A novel phase modulation method for holographic data storage with phase-retrieval reference beam locking is proposed and incorporated into an amplitude-encoding collinear holographic storage system. Unlike the conventional phase retrieval method, the proposed method locks the data page and the corresponding phase-retrieval interference beam together at the same location with a sequential recording process, which eliminates piezoelectric elements, phase shift arrays and extra interference beams, making the system more compact and phase retrieval easier. To evaluate our proposed phase modulation method, we recorded and then recovered data pages with multilevel phase modulation using two spatial light modulators experimentally. For 4-level, 8-level, and 16-level phase modulation, we achieved the bit error rate (BER) of 0.3%, 1.5% and 6.6% respectively. To further improve data storage density, an orthogonal reference encoding multiplexing method at the same position of medium is also proposed and validated experimentally. We increased the code rate of pure 3/16 amplitude encoding method from 0.5 up to 1.0 and 1.5 using 4-level and 8-level phase modulation respectively.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Nowadays massive data is being generated every moment in the information explosion era. Demand for large capacity data storage technology is ever-increasing. Improvement in conventional memory technologies such as magnetic hard disk drives, optical disks and semiconductor memories, has been struggling to keep pace with the demand for larger, faster and longer memories [1,2]. However, strong evidence indicates that these storage technologies are approaching fundamental limits that may be difficult to overcome, such as light wavelength limit and the storage medium thermal stability . Therefore, development of next generation data storage system is of great importance.
Holographic data storage is a promising technology for the storage of large amounts of data with the merits of large capacity and high data transfer rate as two-dimensional data pages can be stored in the medium volumetrically [4,5]. Besides, combined with different multiplexing techniques such as wavelength-multiplexing, shift-multiplexing and angle-multiplexing, stored data density can be improved significantly [6–8].
In typical holographic data storage system, input data pages are displayed on a spatial slight modulator (SLM), which modulates the laser light, and the holograms are written in the recording medium as the interference gratings between object and the reference beams . In 2004, collinear holographic data storage system (CHDSS) was proposed , which shows much more promising potential than conventional 2-axis holography [11–13]. Unique feature of this technology is that two-dimensional data pages are recorded as volume holograms generated by coaxially aligned object and reference beam, which are displayed simultaneously by the same SLM and interfere with each other in the recording medium.
Data encoding is a very important part for data storage. In most conventional holographic data storage systems, digital data are encoded by the amplitude distribution. There are two main shortages of pure amplitude modulation. First, grating intensity formed at the medium is non-uniform. In a practical holographic data storage system, the stored pages do not diffract uniformly due to the non-uniformities in grating formation. When we use an amplitude-based binary data pages as modulation pattern, the intensity of the object beam depends on the number of ON pixels. The variable object beam intensity will affect the strength of grating formation in the multiplexing process. Second, pure amplitude coding suffers from low code rate [14–17]. In general amplitude-modulated CHDSS, the data page codes pattern is designed based on well-known binary 3/16 principle which leads to a low code rate of 0.5.
To increase the storage capacity of holographic data storage, phase modulation methods were proposed. Phase modulation can provide higher data density and data transfer rate in holographic data storage than conventional amplitude modulation . However, the holographic storage system becomes more complex due to additional necessary components in both recording and reconstruction process. Nevertheless, such additional cost can be compensated by the improved storage capacity and more effective utilization of medium dynamic range [19-20].
However, in holographic data storage system, recording and retrieving phase information requires special modulation and detection techniques. In general, two SLMs are applied in modulating the complex amplitude. And to detect the complex amplitude, phase imaging technique is required . Usually, interferometry method is applied to convert phase to amplitude signal that can be detected by CCD or CMOS. Among the interferometry methods, off-axis interferometric technique is limited by the camera pixel size. And both off-axis method and later proposed phase-shifting technique require precise optical alignment and a vibration-free environment [22,23]. There are some further studies about interferometric techniques. Double-referential holography method proposed by Zukeran et al allows phase-detection without external additional beams by recording the phase reading reference beam and data beam at the same position for phase retrieval . However, only binary phase encoding was experimentally verified as a proof-of-concepts. In addition, there are several non-interferometry phase retrieval methods such as the ptycholographic iterative engine (PIE) algorithm, iterative Fourier transform (IFT) algorithm and so on [25,26] The non-interferometry methods require short phase calculation time to retrieval phase information and are susceptible to algorithm performance. Generally interferometry method is still most popular technique to retrieval phase information.
In this paper, we propose a phase modulation method for up to 16 levels for holographic data storage with phase-retrieval reference beam locked together with its corresponding data page at the same medium location through two sequential recording processes. It can eliminate complicated interferometric components such as piezoelectric elements, phase shift arrays and extra interference beam, making the system more compact and phase retrieval easier. Based on this method, we achieved the BER of 0.3%, 1.5% and 6.6% for 4-level, 8-level, and 16-level phase modulation respectively. In coordinate with this method, an orthogonal reference encoding multiplexing technology is proposed and validated experimentally to increase the storage density. The result shows the feasibility for at least four pages multi-recording in the medium.
2. Phase retrieval reference beam locking method
Before getting into the phase retrieval reference beam locking method, let’s review some basic knowledge first. Figure 1(a) shows a typical data page recorded in CHDSS. The inner area is the data pages with outer radial reference lines. Figure 1(b) shows the zoomed region of the red square area in Fig. 1(a) using binary amplitude encoding. Tiny white square spots stand for the ON pixels. 3 out of 16 pixels are chosen as the ON pixels for encoding. Figure 1(c) is the phase modulation encoding based on Fig. 1(b). For each ON pixel in Fig. 1(b), certain phase value from 0 to 2*PI is assigned. From Fig. 1(b) to Fig. 1(c), we can get more information for previous 16 pixels and thus increased code rate.
During the data recording process, reference beam and data page beam are focused onto the medium. Formed gratings are thus recorded in the medium. Figure 2 shows how the reference and data light are recorded in the medium, which lies in the Fourier plane of the objective lens. Based on the Bragg diffraction condition, only identical reference light can reconstruct the data page faithfully.
To retrieve phase information of stored holographic data page, there should be a way to acquire accurate phase value of holographic data page. Here, we record the data page with phase modulation and the same data page with uniform phase, called interference data page (IDP), at the same location sequentially. The IDP serves as the phase retrieval reference beam to transfer encoded phase value into intensity based on interferometry method at the reconstruction process. These two beams are locked at the same position in the recording medium. In the recording process, half of the reference region (A, B, C and D in Fig. 3) was used to record the data page with phase modulation first. Then the other half of the reference region (E, F, G, and H in Fig. 3) was used to record the IDP following the data page recording.
In the reconstruction process, all the reference regions were uploaded to the SLM to reconstruct the data page and the IDP simultaneously shown in Fig. 4 left recording process. These two reconstructed beams will interfere with each other and form an intensity image that can be captured by the CMOS camera shown in Fig. 4 right reconstruction process.
There are mainly two advantages of recording the data page and IDP at the same location. First, the whole system can be compact. There are no additional components to generate an interference beam, which is different from traditional interferometry method using an extra interference beam. Second, the generated interference beam is stable and good for phase retrieval through a stable intensity pattern of interference.
To evaluate our proposed phase retrieval reference beam locking method, we set up a complex amplitude collinear holographic storage system, as shown in the Fig. 5. We set the LCOS (X10468-01, 800 × 600 pixels, 15.8 × 12mm, 98% fill) from Hamamatsu as amplitude SLM using its polarization modulation and polarization state selectivity of PBS. And X10468-01 (phase shift of ) is also used as phase SLM. In the experiment we used the green light of 532nm for recording and reconstruction, used red light for servo system, used LiNbO3 for medium [2, 3, 27–30].
During the experiment there were two steps in the recording process: the first step is recording the data page. Here we recorded four data pages using the above mentioned orthogonal reference encoding. Then the second step is recording the IDP. Only one IDP is recorded serving as the reference beam later for previous recorded four data pages. Two SLMs are applied in this system for amplitude and phase modulation respectively in the system. And the sketch map of the process is shown in Fig. 6.
In the reconstruction process, the reference pattern will be the intact modulated circle. Data page beam and IDP beam are retrieved simultaneously and interferes with each other without external disturbance. The intensity image of interference can be accurate acquired. During the reconstruction process, phase of the IDP beam is set with different phase values by controlling the corresponding phase-SLM. Ideally only 3 IDP phase values are necessary for the phase retrieval. However, in the experiment we acquired 4 interferometric images shown in Fig. 7 with 4 pre-set IDP phase values. Based on phase-shifting detection method, phase values of data page are resolved.
2.3 Results and discussion
We generate random phase modulations and binary 3/16 amplitude modulations on the phase and amplitude SLM respectively. A customized analyzing software that can calculate each subpage signal to noise ratio (SNR), BER and intensity histogram visualization was developed using C#. The graphics user interface is shown in Fig. 8. BER is proportion of incorrectly resolved pixels of total pixels.
We define the SNR as below:
There were three different phase modulation levels applied in the experiment: 4 levels, 8 levels and 16 levels. All of them show a good data page reconstruction with high SNR. There are lower peaks of histogram with higher multilevel phase modulation, the border of each peak is fuzzier, which is in accordance with our expectation that higher multilevel modulation are more difficult to distinguish.
With phase-retrieval reference beam locking modulation, the experiment system preformed quite well in the condition of 4 levels and 8 levels with BER 0.39% and 1.3%. This is quite acceptable for data without error correction code. However, the performance got worse for 16 levels modulation, and BER reached 6.55%. In all experimental results, interferometric intensity images show consistent SNR increase towards page center. The lowest local SNR in 4, 8, 16 levels still reaches 2.67 and the lowest overall SNR reaches 3.92. The interferometric intensity images are maintained in good quality. Based on the 3/16 coding principle of amplitude modulation, the 4 levels phase modulation can reach a code rate of 1.0, which is twice of that in conventional binary amplitude modulation. And the 8 and 16 levels phase modulation can reach the code rate of 1.5 and 2.0 respectively. There are certain disadvantages needs to be pointed out with phase-retrieval reference beam locking modulation and orthogonal reference encoding. First, diffraction efficiency of the material is limited. Storage of the IDP will consume certain dynamic range of the material. The data page’s diffraction efficiency will be halved if equal intensity data page and IDP is stored with equal reference segmentation. To acquire accurate phase distribution, several interferometric intensity pages (four pages is used in our study) are required, which means more time consumption and reduced transfer rate.
3. Orthogonal reference encoding to increase the storage density
Usually to increase the storage density of CHDSS, people want to record as many data pages as possible at the same location of the mediums. The main issue needs to be addressed is to reconstruct these data pages independently without causing cross-talk. Here we propose an orthogonal reference encoding method based on phase-retrieval reference beam locking modulation to prevent cross-talk between multiple data pages recorded at the same position.
In the data page recording process, the reference pattern of data was divided into four parts as shown in Fig. 3(a), (b), (c) and (d) regions. Different phase values were assigned to these four regions. Each region interferes with data page independently, so that the page can be modulated with the assigned phase value. During the reconstruction process, only the reference pattern with identical phase distribution can reconstruct the corresponding data page.
Here we recorded four data pages at the same medium location. Details of the phase encoding are listed in Fig. 9. The principle behind this multiplexing method is that two beams with phase difference interfere with each other destructively.
Using the orthogonal phase modulation of reference pattern, the four data pages can be recorded at same position in the medium without cross-talk in reconstruction process. The principle of orthogonal reference encoding is explained with following equations. We assume the object complex amplitude function is , the writing reference complex amplitude function is and the reading reference complex amplitude function is
According to theory of hologram, the reconstruction complex amplitude can be expressed as Eq. (5) ignoring noise and irrelevant terms:
If orthogonal reference encoding method is applied, data pages to be recorded consist of multiple data pages. During our study, we tested 4 data pages multiplexing. In the recording process, the reference beam was divided into four regions. In the reconstructing process, reading reference beam was also divided into four regions following the same rules as the writing reference beam. Equation (6) expresses the corresponding functions used in four data pages multiplexing. “i” represents for different data page, and “j” represents for different reference region.
Equation (7) can be expanded into the following equation:
For better understanding, here give an example: if we use reference phase encoding of data page 1 for reconstruction, the coefficient of term DP (2) in Eq. (8) can be calculated as
Coefficients of term DP(3) and DP(4) can also be calculated as zeros. Thus only DP(1) can be faithful reconstructed.
The experimental setup in section 2.2 is also used to evaluate the performance of orthogonal reference encoding. The four different 4-level data pages are stored at same position of medium using corresponding reference one by one. The IDP is recorded in the same position of medium for reconstruction process.
Experimental phase histogram results for four data page orthogonal phase encoding recording are shown in Fig. 10. First, all four data pages were reconstructed successfully without cross-talk.
From the experimental results, we calculated the BER of page 1 to page 4 to be 3.55%, 2.64%, 4.54%, 8.02% respectively. The multiplexing results were of higher error compared with single data page recording. However, the phase statistical distribution is still distinguishable and the four pages’ phase distributions are quite similar.
That proves using the orthogonal phase modulation of reference pattern can work well as we expect in multiplexing. And the data page 1 and 2 showed quite similar BER with 0.91% difference, but the data page 3 and 4 showed worse performance. The reason might be the increased noise level due to multiplexing and limited refractive index modulation range of the recording medium.
Currently the BER remains at a relative high level, reduction of the BER will be our future work to do, as it is influenced by many factors including property of recording medium, data encoding regulations, ratio of data page to reference and so on. Nevertheless, it provides a novel method to realize multiplexing at one position of the medium in holographic data storage.
In this big data era, holographic data storage method is a promising candidate solution with its high density, transfer rate and long life time. However precise phase distribution detection is still challenging. In this study a novel phase-retrieval reference beam locking method is proposed for efficient recovery of data encoded in phase-modulated data pages in collinear holographic data storage system. Efficiency of the method was also confirmed experimentally. The BER of 4 levels and 8 levels modulation were 0.39% and 1.3% respectively. With 4 levels phase modulation, the code rate can reach 1.0 which is twice of binary 3/16 amplitude modulation. With 8 levels phase modulation, the code rate can reach 1.5 which is triple of binary 3/16 amplitude modulation. In addition, orthogonal reference encoding method was proposed to realize multiplexing at the same location of medium, which is of great value to improve data storage density, data transfer rate and medium utilization. Our future work will work on the further reduction of the BER through medium optimization and new data encoding development.
National Natural Science Foundation of China (61475019).
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