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A reflection-type integral imaging (InIm) system using a diffuser holographic optical element (DHOE) is proposed for improving the fill factor of displayed three-dimensional images. The DHOE performs an optical function similar to that for a conventional diffuser only for Bragg matched light, while Bragg mismatched light passes through the DHOE. Elemental images projected under Bragg matching condition are scattered by the DHOE. Meanwhile, light reflected by a concave mirror-array becomes Bragg mismatched light, and is integrated into three-dimensional images without the fill factor problem. The optical characteristics of the DHOE are examined by measuring diffraction efficiencies, and the feasibility of the fill-factor-improved InIm is verified by a concave mirror-array and DHOE.
© 2014 Optical Society of America
1. Introduction
Integral imaging (InIm) has been a subject of considerable interest in the field of three-dimensional (3D) displays, since it provides full parallax 3D images with quasi-continuous viewpoint images [1–5]. Typical configurations for implementing InIm use a flat panel display and a lens-array in a transmission geometry. On the other hand, a reflection-type InIm using a projector and a concave (or convex) mirror-array (CMA) has also been extensively studied [6–8]. The reflection-type InIm has the advantage of being space saving, because the observers and the projectors are located at the same side (i.e., in front of the CMA). Moreover, the reflection-type InIm provides a large viewing angle due to the short focal length of the CMA compared to the lens-array used in transmission-type InIm, even though both have the same radius of curvature and pitch.
In the reflection-type InIm, the observer perceives 3D images through images of projector exit pupil corresponding to small portions of elemental images that are reflected from the CMA. The ratio of the effective observing area to whole elemental mirrors of the CMA is defined as a fill factor. The fill factor in the case of a reflection-type InIm is quite low, as are other kinds of projection-type InIms without a diffuser [9–13]. Such a fill factor problem mainly originates from an insufficient emission angle of each pixel in projected elemental images due to the absence of a diffuser, and degrades the visibility of displayed 3D images. As a result, the 3D images in the reflection-type InIm are viewed as a combination of many small dot shaped images corresponding to the images of projector exit pupil, as shown in Fig. 1(a).
Fig. 1 Reflection-type InIm with a CMA: (a) a conventional reflection-type InIm with a fill factor problem, and (b) proposed method for solving the fill factor problem of displayed 3D images.
For solving the fill factor problem in the reflection-type InIm, Okui et al. used a combined structure of a lens-array, a large convex lens, and a mirror [11], and Song et al. used multiple lens-arrays and a retro-reflector screen [12] instead of a single CMA. However, those methods require multiple optical elements, and involve a bulky experimental setup. Recently, Jang et al. proposed a projection configuration which adopts multiple projectors for enhancing the visibility of the reflection-type InIm [13]. However, in that method, since image visibility is enhanced only based on the number of observed points corresponding to the images of the projector exit pupil, the fill factor for each projector remains low.
In this paper, we propose a method in which a diffuser holographic optical element (DHOE) is used in the reflection-type InIm to solve the fill factor problem, as shown in Fig. 1(b). The DHOE scatters the projected elemental images only in the direction towards the CMA, when a projection geometry satisfies Bragg matching conditions. Meanwhile, Bragg mismatched light passes through the DHOE. Since rays which are reflected at the CMA become out of the Bragg condition, they are integrated into the 3D images without scattering by the DHOE. Hence, the DHOE, which has Bragg selectivity, provides fill-factor-improved 3D images with a compact experimental setup by enlarging the emission angle of each pixel in the projected elemental images.
In Section 2, the relationship between projection geometry and the fill factor problem in the reflection-type InIm is analyzed. The principles and recording configurations of the DHOE are then described. In Section 3, a full color DHOE is implemented as an experimental verification of the proposed method. Also, the results of experiments for measuring diffraction characteristics of the DHOE and displaying InIm without the fill factor problem are presented.
2. Principles
2.1. Fill factor problem in a reflection-type InIm
When the elemental images are projected in front of the CMA, rays composing each pixel of the elemental images are reflected at the CMA, and are integrated into 3D pixels. The angle among the rays composing each pixel is the emission angle of the pixel, and determines whether the integrated 3D images have the fill factor problem or not. Suppose that the pixels of the elemental images have identical emission angles, and the elemental images are located in front of the CMA by distance g, as shown in Fig. 2. To prevent the fill factor problem, rays emitted from an upper boundary pixel of a single elemental image should reach a lower boundary of the corresponding elemental mirror of the CMA, and vice versa.
Hence, the required emission angle for each pixel of the elemental images (θmin) is described as
where the pitch of elemental mirror of CMA is Pm. If the emission angles of the pixels are larger than θmin, the projected elemental images are integrated into 3D images without the fill factor problem.However, in the case of a conventional reflection-type InIm, the emission angle of the projected elemental images cannot satisfy Eq. (1), because the elemental image plane is formed without the diffuser. The emission angle of each pixel in the elemental image plane is restricted by an exit pupil of projector as shown in Fig. 3(a). In Fig. 3(a), we assume that centers of the projector and the CMA lie on a common axis, and that the optical axis of the projector is normal to the CMA. In this case, the emission angle of each pixel is determined by the angle among marginal rays which pass through the upper and lower boundaries of the projector exit pupil, and changes according to the position of the pixel.
Fig. 3 The fill factor problem in a reflection-type InIm: schematic diagrams for describing (a) changes of emission angles and chief rays of pixels according to positions, and (b) shift of images of projector exit pupil on a CMA.
In Fig. 3(a), a red pixel represents a center pixel of the projected elemental images. Also a blue pixel is located at position x in the elemental image plane, when the center of the elemental image plane is assumed to be 0. The marginal rays are symmetrically distributed, in the case of red pixel in Fig. 3(a). However, if the pixel is distant from the center of elemental image plane, as shown in the blue pixel of Fig. 3(a), the marginal rays are not symmetrically distributed, and the emission angle differs from that of the center pixel. The emission angle of the pixel located at position x in the elemental image plane is represented as
where Pp and Dp denote a size of the projector exit pupil and the projection distance. In general, θemission of Eq. (2) is smaller than θmin of Eq. (1). For example, if the projector has an exit pupil of 10 mm and a projection distance of 300 mm, the emission angle of each pixel is below 2þ. Meanwhile, θmin in a reflection-type InIm that is needed in practical use, is tens of degrees [7, 8].Moreover, differences in the chief rays of pixels also degrade the fill factor of 3D images. The chief ray of each pixel connects the center of the pixel in the elemental image plane and the center of projector exit pupil. Hence the direction of the chief ray for each pixel changes according to the position of the pixel. It degrades the fill factor, especially for the elemental mirrors at the side of CMA. As presented in Fig. 3(a), if the angle between the optical axis of the projector and the chief ray of the non-central pixel is defined as θchief, the absolute value of θchief increases with the distance of the position of the pixel from the center pixel. The varying chief rays lead to a shift in the image of the projector exit pupil, when the observer perceives 3D images through the CMA [10]. Figure 3(b) shows the shift of images of the projector exit pupil, when a 3 × 3 CMA is used. An aperture stop of the projector is supposed to be a circular shape, and the images of the projector exit pupil, corresponding to the effective observing area of the 3D images, are represented as green circles in Fig. 3(b). The images of the projector exit pupil are partly observed at the side elemental mirrors of the CMA. In other words, compared to the central elemental mirror of the CMA, the fill factor of a boundary elemental mirror decreases.
Since the fill factor of 3D images in the reflection-type InIm is low, the observer perceives the 3D images as combinations of dot shaped images rather than complete images. To enhance the image visibility of 3D images in the reflection-type InIm, a CMA with a large F-number is preferable [10]. However, such a CMA inevitably provides a poor viewing angle, and restrictions on the specifications of the CMA prevent widespread applications of the reflection-type InIm.
2.2. DHOE for solving fill factor problem in reflection-type InIm
In this section, we propose the use of DHOE in a reflection-type InIm for enhancing the fill factor of displayed 3D images. The DHOE enhances the emission angle of each pixel, thus satisfying Eq. (1). Compared to a lens-array holographic optical element (LAHOE), in which the holographic optical element is used as a 3D screen with the function of the CMA in [14, 15], the combination of the DHOE and the CMA has the merit of presenting fill-factor-improved 3D images. Each sub-region in the LAHOE corresponding to the elemental mirror of the CMA effectively represents one pixel of the 3D image, and only a small portion of each sub-region of LAHOE is observed. Since there is also the fill factor problem in the case of LAHOE, experimental verifications have been restricted to using LAHOE with a small pitch [14, 15].
For implementing the DHOE, a reference diffuser and photopolymer are necessary [16–19]. Since the projector and observer are located at the same side from the CMA in the reflection-type InIm, a transmission-type hologram is necessary. The recording geometry of the DHOE involves the use of 4-f optics, as shown in Fig. 4(a). A signal wave passing through the reference diffuser is duplicated at a photopolymer plane by the 4-f optics. A reference wave is incident on the photopolymer with an incidence angle of θr. The interference between the reference wave and the signal wave is recorded in the photopolymer according to principles of a volume hologram. The diffusing angle of the DHOE should be designed so as to be larger than the value for θmin in Eq. (1) by appropriately choosing the specifications of the reference diffuser and two lenses in the 4-f optics. If the diffusing angle of reference diffuser is θd, the diffusing angle of the DHOE after 4-f optics (θDHOE) is determined as
where F1 and F2 represent the focal lengths of lenses consisting of 4-f optics. In the reconstruction process of Fig. 4(b), the original signal wave can be read out by a probe wave which is identical to the reference wave in the recording process of the DHOE. The reconstructed wavefront performs an optical function similar to that of the reference diffuser. If the probe wave does not satisfy the Bragg matching conditions for the DHOE, it passes the DHOE without diffusing.Fig. 4 Recording and reconstruction geometries for DHOE: (a) recording geometry realized with 4-f optics, and (b) reconstruction geometry.
When the elemental images are projected under Bragg matching conditions, each pixel of elemental images is scattered at the DHOE, as shown in Fig. 5(a). Once being scattered by the DHOE, the scattered rays are directed to the CMA, and are reflected at the CMA. When the reflected rays meet the DHOE again after being reflected, their incidence angles become far from the Bragg matching conditions of the DHOE. The reflected rays pass through the DHOE without being scattered, and are integrated into 3D images by the principles of reflection-type InIm as shown in Fig. 5(b). Since the diffusing angle of the DHOE is designed so as to be larger than θmin of Eq. (1), the displayed 3D images are free from the fill factor problems.
Fig. 5 Schematic diagrams of the use of a DHOE in a reflection-type InIm: (a) scattering of elemental images by the DHOE when the elemental images are incident with Bragg matching conditions, and (b) integration of 3D pixels with rays passing through the DHOE after being reflected at the CMA.
Backward scattering, which directs an observation direction in Fig. 5(a), hardly occurs in the case of DHOE [18]. In general, the conventional diffuser scatters the projected images in both the forward and backward directions. The backward scattering of the conventional diffuser makes the observer view the elemental images directly. However, the DHOE only provides the forward scattering, if the reflection at a surface of a substrate where the photopolymer is attached is negligible. The elemental images projected on the DHOE with Bragg matching conditions are scattered only forward, where the CMA is placed, and are not observed by the observer. Hence, the observer views the displayed 3D images without perceiving the elemental images.
Since the diffusing angle of a pixel in the elemental images is enlarged in the proposed method, the emitted rays of pixels in each elemental image cover not only the corresponding elemental concave mirror, but also the neighboring elemental concave mirror in the CMA. Hence when the observer exceeds the viewing angle of the InIm system, he or she perceives the cracking or flipping of the 3D images as the conventional InIm system with the flat panel display [5]. However, the observer within the viewing angle correctly watches the fill-factor-improved 3D images without the cracking or flipping problems by using the proposed method.
3. Experiments
3.1. Experiments on recording DHOE and measuring the diffraction characteristics of DHOE
Figure 6 shows a picture of the optical setup for recording the DHOE. We used crossed lenticular lens sheets as the reference diffuser. As presented in [16], a micro lens-array with a lens size smaller than the projected pixel size can perform the function of diffuser. Regarding the specification of the lenticular lens sheets, θmin of display experiments should be considered. As presented in the next section, the θmin in the display experiments was 33.4þ. Hence, we used lenticular lens sheets with a diffusing angle of 47þ and a lens pitch of 100 lines per inch as the reference diffuser. The diffusing properties of the lenticular lens sheets were recorded in the photopolymer with θr of 40þ. Two lenses with focal lengths of 75 mm make up the 4-f optics. When the DHOE is recorded by using 4-f optics, the θDHOE becomes identical to the diffusing angle of the crossed lenticular lens sheets. A Bayfol HX film, supplied from Bayer Material Science AG, was used as the photopolymer. Three lasers whose wavelengths are 473 nm, 532 nm, and 660 nm were used for wavelength multiplexing in order to present full color images on the DHOE. The diffraction efficiencies are 7.0%, 10.5%, and 11.9% for 473 nm, 532 nm, and 660 nm, respectively, according to the method used to calculate the diffraction efficiency in [20].
We performed the experimental analysis of the diffraction characteristics of the DHOE, and the results are shown in Fig. 7. The optical characteristics of the DHOE were measured in two ways: a diffusing angle measurement, and an angular selectivity measurement. Figure 7(a) shows the measurement geometry. For the diffusing angle measurement, a probe wave of 532 nm was incident on the recorded DHOE with Bragg matching conditions. The variation in intensity of the reconstructed wave was measured, as the position of the photodetector changed. The measurements were performed for half of the diffusing angle, as shown in Fig. 7(a) in order to prevent non-diffracted light from being detected by the photodetector. Also, for the angular selectivity measurement, the intensity of the reconstructed wave was measured as the incidence angle of probe wave changed. Figure 7(b) presents the results of the diffusing angle measurements for the recorded DHOE. Since the measurements were performed for half of the diffusing angle, half of θDHOE is 23þ in accordance with the full width at half maximum (FWHM). Considering that θmin of the display experiments is 33.4þ, θDHOE of 46þ of the recorded DHOE is sufficient for solving the fill factor problem. Figure 7(c) shows the angular selectivity of DHOE, which verifies that the light reflected by the CMA passes through the DHOE without scattering. The FWHM of the angular selectivity measurement is about 3þ. Also, the DHOE reacts hardly to the probe wave which exceeds the angle of deviation of 5þ from θr. Since the direction of propagation of the reflected light by the CMA is inverted compared to that of the probe wave, the incidence angle of the reflected light at the CMA is substantially larger than the angular selectivity of the DHOE.
Fig. 7 Diffraction characteristics of DHOE: (a) a schematic diagram of measuring selectivity and diffusing angle, results of (b) diffusing angle measurements, and (c) angular selectivity measurements of the DHOE.
3.2. Display experiments
Figure 8(a) shows the experimental setup for displaying InIm using the DHOE and CMA. For the display experiments, computer generated elemental images were used, as presented in Fig. 8(b). The elemental images were generated from three letters ‘1’, ‘2’, and ‘3′ with different depths, and were projected on the DHOE using a telecentric lens. The depths of the letter ‘1’, ‘2’, and ‘3′ are 30 mm, 40 mm, and 50 mm, respectively. Since the DHOE is recorded with the plane reference wave, the telecentric lens is necessary for collimated projections [15, 16]. To unequivocally verify the fill factor enhancement, a CMA with large elemental mirrors was used. We performed mirror coatings on a glass lens-array (Edmund Optics Inc.) for implementing the CMA, and the average reflectance of the resulting CMA was about 97% for visible light. The CMA has elemental mirrors of 4 mm × 3 mm, and a focal length of 10 mm. The distance between the DHOE and the CMA was fixed at 13.3 mm. According to the principles of InIm, a central depth plane, where the integrated 3D images show the best quality [5], was located at a distance of 40 mm in front of the CMA. θmin is approximately 33.4þ according to Eq. (1).
Fig. 8 Experimental setup for displaying InIm: (a) a photograph of experimental setup, and (b) elemental images.
Figure 9(a) shows perspective images displayed by the proposed method, which are observed at different positions. The projected elemental images are integrated into the three letters with different depths with a high fill factor. Even though the elemental mirrors of the CMA are large, 3D images are formed without the discontinuity. The viewing angle of the InIm system is determined by the pitch of the elemental concave mirror (Pm) and the gap between the DHOE and CMA (g) [5]. Since g is 13.3 mm and Pm is 4 mm in the horizontal direction and 3 mm in the vertical direction, the viewing angle is approximately 17þ in the horizontal direction and 13þ in the vertical direction. Within this viewing angle, the continuous viewpoint images are presented as shown in Media 1 of Fig. 9(a).
Fig. 9 Experimental results: integrated images by using (a) CMA with DHOE (Media 1), and (b) CMA with directly projecting elemental images.
For the sake of comparison, the integration result from the conventional reflection-type InIm system without the DHOE is also presented in Fig. 9(b). In this case, the computer generated elemental images have the same specifications of 3D objects as in Fig. 8(b). In Fig. 9(b), it is difficult to recognize the shape of the displayed 3D images due to the poor fill factor. In contrast, the proposed method successfully increases the fill factor by enlarging the diffusing angle of each pixel in the elemental images.
Even though the ideal DHOE has only a forward scattering component without backward scattering as addressed in the previous section, reflections occur at the surface of the substrate and the photopolymer in practice. Such reflections may cause the leakage components in the reconstruction process. However, in the case of the implemented DHOE, the peak intensity of the backward scattering components for the probe wave of 532 nm was found to be about 4% of that of forward scattering components. Hence, the intensity of the integrated images is much brighter than that of the backward scattering components, and the observer views the correct 3D images without perceiving elemental images due to the backward scattering of the DHOE.
4. Conclusion
A fill factor enhancement method for use in reflection-type InIm is proposed by using the DHOE. The DHOE scatters the elemental images which satisfy the Bragg matching conditions. The rays reflected from the CMA become Bragg mismatched light, and are integrated into 3D images when they pass through the DHOE. The recording process of the DHOE is realized by 4-f optics. Full color DHOE is implemented by using the wavelength multiplexing technique with the similar diffraction efficiencies for 473 nm, 532 nm, and 660 nm lasers. An experimental analysis of the diffraction characteristics of the recorded DHOE is presented. The diffusing angle of 46þ satisfies the conditions required for solving the fill factor problem in the display experiments, and the FWHM of 3þ in the angular selectivity measurement verifies that the reflected rays at the CMA hardly activate the DHOE. The experimental results for displaying InIm show that fill-factor-improved 3D images can be achieved using DHOE and CMA.
Acknowledgment
This research was supported by “The Cross-Ministry Giga KOREA Project” of The Ministry of Science, ICT and Future Planning, Korea [GK14D0200, Development of Super Multi-View (SMV) Display Providing Real-Time Interaction]. The authors acknowledge the support by Bayer Material Science AG for providing the photopolymer Bayfol HX film used for recording the DHOE.
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