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We have developed a new type of transparent volumetric three-dimensional (3D) image display in which a thin photopolymer sheet containing Lanthanide(III) complexes is used as a rotational screen. The Lanthanide(III) complexes used in our system are Eu(TTA)3 Phen, designed for achieving red luminescence (615nm) for an excitation light of 395 nm. An arbitrary luminous point (voxel) is identified by controlling the excitation laser beam direction in synchronization with the photopolymer sheet rotation. The full colorization of the proposed volumetric 3D image display can be realized by using, for example, Eu(TTA)3 Phen, Tb(ACAC)3 Phen, and Coumarin 337, simultaneously.
©2007 Optical Society of America
1. Introduction
Several techniques for autostereoscopic three-dimensional (3D) image display systems [1], such as integral imaging (InIm) [2, 3], which is based on an integral photography technique [4, 5], and volumetric 3D image display systems [6] have been developed.
Current multi-view techniques such as InIm provide some of the most promising and practical 3D image display systems that do not use any special glasses. InIm provides full-color 3D images with adequate detail and depth levels and supports multiple simultaneous viewers. However, they have a critical problem; an observer can view the 3D images only from the front side of the display unit. Moreover, the viewing angle is limited.
The problems arising from the limited viewing angle can be solved by using volumetric 3D image display systems. Generally, volumetric techniques can be divided into two basic categories -swept volume displays [7–9] and static volume displays [10]. In the case of swept volume displays, the display volume is created by either the vibrational or rotational mechanical motion of a target opaque screen. Although observers can view 3D images from a wide angle, hidden zones continue to exist. The most common principle used in static volume displays is the two-frequency, two-step upconversion technique [11–13]. The advantage of this approach is that there are very few hidden zones, which leads to a larger field of view and a larger viewing zone. The main disadvantage is the small size of the currently used fluoride crystals.
In this paper, we present a new type of volumetric 3D image display in which 3D objects are displayed on a transparent rotating photopolymer sheet containing Lanthanide(III) complexes. The 3D images are constructed as an aggregation of luminous points (voxels) of the transparent sheet instead of employing the scattered light field from the opaque screen. These images are integrated with the real background because of the transparent volumetric display. The main advantages of our approach are that (1) there are very few hidden zones, (2) the display size is large as compared to that of the conventional static-type volume display, and (3) our display can easily be extended to a full-color system.
2. Principle of Operation
Figure 1(a) schematically shows the operation principle of our system. A spinning thin photopolymer sheet containing Lanthanide(III) complexes is used to sweep out a volume cyclically at a frequency higher than one that can be resolved by the eye. The specific voxel point of the 3D image is expressed by the luminescence of the Lanthanide(III) complexes dissolved in the photopolymer sheet. The voxel is excited by a laser diode beam. The direction of the excitation laser beam is changed by two galvanometer scanners. By controlling the laser beam direction (α, β) as a function of the rotational angle θ of the photopolymer sheet, the specific voxel is indicated. The 3D images are expressed as an aggregation of these voxels. The constructed 3D image is the so-called phantom image through which all objects in the background are observed.
Figure 1(b) shows the model for the calculation of α(θ) and β(θ). These parameters denote the horizontal and the vertical directions, respectively. The function to be displayed is assumed to be f(x,y,z). The function representing the spinning thin photopolymer sheet surface is assumed to be g(x,y,z). The point of intersection of the two functions f(x,y,z) and g(x,y,z) is shown in Fig. 1(b) as p(xp(θ),yp(θ),zp(θ)). The function representing the excitation laser beam is expressed as h(α,β) in the figure. The relations between the laser beam directions (α(θ), β(θ)) and the coordinates of the points of intersection p(xp(θ),yp(θ),zp(θ)) are expressed as
Fig. 1. Principle of operation (92 kB). (a) Operation principle of the system. The specific point of the 3D object is expressed by the luminescence of the Lanthanide(III) complexes excited by the laser diode beam. [Media 1] (b) The calculation model used to derive the relation between θ and each angle of the galvanometer scanners, α and β. f(x,y,z) is the 3D image function to be displayed.
Here, L denotes the distance between the galvanometer scanners and the axis of revolution.
Let us calculate the functions α(θ) and β(θ) to construct a straight line that passes through points A(xa,ya,za) and B(xb,yb,zb). Such a straight line f(x,y,z), can be represented as
Here, T is a parameter expressed as
From Eqs.(1)–(6), α(θ) and β(θ) for the straight line are expressed as
Fig. 2. Manufacturing procedure for the transparent photopolymer sheet containing Lanthanide(III) complexes.
Fig. 3. Photographs of a luminous transparent photopolymer sheet. (a) Photograph taken under a usual lighting. (b) Photograph taken under no illumination. (c) The entire sheet is excited by UV lamp. (d) The sheet is excited by a laser diode. The excitation wavelength is 410 nm.
3. Experiment
3.1. Transparent photopolymer sheet containing Lanthanide (III) complexes
Figure 2 shows the manufacturing procedure for a transparent photopolymer sheet. The Lanthanide(III) complex used in our system is Eu(TTA)3 Phen, designed for achieving red luminescence (615 nm) for an excitation light of 395 nm [14]. The Lanthanide(III) complexes are added to the photopolymer (Technovit) and dissolved with the aid of an ultrasonic washing machine that is operated for 30 min. Subsequently, the photopolymer is injected into a transparent mold. Ultraviolet (UV) rays are irradiated onto the transparent mold so that the photopolymer stiffens. The photopolymer sheet is nipped in polyester film to reduce unwanted scattering of the excitation laser beam at the surface. The resultant thickness of the thin photopolymer sheet is 0.5 mm. Eu(TTA)3 Phen is dissolved in the photopolymer with a weight ratio of 0.04 %.
Figure 3 shows our photopolymer sheet. The size of the developed sheet is 8 cm×6 cm. Therefore, the display volume becomes 22.6×104mm3 (with a radius of 3 cm and a height of 8 cm). As shown in Fig. 3(a), good transparency is achieved. Figure 3(c) shows the red luminance of the photopolymer sheet excited by a UV lamp. The Lanthanide(III) complexes are dissolved thoroughly, and luminescence without irregularity is achieved. Figure 3(d) shows the spot luminance of the sheet excited by a 410-nm-laser-diode.
Fig. 4. Experimental setup. Control signals are supplied from the PC. Two mirrors are controlled by analog servo drivers. The rotation of the photopolymer sheet is phase-locked to the stable reference clock signal supplied from the PC.
The voxel luminescence propagates from the exited point toward the edge of the sheet. If the transparency of the photopolymer sheet is not sufficient, unwanted scattered light causes a blurring of the 3D images. The scattered luminescence at the edge can be observed, as shown in Fig. 3(c). In the experiment, the edges of the sheet are sealed by an opaque tape to hide this unwanted scattered light. This results in some hidden zones.
3.2. Experimental setup
Figure 4 shows our experimental setup. The distance between the galvanometer scanners and the thin sheet is set to be L=30 cm. For convenience, we used a 410-nm-laser-diode for the excitation. The control signals are supplied from a PC through an I/O board (CONTEC: ADA-16-32/2(PCI)F) to two galvanometer scanners (GSI LUMONICS: VM500). Two mirrors are controlled by analog servo drivers (GSI LUMONICS: MiniSAX). The mirror aperture is 6 mm. The maximum scan angle is ±50 degree. The small step time is less than 175 μs. The full step time is less than 800 μs. A DC motor (MAXON: A-max22) is used. The rotation speed of the photopolymer sheet is controlled through the DC motor driver with the aide of pulse width modulation (PWM) and is set to be 900 rpm. The rotation phase is detected by the photo interrupter and locked to that of the stable reference clock signal supplied from the PC so that the rotation of the photopolymer sheet and the signals supplied to the two galvanometer scanners are mutually synchronized.
3.3. Model of the 3D object
Figure 5(a) shows the model of the 3D object. The object size has been normalized. The 3D object comprises six straight lines. α(θ) and β(θ) can be calculated from Eqs. (7) and (8), respectively. The calculated angles are shown in Fig. 5(b). The 3D model is drawn using a single stroke of the laser beam while one lap of the transparent sheet spins.
3.4. Results
Figure 6 shows the constructed 3D image. The two pictures have been taken from mutually different positions. The 3D image can be viewed from any perspective. Because the edge of the photopolymer sheet is sealed to prevent unwanted scattered light, there are few hidden zones (width of approximately 0.5mm), as clearly shown in Fig. 6(b). The 3D image is integrated with the real background because the spinning thin sheet is transparent (transparent volumetric 3D display). Because the 3D image is constructed as an aggregation of voxels luminous points of the transparent sheet, there is no accommodation-convergence conflict.
Figure 7 shows the movie of a 3D animation of fluttering triangles. One period of the animation comprises 18 laps of transparent sheet spins.
4. Discussion
In our system, the voxel size is a function of θ. The minimum and the maximum voxel sizes can be achieved at θ = (n+1/2)π and θ = nπ, respectively, where n = 0,1,2... The voxel size v can be estimated as
Here, r denotes the radius of the excitation laser beam and d and w are the depth and width of the transparent thin sheet, respectively. In our experiment, r = 0.25 mm, d = 0.5 mm, and w = 60 mm. From these expressions, we estimate that the developed system has approximately 147 × 104 voxels. It is easy to enlarge the height and the width of the thin sheet containing Lanthanide(III) complexes. It is also easy to make the sheet thinner. However, from the viewpoint of sheet strength, there is a trade-off between the sheet dimension and the rotational speed. For drawing a more complicated 3D image with low rotational speed, we have to optimize the rendering algorithms of vector scanning for the excitation laser beam [15]. The proposed system can also generate 3D images by projecting a sequence of two-dimensional patterns of UV images onto a spinning thin sheet containing Lanthanide(III) complexes.
In the experiment, we used Eu(TTA)3 Phen for achieving red luminescence (615 nm) for an excitation of 395 nm. The intensity of the luminescence of our transparent sheet can be linearly controlled by the excitation laser intensity. We can achieve green luminescence (550 nm) for an excitation of 300 nm by using Tb(ACAC)3 Phen; we can also achieve blue luminescence (488 nm) for an excitation of 443 nm by using Coumarin 337. By using a transparent thin sheet for containing the three abovementioned materials for the three colors (RGB) and by controlling the excitation intensity for each color, we can realize a full-color transparent volumetric 3D display.
5. Conclusion
We have proposed and demonstrated a new type of transparent volumetric 3D image display in which 3D objects are displayed on a transparent rotating photopolymer sheet containing Lanthanide(III) complexes. The volume of the developed display was 22.6×104mm3, and there were approximately 147×104 voxels. We experimentally confirmed our results that the displayed 3D image was integrated with the real background. The main advantages of our approach are that (1) there are very few hidden zones, (2) the display size is large as compared to that of the conventional static-type volumetric display, and (3) our display can easily be extended to a full-color system.
Acknowledgments
We wish to thank Dr. Yasuchika Hasegawa of the Nara Institute of Science and Technology for his helpful comments and for providing us with Eu(TTA)3 Phen. We also thank Mr. Yusuke Nakamura for the early implementation of the experimental setup.
This research was supported in part by the Ministry of Education, Science, Sports, and Culture, (Grant-in-Aid for Scientific Research (B), 18360038, 2006) and the Japan Science and Technology Agency (Research for Promoting Technological Seeds).
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