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A novel full parallax and viewing-angle enhanced computer-generated holographic (CGH) three-dimensional (3D) display system is proposed and implemented by combining an integral lens array and colorized synthetic phase holograms displayed on a phase-type spatial light modulator. For analyzing the viewing-angle limitations of our CGH 3D display system, we provide some theoretical background and introduce a simple ray-tracing method for 3D image reconstruction. From our method we can get continuously varying full parallax 3D images with the viewing angle about ±6°. To design the colorized phase holograms, we used a modified iterative Fourier transform algorithm and we could obtain a high diffraction efficiency (~92.5%) and a large signal-to-noise ratio (~11dB) from our simulation results. Finally we show some experimental results that verify our concept and demonstrate the full parallax viewing-angle enhanced color CGH display system.
©2005 Optical Society of America
1. Introduction
Study on three-dimensional (3D) display systems has been mainly focused on real-time full color autostereoscopic 3D displays, such as integral imaging (InIm) [1, 2], holographic stereography [3, 4], partial pixel structures [5], and micro mirror array architecture [6]. Holography is the only 3D imaging technique that is capable of providing all the depth cues and can produce images with virtually unlimited resolution. However, the size and complexity of holographic fringe patterns for general digital holography often preclude their computation at interactive rates. Especially, it has drawbacks such as limited viewing angle, large required bandwidth, and daylight unusability. InIm or integral photography is considered to be a practical 3D displaying method because it provides continuous viewing points, full parallax 3D images, and does not require special viewing devices. InIm was first proposed by Lippmann [7] in 1908, and at that time it had several disadvantages such as depth inversion and difficulties in fabricating lens arrays. Recently, after the proposal of active pickup display devices [8] much attention has been focused on InIm, and many papers have been published regarding improved technologies or theoretical analyses. [9–25].
Computer-generated hologram (CGH) or digital hologram [26] is a hologram made by a computer calculating the interference pattern that would be produced by an imaginary object wave and a reference beam. The amplitude or phase modulation of the CGH is implemented by a semiconductor process or encoded by a programmable real-time spatial light modulator (SLM). Especially, the phase hologram has the advantage of having high diffraction efficiency and variety applications including a diffractive optical element (DOE) [27], optical communication [28], optical information processing [29], and 3D display [30]. The possibility of a real-time holographic display has only recently emerged due to advances in computers and computational methods, which allow the rapid computing of a holographic representation of a given set of 3D data, as well as new electro-optical technologies for their display. Especially, the development of SLMs [31, 32] with high resolution and fast response time is helping to create dynamic real-time digital holographic display system [33–39]. However, real-time holography is still handicapped by the limited information bandwidth available in present-day electronic, computing, and communication systems. In order to reduce the information content of the holographic fringe patterns and to eliminate its information redundancy, we recently proposed and implemented a Fourier-transformed synthetic phase hologram (SPH) for an autostereoscopic 3D image display system using a phase-only SLM and a simple projection lens module [38]. And also, we implemented a dynamic autostereoscopic 3D display system using color-dispersion-compensated (CDC) SPHs for achieving a full-color 3D image [39]. The Fourier transform holograms (FTHs) provide excellent design flexibility and make the most efficient use of the hologram space-bandwidth product. In addition, they have robustness with respect to damage, such as localized defects and degradation of the hologram. However, the FTHs still have a small viewing angle, limited bandwidth, and low-resolution problems due to the two-dimensional imaging property of the lens system and low resolution of the SLM. In this paper we propose and implement a full parallax viewing-angle enhanced color CGH 3D display system combined with integral imaging technology using a phase-type SLM and a conventional lens array.
2. Principle of the proposed full parallax CGH 3D display system
Figure 1 shows the schematic diagram of our full parallax and viewing-angle enhanced CGH 3D display system combined with integral lens array. In Fig. 1, a real 3D object can be obtained by a 3D pickup lens array system. The captured elemental images can be then encoded into a CGH and stored or transmitted without any compression. The CGH can be calculated fast by our previously proposed IFTA method [38]. The modified IFTA has scaling constraints for color dispersion compensation and different phase quantization levels for compensating the phase difference error with respect to each red, green, and blue light source. The encoded CDC holograms are then loaded to a single phase-type SLM. The phase-modulated information is Fourier transformed and magnified through the relay optics. The transformed images are observed through the elemental lens array to form a 3D integrated image. From these procedures we can observe the full parallax 3D integral images with a large viewing-angle without any glass and color dispersion errors. In this paper, we used a computer-generated 3D input image that has the size of 256×256, two illumination laser diode sources with the wavelengths of 635nm (red) and 532nm (green), an SLM that consists of 832×624 pixels with the pixel size of 32μm, and a 13×13 elemental lens array that has the focal length of 22mm and the elemental lens pitch of 10mm.
Fig. 1. Schematic diagram of our proposed full parallax viewing-angle enhanced CGH 3D display system.
In conventional CGH system the viewing angle is inversely proportional to the resolution, i.e., the minimum pixel pitch of the display panel. The size of pixel pitch in liquid crystal display system is about 250μm and the pixel pitch of the SLM in our system has the value of about 32μm. So we can obtain higher resolved reconstructed elemental images. The elemental images in conventional InIm system are calculated by the ray-tracing method considering the elemental lens size and minimum pixel pitch. However the CGH is calculated by the scalar diffraction theory. In our example, we assumed the elemental lens has a pitch of 10mm. Each elemental image has only 40×40 pixels in the conventional InIm system, while it has 312×312 pixels in our CGH display system. In other words, the CGH system can obtain the highly resolved elemental images so that the viewing angle is enhanced. The viewing angle θ of a CGH 3D display system depends on the illumination wavelength, the maximum representative pixel size and minimum sampling size of the SLM as shown in Eq. (1).
where, h and w are the height and width of the hologram, λ is the wavelength of the diffracted light, and N is the sampling number of the hologram. For example, to display a hologram with dimensions h = 1mm, w = 1mm, λ= 632.8nm, and N = 1024×768, we can obtain a viewing angle θ = 0.3559°. However, the viewing-angle of our proposed CGH 3D display system combined with an integral lens array has the full parallax and large viewing angle as the conventional CGH 3D display system.
From scalar diffraction theory [40], the light complex amplitude W(ξ,η) in the hologram plane is related to the light complex amplitude F̂(x,y) in the observation plane. The intensity distribution of the reconstructed image is formed by the square of the following Fresnel integral equation.
where, z is the propagation distance, H means the transfer function of propagation through free space, and λ is the wavelength of the reconstructing illumination light. For colorized synthetic elemental image acquisition, the reconstructed image size is proportional to the light wavelength. Assuming that we use two laser diode sources with wavelengths of 635nm (R) and 532nm (G), a minimum pixel size of the SLM of 32μm, and an achromatic lens with a focal length of 300mm, we can obtain the size of the reconstructed color image component at the image plane of the values about 6 and 5mm for R and G, respectively. To minimize the color difference error each size of the desired color target image should be inversely scaled by the scaling ratio of 1/635:1/532 ≅ 0.838:1 in an iterative Fourier transform algorithm (IFTA) optimization process. The IFTA [41–45] consists of two stages: one stage involving the Fourier transform, and another stage where the constraints are imposed in both the hologram plane and the image plane. These two stages are repeated until the error between the intensity distribution of the reconstructed image and the target image reaches a predetermined tolerance, or when a predefined number of iterations have been achieved; i.e., this procedure is iterated until the error criterion is satisfied. To design CDC-SPHs, the IFTA should be considered carefully for imposing constraints, such as the different reconstruction wavelengths, scaling ratio, each phase quantization level, the minimum pixel size of the phase-type SLM, and the viewing distance.
Table 1 shows the design parameters and the characteristics of our designed CDC-SPHs for generation of the elemental images in our previously proposed IFTA method [38]. The parameter ρ denotes the pitch of each elemental image region. Although 1mm value is used for it, the elemental images are enlarged with a projection lens module to fit 10mm elemental lens pitch. The parameters f and dc denote focal length of each elemental lens and the location of the integral real image from the lens array, respectively. Although the optimization process of the CDC-SPHs in the modified IFTA has some complexity, a quasi-optimized phase hologram can be produced with a fast calculation time of 3 minutes at a personal computer with a Pentium4 2GHz CPU machine. The diffraction efficiency was defined as the ratio of the diffracted signal beams in the signal region to all the diffracted light. The root mean square error (RMSE) was determined for the reconstructed image quality, and was computed from the difference between the normalized reconstructed image and the normalized target image that contained M×N pixels. The signal-to-noise ratio (SNR) was defined as a value of the sum of the intensity of the reconstructed signal beams divided by the sum of the intensity of the remainder beams in the noise region. Using our method, we could theoretically obtain a high diffraction efficiency of 92.5%, a large SNR of 11.0dB, and the averaged reconstruction error of 0.812. To implement the proposed full parallax viewing-angle enhanced CGH 3D display system using CDC-SPHs and integral lens array, we used two crossed-view 3D color images. The sizes of the desired red and green target elemental images were 191×191 and 214×214, respectively. Each size of the designed CDC-SPHs was 256×256, and the size of the composed hologram was 832×624.
Table 1. Performance characteristics of our designed CDC-SPHs.
Figure 2 shows the original images, computer-generated elemental images (the objective to achieve by holograms), the calculated holograms for R and G elemental images, and their reconstructed images. The 3D effect of reconstructed elemental images can be observed from these reconstructed images through a proper magnification optics and integral lens array.
Fig. 2. Original input images (a) and (b), (c) computer-generated elemental image with the central depth plane of 100mm and the position difference of 6mm and depth difference of 20mm between two characters, each designed CDC-SPH for red (d) and green (e) images, and (f) the reconstructed elemental image from the synthetic phase holograms (simulation).
3. Experimental setup and result
The designed CDC-SPHs for elemental image reconstruction were experimentally implemented using a simple Fourier optic system employing a single-phase-type SLM, two laser diode sources (for colorized 3D image display), an achromatic lens, a projection lens module, and an integral lens array. Figure 3(a) shows the optical setup of our proposed full parallax viewing-angle enhanced colorized CGH display system.
Fig. 3. Experimental setup and results of the proposed full parallax viewing-angle-enhanced colorized CGH display system with integral imaging lens array: (a) schematic diagram and picture of our experimental setup, (b) acquired 3D images at different viewing angles -6°, 0°, and 6°, and reconstructed 3D image of the proposed CGH system with respect to the viewing-angle variations (c) simulated result [movie] (d) experimental result [movie]. [Media 1] [Media 2]
In our setup two red and green laser diode sources with wavelengths of λ = 635nm and λ = 532nm were collimated and used to illuminate different areas of the phase-type SLM. Each laser was modulated by the designed CDC-SPHs through the SLM. The diffracted beams from the SLM produced an overlapped colorized elemental image on a color charge coupled device (CCD) plane through a precision achromatic doublet lens having a focal length of 300mm. The color CCD produced the photographs of the acquired elemental images using an image capturing software LabVIEW.
Figure 3(b) shows the captured 3D integral image at the different viewing angles of -6°, 0°, and 6°. From the experimental result we could convince the validity of the proposed full parallax viewing-angle enhanced CGH images with a little image distortion. However, some speckle problems occurred because we used high coherence laser diodes as the illumination sources. To reduce the speckle noise effect some methods [46], such as a rotating or vibrating transmission-type diffuser or a partially coherent light source array, have already been presented and might be usefully applied for our system. And also, some small color dispersion error occurs that is the result of the center-axis mismatch of the designed CDC-SPHs on the SLM. We think that this error can be reduced by placing the CDC-SPH on circular symmetrical position on the SLM. The white noise at the center region of the experimentally captured images is due to the superposition of the undiffracted waves of our SLM. In general, the color sensitivity of the captured image depends on the spectral response of the image-capturing device. To represent a natural full-colorized 3D image, we need to control the power ratio of the three illumination sources with carefulness.
To analyze the viewing-angle limitation of our proposed CGH display system we used a simple lens equation and a viewing-angle condition of a conventional InIm system as follows.
where g is the gap between the integral lens array and the elemental images, b is the distance from the lens array to the integrated image plane, and ρ is the pitch of an elemental lens. Equation (3) can be used in simulating reconstructed 3D images for elemental images at the observer’s plane.
Figure 3(c) shows the 3D image reconstructed from our designed CDC-SPHs with respect to the horizontal viewing-angle variations. Figure 3(d) shows our experimentally captured video frames at the observer's viewing positions having the viewing-angle variations about ±6°. In principle, InIm system has the characteristic of full parallax 3D system. For simplicity in this paper we have only shown the horizontal parallax viewing-angle enhanced CGH 3D simulation and experiment results. The vertical viewing-angle characteristic is similar to the horizontal viewing-angle properties. From Figs. 3(c) and 3(d) we verified that the theoretical and experimental results were well matched together.
Fig. 4. Real-time reconstruction of the proposed full parallax viewing-angle enhanced CGH 3D system of rotating 3D characters: (a) elemental image frames [movie], (b) simulated result [movie], and (c) experimental result [movie].
Currently, the proposed viewing-angle enhanced CGH 3D system has disadvantages of some complexity for calculating the CDC-SPH and real-time processing for simultaneously 3D pick-up and reconstruction. However, we think that the proposed method can be used for real-time 3D broadcasting system if supported with a parallel processing and a specialized application-specific integrated circuit chip for fast IFTA calculation. Because our system generates elemental images with CGH, it might have advantages such as mitigation of flipped images, superposition of multiple viewing images and correction of distorted images. To reveal these advantages, the diffuser in Fig. 3(a) needs to be removed and the diffracted images from phase-type SLM need to be directly input to the elemental lens array. Because CGH has flexibility in designing diffracted beam directions and images, it might show such advantages. This would be an interesting research topic that would require further study.
Figure 4 shows elemental video frames and the simulated and experimentally captured reconstruction results of rotating 3D characters for real-time full parallax viewing-angle enhanced CGH 3D reconstruction system.
4. Conclusion
In this paper, we proposed and implemented a novel full parallax viewing-angle enhanced colorized CGH 3D display system using CDC-SPHs and an integral imaging lens array. To reduce the color dispersion and the phase difference error arising from the use of two different laser sources for color superposition, we applied scaling constraints and phase quantization leveling method in the modified IFTA optimization process. From the simulated reconstructed images using this method, we obtained a high diffraction efficiency (~ 92.5%) and a large signal-to-noise ratio (~ 11dB). Each optimized phase hologram was reconstructed for the red and green wavelengths to achieve a colorized 3D image display. The CDC-SPHs were composed and modulated using only one phase-SLM. Experimentally, we demonstrated that the proposed full parallax viewing-angle enhanced CGH display system works well for 3D image display without using any glasses. However, some discrepancies between the simulated results and the experimentally obtained results occurred due to a low transmission efficiency of our phase-type SLM, some speckle problems, a little chromatic error, and some color-saturation characteristics of our image capturing device.
Acknowledgments
This work was supported by the Next-Generation Information Display R&D Center, one of the 21st Century Frontier R&D Programs funded by the Ministry of Commerce, Industry and Energy of Korea.
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