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Abstract
A novel technique is presented for the full-color reconstruction of large-scale computer-generated holograms (CGHs). In this method, three printed CGHs are transferred to three volume holograms at the wavelengths corresponding to red–green–blue (RGB) colors and then stacked to superimpose the RGB color images. The developed CGHs are compact and portable. The reconstructed image is sharp and vivid as compared with that developed using RGB color filters. A technique for correcting the original CGHs is proposed to compensate for the aberration caused by the thick glass substrate because the RGB images exhibit a considerable position shift owing to the aberration. Fabricated large-scale full-color CGHs are demonstrated to verify the techniques.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. INTRODUCTION
Traditional optical holography can produce amazing full-parallax full-color three-dimensional (3D) images by white-light reconstruction [1]. The 3D images are very sharp, bright, and vivid, and have a large viewing angle in full parallax. In many cases, the optical color holograms are a reflection hologram, recorded using a technique of the Denisyuk hologram [2]. Here, optical holograms can be classified into two categories: “thick,” or volume holograms, and thin holograms. The former holograms have a 3D fringe structure and thus, feature wavelength selectivity and multiplexed recording. As a result, the color images can be reconstructed by white-light illumination.
Optical color holography can produce excellent 3D images. However, there is a considerable disadvantage: when creating a 3D image, we have to prepare the physical object prior to recording. Sometimes, a physical model of the 3D image must be made by some device, e.g., a 3D printer. This is a strange situation in a sense. To get over the restriction of traditional color holography, holographic printers based on direct-write digital holography have been developed [3,4]. However, the hologram printed through this method reconstructs a holographic stereogram, which does not present exact accommodation cues and commonly causes vergence–accommodation conflicts in the reconstruction of deep 3D scenes.
Another technique to reconstruct virtual objects and scenes is computer holography, which has been steadily developed over the past decade. In this technique, the object field is numerically calculated from 3D computer-graphics (CG) models and digital pictures; then, the fringe pattern is generated by numerical interference with a reference field. Physical objects are no longer required to reconstruct the 3D image. The synthetic fringe pattern is commonly printed by homemade fringe printers [5,6] or e-beam lithography [7]. The latter technique features very high-resolution printing; however, it is time-consuming and is commonly restricted to printing a small computer-generated hologram (CGH) suited for optical devices, such as a diffractive optical element.
Printed CGHs are generally a type of thin hologram that reconstruct only monochromatic images. Multicolor reconstruction in CGHs is achieved using the technique of rainbow holograms [5,8–11]. However, it is difficult for rainbow holograms to reconstruct the true color of the 3D model when the viewpoint varies. In addition, because rainbow holograms only present horizontal parallax, it is essentially difficult to reconstruct deep 3D scenes. Full-color reconstruction of thin CGHs can also be realized by combining red–green–blue (RGB) images using dichromatic mirrors at the sacrifice of portability [6,12]. In another technique to produce thin color CGHs, a multiplane phase hologram was proposed; however, the optical reconstruction was not reported [13].
Instead of thin CGHs, direct printing of computer-generated volume holograms (CGVHs) has been proposed in the same vein as the holographic printers [14–18]. This type of printer, often called a wavefront printer, seems to have the same structure as holographic printers; however, the hologram printed by a wavefront printer reconstructs the synthetic object field, unlike the holographic printers, which reconstruct only parallax images. Full-color CGVHs have also been reported as generated from the wavefront printer; unfortunately, the reported 3D image is not very clear [16]. This is most likely due to the phase discontinuity caused by tiling subholograms [17,18].
Computer holography has suffered from the space-bandwidth product problem for a long time, in which a gigantic space-bandwidth product is required for creating high-quality holograms, whose screen size and viewing angle are at a given level necessary for practical display. This is not only the problem of printing but also of the calculation of the object field, because the object field must be composed of more than several billion sample points in high-quality CGHs. We can overcome the calculation problem through the polygon-based method [19] and silhouette method for occlusion processing [20] and overcome the printing problem through laser lithography, which is one more technique that can be used to print CGHs [21]. We reported some large-scale CGHs called high-definition CGHs [20–25] and exhibited a few of them in museums. These high-definition CGHs are composed of more than one billion or sometimes tens of billions of pixels. As a result, very impressive deep 3D scenes are reconstructed in monochrome with continuous and natural-motion parallax in full parallax. The reconstructed 3D images are almost comparable to those constructed by monochromatic optical holography.
However, it was very difficult to reconstruct full-color images by these high-definition CGHs because the CGHs printed using laser lithography are also a type of thin hologram. The 3D images are reconstructed with many smears under white-light illumination because of chromatic aberration. Several methods have been attempted to reconstruct full-color images from high-definition CGHs. For example, dichroic mirrors are used to superimpose RGB color images [12]. In this technique, sharp full-color images are reconstructed with high contrast; however, complicated, expensive, and nonportable optical systems are required. Therefore, the CGHs are unsuitable for any exhibition.
We also reported another technique using RGB color filters [26,27]. In this technique, RGB color filters that are very similar to those used in LCD panels are attached to the large-scale fringe pattern, and the fringe pattern behind the filters is generated at the appropriate wavelength corresponding to the RGB colors. The CGHs produced by this technique are portable and able to reconstruct full-color images very easily; however, the image is not very sharp or vivid. There are two reasons: (a) The spectral property of the RGB color filters is commonly not narrow enough to reconstruct the thin CGHs, and (b) the fringe pattern is spatially divided to fit with color filters.
To overcome this problem, better color filtering is required. In addition, the fringe pattern should not be divided into blocks or subholograms. An excellent technique called stacked CGH has been proposed and meets these conditions [28]. In this technique, the fringe patterns for RGB colors are individually printed on the corresponding dichroic mirrors; more exactly, the fringe is formed by the pattern of dichroic mirror films. Three fringes are stacked on a substrate. The R layer, for example, reflects and modulates only the red component of white light. The G and B components passing through the R layer are reflected at the corresponding layer. As a result, it is expected that a very clear full-color image would be reconstructed because of the narrow bandwidth and lack of discontinuance of the dichromatic fringe pattern. However, very sophisticated film and pattern formation technology is needed to realize the stacked CGH.
We propose a novel technique to realize a type of stacked CGH [29]. In this method, three printed CGHs are transferred to three volume CGHs at the wavelength corresponding to RGB colors and are then stacked to superimpose the RGB images. We call this a stacked CGVH. The stacked CGVH is as portable as the CGH using RGB color filters; however, the reconstructed image is sharper and definitely more vivid. A color shift due to the aberration caused by the thick glass substrate can be exactly compensated for by correcting the original CGH.
In this paper, we present the principles for creating the stacked CGVH in Section 2 and the technique to compensate for the thickness and refractive index of the glass substrate in Section 3. Fabrication of an actual stacked CGVH and its full-color reconstruction are demonstrated to verify the proposed techniques in Section 4.
2. PRINCIPLE OF STACKED CGVH
A. Fabrication of Reflection-Type CGH by Laser Lithography
Laser lithography is one of the best methods to create a large-scale CGH [21]. In this technique, a fringe pattern is printed as the transmittance pattern of metal thin films, chromium thin films in many cases. Because metal films have high reflectivity, the fringe is formed not only as the pattern of transmittance but also of reflectance. As a result, the CGH can be reconstructed by reflected illumination, as shown in Fig. 1(a). This is a notable feature of the CGHs printed by the laser lithography because ordinary printed CGHs are commonly reconstructed only by transmittance illumination.
Fig. 1. (a) Reconstruction of CGHs printed by laser lithography and examples of optical reconstruction by (b) monochromatic and (c) white-light illumination.
Figure 1(b) shows an example of the optical reconstruction of a large-scale CGH printed using laser lithography. In this case, a monochromatic light source is used for the illumination to reconstruct. The 3D images are very clear and bright. However, when using white-light sources, such as white LEDs, the optical reconstruction causes a severe color smear, as shown in Fig. 1(c). This is because the printed CGH is a thin hologram. To reconstruct full-color images, some optical element exhibiting wavelength selectivity is generally required, e.g., RGB color filters [26].
B. Transfer of Original CGH to Volume Hologram
The feature of CGHs printed by laser lithography, reflection reconstruction, can be used to transfer the original CGH to a volume hologram. A thick photosensitive material, such as a photopolymer, is attached to the surface of the printed CGH to transfer the image of the printed original CGH, as shown in Fig. 2(a). When the original CGH is reconstructed using a coherent light source, which illuminates the CGH through the recording material, the reconstructed light of the CGH is recorded on the material.
Fig. 2. (a) Fabrication and (b) reconstruction of a volume hologram transferred from the original CGH using contact copy; (c) example of optical reconstruction of the transferred CGH using white-light illumination.
Because the hologram transferred by this technique is a type of volume hologram, it has the property of wavelength selectivity, i.e., the hologram is reconstructed only at the same wavelength as that used in the transfer. Accordingly, when we illuminate the transferred hologram with a white-light source, as shown in Fig. 2(b), the 3D image is reconstructed in a single color, and any color smear is no longer caused, as in Fig. 2(c). This is the same technique as contact copy, used in analog holography. The contact-copy technique features simplicity of the optical system and excellent vibration resistance.
C. Stacking Transferred CGHs
The contact copy allows us to reconstruct the CGHs by white-light illumination, because the transferred volume hologram has wavelength selectivity. The transferred hologram is nearly transparent at wavelengths other than that used in the contact copy. Thus, we can realize almost the same structure as that of the stacked CGH, proposed for full-color reconstruction [28].
In the fabrication of the stacked CGVH, three volume holograms are transferred from the three original CGHs at wavelengths corresponding to the RGB color; then, they are stacked, as shown in Fig. 3. By using white-light illumination, full-color images are reconstructed by the superposition of the RGB color images. Here, note that the transferred CGHs must be aligned carefully so that the reconstructed 3D images do not cause any color shift.
It may also be possible to transfer all RGB images to a single volume hologram instead of three holograms. In this case, because the aligning work of RGB color images must be done in a dark room, special aligning equipment is required. In addition, the recording material commonly has problems of limited writing capacity. In multiple exposures, we must control the degree of exposure very carefully to produce a well-balanced and bright full-color image. These difficulties are not present when stacking multiple holograms.
3. COMPENSATION FOR THICKNESS AND REFRACTIVE INDEX OF SUBSTRATE
Each transferred CGVH is recorded on the photosensitive material coated on a glass substrate. In the original CGHs, the fringe pattern made of chromium is also printed on a glass substrate. Therefore, when we simply generate the three original CGHs corresponding to RGB wavelengths, the images reconstructed by the three volume CGHs are not superimposed perfectly because of the position shift and aberration caused by the substrates. To compensate for the thickness and refractive index of the glass substrate, the fringe patterns of the three original CGHs are generated by the following procedure.
A. Compensation for Substrate of Recording Material
Suppose that the origin of the coordinate system is placed at the forefront of a stacked CGVH, as shown in Fig. 3. Object waves at three wavelengths are first calculated from the object model in a plane including the origin, as shown in Fig. 4. Let $ O(x,y;{\lambda_p}) $ represent the wave field of the object wave. Here, $ {\lambda _p}(p = {\rm{R}},{\rm{G}},{\rm{B}}) $ is a wavelength corresponding to RGB colors. This wave field is referred to as an ideal field in the following discussion.
Fig. 3. Reconstruction of a full-color image from the stack of transferred CGVHs and the coordinate system used for compensation.
In the optical reconstruction of a stacked CGVH, the field reconstructed by the volume hologram reaches the forefront after passing through the glass substrates. Therefore, we numerically propagate the ideal field backwardly to the position of the recording material through the glass substrates, as shown in Fig. 5. Here, we assumed that the transferred holograms are stacked in the order of BRG from the forefront because the diffraction efficiency of the recording material increases in this order. We also assume that the recording material is coated on the back of the substrate and thin enough to ignore the thickness.
Fig. 5. Backward propagation of the ideal object field through the glass substrate. The propagation is depicted in the case of G, for example.
To compensate for the aberration caused by the substrate, the object field $ O(x,y;{\lambda_p}) $ must be numerically propagated at the wavelength inside the glass substrates. The wavelength is properly calculated by the refractive index of the glass,
where $ {n_p} $ is a refractive index of the substrate for color $ p $. Because we adopt the band-limited angular spectrum (BLAS) method as the technique of numerical propagation [30], the wave field at the recording material for green, for example, is given byB. Compensation for Substrate of Original CGH
In the original CGHs, the fringe pattern of the chromium thin films is also printed on the back side of the glass substrate, as shown in Fig. 6. On the other hand, when we transfer the original CGH, the recording material is attached to the front side of the substrate of the original CGH, as in Fig. 6. Thus, the field $ O^\prime(x,y;{\lambda_p}) $ given at the position of the recording material should again be propagated backwardly at the wavelength in the glass substrate of the original CGH,
Finally, the fringe pattern of the original CGH is generated by numerical interference with a reference field as follows:
4. FABRICATION AND OPTICAL RECONSTRUCTION OF STACKED CGVH
A. Fabrication of Original CGHs with Compensation for Substrate Aberration
Three original CGHs, i.e., three fringe patterns, were actually printed on the chromium thin film using a DWL $66^{+} $ laser lithography system made by Heidelberg Instruments. The parameters and 3D scene are shown in Table 1 and Fig. 7, respectively. The ideal object field was calculated by using the polygon-based method [19]. Occlusion was processed by the silhouette method using the switch-back technique [20]. As a result, the CGHs reconstruct full-parallax images with continuous-motion parallax.
Table 1. Parameters Used for Creating the CGH
The ideal object field was propagated backwardly using Eqs. (1)–(3) to compensate for the effect of the glass substrates, as mentioned in Section 3. We used Bayfol HX200, a photopolymer provided by Covestro, for the recording material of the transferred hologram. The thickness and refractive index of the glass substrates of the recording material and original CGH are shown in Table 2.
Table 2. Parameters of the Glass Substrate of the Recording Material and Original CGH
B. Fabrication of Stacked CGVH
The original CGHs were transferred to the recording material by using the optical system shown in Fig. 8. All light sources used for transfer are narrowband diode-pumped solid-state (DPSS) lasers. The outputs of the lasers are combined into a coaxial beam using dichroic mirrors and then converted to spherical waves using a spatial filter, because the fringe pattern of the original CGHs are generated with a reference spherical wave. The beam expander, inserted into the path of the blue laser, is necessary to spread the spherical wave sufficiently; this is because the blue laser used in the experiment outputs a very narrow beam. The position of the pinhole of the spatial filter was adjusted carefully so as to agree with the center of the spherical field used in the numerical generation of the fringe pattern. The exposure was optimized depending on the color sensitivity of the material.
Parameters for transfer are shown in Table 3. Optical reconstructions of the individual transferred CGH are shown in Fig. 9. Here, a pigtail white LED is used for the illuminating light source.
Table 3. Parameters for Transferring the Original CGHs to Volume Holograms
Fig. 9. Optical reconstructions of the individual transferred CGHs. A pigtail white LED is used for the illumination light source. (a) Red, (b) green, (c) blue.
Fig. 10. Optical reconstruction of the stacked CGVH using a pigtail white LED. (a) Setup and (b) a distant picture (see Visualization 1).
Fig. 11. Close-up photographs of the 3D image reconstructed by the stacked CGVH. The pictures are taken from (a) left, (b) center, and (c) right viewpoints (see Visualization 1).
Fig. 12. Comparison between optical reconstructions of (a) the stacked CGVH (this work) and (b) full-color CGH using RGB color filters [26].
C. Optical Reconstruction of Stacked CGVH
The transferred CGHs were stacked to fabricate the full-color CGVH. The position of the CGVHs was adjusted as the RGB images were reconstructed by the white-light illumination. Optical reconstructions of the fabricated stacked CGVH are shown in Fig. 10, in which a pigtail white LED is again used for the illuminating light source because of its excellent spatial coherency. Close-up photographs of the 3D image reconstructed by the stacked CGVH are shown in Fig. 11. The pictures are taken from different viewpoints. Little color shift is detected at any viewpoint. The stacked CGVH successfully reconstructs the full-color 3D images in full parallax. Continuous-motion parallax, inherited from the original CGHs, is also reconstructed, as shown in Visualization 1.
Figure 12 shows a comparison of the 3D image reconstructed by the stacked CGVH with that of the full-color CGH using RGB color filters [26]. In the technique that uses RGB color filters, three fringe patterns calculated for RGB colors are combined into a single fringe pattern. Each fringe pattern for the color shapes stripes. The RGB color filters, which are essentially the same as those used in LCD panels, are attached to the corresponding fringe pattern in an accurate manner. As the broadband transmittance of the RGB color filters degrades the optical reconstruction owing to chromatic aberration, the CGH is reconstructed by a multichip white LED to narrow the effective bandwidth even slightly.
Fig. 13. Comparison between spectra of (a) measured reflectance of the volume holograms and (b) estimated effective illuminations with use of RGB color filters [26].
The reconstruction of the stacked CGVH definitely results in a clearer 3D image than that using RGB color filters. The 3D image by the stacked CGVH is also brighter than that by the CGH using RGB color filters. This is most likely because the wavelength selectivity of the volume holograms is better than that by the RGB color filters. To verify this fact, another experiment was performed in which simple reflection holograms were recorded by a two-beam interference exposure using the same material and lasers as those used in creating the CGVHs. The measured reflectance spectra are shown in Fig. 13(a). The bandwidths of the volume holograms are 15, 10, and 9 nm in order of RGB, respectively, and are quite narrower than those of the effective illumination for the CGH using the RGB color filters shown in Fig. 13(b). Thus, the volume hologram provides better wavelength selectivity and less chromatic aberration to the CGH. In addition, the spatially divided fringe pattern most likely degrades the optical reconstruction of the CGH using RGB color filters.
Fig. 14. Comparison between optical reconstructions of the stacked CGVHs (a) with and (b) without the substrate compensation. Both pictures are taken from a left viewpoint.
Figure 14 verifies the technique of compensation for the aberration caused by glass substrates. The fringe pattern in Fig. 14(b) is not generated with compensation for the aberration, whereas compensation is involved in the fringe in Fig. 14(a). The pictures are taken from a left viewpoint. Color shifts are clearly detected and the 3D image is drastically degraded in Fig. 14(b). This means that the technique proposed in Section 3 is always necessary to decrease the aberration by the glass substrates in stacked CGVHs.
5. CONCLUSION
We proposed a method to create full-color CGHs by stacking RGB CGVHs that are transferred from the original high-definition CGHs printed by laser lithography. The technique of contact copy can be applied to the transfer because the original thin CGHs are reflection holograms owing to the fringe made of metal films. A technique is also proposed to compensate for the aberration caused by the thick glass substrates of the recording material and original CGH. An actual stacked CGVH was fabricated and demonstrated to confirm the validity of the proposed techniques. The reconstructed full-parallax full-color 3D image is very sharp and vivid and presents natural-motion parallax, which is an excellent feature of the original high-definition CGHs.
Stacking multiple holograms does not present the problems of the aligning and limited writing capacity of the recording material that arise in single-layered full-color holograms produced by multiple exposures for RGB colors. However, as single-layered full-color holograms have the advantages of simplicity and thinness of the produced hologram, the development of this technique is a feature of our work.
Funding
Japan Society for the Promotion of Science (KAKENHI 18H03349).
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