3. Application of HOE

#### 3.1. Waveguide and wedge-shaped holographic optical element (HOE) waveguide HMD

HMD is a display device, worn on the head or as part of a helmet that has a small display optic in front of one or each eye. HMD has been widely used in virtual reality and augmented reality applications [23–25]. There are two main kinds of HMD: "curved mirror"-based HMD and "waveguide"-based HMD. The curved mirror HMD uses semi-reflective curved mirrors placed in front of the eye with an off-axis optical projection system. This system suffers from a high mount of distortion which needs to be corrected optically or electronically adding cost and reducing image resolution. Moreover, a small heavy "eye motion box" will be needed, which is uncomfortable and requires mechanical adjustment, further adding to cost. The waveguide HMD removed the side electronics and display using a waveguide; it reduces the cumbersome display optics and provides a fully unobstructed view of the scenes. Among the waveguide techniques, the holographic waveguide method focuses on the advantage of having a small volume, low price, and command of angular and spectral selectivity of optical elements. In this chapter, we will mainly talk about the holographic waveguide HMD based on HOE. Note that among a lot of types of recording materials, these holographic waveguide HMD techniques are utilized the photopolymer which is high-efficiency material and most widely used in various research fields. In addition, other HOE-based techniques which will be reviewed in next sections, section 3.2 and 3.3, also used the photopolymer.

By the same way as it was described above for angular selectivity, spectral selectivity could be

The HWFZ wavelength selectivity also could be considerably simplified for un-slanted grat-

Figure 15 shows dependence of wavelength selectivity on spatial frequency for different grating thicknesses. HWFZ wavelength selectivity of reflection volume grating could be easily varied from values below 0.1 nm to more than a dozen nm by proper choosing of grating parameters.

3.1. Waveguide and wedge-shaped holographic optical element (HOE) waveguide HMD

HMD is a display device, worn on the head or as part of a helmet that has a small display optic in front of one or each eye. HMD has been widely used in virtual reality and augmented reality applications [23–25]. There are two main kinds of HMD: "curved mirror"-based HMD and "waveguide"-based HMD. The curved mirror HMD uses semi-reflective curved mirrors placed in front of the eye with an off-axis optical projection system. This system suffers from

Figure 15. Wavelength selectivity (HWFZ) of reflecting volume grating with 99% diffraction efficiency at λ = 532 nm and n<sup>0</sup> = 1.5 on spatial frequency for optimal refractive index modulation with grating thickness in 0.5, 2, 5, and 10 mm.

q

sinh<sup>2</sup>

<sup>1</sup> � <sup>λ</sup>0<sup>f</sup> 2 Δλ 2n0Δn � �<sup>2</sup>

2πn0dΔn λ0 2f � �<sup>2</sup>

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

� �<sup>2</sup> <sup>r</sup>

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi atanh ffiffiffiffiffi η0 � � <sup>p</sup> <sup>2</sup> <sup>þ</sup> <sup>π</sup><sup>2</sup>

� <sup>π</sup>dfΔλ λ0

�1

<sup>π</sup>df (35)

(34)

expressed by substitution of Eqs. (26) and (28) to Eq. (25) at Δθ = 0:

ΔλHWFZ <sup>R</sup> <sup>¼</sup> <sup>λ</sup><sup>0</sup>

ηRð Þ¼ Δλ 1 þ

ings with diffraction efficiency of Eq. (29):

114 Holographic Materials and Optical Systems

3. Application of HOE

Ando et al. proposed and fabricated an HMD using HOEs instead of half mirror [26]. The benefit of this system is that all functions of lens, combiner, and binocular stereoscopy can be kept within single HOE. However, this method has limited size reduction, because they did not use waveguide-type HMD. As shown in Figure 16, two small LCD displays are replaced in both sides of the head and prevent the reflection light from the HOE to the human eyes. The HOE was recorded in 120° of recording angle between an object beam and a reference beam. The binocular images are modulated by illumine light for reconstruction.

Figure 16. The optical specification of HOE for binocular stereoscopy-type HMD.

Amitai et al. and Kasai et al. reported a monochrome eye display using a volume hologram or grating [27] as the optical combiner in front of the eyes on a waveguide [28, 29]. Although the size of the optics is minimized, this method did not yield high diffraction efficiency. Subsequently, full-color eyewear display was proposed by Mukawa et al. [30]. In this method, the issue of color uniformity should be solved. Figure 17 shows the basic structure of the HOE for waveguide-type HMD. As shown in this figure, the system has three optical parts, the couplein part, couple-out part, and waveguide plate. In couple-in part, an image is magnified by micro-display, and the light is refracted into the waveguide; then the light was reflected by the first HOE guided in the waveguide plate with the total internal reflection. In couple-out part, the guided light refracted by the second HOE projects the image to the observers.

Figure 17. A basic structure of the HOE for waveguide-type HMD.

Recently, Piao et al. proposed a reflection-type HOE with high diffraction efficiency for a waveguide-type HMD using a photopolymer and present a laminated structure method for fabricating full-color HOE [31]. A photopolymer is one of the hologram recording materials that has high diffraction efficiency and low cost. Furthermore, it does not require any chemical or wet processing after recording the holograms. As mentioned earlier, the photopolymer is applied in various fields such as optical elements, holographic storage, holographic display and so on. Piao et al. analyzed the optical characteristic of the photopolymer using three lasers operated at 473, 532, and 633 nm, respectively. Figure 18 shows the efficiency of full-color HOEs: (a) combined structure, (b) three-layer laminated structure, and (c) two-layer composited structure.

In this experiment, the diffraction efficiencies of the photopolymer were more than 90% for each R, G, and B color that provides wide angular selectivity. And, the output efficiencies of full-color HOEs are 40%, 44%, and 42% for R, G, and B colors. The proposed method reduced the volume of the system by using photopolymer, and the system also has good color uniformity, brightness performance, and high diffraction efficiency. Figure 19 shows the experimental results for the full-color HOEs which were fabricated using the proposed two-layer composited structure.

However, based on the design configuration of the system, the thickness, weight, color uniformity, and field of view (FOV) issues of the system were not solved entirely.

According to the previous work, M. Piao et al. designed waveguide glass specifications for the HMD system in accordance with wedge-shaped waveguide design [32]. Figure 20 is the designed waveguide structure. This system includes a lens positioned proximate to the micro-display and two reflection holographic volume gratings (HVGs) in HOEs attached on either side of a waveguide.

waveguide-type HMD. As shown in this figure, the system has three optical parts, the couplein part, couple-out part, and waveguide plate. In couple-in part, an image is magnified by micro-display, and the light is refracted into the waveguide; then the light was reflected by the first HOE guided in the waveguide plate with the total internal reflection. In couple-out part,

Recently, Piao et al. proposed a reflection-type HOE with high diffraction efficiency for a waveguide-type HMD using a photopolymer and present a laminated structure method for fabricating full-color HOE [31]. A photopolymer is one of the hologram recording materials that has high diffraction efficiency and low cost. Furthermore, it does not require any chemical or wet processing after recording the holograms. As mentioned earlier, the photopolymer is applied in various fields such as optical elements, holographic storage, holographic display and so on. Piao et al. analyzed the optical characteristic of the photopolymer using three lasers operated at 473, 532, and 633 nm, respectively. Figure 18 shows the efficiency of full-color HOEs: (a) combined structure, (b) three-layer laminated structure, and (c) two-layer

Figure 17. A basic structure of the HOE for waveguide-type HMD.

In this experiment, the diffraction efficiencies of the photopolymer were more than 90% for each R, G, and B color that provides wide angular selectivity. And, the output efficiencies of full-color HOEs are 40%, 44%, and 42% for R, G, and B colors. The proposed method reduced the volume of the system by using photopolymer, and the system also has good color uniformity, brightness performance, and high diffraction efficiency. Figure 19 shows the experimental results for the full-color HOEs which were fabricated using the proposed two-layer composited structure.

However, based on the design configuration of the system, the thickness, weight, color unifor-

According to the previous work, M. Piao et al. designed waveguide glass specifications for the HMD system in accordance with wedge-shaped waveguide design [32]. Figure 20 is the designed waveguide structure. This system includes a lens positioned proximate to the micro-display and two reflection holographic volume gratings (HVGs) in HOEs attached on

mity, and field of view (FOV) issues of the system were not solved entirely.

composited structure.

116 Holographic Materials and Optical Systems

either side of a waveguide.

the guided light refracted by the second HOE projects the image to the observers.

Figure 18. Efficiency of the full-color HOEs for (a) combined structure, (b) three-layer laminated structure, and (c) twolayer composited structure.

Unlike the previous method [31], the both ends of waveguide are wedge-shaped by the certain angle and the HOEs are mounted onto the wedge-shaped sides. Structurally, the thickness of the waveguide can be reduced by a large angle of total internal reflection. In addition, the wide angular selectivity of the HVGs allows for a large FOV, and the narrow spectral selectivity can be used with broad spectral sources, such as light-emitting diodes (LEDs). By observing the optical path of light in the waveguide, they theoretically analyzed the angular and spectral selectivity of the HVG, presented the correlation of the spatial frequencies of the HVG with the slope of the wedge-shaped waveguide, and determined the specific waveguide structure. According to the Bragg condition, Kogelnik's theory [21], their experiment shows θ<sup>1</sup> = 40<sup>∘</sup> and θ<sup>2</sup> = 30<sup>∘</sup> are suitable for recording the incident angle of the HVGs (Figure 21), which were attached on both sides of the wedge-shaped waveguide, because the large total internal reflection angle leads to a thin waveguide design.

Figure 19. Experimental results (a) using full-color HOE for HMD system, (b) input image, and (c) output image.

Figure 20. Structure of the wedge-shaped holographic waveguide wearable display.

The fabricated holographic waveguide using a photopolymer was tested using the optical setup shown in Figure 22. To confirm the light path in the designed waveguide, each monochromatic holographic waveguide HMD system was investigated. And the plane wave of the three combined beams (633 nm, 532 nm, 473 nm) illuminated a reflection-type spatial light modulator (SLM).

The image illuminated by an LED captured by the demonstration system is shown in Figure 22. Figure 23(a) shows the original test image. Figure 23(b–d) shows each monochromatic HVG of the input image with accurately guided in the designed waveguide. Figure 23(e) shows that the results of the full-color HVG fabricated using a GBR sequential recording on one photopolymer

Figure 21. Designed angle of the light path in the waveguide.

The fabricated holographic waveguide using a photopolymer was tested using the optical setup shown in Figure 22. To confirm the light path in the designed waveguide, each monochromatic holographic waveguide HMD system was investigated. And the plane wave of the three combined beams (633 nm, 532 nm, 473 nm) illuminated a reflection-type spatial light modulator (SLM).

Figure 20. Structure of the wedge-shaped holographic waveguide wearable display.

118 Holographic Materials and Optical Systems

Figure 19. Experimental results (a) using full-color HOE for HMD system, (b) input image, and (c) output image.

The image illuminated by an LED captured by the demonstration system is shown in Figure 22. Figure 23(a) shows the original test image. Figure 23(b–d) shows each monochromatic HVG of the input image with accurately guided in the designed waveguide. Figure 23(e) shows that the results of the full-color HVG fabricated using a GBR sequential recording on one photopolymer

Figure 22. Experimental setup for testing the fabricated wedge-shaped holographic waveguide using SLM. M, mirror; DM, dichroic mirrors; SF, spatial filter; L, collimating lens; and PBS, polarizing beam splitter.

Figure 23. Experimental results captured from the wedge-shaped waveguide wearable display: (a) the original test image; output image fabricated by (b) 633 nm, (c) 532 nm, and (d) 473 nm; and (e) GBR sequential exposure in the DMD system.

layer with good quality. The image clearly was reproduced with a white color, the same as the ideal one shown in Figure 23(e).

In addition, they successfully fabricated a compact full-color HVG, which performed with high levels of optical efficiency, using one layer of photopolymer based on a color analysis of the HVG.

Recently, Yeom et al. proposed a bar-type waveguide 3D holographic HMD using HOE with astigmatism aberration compensation [33]. Here, a conventional bar-type waveguide HMD structure is used, and 3D holographic images are displayed in both SLMs without the accommodation-vergence mismatch. Also, the ray tracing based on the H. Kogelnik-coupled wave theory has been analyzed. Figures 24(a) and 24(b) show the simulated footprint image of in-coupling and out-coupling HOEs on the waveguide, respectively, where the light rays which come from the SLM are diffracted on the in-coupling HOE and go to the out-coupling HOE through the waveguide glass. When the light rays are transmitting between two HOEs, in-coupling and out-coupling, too much of distortion occurs due to the asymmetric diffraction of HOEs, i.e., the optical path length of the light ray experience in the waveguide. Naturally, this issue makes the astigmatism in the final images. In order to eliminate the distortion, a constant difference Δzparameter is added in the hologram generation process as the following:

$$H(u,v) = \sum\_{i} A\_i \exp\left\{\frac{jk\_{o,air}}{2} \left(\frac{(x\_i - u)^2}{z\_i} + \frac{(y\_i - v)^2}{z\_i - \Delta z}\right)\right\} \tag{36}$$

Figure 25 shows the reconstructed image from the hologram which is applied in holographic compensation. Figure 25(a) shows the 3D image generated from the hologram without compensation; the aberration is visible. Then, in Figure 25(b), the 3D image reconstructed from the hologram with compensation is presented. Figure 26(a) shows the experimental setup, and Figure 26(b) shows the combined visualization for real object and holographic images displayed on the HOE-based HMD.

Figure 24. Footprint of ray on the bottom side of the waveguide: (a) in-coupling HOE and (b) out-coupling HOE.

Figure 25. Reconstructed image of holographic compensation: (a) without compensation and (b) with compensation.

Figure 26. (a) Experimental setup and (b) real object and holographic images with the holographic compensation.

#### 3.2. Lens-array HOE

Recently, Yeom et al. proposed a bar-type waveguide 3D holographic HMD using HOE with astigmatism aberration compensation [33]. Here, a conventional bar-type waveguide HMD structure is used, and 3D holographic images are displayed in both SLMs without the accommodation-vergence mismatch. Also, the ray tracing based on the H. Kogelnik-coupled wave theory has been analyzed. Figures 24(a) and 24(b) show the simulated footprint image of in-coupling and out-coupling HOEs on the waveguide, respectively, where the light rays which come from the SLM are diffracted on the in-coupling HOE and go to the out-coupling HOE through the waveguide glass. When the light rays are transmitting between two HOEs, in-coupling and out-coupling, too much of distortion occurs due to the asymmetric diffraction of HOEs, i.e., the optical path length of the light ray experience in the waveguide. Naturally, this issue makes the astigmatism in the final images. In order to eliminate the distortion, a constant difference Δzparameter is added in the hologram generation process as

the following:

120 Holographic Materials and Optical Systems

H uð Þ¼ ; <sup>v</sup> <sup>X</sup>

displayed on the HOE-based HMD.

i

Aiexp jko, air 2

Figure 25 shows the reconstructed image from the hologram which is applied in holographic compensation. Figure 25(a) shows the 3D image generated from the hologram without compensation; the aberration is visible. Then, in Figure 25(b), the 3D image reconstructed from the hologram with compensation is presented. Figure 26(a) shows the experimental setup, and Figure 26(b) shows the combined visualization for real object and holographic images

Figure 24. Footprint of ray on the bottom side of the waveguide: (a) in-coupling HOE and (b) out-coupling HOE.

ð Þ xi � u 2

( ) !

<sup>þ</sup> yi � <sup>v</sup> � �<sup>2</sup> zi � Δz

(36)

zi

Integral image is one of the most attractive ways to create autostereoscopic 3D display providing real-time full parallax information without requiring special glasses [34]. However, integral image still has a problem with limitation of resolution, viewing angle, and depth of field. Among these, the narrow viewing angle is the main disadvantage. Several methods have been proposed to increase the viewing angle of integral imaging displays. Curved lens array and curved screen can be one solution, though the necessary physical configurations make these systems difficult to implement.

A wide-viewing-angle 3D display system using HOE lens array is proposed by H. Takahashi et al. where the system consists of a projector and HOE lens array [35]. Here, the main role of HOE lens array is virtual curved lens that each individual axis is not perpendicular to HOE plane. The basic procedure of the display system is that the elemental images are projected as parallel beams to the corresponding elemental lens areas; the HOE lens array reconstructs the 3D image. As mentioned above, the HOE lens array has manufactured that all of the transmitted light rays through the elemental lenses can be crossed onto the single point, similar with the curved-type lens array, so the viewing angle of reconstructed image is much wider than original object's viewing angle acquired into the elemental images. Figure 27 shows the schematic configuration of HOE lens array-based wide-viewing-angle 3D display system, where p is the pitch of elemental lens recorded onto HOE, r is the radius of virtual curvature of HOE lens array, and ψ is viewing angle of the reconstructed image.

Figure 27. The scheme of HOE lens array-based 3D display system.

In the experiment, HOE lens array consists of 17 · 13 elemental lenses, as shown in Figure 28, where each of them is 4.4 · 4.4 mm, the focal length of the central elemental lens is 18.3 mm, and the radius of virtual curvature of HOE lens array, i.e., the distance from HOE lens array to reconstructed image, is 50 mm. Here, the viewing angle of central elemental lens is approximately 7° on each side of the individual axis, and the entire viewing angle of reconstructed image is much wider, approximately 35°, where the theoretical angle is 37°. Note that if the common lens array has been used in the reconstruction, the reconstructed image viewing angle would be approximately 7°, because the elemental lens axes are parallel with each other. Also, the HOE lens array reconstructs the flipped ray-free 3D images, and if the virtual curvature of HOE lens array is desired by 2D lens array configuration, the full viewing angle, horizontal and vertical, can be widened.

Figure 28. HOE virtual lens array in experimental system.

image still has a problem with limitation of resolution, viewing angle, and depth of field. Among these, the narrow viewing angle is the main disadvantage. Several methods have been proposed to increase the viewing angle of integral imaging displays. Curved lens array and curved screen can be one solution, though the necessary physical configurations make these

A wide-viewing-angle 3D display system using HOE lens array is proposed by H. Takahashi et al. where the system consists of a projector and HOE lens array [35]. Here, the main role of HOE lens array is virtual curved lens that each individual axis is not perpendicular to HOE plane. The basic procedure of the display system is that the elemental images are projected as parallel beams to the corresponding elemental lens areas; the HOE lens array reconstructs the 3D image. As mentioned above, the HOE lens array has manufactured that all of the transmitted light rays through the elemental lenses can be crossed onto the single point, similar with the curved-type lens array, so the viewing angle of reconstructed image is much wider than original object's viewing angle acquired into the elemental images. Figure 27 shows the schematic configuration of HOE lens array-based wide-viewing-angle 3D display system, where p is the pitch of elemental lens recorded onto HOE, r is the radius of virtual curvature of HOE

In the experiment, HOE lens array consists of 17 · 13 elemental lenses, as shown in Figure 28, where each of them is 4.4 · 4.4 mm, the focal length of the central elemental lens is 18.3 mm, and the radius of virtual curvature of HOE lens array, i.e., the distance from HOE lens array to reconstructed image, is 50 mm. Here, the viewing angle of central elemental lens is approximately 7° on each side of the individual axis, and the entire viewing angle of reconstructed image is much wider, approximately 35°, where the theoretical angle is 37°. Note that if the common lens array has been used in the reconstruction, the reconstructed image viewing angle would be approximately 7°, because the elemental lens axes are parallel with each other. Also, the HOE lens array reconstructs the flipped ray-free 3D images, and if the virtual curvature of HOE lens array is desired by 2D lens array configuration, the full viewing angle, horizontal

systems difficult to implement.

122 Holographic Materials and Optical Systems

and vertical, can be widened.

lens array, and ψ is viewing angle of the reconstructed image.

Figure 27. The scheme of HOE lens array-based 3D display system.

Recently, Hong et al. proposed a full-color 3D display on the basis of a projection-type integral imaging for the optical see-through AR by making use of a full-color lens-array HOE as the image combiner [36]. Here, the HOE lens array has been manufactured by the interference pattern which includes all of characteristics of the given common lens array recorded onto the photopolymer where the interference pattern is formed by spherical-wave-type object beam and plane-wave-type reference beam. The photopolymer is provided from Bayer MaterialScience AG, and the thickness of the photopolymer is 14–18 μm. Then, the wavelength multiplexing and spatial multiplexing methods in order to display the full-color virtual 3D images and record the large-sized HOE lens array are proposed [37]. Figure 29 is showing the schematic diagram of experimental setup for recording the full-color lens-array HOE. And, experimental setup for displaying 3D virtual images in the proposed optical see-through AR system is shown in Figure 30(a). Figure 30(b) shows the computer-generated elemental images of S, N, and U, which were used in experiment. They used a telecentric lens with the relay optics for collimated light of projection to avoid the Bragg mismatch.

Figure 29. The schematic diagram of experimental setup for recording the full-color lens-array HOE.

The collimated reference beam in the recording setup and the imaging device for a display setup should also project collimated light on the full-color lens-array HOE to avoid the Bragg mismatch.

Figure 30. (a) Experimental setup for displaying 3D virtual images in the proposed optical see-through AR system. (b) The elemental images for three characters (S, N, and U) projected on the lens-array HOE for 3D virtual imaging.

Figure 31 shows the results of see-though 3D virtual images captured in the display experiments from five different viewing points relative to the proposed optical see-though AR system. It is clearly confirmed that the disparities among the images captured from top, left, center, right, and bottom provided a binocular disparity and give a 3D perception to the observer.

Figure 31. Perspective see-through 3D virtual images of three characters (S, N, and U) with a real object cube for a background, which were captured from five different view positions in the display experiment.

#### 3.3. Holographic solar concentrator

Figure 31 shows the results of see-though 3D virtual images captured in the display experiments from five different viewing points relative to the proposed optical see-though AR system. It is clearly confirmed that the disparities among the images captured from top, left, center, right, and

Figure 31. Perspective see-through 3D virtual images of three characters (S, N, and U) with a real object cube for a

background, which were captured from five different view positions in the display experiment.

Figure 30. (a) Experimental setup for displaying 3D virtual images in the proposed optical see-through AR system. (b) The elemental images for three characters (S, N, and U) projected on the lens-array HOE for 3D virtual imaging.

bottom provided a binocular disparity and give a 3D perception to the observer.

124 Holographic Materials and Optical Systems

Recently, HOEs have been studied for use in various solar applications to substitute optical mechanisms in solar concentrators [38–40]. The recording material of HOEs is usually flat and thin. It is possible to multiplex several holographic elements into the same material and collect solar energies with different incidence angles. Moreover, HOEs have the ability to diffract the light in a specific direction, and they also have the potential to provide angular or wavelength multiplexing. By applying the angular multiplexing method to the HOE recording, the angular multiplexing-based HOEs could act as the sun tracker. The HOEs that operate at specific wavelengths are able to diffract the desired specific wavelengths and remove other unwanted wavelengths, such as UV rays.

HOEs were suggested to be used in solar applications for the first time in 1982 [38]. The major attraction of holography is that it appears possible to make a holographic concentrator that has no moving parts and is able to track the daily movement of the sun and concentrate the sun's rays onto an absorber. Afterward, a variety of designs have been suggested over the years [41, 42]. For example, it was demonstrated that a volume holographic lens allows a single-axis tracking over 55° angular variation [43, 44].

Designs of multiplexed holographic lenses have been also proposed by Naydenova et al. [45]. Here, the multiplexed HOEs are recorded in the same photopolymer layer. Figure 32 shows the optical setup for recording the holographic lens in the photopolymer plate with focusing lens. Then, the recorded HOE has the characteristic of focusing the light in the recording direction.

Figure 32. A schematic configuration of experimental setup for recording a holographic lens.

For focusing the light from the multiple directions, a schematic configuration for recording multiplexed HOEs is illustrated in Figure 33. The reference beam reflects the light in five different mirrors to record the multiplexed transmission gratings with the object beam. The object beam and the different reference beam are recorded by adjusting the photopolymer material to bisect the inner beam angle. By variability of exposure time and intensity, the multiplexed HOEs can obtain optimum diffraction efficiencies.

Recently, the angular multiplexed holographic solar condensing lens has been proposed by J. H. Lee et al. [46]. In order to combine the solar concentrator and sun tracking functions in a single photopolymer, a convex lens was used as a recording object while multiplexing the incident

Figure 33. A schematic configuration of experimental setup for recording multiplexed HOEs.

beams of three angles. Generally, the performance of a HOE is determined by the diffraction efficiency. The diffraction efficiency is defined as the ratio of the intensity of the diffraction beam to the sum of the intensity of diffraction beam and transmission beam. However, it is difficult for the diffraction efficiency to evaluate the performance of the HOE as a solar concentrator. Therefore, they newly suggest the concentrated diffraction efficiency (CDE) calculation method that uses an effective concentration rate (ECR). ECR is a metric measure, i.e., already proposed for measuring the concentration rate of the solar concentrator. The ECR was calculated from the equation

$$E\mathbb{C}\mathbb{R} = \eta\_{opt} \times \mathbb{R}\_{\mathfrak{c}} \tag{37}$$

where ηoptis the optical efficiency which is the ratio of condensed light intensity to incident light intensity and Rc is the geometric concentration rate which is the ratio of area of incident beam and condensed beam. The CDE, ηc, is defined by ECRh of HOE and ECRl of the convex lens as follows:

$$
\eta\_c = \text{ECR}\_h / \text{ECR}\_l \times 100 (\%) \tag{38}
$$

Eq. (2) shows the actual performance of the recorded HOE as a solar concentrator. Figure 34 shows the schematic diagrams of the hologram recording for the solar concentrator. In this experiment, holograms are recorded by transmission geometry because it is advantageous for the HOE solar concentrator.

In solar concentrator systems, the sun tracking systems are necessary owing to the movement of the planet. In order to realize the effective sun tracking system, an interval within 10 am–2 pm is widely used, as shown in Figure 35. This scheme shows the schematic diagram that condenses the light coming from three different angles to a fixed single point. Note that the interval degrees between each angle are decided as 10° because it matches the movement interval of the sun at 10 am–2 pm.

The iterative recording method is used to improve efficiency and uniformity. The iterative method is applied to make holograms through repetitive exposure in one photopolymer that each of the N holograms is recorded with a series of short exposure time within the material's saturation time. At 0.5 second, 0.25 second and 0.125 second of the exposure time and from twice to six times of the iteration number were applied. And, the order of recording is A, B, and C. This schedule is laid out with consideration of saturating condition. And, the result is shown in Figure 36. It shows the possibility of increasing the efficiency by using iterative recording method.

beams of three angles. Generally, the performance of a HOE is determined by the diffraction efficiency. The diffraction efficiency is defined as the ratio of the intensity of the diffraction beam to the sum of the intensity of diffraction beam and transmission beam. However, it is difficult for the diffraction efficiency to evaluate the performance of the HOE as a solar concentrator. Therefore, they newly suggest the concentrated diffraction efficiency (CDE) calculation method that uses an effective concentration rate (ECR). ECR is a metric measure, i.e., already proposed for measuring the concentration rate of the solar concentrator. The ECR was calculated from the

Figure 33. A schematic configuration of experimental setup for recording multiplexed HOEs.

where ηoptis the optical efficiency which is the ratio of condensed light intensity to incident light intensity and Rc is the geometric concentration rate which is the ratio of area of incident beam and condensed beam. The CDE, ηc, is defined by ECRh of HOE and ECRl of the convex

Eq. (2) shows the actual performance of the recorded HOE as a solar concentrator. Figure 34 shows the schematic diagrams of the hologram recording for the solar concentrator. In this experiment, holograms are recorded by transmission geometry because it is advantageous for

In solar concentrator systems, the sun tracking systems are necessary owing to the movement of the planet. In order to realize the effective sun tracking system, an interval within 10 am–2 pm is widely used, as shown in Figure 35. This scheme shows the schematic diagram that condenses the light coming from three different angles to a fixed single point. Note that the interval degrees between each angle are decided as 10° because it matches the movement

ECR ¼ ηopt · Rc (37)

η<sup>c</sup> ¼ ECRh=ECRl · 100ð Þ % (38)

equation

lens as follows:

the HOE solar concentrator.

126 Holographic Materials and Optical Systems

interval of the sun at 10 am–2 pm.

Figure 34. Schematic diagrams of the transmission hologram for the HOE solar concentrator on the photopolymer film.

Figure 35. Schematic diagram for angular multiplexed holographic solar concentrator.

Figure 36. Result of iterative recording at 0.25 seconds of exposure time.
