexing manner

Figure 11 shows the configuration of the proposed holographic display system. In order to remove the gap between guided images in the display process, the relay lenses L₁ and L₂ are designed as square shape. The three order diffraction images of the SLM can be regarded as three virtual SLMs located at different depths along z axis. Thus, a set of relay lenses (L₁), which have the different focal lengths, are used to imaging them at the same depth plane and with the same magnification. The parameters of the relay lenses and the virtual SLMs are listed in Table 1.

Fig. 11 Configuration of proposed holographic display system.

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Table 1. Parameters of the relay lenses and virtual SLMs.

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In order to make the system function as if three SLMs are arranged in the horizontal direction, they are displayed in a temporal-multiplexing manner. In the system, three electro-shutters (Thorlabs Co., SHB05T high speed shutter) whose maximum operation speed are 15 Hz, are synchronized with the corresponding order parts, and an Arduino UNO R3 micro controller board is used for sending the signal to the shutters. According to the frequency specified at the output port of the control board, it sends on/off signals to the shutters and the computer simultaneously. OpenGL and OpenCV library are used for enhancing the display speed of the holograms. The size of the viewing window and the viewing angle of the ultimate display part in the horizontal direction are 50.8 mm and 4.3°, respectively. Figure 12 shows the experiment setup of the proposed holographic display.

Fig. 12 Experimental setup of the proposed holographic display system.

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In order to confirm the advantage of the SBP enhancement, the apertures of the three shutters are released sequentially as shown in Fig. 13. By utilizing the temporal-multiplexing technique, holograms of letters “S”, “N”, and “U” are modulated by −1st, 0th, and 1st order of the SLM, respectively. In Visualization 1 of the Fig. 13, each order term image and the corresponding shutter are displayed with 6 Hz. The result shows that it is able to obtain three-fold increase in SBP of a single SLM. Thus, tripled size of the viewing aperture is provided by the proposed system. Note that, if the virtual SLMs are arranged in a curved structure, the increased SBP is also able to perform a viewing angle enlargement effect.

Fig. 13 Experimental results of the reconstructed holograms by the holographic display with increased SBP (see Visualization 1).

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5. Conclusion

In this paper, an SBP enhancement method is proposed by using high-order diffraction of an SLM. Three HOEs are designed for guiding them to an identical direction with the same intensity. Before using the HOEs as the guiding optics for the proposed holographic display, several optical characteristics of the recording material are measured. In order to achieve Bragg-matching condition in the display process, the HOEs are recorded using compensated reference and the signal waves. The experiment shows that HOE can be used as the guiding optics in holographic display system. A set of relay lenses and electro-shutters are used to implement the display as if three SLMs are arranged with seamless effect. Furthermore, it would be possible to fabricate a color HOE by applying the technique of wavelength multiplexing for implementing a full color display system. In this case, an SLM having higher speed framerate is required. The proposed method can be a solution for getting a high SBP holographic display by using fewer number of SLMs.

Acknowledgment

This work was supported by the IT R&D program of MSIP/KEIT (fundamental technology development for digital holographic contents). The authors acknowledge the support by Covestro AG (formerly Bayer Material Science AG) for providing the photopolymer Bayfol HX film used for recording the HOE.

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Relay lenses				Virtual SLMs
item	center coordinates in x-z plane (mm)	width(w)/diameter(d) (mm²)	focal length (mm)	item	center coordinates in x-z plane (mm)
L_1,1	(−25.4,-23.8)	25.4(w)	341	SLM₁	(−25.4,-705.8)
L_1,2	(0,-10.4)	25.4(w)	335	SLM₂	(0,-680.4)
L_1,3	(25.4,0)	25.4(w)	328	SLM₃	(25.4,-655)
L_2,1	(−25.4,691)	25.4(w)	367
L_2,2	(0,691)	25.4(w)	367
L_2,1	(25.4,691)	25.4(w)	367
L₃	(0,991)	127(d)	300
L₄	(0,1491)	50.8(d)	200

Space bandwidth product enhancement of holographic display using high-order diffraction guided by holographic optical element

Abstract

1. Introduction

2. HOE design for guiding high-order diffraction terms of an SLM

2.1 Condition for using HOE to guide high-order diffraction terms of an SLM

2.2 HOE recording and reconstruction process

3. CGH algorithm for compensating wavefront distortion caused by use of HOE

4. Experiments

4.1 Optical characteristics measurements of the HOE recording material

4.2 HOE recording and reconstruction

4.3 Experiments for confriming the CGH compensation algorithm

4.4 Holographic display using three different order diffraction images with temporal-multiplexing manner

5. Conclusion

Acknowledgment

References and links

Supplementary Material (1)

Cited By

Figures (13)

Tables (1)

Equations (13)

Optics Express