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We describe a coaxial holographic recording system for achieving high recording density. We implement several techniques, such as an objective lens with high numerical aperture (NA), high capacity page data format, a random binary phase mask, and an optical noise reduction element. Our system successfully realizes a hologram recording/retrieving at a low diffraction efficiency less than 2.0×10-3 and achieves a raw data density of 180 Gbit/in.2, thus demonstrating the potential of a coaxial holographic system for high-density optical storage systems.
©2007 Optical Society of America
1. Introduction
Holographic data storage (HDS), which volumetrically records two-dimensional page data in a recording medium, is a promising breakthrough for advanced optical storage systems due to its potential for high data capacity and high data-transfer rate. The technique of holographic data storage has been widely researched [1], and coaxial recording has been studied as an attractive technique [2,3]. In coaxial recording, signal and reference beams share the same optical axis, and can record/retrieve a hologram in a recording medium through a single objective lens. Holograms are multiplexed by shifting a medium with a certain pitch. Thus, its optical system can be designed similar to those used in conventional optical disc systems, such as CDs and DVDs, and it can be made compact and compatible with a disc drive system by applying existing servo control techniques.
Stanford University and Siros Technologies have designed and implemented a digital holographic storage disc system including electronic hardware for channel decoding, and have demonstrated a transfer rate of 10 Gbit/s [2]. Horimai et al. have presented their basic specifications of a coaxial system, such as optical configuration, disc structure, and page data format, and demonstrated its fundamental recording/retrieving characteristics [3].
While recent researches, including the two above-mentioned studies, are quite interesting, we have not come across studies that have experimentally demonstrated multiplexed recording performance in a coaxial system with a large number of multiplexed holograms, and therefore, its characteristics are still unknown.
In this paper, we demonstrate our developed coaxial recording system for high recording performance. Various techniques were introduced into our system, and the details of them are presented. We evaluate system characteristics for single hologram recording and its selectivity. In addition, we also perform multiplexed recording and discuss recording performance.
2. Coaxial recording system
In HDS, one can obtain high data capacity by multiplexing holograms in the same region of a recording medium; however, this would require the recorded holograms to share the medium. Hence, given a finite dynamic range of the medium and a large number of multiplexed holograms, it is necessary to realize a recording/retrieving operation with low diffraction efficiency and utilize the medium as effectively as possible to improve the recording density of a holographic system.
We have carefully designed and implemented the coaxial holographic recording system taking the above conditions into account. Figure 1 shows the schematic diagram of the coaxial holographic recording system. In addition to typical devices, such as a digital micromirror device (DMD™, Texas Instruments) that serves as a spatial light modulator (SLM), and a complementary metal-oxide semiconductor (CMOS) image sensor as a two-dimensional detector, we have introduced a blue external cavity laser diode (ECLD), an objective lens with high numerical aperture (NA), a phase mask, and a polarizing beam diffractor (PBD). In this section, we present the detail of each component.
2.1 Blue external cavity laser diode
In HDS, a shorter wavelength laser has an advantage in increasing recording density, because it can decrease the size of a recorded hologram compared to longer wavelength lasers. Hence, we selected a blue light as the light source, and used the blue ECLD that was originally developed by our group [4]. The blue ECLD offers a large output power of 80 mW and long coherent length of 14 m, thus making it suitable for holographic data storage. The wavelength of the ECLD used in the experiment was 407 nm.
2.2 High NA objective lens
The objective lens is a key element in HDS, because it determines not only the effective page size (or page data capacity) but also the size of a recorded hologram. A smaller page size requires an increase in the number of multiplexed holograms to achieve the same recording density, leading to a rapid decrease in diffraction efficiency [5]. Therefore, the objective lens needs to have a sufficient diameter to maintain an adequate page size. From the viewpoint of hologram size, the objective lens needs a short focal length to produce small holograms. To satisfy both conditions, i.e., sufficient size and a short focal length, the lens must have a high NA. Moreover, in the case of a page-oriented HDS, the wavefront aberration of the objective lens in a telecentric system is also important; a small aberration is necessary to maintain quality in the detected signal image.
Fig. 1. Schematic diagram of coaxial holographic recording system. ECLD denotes the external cavity laser diode; HWP, half-wave plate; DMD, digital micromirror device; PM, phase mask; PBD, polarizing beam diffractor; and L1–L4, lenses. Focal lengths of L1–L4 and objective lens are 50 and 5 mm, respectively. Irises are square and twice the Nyquist size. Retrieved data is detected with an over-sampling ratio of 2.0 using zoomed optics placed in front of the CMOS image sensor.
We designed a special objective lens for the HDS considering the above-mentioned conditions. Figure 2 shows an overview of the objective lens. The focal length and effective diameter were 5.0 and 6.5 mm, respectively. The corresponding NA was 0.65, and the aberration was less than 0.03 λrms at all image position. The lens also satisfied the Abbe sine condition. The lens dimensions were ϕ 17×16 mm, which is small enough for making a holographic system compact.
2.3 Phase Mask
The recording media used in HDS are usually photopolymers or photorefractive crystals, whose refractive index change are limited in nature. Thus, the DC peak of the Fourie image from an objective lens, which has extremely high intensity, is never suitable for hologram recording, because it exceeds the media limit and the resultant hologram has insufficient quality.
There are two methods to avoid this adverse effect of the DC peak. One is to create a gap layer between the recording material and the reflective layer in the recording medium [3]. This prevents the recording material from being illuminated at a focused plane, where the DC peak intensity is maximum. However, this method inevitably decreases the effective dynamic range of the medium and increases the size of recorded holograms due to the gap layer. This eventually degrades the overall multiplexed recording performance. The other method is to suppress the DC peak optically. One can realize this by applying a random binary phase mask [6]. A random binary phase mask can homogenize the spectrum and suppress the DC component on the Fourier plane. An example of calculated profiles is shown in Fig. 3, which has the following calculation conditions: the pixel number is 128×128, the input pattern is a random pattern with a white rate of 0.5, the pixel pitch d is 13.68 µm, the wavelength λ is 407 nm, and the focal length f is 5.0 mm (the corresponding Nyquist size λf/d is approximately 150 µm). It can be seen that the DC component is greatly suppressed and becomes comparable with the intensity of AC component. In general, the peak intensity decreases as 1/N when the number of bright pixels is N. Thus, one can effectively utilize the dynamic range of the recording medium. In addition, the phase mask can spread the intensity distribution over a wide range, greatly increasing the interference efficiency between the signal and reference beams in the recording medium. Because of these advantages, we used the random binary phase mask.
An optical microscopic image of the fabricated random binary phase mask is shown in Fig. 4. The pixel pitch was set to be equal to that of the SLM. The change in thickness was determined to be λ/(2(n-1)), where λ is the wavelength of light, and n is the refractive index of a substrate, so that a two-phase status [0,π] was realized. The phase mask was placed at the conjugate plane of the SLM as shown in Fig. 1.
Unfortunately, a random binary phase mask usually accompanies interpixel interference (IPI) [7]. IPI occurs at the pixel boundaries where neighboring phase status is different, leading to degradation of data image quality. From this point of view, we used a square iris with the size twice the Nyquist size at the focal plane of relay lenses, because it restricts the degradation to be minimum.
2.4 Polarizing beam diffractor
The optical scattering noise from a reference beam is a major problem in coaxial HDS. The reference and signal beams both propagate along the same optical axis, and the reference beam’s scattering noise disturbs data retrieval at low diffraction efficiency. To solve this problem, several techniques have been proposed [8,9]. Although these techniques are effective for noise reduction, the schemes are rather complex and make the total optical system more complicated compared to a typical coaxial system. Therefore, we applied a new optical noise reduction element, which we call polarizing beam diffractor (PBD).
Figure 5 shows the principle of working of the PBD. The PBD is capable of polarization-selective diffraction and only diffracts S-polarized light. In retrieving a hologram, the reference beam, which is controlled in the P-polarized state, propagates through the PBD without diffraction and the polarization state is changed into the circular polarization by the quarter-wave plate. After retrieving a recorded hologram from the recording medium, the reference beam goes back toward the PBD along the optical axis, and the polarization state is changed into the S-polarization by the quarter-wave plate. Consequently, the reference beam is diffracted away from the optical axis by the PBD. The polarizing diffraction grating consists of a birefringent material, and it is patterned according to the reference beam area (Fig. 5(c)). The PBD has the following characteristics for a blue light: the transmissivity is more than 90 %, the diffraction angle is 15 degrees, and the extinction ratio as a polarizer is more than 70, which are sufficient for practical application. The PBD is located at the front-focal plane of the objective lens.
Figures 6(a) and (b) show representative CMOS sensor images with and without the PBD. These results show that the PBD can diffract the reference beam and greatly decrease its scattering noise. The dependence of error rate on diffraction efficiency was also examined (Fig. 6(c)). Without the PBD, the error rate begins to increase around a diffraction efficiency of 8.0×10-3. On the other hand, with the PBD, the error rate performance significantly improves, and an equivalent error rate is obtained at a diffraction efficiency of 4.0×10-3. These results reveal that the PBD is effective for noise reduction and can realize data retrieval with lower diffraction efficiency.
Fig. 5. (a) Principle of working of PBD. PBD has a polarization-selective feature, and can only diffract S-polarized light. (b) Structure of PBD. (c) Photograph of PBD. Grating area is patterned according to reference beam area.
Fig. 6. CMOS sensor images (a) without and (b) with PBD. (c) Dependence of error rate on diffraction efficiency.
2.5 Page format
The page data format used in the experiment is shown in Fig. 7(a). We designed the signal pattern to be circular for effective use of the SLM area. This allowed us to increase the capacity available in a single page, leading to a decrease in the total number of multiplexed holograms. The reference pattern was a random pattern with a white rate of 0.5. Note that changing the reference pattern does not significantly affect the recording performance, because the random binary phase mask widely spreads the distribution of the reference light. The diameter of the signal pattern and the outer diameter of the reference pattern were 4.7 and 6.4 mm, respectively, and the corresponding NAs were 0.47 and 0.64. The gap width between the signal and reference patterns was 0.45 mm.
The details of the signal format are shown in Figs. 7(b)–(d). Figure 7(b) shows a magnified pattern that illustrates four subpages in the central area of the signal pattern. Each subpage consists of 24×24 pixels, and contains a sync mark in the upper-left corner that is used for position detection. Note that the subpage in the outer signal area was partially cut to make it circular. The minimum data unit, called a “symbol,” consists of 4×4 pixels (Fig. 7(c)). As a symbol modulation code, we applied the E(16, 3, 8) sparse code that has three bright pixels in sixteen pixels [10]. Figure 7(d) shows the pattern of the sync mark. The sync mark occupies only 4×4 pixels, thus contributing to an increase in page data capacity. An error correction code (ECC) was not applied in this experiment.
In the procedure of the data position extraction and error detection from retrieved page data, we applied a two-dimensional clock extraction method that was originally developed by our group [11]. This method has significant advantages over conventional detection methods in precision of pixel detection and robustness against misalignment (e.g., due to magnification or rotation of a page), thus improving error detection performances.
Fig. 7. (a) Page format used in experiment. Signal and reference patterns are placed in central area and outer areas, respectively. (b) Magnified signal pattern with four subpages. One subpage consists of 24×24 pixels. Gray line is drawn for help in visualization. Patterns of (c) symbol data and (d) sync mark. Each pattern is 4×4 pixels.
3. Experimental results and discussion
In this section, we describe a series of experimental evaluations, including single recording characteristics, shift selectivity, and multiplexed recording performance. Figure 8 illustrates the structure of the recording medium used in the experiment. The material and cap layer thickness were both 600 µm, and an anti-reflection coating was applied on the top of the cap layer. A photopolymer was utilized as a recording material. The fundamental characteristics of the material were analyzed and discussed in Ref. [12].
3.1 Single recording characteristics
Figure 9 shows recording characteristics of a single hologram. In the experiment, read energy was set to 1.4 mJ/cm2. Write energy dependence shown in Figs. 9(a) and (b) indicate that as the write energy decreases, the diffraction efficiency decreases and the symbol error rate degrades; at a write energy of 1.4 mJ/cm2, a diffraction efficiency of 5.0×10-3 is obtained and no symbol error is detected. Note that ECC was not applied in the experiment. The retrieved page data and its histogram are shown in Figs. 9(c) and (d). It is shown that bright pixels “1” and dark pixels “0” are well separated, which means that the page data is clearly retrieved. These results indicate that the techniques introduced in our system work effectively, thus realizing hologram recording and retrieval with low diffraction efficiency.
3.2 Shift Selectivity
Fig. 9. Recording characteristics of single hologram. Dependence of (a) symbol error rate and (b) diffraction efficiency on write energy. (c) Retrieved hologram data and (d) its histogram at a write energy of 1.4 mJ/cm2; “1” and “0” correspond to bright and dark pixels, respectively.
Selectivity is a significant feature of a holographic storage system, because it affects both, system tolerances and interactions among multiplexed holograms. As mentioned above, we applied a coaxial shift multiplexing system with a random binary phase mask, in which shift selectivity is usually determined by the auto-correlation length of the speckle of the reference beam [13]. Now, we theoretically and experimentally examine the shift selectivity.
The intensity distribution of the reference beam on the Fourier plane is shown in Fig. 10(a), which was calculated with following conditions: the input pattern was the reference pattern shown in Fig. 7(a) with a random binary phase mask, the pixel pitch was 13.68 µm, the wavelength was 407 nm, and the focal length was 5.0 mm. Due to the effect of the random binary phase mask, the distribution spread twice the Nyquist Size (300 µm) at the first null distance, which is equivalent to the distribution of a single pixel [6]. The magnified distribution shown in Fig. 10(b) indicates that sub-micron speckles are generated over the entire area. To estimate shift selectivity, we directly calculated the auto-correlation length of the speckle (Fig. 10(c)). The obtained auto-correlation length is approximately 0.6 µm, according to the definition of the full width between the first two minimum points. Following this calculation, we experimentally evaluated shift selectivity. The shift selectivity shown in Fig. 10(d) indicates that the selectivity curve forms like a sinc function, and the shift for the first minimum is 0.28 µm, which gives a full width of 0.56 µm. This result is in good agreement with the calculated results. From the viewpoint of practical application, a shift selectivity of ±0.28 µm is sufficiently large for disc position control when using conventional servo techniques, and small enough for multiplexing holograms to realize high recording density.
Fig. 10. (a) Calculated intensity distribution of reference pattern on Fourier plane. Area size: 600×600 µm. Gray scale is 1/100 of maximum intensity for better visualization. (b) Magnified intensity distribution of central area of (a). Area size: 20×20 µm. (c) Profile of calculated auto-correlation intensity. (d) Evaluated shift selectivity in experiment.
3.3 One-dimensional Multiplexed recording
Next, we perform one-dimensional multiplexing to reveal fundamental characteristics of shift multiplexed holograms. The multiplexed condition is shown in Fig. 11. The multiplexed area of the center position of holograms was fixed to be constant (800 µm), and the shift pitch p was changed from 2 to 16 µm. The multiplexed hologram number M was determined so that it satisfied the condition of p×(M-1)=800. The five holograms shown as black marks in Fig. 11 were retrieved for evaluation. The write energy and read energy were 1.4 mJ/cm2, and no scheduling was applied.
Figures 12(a) and (b) show the change of diffraction efficiency and symbol error rate (SER) for each shift pitch condition, respectively. These results indicate that the diffraction efficiencies of the three central holograms are lower than those of the first and last holograms, and the SERs are much higher. This is due to the difference in the multiplexing degree (for example, the multiplexing degree of the center hologram is twice as high as that of the first or last hologram). It is also shown that the diffraction efficiencies and SERs of the three central holograms are almost equivalent, which suggests that the multiplexing degree are almost same for these holograms. While the distance between these holograms (200 µm) seems to be rather small for the saturation of the multiplexing degree from the viewpoint of hologram size (300 µm at the focal plane and 560 µm at the material top plane), we consider that the energy distribution of a recorded hologram, which forms a sinc function due to the effect of a random binary phase mask, is related to this result. The dependence of characteristics of the center hologram on the shift pitch are shown in Figs. 12(c) and (d). The lateral axes of Figs. 12(c) and (d) are the multiplexing degree instead of the shift pitch itself, which is inversely proportional to the shift pitch. It is shown that when the multiplexing degree increases (the shift pitch decreases), the diffraction efficiency decreases almost linearly and the SER increases. Especially, the SER drastically degrades at p=2 µm, indicating that it is appropriate to apply a shift pitch more than 4 µm from a practical viewpoint.
Fig. 11. Multiplexed condition in one-dimensional recording. Black marks indicate retrieved holograms for evaluation.
Fig. 12. Multiplexed characteristics in one-dimensional recording. Change of (a) diffraction efficiency and (b) symbol error rate for each shift pitch condition. Retrieved hologram number corresponds to the number shown in Fig. 11. Note that symbol error rates for p=8 µm and p=16 µm are almost zero. Dependence of (c) diffraction efficiency and (d) symbol error rate on multiplexing degree. Multiplexing degree is inversely proportional to shift pitch and is normalized to that of p=16 µm.
3.4 Two-dimensional Multiplexed recording
Finally, we discuss two-dimensional multiplexed recording performance. In this evaluation, we applied a raster scan method as the recoding sequence (Fig. 13). After writing the first hologram, holograms are first recorded along the shift direction, and then along the track direction. For evaluating the performance, we retrieved the eleven holograms shown as black marks in Fig. 13, which includes the first, center, and last holograms. Experimental conditions are summarized in Table 1. The shift pitch was set to 8 µm, and the track pitch was changed according to the recording density. The number of multiplexed holograms was determined by the recording pitch and hologram size, and almost satisfied the (2n-1) regime [14]. We used the same write energy for all holograms. This reason is as follows: while angular multiplexing separates a recorded area into a book unit [15], shift multiplexing utilizes the entire recorded area in a continuous manner. Thus, all holograms have to be taken into account in determining the write scheduling. However, it is not practical to individually define the write energies for a large number of holograms on a disc. In addition, the scheduling should be such that the write energy is constant because the degree of multiplexing saturates and becomes constant when holograms are sufficiently multiplexed.
Fig. 13. Raster scan method in two-dimensional multiplexed recording. Black marks indicate retrieved holograms for evaluation.
Table 1. Experimental conditions for each data density.
Fig. 14. Multiplexed characteristics in two-dimensional recording at a raw data density of 180 Gbit/in.2. Retrieved hologram data and histograms for the first hologram ((a) and (b)), the center hologram ((c) and (d)), and the last hologram ((e) and (f)); “1” and “0” correspond to bright and dark pixels, respectively. (g) Diffraction efficiencies and (h) symbol error rates of retrieved holograms.
Figure 14 shows an example of retrieved data with a raw data density of 180 Gbit/in.2. The retrieved page data and histograms for the first, center, and last holograms are shown in Figs. 14(a)–(f). It is found that the brightness of the center hologram is low, and its histogram degrades compared to the first and last holograms; the overlapped area between bright pixels and dark pixels is enlarged. From the viewpoints of diffraction efficiency and SER (Figs. 14(g) and (h)), we can see that the three central holograms in the center track have lower diffraction efficiencies and higher SERs compared to other holograms because of the difference in the multiplexing degree. In addition, similarly to the case of one-dimensional multiplexed recording, the diffraction efficiencies of the three central holograms in the center track are almost equivalent, which suggests that the multiplexing degree of these holograms are almost same. In the case of the center hologram, an SER of 8.0×10-2 and diffraction efficiency of 1.4×10-3 were obtained. Diffraction efficiency and SER dependence on raw data density are shown in Figs. 15(a) and (b). While the diffraction efficiency decreases and the SER degrades with an increase in raw data density, we obtained a raw data density of 100 Gbit/in.2 at an SER of 1.0×10-2, and also achieved 180 Gbit/in.2 with an SER of less than 10-1, which can be corrected with 40–50% ECC. To our knowledge, this is the first instance of successfully multiplexing a few thousand holograms in a coaxial holographic system and experimentally evaluating its recording performance.
As for the consumption of medium dynamic range, it is usually considered that when a large number of holograms are multiplexed and the modulation of the recording medium becomes saturated, the diffraction efficiency of a recorded hologram drastically decreases as discussed in Ref. [5]. However, the obtained diffraction efficiency change is almost linear as shown in Fig. 15(a). We consider that this linear and continuous change indicates that the medium dynamic range was not consumed to a full extent and the overmodulation of the medium did not occur in this experiment.
To analyze multiplexing characteristics in detail, we examined signal and noise intensity changes (Fig. 16). Here, the signal and noise intensities are determined simply by the average intensities of bright pixels “1” and dark pixels “0”, respectively. The result reveals that although the noise intensity is almost constant, the signal intensity decreases with an increase in raw data density. This suggests that the main reason for SER degradation is not related to the noise increase, but to the signal decrease. We consider that this is mainly due to the increase in the multiplexing degree (overlapping of recorded holograms). Therefore, a decrease in hologram size and an increase in page data capacity will further improve recording performance.
4. Summary
In this paper, we described the development of our coaxial holographic recording system for realizing high recording density. We implemented several techniques, such as a high NA objective lens with NA=0.65, circular page format for high page data capacity, a random binary phase mask for the homogenization of intensity distribution, and a polarizing beam diffractor for noise reduction. Acceptable symbol error rate was successfully obtained at a low diffraction efficiency less than 2.0×10-3, and we confirmed a high shift selectivity of 0.58 µm. We performed both one-dimensional and two-dimensional multiplexing and revealed fundamental characteristics of shift multiplexed holograms. In addition, we evaluated the multiplexed recording performance with a few thousand holograms, achieving a raw data density of 180 Gbit/in.2. This work demonstrated the potential of the coaxial holographic system and will contribute to the development of high-density optical storage systems in future.
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