An integral imaging system enabling extended depth of field was proposed and demonstrated based on a birefringence lens array (BLA) whose focal length was switched via the light polarization. The lens array system was constructed by combining two different liquid crystal(LC) embedded lens arrays, BLA I and II, which were fabricated by injecting a ZLI-4119 LC and an E-7 LC in between a lens array substrate and an ITO (indium-tin-oxide) glass plate respectively. The BLA I played a role as a convex lens only for the polarization parallel to the ordinary axis of the corresponding LC, but it serves as a plain medium for that along its extraordinary one since the refractive indexes of the lens and the LC are almost identical. Meanwhile, the BLA II played a role as a concave lens only for the polarization parallel to the extraordinary axis of the LC but as a plain medium for that along its ordinary one. As a result, the focal length could be switched via the polarization, and it was measured to be 680 mm and −29 mm. For the proposed system with the prepared BLAs, both real and virtual three-dimensional (3D) images were efficiently reconstructed at the positions of z=1300 mm and z=−30 mm with no significant degradation in the resolution, indicating its depth of field range.
©2009 Optical Society of America
Recently the three dimensional (3D) display, which is regarded as one of the most prominent cutting edge technologies leading to next generation value-added display industries, has advanced drastically with the advent of flat panel display devices such as the plasma display panel (PDP) and the liquid crystal display (LCD). The integral imaging (InIm) is known to be one of viable schemes for the implementation of the 3D display system, and it is composed of two basic steps including the pickup and the reconstruction  as illustrated in Fig. 1 . In the pickup step an optical information of object is recorded through a micro-lens array (MLA) on a pickup device such as a charge coupled device (CCD), producing a 2D elemental image array. And, in the reconstruction step the elemental image is loaded on a display device like the LCD and then integrated via a similar lens array to feel a 3D object through our eyes. The InIm scheme is attractive because it affords to offer a continuously varying viewpoint within a certain viewing angle without the wearing of special glasses [2–11]. Yet some issues have been revealed related to the depth of field, the resolution and the viewing angle. To mitigate their limited depth of field various configurations of InIm systems were especially suggested based on: a variable focusing lens array (VFLA) , multiple image planes using a multilayered display device like transparent LC panels , and multiple images employing a dynamic polarizer, a sliding slit array mask, and a transparent uniaxial crystal plate . A depth-enhanced InIm system incorporating an electrically variable image plane with polymer dispersed liquid crystal (PDLC) layers was also reported .
In this paper an InIm system exploiting a birefringence lens array (BLA) allowing two different focal lengths was proposed and implemented. The BLAs were fabricated by placing two different types of LC in between a lens array substrate and a glass plate, and their focal length was varied by switching the light polarization. The real and imaginary 3D images for an object were reconstructed at two different locations with a certain depth of field respectively, supporting that the depth of field for the reconstructed images could be readily extended by combining them properly.
2. Proposed InIm system and its operation
Figure 2 illustrates the configuration of the proposed InIm system involving a polarization selective lens array composed of BLA I and II and an LCD providing pickup elemental images. The BLA I and II are first aligned in such a way that their principal axes, the ordinary and extraordinary axis, are matched together. A polarizer is used to dynamically change the polarization of the incident light. Dynamically changing polarizer means a temporally rotating polarizer. Either of the two BLAs whose axis matches that of the polarizer is selected to play a role as lens. For the polarization parallel to its ordinary axis, the BLA I acts as a convex lens and thus a real integrated image is obtained in front of it. Meanwhile, for the polarization parallel to its extraordinary axis the BLA II functions as a concave lens generating a virtual integrated image at the back of it. The propagation of rays for the two BLAs is depicted in Fig. 3 depending on the light polarization. Here the BLA I and II were made by placing ZLI-4119 and E-7 nematic LCs in between a lens array substrate and an indium-tin-oxide (ITO) glass plate respectively. As shown in Fig. 3, the incident light polarized in the extraordinary direction is refracted by the BLA II alone but bypasses the BLA I working as a plain retarder. On the contrary, for the light polarized in the ordinary direction only the BLA I plays a role as a convex lens.
An enlarged view of the proposed BLA is given in Fig. 4 . Its focal length may be estimated by taking into account the distribution of the refractive index profile along the light propagation direction. To extend the depth of field of the integrated images without degrading the resolution the focal length of the BLAs used is to vary over a wide range as long as the light polarization is switched instantly.
The position of the center of the reconstructed image can be expressed as Eq. (1). Here g is the gap between the display panel and the BLA in effect, and L denotes the distance of the resulting integrated image from the corresponding BLA, which is dependent upon the magnitude of the birefringence available the lens. f 1 and f 2 denote respectively the convergent and divergent focal length leading to the real and virtual integrated image, and they are given by Eq. (2). Here nl and np are the effective refractive index of the LC and the lens respectively, and C is the radius of curvature of the lens. no and ne represent the ordinary and extraordinary refractive index of the LC and θ is the tilt angle thereof. The position of the integral image plane can be adjusted by altering the focal length of the lens, which is determined by the refractive index contrast between the LC layer and the lens array substrate. Therefore the depth of field for the proposed system may be defined as the separation between the focal point where the spot size becomes ideally zero and the position where it is enlarged to be equivalent to one pixel size d of the LCD, as given in Eq. (3). Finally the total depth of field is given by Δz total=Δz 1+Δz 2.
In this work two kinds of LCs including the E-7 (no=1.5216, Δn=0.2246 @580 nm) and the ZLI-4119 (no =1.4712, Δn= 0.0603 @580 nm) were practically used to form a birefringent layer on a lens substrate, which is 10 μm thick at the center. The focal length of the BLA I and II was designed to be 630 mm and −29 mm respectively. For instance, for d =0.2 mm and W=4 mm, we will get Δz total=~33 mm from Δz 1= 31.5 mm and Δz 2=1.45 mm.
3. Simulation and experimental results
A conventional InIm system employing a plain non-birefringent lens array was first designed and analyzed by using the LightTools® . The elemental image for the two objects of letters ‘I’ and ‘P’, which were located at z=9 mm and z=30 mm respectively, was produced with the resolution of 609 x 609 pixels as shown in Fig. 5(a) . They were reconstructed at z=9 mm and z=30 mm respectively as displayed in Fig. 5(b) and 5(c). At each of the reconstruction image planes one object is shown to be clearly imaged but the other blurred severely, reflecting the limited depth of field for the current system as anticipated. This problem may be however addressed by adaptively controlling the focal length of the lens arrays in accordance with the reconstruction position of each object.
We have then produced and evaluated the proposed BLA, which will be used for the implementation of our InIm system. The BLA I and II were first prepared by following a standard LCD fabrication procedure: RN-1702 polyimide films were spin-coated on an ITO glass plate and a lens substrate, which was containing an array of 10 × 12 plano-convex lenses with the footprint of 4 mm x 3 mm. The films were baked on a hot plate and rubbed to serve as an alignment layer for the LCs to be formed. And a spacer layer of 10-μm thickness was prepared upon the ITO plate. The lens array substrate was then attached to the ITO plate in such a way the rubbing directions for the two become anti-parallel. Next a proper amount of ZLI-4119 and E-7 LCs was injected into the space between a conventional lens array substrate and an ITO glass plate via the capillary effect, thereby completing the proposed BLAs. A 10-μm thick LC layer was found to be formed on top of each elemental lens, which was 500 μm high. The focal length of the BLAs was examined by using the setup given in Fig. 6(a) , where a collimated beam at 633 nm coming out of a spatial filter in conjunction with a collimating lens was launched to the BLAs and captured by a photodetector. As expected, the BLA I and BLA II exploiting the ZLI-4119 LC and E-7 LC gave birth to a converging beam and a diverging beam respectively. The BLA I provided the focal length of 680 mm for the light polarization along the ordinary direction as shown in Fig. 6(b), while it failed to function as lens for the polarization parallel to the extraordinary axis BLA I as implied from Fig. 6(c). And the BLA II exhibited the opposite operation characteristics: it worked as a lens only for the polarization in the extraordinary direction giving the focal length of −29 mm.
Finally the proposed InIm system introduced in Fig. 2 was built and evaluated by utilizing the fabricated BLAs. Figure 7 depicts the setup for the reconstruction procedure in detail and Fig. 8(a) and 8(b) display part of the 8×8(one of them is 4 mm x 3 mm) elemental image array of an original object with the shape of a car, which will be used for the real and virtual reconstruction. The elemental images emanating from a projector went through the polarizer and the optic relay comprising lenses. Currently used polarizer is general glass type and the rotation of polarization is performed mechanically. For now, temporal frequency is several seconds but if Motor or electro optic device is used, it can be below several ms. Light loss should be about 50% for white light theoretically. The used projector has the different polarized light according to color because of chromatic prism in projector. Thus, it is supposed that because used light is red and green, the light efficiency is below 30%. By adjusting optic relay elemental images were matched to each elemental lens of BLAs, and g is decided as the effective gap which is estimated to be large. The number and size of the lenslets is limited by the beam diameter passing through the optical relay, which is used to modulate the beam coming from the projector. The object was finally reconstructed either on the real image plane or on the virtual image plane for the case of the BLA I and II respectively. And the restored images were photographed with a digital camera. Figure 9(b) and 9(c) show the images reconstructed via the proposed system based on the BLA I and II respectively, while the image obtained by employing the conventional system is included in Fig. 9(a). The color of the images varied with the light polarization of concern. Our display system might exhibit a slight chromatic dispersion effect caused by the liquid crystals of ZLI-4119 and E-7. They are known to cover the spectral band around the center wavelength of 540nm for the case of perpendicular light incidence. The dispersion undergone by the liquid crystal layer is dependent on its incidence angle. The dispersion might become only significant when the focal length the BLA is short and as a result the incidence angle is large. Currently, the incidence angle is about 0.05o (=1.5 mm (radius of a lens)/30mm) considering the maximum thickness of 500 um of the liquid crystal layer near the edge of the lens. The focal length is longer than 30 mm, so that the dispersion effect might be neglected. We have succeeded in restoring a real 3D object at z=130 cm and a virtual 3D object at z=−3 cm. It was confirmed from the above experimental results that the proposed InIm system was capable of producing either a real image in front of the BLA or a virtual image at the back of it. The switching speed of the focal length is faster for the proposed system than the previous VFLA based system because the tilting response time of LC layers which is altered via an external electric field are longer than the switching time of the light polarization. At ahead section, it is mentioned that Δz total=~33 mm would be obtained for d =0.2 mm, f 1=630, f 2-29mm and W=4 mm. However optically Δz total is larger than computational Δz total if wave optical theory is considered. Thus, in Fig. 9(b), (c), the reconstructed image has nearly no degradation due to this effect.
An InIm system taking advantaging of a BLA with polarization selective focal lengths was presented. Both real and virtual images of a 3D object were decently reconstructed at two widely separated positions with no remarkable degradation in the resolution. In the future an InIm system exhibiting a continuously varying reconstructed image will be attempted. A lens with shorter focal lengths might be required to overcome the narrow viewing angle resulting from the limited amount of birefringence available from BLAs. The aberration of the BLAs and the range of depth enhancement should be also considered.
This research was supported by the MKE (Ministry of Knowledge Economy), Korea under the ITRC (Information Technolgy Research Center) Support program supervised by the IITA (Institute of Information Technology Advancement) (IITA-2008-C1090-0801-0018).
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