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Abstract
We propose a simultaneous dual-page reproduction for holographic data storage (HDS) with high-efficiency and high-speed data reproduction by reusing a transmitted reference beam that passes through a recording medium after data reconstruction. The transmitted reference beam enters the recording medium at a different incident angle to reproduce different data pages; thus, this technology can double data-transfer rates without increasing the laser’s output power or preparing another laser source. In the experiment, neighboring angle-multiplexed two data pages were simultaneously reconstructed and a data transfer rate of 1.0 Gbps was obtained.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Recently, not only broadcasters but also various video services on the internet have begun handling high-resolution video, and ultra-high definition (UHD) video is becoming increasingly popular. Since cameras, monitors, and other devices compatible with the UHD standard are now commercially available, not only 4K but also 8K UHD video has become commonplace. The 8K UHD system has 7,680 × 4,320 pixels, which is 16 times higher than conventional high definition (HD) [1]. Additionally, the 8K format can offer a frame rate of up to 120 Hz and a bit depth of 12 bits with a high dynamic range [2], thus an uncompressed video signal has a maximum data-transfer rate of 144 Gbps. When audio signals are added; the 8K UHD content becomes high bit rate and thus large capacity. The 8K satellite broadcasting has been launched in Japan in 2018 [3], thus broadcasters can handle a tremendous amount of information every day, including 4K and HD videos.
Holographic data storage (HDS) is a promising next-generation optical storage technology with a large capacity and a high data transfer rate [4,5]. In particular, one of the features of HDS is its ability to store data for more than 50 years on low-cost recording media [6]. As the amount of data that needs to be stored increases rapidly year by year, the development of recording media such as magnetic recording media and semiconductor memory with high speed and large capacity is also remarkable. In light of the increase in the amount of data that must be stored for a long period of time but is inactive, called “cold data, “ there is a need for storage that is not only high-speed and high-capacity but also low-cost and can be stored for a long period of time. So far, HDS with a high recording density of 1 Tbit/in2 [7], 2.2 Tbit/in2 [8], and 2.4 Tbit/in2 [6] have been reported. In terms of data transfer rate, some works have over 100 Mbps [9] and 1 Gbps [6]. These reports used a binary modulation scheme for recording and reproduction, whereas recent studies have explored the introduction of multi-level modulation [10–13]; therefore, it is expected that these values can be increased several times. In our open house 2015 and 2017, we successfully demonstrated a real-time playback of a compressed 8K UHD video file with a data-transfer rate of 85 Mbps from angle-multiplexed HDS [14,15]. This transfer rate is the same as the video bit rate used in Japanese 8K satellite broadcasting [16]; hence, we show the HDS’s promise of meeting the requirements for archiving 8K video data. Therefore, HDS will meet the demand for data centers and for broadcasters like us that store a vast array of broadcast materials and videotapes in its archives. However, to archive videos as editable material, HDS must archive 8K contents at a lower compression rate, and a higher data-transfer rate technology is required.
The data format used in HDS is known as “data page,” which is a two-dimensional (2D) data array. In typical HDS, a data transfer rate is expressed as a multiple of the amount of the data in one data page reproduced by a beam exposure and the number of reproduced data pages per unit time. The amount of data in a data page increases as the SLM and camera with narrow pixel pitches and many pixels are used, thus the data-transfer rate becomes higher. A data transfer rate of 1 Gbps was achieved using a spatial light modulator (SLM) and a camera with 4-megapixels [6]. However, the number of pixels in these devices limits the increase in transfer rate. Furthermore, it is necessary to use not only the SLM and camera but also optical components such as large-diameter lenses to support large-area data pages, which increases the size of the optical setup in HDS. Another solution is to improve the recording format with high coding efficiency. As previously stated, more information can be handled by configuring the data page not only with binary values of light and dark but also with multi-level values. By using one of the most characteristic properties of holograms, the ability to record phase information, modulation codes that combine phase, and light intensity have been proposed in numerical simulation [17–22]. The amount of information per data page can be increased by increasing the number of gradations through multi-level modulation. Although the HDS using complex amplitude modulation is promising, it will take more time to demonstrate it in experiments because the noise sensitivity is severe.
Therefore, in this study, we focus on the number of reproduced data pages per beam exposure. A previous study investigated the simultaneous reproduction of two data pages to increase the data transfer rate in the HDS [23]. While a hologram in conventional HDS is usually reproduced by a single polarized reference beam, two reference beams with different types of polarization (p-and s-polarization) irradiate the medium simultaneously. These reference beams are adjusted to have an angle difference equal to the angle difference of neighboring data pages in angle-multiplexed holograms. The data pages are then captured individually and simultaneously by two cameras. The number of reproduced data pages per unit time then increases by two, doubling the data transfer rate. This scheme is promising because it applies also to large-area data pages and multi-level modulation schemes; thus, by combining these techniques, ultra-high capacity, and ultra-high-speed HDS can be realized.
We consider the power of the reference beam to improve this technology for practical use. Two reference beams with different polarizations were generated by splitting the original reference beam in the previous study. If the beam power of the two reference beams is lower than that of the conventional reference beam, the irradiation time per unit data page increases and the data transfer rate remains unchanged. Therefore, in the optical setup, a laser source with twice the power was required. However, the output of laser sources with blue-violet wavelengths, which can increase recording density by increasing NA (numerical aperture), is significantly lower than that of other laser sources with green or other wavelengths, hence it cannot be easily doubled. Although using a different laser source may prevent power reduction of the reference beam, it does not prevent an increase in size or cost of the optical setup; thus, a more efficient method is required.
In this paper, we propose to reuse a transmitted reference beam that passes through a recording medium after data reconstruction. Two data pages can be reproduced simultaneously by changing the polarization state of this beam and re-irradiating the recording medium again. We created an optical setup, evaluated the quality of the reproduced data pages, and finally estimated the data transfer rate using two beams.
2. Overview of dual page reproduction with a transmitted reference beam
2.1 Principle of data reproduction
Figure 1 shows a dual page reproduction principle using a transmitted reference beam. Data pages are angle-multiplexed at the same location by changing the angle of the reference beam when recording data, which enables a large recording capacity. When the reference beam irradiates recorded holograms, a reconstructed beam is then diffracted by the hologram. The reconstructed beam has the same polarization state as the reference beam [23]. Therefore, in the example shown in Fig. 1, the p-polarized reproduced beam is first reproduced when the reference beam is p-polarized. This beam with a data page is captured by camera1 in the same manner as with a conventional HDS. The reference beam that passes through the photopolymer recording medium is extracted and reused. The transmitted reference beam becomes the second reference beam, whose polarization state is orthogonal to the original reference beam. In the example shown in Fig. 1, the transmitted reference beam with s-polarization re-enters the recording medium. The angle of incidence of the s-polarized reference beam differs from that of the p-polarized reference beam by an angle $\Delta \theta $. The s-polarized beam reproduced by the reused reference beam is reflected by polarizing beam splitters (PBS) and captured by camera2. The angle difference between the original and transmitted reference beams is set to be equal to the angle between the neighboring data pages in angle-multiplexing. Therefore, the proposed reproduction method uses the original reference beam to reproduce odd-numbered data pages and the transmitted reference beam to reproduce even-numbered data pages, whereas angle-multiplexed data pages are reconstructed by sequentially changing the angle of the reference beam in the conventional HDS. This enables two different data pages to be reproduced simultaneously, thus doubling the data transfer rate. Furthermore, there is no need to prepare another laser source or increase the output power of the laser source; the beam can be efficiently reused to increase the speed.
2.2 Power loss of the reference beam
The optical power of the transmitted reference beam decreases slightly as it passes through the recording medium, because of the diffraction for reproduction, as well as absorption and reflection on the surface. The diffraction efficiency $\eta $ of the holograms with many multiples can be expressed as:
where $M\# $ is known as “M-number” which represents the dynamic range of the recording medium [24], N is the number of recorded holograms in one location. The higher the recording density, the lower the diffraction efficiency, which is desirable in terms of reusing the reference beam because of the low diffraction loss (typically less than 0.3% [25]). The loss due to the recording medium absorption is negligible in data reproduction [26]. The influence of reflection is the most important factor to consider. When p-polarized and s-polarized beam enters the medium at an angle of incidence $\alpha$, the reflectance can be expressed by the following equation:3. Optical setup
3.1 Recording
Figure 3 shows an optical setup used for data page recording. Note that the optical system is a two-story structure, and only the area around the recording medium on the second floor is shown in this figure. On the first floor, a spatial filter is used to remove the beam’s spatial noise, after which the beam diameter is adjusted. The laser is then divided into two beams (for signal and reference), both of which are adjusted to p-polarization.
A signal beam passes through PBS1, and an SLM, which displays the data pages modulates the beam. The modulated beam becomes a signal beam with s-polarization. The signal beam is adjusted to p-polarization by half-wave plate 1 (HWP1) to pass through PBS2. It is possible to record data with an s-polarized signal beam without installing HWP1 and PBS2 at the time of recording; however, the optical system is different between recording and reproduction, and the data quality will be degraded as phase-conjugated readout (described in Chapter 4.3) is not possible. The p-polarized signal beam passes through PBS2 and focuses on the recording medium. A p-polarized reference beam without modulation irradiates the recording medium simultaneously to interfere. Angle-multiplexing occurs when a galvanometer mirror 1 (GM1) changes the incident angle of the reference beam to the relay lens 1 (RL1), causing the reference beam to irradiate the same spot on the recording medium at different angles.
3.2 Reproduction
Figure 4 shows the optical path in the data reproduction. Beam formed on the first floor of the optical system is reflected by a mirror and travels up to the second floor of the optical system, as in the recording. The p-polarized beam transmitted through PBS3 is used as the first reference beam for data reproduction. GM2 and GM3 adjust the angle of incidence to the recording medium in two axes with high precision, resulting in an accurate reproduction of the target data page from the angle-multiplexed holograms. RL2 enables the reference beam to irradiate the same spot on the recording medium. As the optical axis of HWP1 is adjusted to maintain the polarization direction of the passing beam, the reproduced beam with p-polarization passes through PBS2 and PBS1 to reach camera1.
The first reference beam passed through the recording medium. Although the angle of the transmitted beam’s emergence changes depending on the data page to be read, the transmitted beam reaches GM4 by passing through RL1. This transmitted beam is adjusted to the s-polarized state by HWP2 and becomes the second reference beam. GM5 and GM6 reflect the beam and adjust the incident angle to the recording medium so that the angle difference between the two references beams equals the angle interval of angle-multiplexed holograms. The s-polarized reference beam reflected by PBS3 also irradiates the recording medium, and the s-polarized beam with a different data page is reconstructed. The second reconstructed beam is s-polarized; thus, PBS2 reflects the beam and camera2 captures it.
4. Experimental results
4.1 Conditions for recording and reproduction
Table 1 summarized the experimental conditions. Data to be recorded is encoded using spatially coupled low-density parity-check (SC-LDPC) code for error correction [27,28], and then converted into data pages using 5:9 modulation code [29]. The symbol size of the data page is equal to that of the SLM pitch. As shown in section 2, the amount of beam incident on the recording medium changes depending on the polarization direction, which is especially noticeable when the beam is s-polarized. Although only the p-polarized beam is used in recording, the reference beam with p- and s-polarization are used in reproduction. Furthermore, the optical power of the transmitted reference beam decreases as it passes through optical components such as lenses and prisms before re-entering the recording medium. Therefore, we scheduled the irradiation time to record data pages according to the data page number, minimizing the difference in exposure time between the two cameras in the data reproduction because of the difference in reproduced beam power. As shown in Fig. 5, odd-numbered data pages reproduced with p-polarized beams were irradiated for a constant time at any angle, whereas even-numbered data pages reproduced with s-polarized beams were irradiated for a longer time as the angle of incidence increased, resulting in high diffraction efficiency of the gratings, and high light intensity in the reconstructed beams were reproduced even with the low light intensity s-polarized reference beam. The recording medium is a photopolymer material sandwiched between two pieces of cover glass. This material is isotropic and has no difference in absorption or transmission properties depending on the polarization direction.
Table 1. Experimental conditions
4.2 Reproduced data quality
Figure 6 shows examples of reproduced data pages. The area around the data page has markers for detecting the data area and the data page number, as shown in the enlarged view in Fig. 6. Odd-numbered and even-numbered data pages were well reproduced. The quality of the reproduced data pages is shown in Fig. 7, and the bit error rate differs between odd- and even-numbered data pages. The bit error rate for data pages reproduced with the s-polarized reference beam is higher than for data pages reproduced with the p-polarized reference beam. This is because of the difference in the optical paths of the reconstructed beams. The optical paths of the two beams propagating from the recording medium to the cameras are shown in Fig. 8. A phase-conjugate readout system [30–32] is used to configure the optical setup. The reference beam is irradiated from the backside of the recording medium to generate the reconstructed beam in reproduction. A phase conjugate of the signal beam is the reconstructed beam that propagates in the same optical path as the signal beam in the opposite direction. This cancels the inherent aberrations of optical components such as lenses, preventing the quality of the reproduced data from degrading. The p-polarized reconstruction beam propagates along the same optical path (including lens1, HWP1, and PBS1) as the signal beam, as shown in Fig. 8. However, the s-polarized reconstructed beam is split by PBS2, passes through lens2, and propagates along a different optical path than that used during recording toward the camera2. Therefore, the superimposed aberration during recording was not canceled, and bit errors in even-number data pages increased. To compensate for aberration errors, HWP3 and PBS4, which were not originally required in data reproduction, were added to the optical path of the s-polarized side, as shown in Fig. 8. This enables the s-polarized reference beam to pass through the same optical components as the p-polarized beam side. Although the optical path of the s-polarized reproduction beam is not the same as the recording optical path of the recording, the aberration is not completely canceled; however, the bit errors are reduced by approximately 15%.
Another factor that can cause more bit errors on even-numbered data pages is crosstalk caused by PBS2 because the extinction ratio of the reflected beam is slightly lower than that of the transmitted beam. A previous study reported that the subtraction process using other reproduced data pages removed crosstalk noise and reduced bit errors by approximately 24% [23]. However, in this study, even if a part of the p-polarized beam is reflected by PBS2, the HWS3 converts the crosstalk components into the s-polarized beam, which is reflected by PBS4 so that the undesired beam does not enter camera2. Thus, the combination of HWP3 and PBS4 contributes significantly to suppressing the crosstalk noise in the reproduced data page captured by camera2 without signal processing.
The average bit error rates of odd-numbered and even-numbered data pages were 1.07 × 10−3 and 9.01 × 10−3, respectively. Although the wavelength of the laser and the pitch of the camera and SLM are different, even in the study of the conventional method of simultaneously reproducing two data pages by dividing one beam into two reference beams [23], many of the reproduced data had a bit error rate in the order of 10−3. In our system, the allowable bit error rate for error-free by error correction processing with SC-LDPC code is 8.0 × 10−2 [28], which means that all data pages were successfully reproduced using a combination of the p-polarized reference beam and the reused s-polarized reference beam.
4.3 Data transfer rate
We estimated the system’s data transfer rate. The exposure times of camera1 and camera2 were 0.5 ms and 0.6 ms, respectively. As described in section 4.1, the exposure time difference of the camera between odd- and even-numbered data pages is reduced by increasing the irradiation time during recording only for even-numbered data pages. However, as the hologram diffraction efficiency increases, the number of pages that can be multiplexed at the same location decreases, as shown in Eq. (1). Therefore, the exposure time of camera2 is slightly changed to compensate for this trade-off relationship.
The data transfer rate $DTR$ is calculated as follows [6].
where C is the capacity of reproduced data, ${T_e}$ is the exposure time of the camera, ${T_m}$ is the moving time of GM to reproduce the next angle-multiplexed data page. The data transfer rate is twice as fast as conventional, as two data pages are simultaneously reproduced in this system. From the data page size and modulation code efficiency, C is ${1,740 \times 1,044 \times }({{{5} / {9}}} ){ = 1,009,200}$ bits. ${T_e}$ was 0.6 ms because the camera with the longer exposure time becomes the bottleneck. ${T_m}$ was 1.4 ms; thus, these conditions resulted in $DTR$ 1.0 Gbps. For example, this data transfer speed can be doubled and exceed the data transfer rate of 1.8 Gbps which is required to archive 8K UHD contents as playout format using AVC-intra codec [33], by using a data page format twice the number of pixels [6]. This speed can be further increased by introducing multi-level modulation codes with high modulation efficiency. Compared with the 5:9 modulation code used in this study, the 10:9 modulation code using multi-level amplitude [34] and 20:9 modulation code using complex amplitude [19] can increase the data transfer rate by two and four times, respectively. The combination of these technologies enables HDS to archive re-editable UHD video materials at a lower compression rate.5. Conclusions
We developed an efficient and fast data reproduction method in HDS that reuses a transmitted reference beam to reproduce two angle-multiplexed data pages simultaneously. There is no need to prepare a high-power laser source or another laser source for this high-light usage efficiency reproduction method. Although extra optical elements such as GMs and PBSs are required to re-irradiate the transmitted reference beam to the recording medium, they are less expensive and space-saving than updating the laser source. This is especially useful for optical systems using blue-violet wavelengths, where the output power of the laser source is limited. The amount of light incident on the recording medium varies depending on the polarization direction and the angle of incidence of the reference beam. In data recording, the diffraction efficiencies of the holograms to be recorded were adjusted by changing the beam irradiation time according to the polarization direction and the incidence angle of the reference beam. This ensures that the intensity of the p-polarized and s-polarized reconstructed beam is equal, regardless of the reference beam’s conditions, ensuring that the camera’s reproduction exposure time is constant. In data reproduction, the first reference beam was set to p-polarization to reproduce odd-numbered data pages, which has less reflection on the recording medium’s surface, and the reused second reference beam was set to s-polarization to reproduce even-numbered data pages. With evaluating the bit errors in the reproduced data pages, a difference in quality was observed between the odd-numbered and even-numbered data pages. This is because the p-polarized reconstructed beam’s phase-conjugate optical path cancels the aberration that occurred during recording, whereas the s-polarized reconstructed beam’s optical path does not. Therefore, we configured the optical path on the s-polarized beam side to be as similar as possible to the p-polarized beam side to suppress the aberration. This also contributes to the suppression of crosstalk noise. The bit error rate of the reproduced data was less than the allowable rate in our HDS system with the error correction process; thus, we confirm that the data were read correctly. The estimated data transfer rate was 1.0 Gbps. This reproduction method is an effective and promising technology for the realization of HDS to archive 4 K/8 K UHD video materials, with room for improvement in modulation efficiency and other areas.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this study are not publicly available at this time but may be obtained from the authors upon reasonable request.
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