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This research proposes a method that uses a single object beam to record multiple images in a photorefractive crystal medium without having to use any reference wave. The object beam in this study is modulated using a lenticular lens array sheet to produce a set of sub-object beams. These beams are then angularly separated on the recording plane and their scattered waves overlapped in an iron-doped photorefractive LiNbO3 crystal. This single-exposure, multiple-holographic-recording method is simple and proven successful via the experiments that recorded four holograms in a 30 × 30 × 1 mm3 LiNbO3:Fe crystal with single exposure.
©2012 Optical Society of America
1. Introduction
The requirement for higher speed and greater volume for the information storage has made the study of optical information storage a hot research topic in the optoelectronics field. To holographic technique is the best to meet the need for speed and volume [1] as it allows fast access, fast writing, and high storage density [2].
Holographic multiplexing is the process of recording multiple holograms, either in the same physical location of a medium or in many locations. Among the methods for information storage enhancement are multiplex recording, space multiplexing [3], angular multiplexing [4], wavelength multiplexing [5], peristrophic multiplexing [6], shift multiplexing [7] and phase-code multiplexing [8–10]. These holographic data storage methods take much space because they require complex holographic systems for the recording of the interferences between object wave and reference wave.
In 1993, Kukhtarev et al. [11], for the first time, demonstrated the holographic recording using only one input beam. Their single beam holographic grating recording based on the photogalvanic coupling between orthogonal birefringent modes is demonstrated in a photorefractive BaTiO3 crystal. The periodic variation in refractivity induced is used for information storage. In 1997, Naruse et al. [12] proposed a holographic memory configuration with one-beam geometry in a photorefractive crystal. The incident beam enters the crystal and splits into an object beam and a reference beam. The two beams eventually cross and interfere with each other within the crystal. Their experiments have demonstrated the capability to record ten angle-multiplexed holograms in a Fe:LiNbO3 crystal. Mitsuhashi and Obara [13] later demonstrated a compact holographic memory system via one-beam geometry. Using a 635 nm laser diode as the light source and a Fe-doped 45° cut LiNbO3 photorefractive crystal as the recording media, this system have eliminated the need for splitting the incident beam into object and reference beams.
Liu, et al. [14] have proposed another method that uses a single object beam to record images in a photorefractive LiNbO3 crystal. They have accomplished recording by fanning the resulting holograms from interference between the object beam and its scattered beam. The recorded pattern can be viewed with white light as well as with a laser beam entered within a certain angular range. In 2005, Horimai, et al. [15] developed a reading and writing method for a holographic storage system called collinear holography. This method allows recording two-dimensional page data and constructing a small volumetric optical disk storage system with CD and DVD upward compatibility. In further research, Hideyoshi and Tan [16] have applied collinear holography to a holographic versatile disk (HVD) system. This research has introduced a selectable-capacity HVD recording standardized format which allows the construction of a small HVD system with CD and DVD upward compatibility. In 2007, Sun, et al. [17] proposed a paraxial solution to the coaxial holographic storage algorithm based on the scalar diffraction theory and a VOHIL (volume hologram being an integrator of the lights emitted from elementary light sources) model. Their study has shown that the bit error rate of the system can be improved via changing the reference pattern. This solution is helpful for designing a reference pattern to produce a high-quality readout pattern in the coaxial holographic storage system. Following this study, Yu, et al. [18] have proposed a reference modulation approach in a collinear holographic storage system to increase the signal-to-noise ratio (SNR). They have shown that the point-spread function is related to the autocorrelation function of the reference pattern times a defocusing phase term. They have proposed and demonstrated lens-array phase modulation that can enhance the system SNR to 63.2 from the traditional 2.3.
The methods described above, while only needing a single beam for information recording, allow to recording only one image at a time. That means each image has to be processed one at a time when multiple-image recording is needed. Accurate calculation of the exposure sequence is also required in order to achieve greater storage capacity and uniform diffraction efficiency [19].
This paper proposes a method that helps to reduce the recording procedure complexity and simplify the recording system wave path. This method uses a single object beam to record multiple images in a medium without the need for a reference wave and thus is less complicated than the traditional holographic storage mechanism. The feasibility of this single-exposure, multiple-hologram recording technique is verified via an experiment that records four holograms in a 30 × 30 × 1 mm3 LiNbO3:Fe crystal with a single exposure.
2. Working principle
This study is conducted using a Lenticular Lens Array (LLA) that consists of multiple lenticular lenses of the same size [20, 21] as depicted in Fig. 1c , where R is the radius of curvature, n is the refraction index and f is the focal length as well as the thickness of each lens. The LLA density is defined as the number of lenticular Lenses Per Inch (LPI) and 1/ LPI represents the width of a single lens. A 20 LPI LLA and a set of four source images (i.e. an A, a B, a C, and a blank) of identical resolution and size (1” x 1” as shown in Fig. 1a) are selected for this study. As shown in Fig. 1b, strips of 1/20” are cut out from each of these source images at an equal distance 1/20”. The remaining 1/20” strips of each letter image are numbered sequentially (namely; A1, A2…, A19, A20; B1, B2…, B19, B20; and C1, C2…, C19, C20; respectively). The prepared images are then incorporated into a set with each corresponding strip overlapped (i.e. A1 on B1 on C1, A2 on B2 on C2, …, A19 on B19 on C19, A20 on B20 on C20). However, each image should shift a bit so that part of the image would be recognizable through the cut-out space. The set, called the LLA-input-pattern, is then stamped on the focal plane of the LLA as the input images.
Fig. 1 LLA input image design process: (a) selecting source images, (b) cutting out strips from each image, and (c) incorporating the cut images.
When an incident ray hits the LLA-input-pattern, the ray that passes the spot on the same curvature on each respective lens in the array should refract to the same direction. When each fragmented image strip is placed on the same corresponding focal location of each lens in the array, the observer will see a different regrouped image at a different viewing angle. Take the case shown in Fig. 2 for example, as the light propagates through the LLA-input-pattern, the fragmented images A1 through A20 should refract through each lens of the array to one direction and integrate to form a complete image A. The strips B1 through B20 should refract through each lens of the array to another direction to rebuild image B. The strips C1 through C20 should go through the same process to rebuild image C.
With the LiNbO3:Fe crystal closely attached behind and the plane wave incident on the LLA-input-pattern, the sub-object beams refracted within the crystal could mutually interfere to produce an index grating as shown in Fig. 3 . When the input image is removed during the reconstruction process, the plane wave modulated by the LLA will produce identical optical fields as the recording wave. The modulated waves would each read the index grating within the crystal via the same angle to reconstruct the source images that have been recorded.
Let be the electric field vector of the fragmented image, A1, then the interference fringe distribution of A1 and the object beams of other images can be expressed as
Of the four terms on the right hand side of Eq. (1), the 1st and the 2nd terms constitute the DC term and the 4th term is the interference term between the object beams other than A1. These terms are object beams of the non-A images and as a result cannot be used to reconstruct image A1. The 3rd term, through which the A1 image can be reconstructed, is the interference term between image A1 and the non-A images. As image A = , image A can be reconstructed from the interference term .3. Experiments
Figure 4 shows the scheme for a single beam storage setup used to record multiple holographic images. The polarization of the laser beam is first identified with the polarizer. The beam moves through the spatial filter, into the iris and then the lens. The incident beam is then expanded and collimated. Multiple images are then recorded with the single beam via the recording platform. The light source used in the experiment is a 532 nm Verdi laser and the recording media is the 1,000 ppm LiNbO3:Fe crystal. The input pattern, which comprises images A, B, C, and a blank image, is incorporated using a 62 LPI LLA manufactured by PACUR. The blank image is used as the input image for the reference beam in the hope that the information from both the reference and object beams can be fully recorded in the LiNbO3:Fe crystal. This design also avoids image distortion and uneven distribution of the rebuilt object beam image. At the image rebuilding stage only the reference beam image is applied to assure that the object beam image information stored in the LiNbO3:Fe crystal is a hologram rather than a burnt in picture.
Figure 5 shows the design schemes of the input image and the rebuilt reference beam. To reduce the crosstalk among the images, a black background is inserted between each of the images A, B, C, and the blank.
Figure 6 is a beam positioning platform scheme designed to solve the position alignment issue for the input and the rebuilt images during recording. The platform is equipped with a five-axle adjustment device to provide rotation, inclination, and shifting functions via which the input image and LLA positions can be accurately aligned. An inclinable stand on the platform base maintains the incident beam and system at a right angle.
To start, apply a 300 mW laser light to the LLA input pattern. The film of the input image is removed after recording and replaced with the film that contains only the reference beam. To keep the recorded information in the crystal from being interfered with or erased, the same incident ray with reduced power less than 300μW is applied instead. Image capturing part of this experiment is accomplished via CCD camera, which captures the image at the imaging plane of the lens. The angle of the reconstructed images can be accurately measured with the help of the platform that can be precisely rotated and titled when the laser beam projects each image to the center of the LiNbO3 crystal. The results are shown in Tables 1 and 2 .
Table 1. Experimental Parameters of Single-Beam-3-Holographic Image Storage
Table 2. Experimental Results for Single-Beam-3-Holographic Image Storage
The study starts with a single-beam experiment that stores a hologram of three images (i.e. A, B and C). The corresponding power of the incident beams and the angles between the optical axis and each image are measured prior to the recording. The parameters shown in Table 1 indicate that the power ratios of the incident beam and each of the recording beams are similar. Table 2 shows that the crosstalk interference among the diffraction images is minor. The reconstructed images are clear and the diffraction efficiency, while having a tendency to attenuate when the incident angle increases, are distributed evenly.
The subsequent experiment uses a single-beam to store four holographic images (i.e., △, ◻, ☆, and ◯). Again, the corresponding power of the incident beams and angles between the optical axis and each image are measured prior to recording. The parameters shown in Table 3 indicate that the power ratios of the incident beam and each of the recording beams are not as close as the previous experiment. Nevertheless, the crosstalk interference among the diffraction images is still minor, as shown in Table 4 . The reconstructed images are clear and the diffraction efficiency is distributed evenly with a tendency to attenuate as the incident angle increases.
Table 3. Experimental Parameters of Single-Beam-4-Holographic Image Storage
Table 4. Experimental Results of Single-Beam-4-Holographic Image Storage
4. Conclusion
The researchers have used a Lenticular lens array design to integrate the input images for a single beam recording device that allows the recoding of multiple holograms. This one-exposure, multi-hologram recording method eliminates the need to divide the incident wave into object and reference beams and consider the exposure sequence. The study has shown, without the need to rotate the recording film, the feasibility to record four holograms in a 30 × 30 × 1 mm3 LiNbO3:Fe crystal with a single exposure. The respective imaging angles of the four reconstructed images are the same as their original images. Only one parallel beam is needed to read back the recorded information. This constitutes accelerated information access as well as great process simplification and capacity enhancement in optical information storage. These experiments have demonstrated uniform diffraction efficiency distribution in similar diffraction angles.
The resolution of each picture tends to blur, as the input contains more images. This image deterioration issue can be partially resolved when the incident beam has a shorter wavelength. With this in mind, future study can be directed to explore the feasibility of recording even more holograms in an even smaller medium with a single exposure.
The lengthy process in fabricating the input images of the LLA-input-pattern makes this approach in its current form not applicable for real-time applications. Nevertheless, it is possible to incorporate an SLM or similar device that interlaces multiple images and records arbitrary and changeable patterns using this method, which is the next project of this research team.
Acknowledgments
The authors would like to thank the National Science Council of the Republic of China, Taiwan, for financially supporting this research under Contract No. NSC 100-2221-E-451-007. Corresponding author Chi-Ching Chang’s e-mail address is chichang@mdu.edu.tw.
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