High-speed optical correlator with coaxial holographic system

Investigations into optical pattern recognition that can perform highly parallel processing have been ongoing and many algorithms and applications, such as face recognition, fingerprint recognition, target recognition, and video identification, have been proposed.^1–4) Optical correlators based on the Vanderlugt correlator⁵⁾ and used in optical pattern recognition can be divided into the following two types: (1) a device that stores a database as a matched filter pattern in a digital computer to be read sequentially on a spatial light modulator (SLM), and (2) a device that stores a database in holographic optical memory and then reads directly modulated signal light.

The first types of device reads the images stored in the hard disk drive, for example, and is flexible in that it can be applied to scene matching^2,6–8) that is suitable for a small capacity database. However, its data transfer rate is limited by the frame rate of the SLM. In the second types of device on the other hand, where the database is stored in optical memory,^1,9,10) the database can be read directly so, in principle, ultrahigh-speed transfer and correlation rates can be achieved. While being high recording density, a coaxial holographic recording system has a simple configuration and is tolerant to environmental disturbances, therefore, it has become one of the promising candidates for use in such optical memory devices.^11–15) A coaxial holographic system is compatible with existing disk storage systems such as CDs, DVDs, and Blu-ray Disks. Therefore, data can be recorded and read with high-speed rotation, and can be accessed at addressed positions. In addition, ultrahigh-speed optical correlation with more than 100 Gbps data transfer speed and a terabyte storage capacity should be achievable by maximally utilizing a coaxial holographic system. We previously demonstrated an optical correlation system with coaxial holography using a holographic optical disk¹⁰⁾ and developed a video identification system consisting of a digital server and an optical correlator.¹⁶⁾ However, in that previous work, the shift pitch in the shift multiplex recording was 20 µm and was not optimized for the signal and reference patterns. The disk rotation speed has also been limited to 300 rpm in previous studies, because of the use of an actuator designed for holographic memory systems.

In this paper, we present the development of an ultrahigh-speed optical correlator using a coaxial holographic system with the capability to calculate the enormous inner products stored in a holographic optical disk. To speed up the optical correlation, we propose and design a signal pattern for improving the shift multiplex recording shift pitch. We show a new configuration of the optical correlation system, and evaluate and demonstrate the functionality of the system through ultra-high-speed optical correlation experiments.

The optical correlation system involves two processes: the hologram recording process for registering reference images in the database in the holographic optical disk and the optical correlation process used to correlate the database images. The data transfer and correlation speed is given by

$$\begin{equation} V = P_{x}\cdot P_{y}\cdot \frac{2\pi r}{d}\cdot \frac{R}{60}, \end{equation} \tag{ 1 }$$

where r (mm), P_x (pixel) and P_y (pixel), R (rpm), and d (mm) represent the diameter of the disk, input image size, disk rotation speed, and circumferential shift pitch in the multiplex recording, respectively. To increase the optical correlation speed, it is necessary to optimize the above parameters. The circumferential and radial shift pitches in the multiplex recording are shown in Figs. 1(a) and 1(b). A diagram of optical correlation signals is shown in Fig. 1(c), and the relationship between circumferential shift pitch and correlation speed is given by Eq. (1). We define a simple similarity with two vectors, q₁ and q₂. The similarity, denoted by $S_{\text{s}}(\boldsymbol{{x}},\boldsymbol{{y}})$, is given by the following equation: $S_{\text{s}}(\boldsymbol{{q}}_{1},\boldsymbol{{q}}_{2}) = (\boldsymbol{{q}}_{1}\cdot \boldsymbol{{q}}_{2})/(||\boldsymbol{{q}}_{1}||\cdot ||\boldsymbol{{q}}_{2}||)$. The vectors q₁ and q₂ correspond to the input and database images, respectively. In this paper, we obtain calculated values which are determined using S_s. We have designed and implemented a coaxial holographic recording and a correlation system taking these parameters into account, which is shown in Fig. 2(a). We used a Q-switched (Q-SW; Spectra-Physics Navigator II J80-YHP70) laser to input page data into a rotating holographic disk, and a red laser to operate a servo system and realize high-accuracy recording and correlating. A CW laser (Showa Optronics H6780-01) was used in the correlation process. The trigger signal, which is based on the disk rotation frequency, controls the SLM and a shutter. When the shutter is opened, the pulse from the Q-SW laser propagates to the holographic disk and writes a matched filter hologram on the holographic disk. It was possible to write the matched filter hologram accurately on the same spot of the holographic disk. A schematic representation of a crosssection of our holographic optical disk is shown in Fig. 2(b). The medium consists of a glass, photopolymer and a mirror, their thickness are 0.62, 0.50, and 0.62 mm, respectively. The material polymerize with the green laser and does not react with the red laser; therefore, the laser can be used for a servo, which keeps the system on focus. In the correlation process, after passing through the matched filter in the hologram disk, the correlation signal appears on the output plane. A photomultiplier tube is utilized to detect signals of small intensity, and the intensity of the correlation signal is used to classify the resemblance level between images.

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We changed the image display device from the digital micromirror device (DMD) in the previous system¹⁰⁾ to a liquid crystal on silicon-spatial light modulator (LCOS-SLM; Displaytech SLM-1216-1). Therefore, we can increase the storage capacity on a spot by 1.64 times that achievable with a DMD, because the pixel width of the LCOS-SLM is 10.7 µm, which is smaller than that of the DMD. A custom-designed high-speed actuator was installed in this system. A conventional actuator combines three groups of lenses;¹⁷⁾ therefore, the lens can handle a disk rotation speed as low as 300 rpm. In contrast, the new actuator, in which a single lens for CDs (Edmund Optics 48137, 0.62 NA, 4.03 FL) was installed, can manage a disk rotation speed as high as 1200 rpm. Consequently, the new actuator allowed for increased data transfer speed.

3.1. Design of signal pattern

To improve recording density, several groups have tried to solve the problem of inhomogeneous intensity distribution recorded in a holographic medium, which reduces the dynamic range of a recording material.^14,18) Here, we propose a new design method for a signal pattern for optical correlation, which alleviates this problem, by conducting random address-rearrangement of the diced input images. Through application of this process, recording density has been dramatically improved, as will be discussed below. Figure 3 shows the design flowchart for the production of this random address-rearranged signal pattern. (a) An input image with RGB colors from a TV, a DVD, for example, is prepared. (b) The image undergoes grayscale conversion, edge extraction, and binarization. Conventional preprocessing is performed in the same way until an image similar to that shown in Fig. 3(b) is obtained. To create the address-rearranged signal pattern, the preprocessed image (P_x × P_y pixels) is diced into multiple blocks (each block consists of p × p pixels), as shown in Fig. 3(c), and the address of each block is rearranged to a random address, as mapped out in Fig. 3(d). These addresses are determined using a random number table; for one specific database the same random number table should always be used. Figure 3(e) shows an example of the address-rearranged signal pattern produced from an input image size of 240 × 180 pixels, where each diced block has a size of 2 × 2 pixels. Since the block size can be set sufficiently small, the rearranged signal pattern can form a circle shape while the input image can be any other shape.

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3.2. Simulation results

We performed a scalar analysis simulation to verify that this address-rearrangement design method is effective for achieving a homogenizing intensity distribution in the recording medium. Figure 4(a) shows the simulation model of the hologram recording process. The recording medium is divided into M layers. We simulated the diffraction spectrum at Z_i in the medium by the fast Fourier transform (FFT) method, which includes a defocusing factor at the ith layer.^19,20) These parameters are summarized in Table I. The complex amplitude is

$$\begin{align} U_{m}(\nu_{x},\nu_{y},z_{i}) &= \iint U_{\text{SLM}} \cdot \exp \left[j\frac{2\pi}{\lambda}z_{i}(x^{2} + y^{2})/f^{2}\right] \\ &\quad \times \exp [j2\pi (\nu_{x}x + \nu_{y}y)]\,d\nu_{x}\,d\nu_{y}, \end{align} \tag{ 2 }$$

where $(x,y)$, f, and Z_i are respectively the position in the SLM plane, the focus length of the Fourier transform lens, and the defocus amount, which is the distance between the focus plane and the ith layer. The optical intensity distribution is calculated using the complex amplitude. A hologram is recorded phase distribution which was formed by the optical intensity distribution. We simulated that with the following simulation parameters: calculation area 2048 × 2048 pixels; pixel size 2.675 µm; focal plane resolution 194 nm; wavelength (λ) 532 nm; focal length 4.00 mm; 100 layers; and medium thickness, 0.5 mm. These parameters are summarized in Table I.

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Table I. Simulation parameters.

Calculation area (pixels)	2048 × 2048
Pixel size (µm)	2.675
Resolution of focal plane (nm)	194
Wavelength, λ (nm)	532
Focal length, f (mm)	4.00
Number of layers, M	100
Medium thickness (µm)	500

We then calculated the standard deviation using Eqs. (3) and (4) below, and compared the differences between the conventional and address-rearrangement methods. The intensity deviation on y = 0 plane in the medium (from N different images) is given by

$$\begin{align} \mu (x,Z_{i}) &= \frac{1}{N} \sum_{n = 1}^{N}I_{n}(x,Z_{i}), \end{align} \tag{ 3 }$$

$$\begin{align} \sigma^{2}(x,Z_{i}) &= \frac{1}{N} \sum_{n = 1}^{N}\{I_{n}(x,Z_{i}) - \mu(x,Z_{i})\}^{2}, \end{align} \tag{ 4 }$$

where $I_{n}(x,Z_{i})$ is the intensity at position x, Z_i on image n, as shown in Figs. 4(b)–4(e). In this study, the intensity deviation from 10 different images (N = 10) was calculated, and an average value of 0.417 for $\overline{\sigma _{\text{r}}^{2}}/\overline{\sigma _{\text{c}}^{2}}$ was obtained. Here, $\text{ }\overline{\sigma _{\text{c}}^{2}}$ and $\text{ }\overline{\sigma _{\text{r}}^{2}}$ denote the average of $\sigma ^{2}(x,Z_{i})$ over the image, calculated from images by conventional preprocessing and by preprocessing with the address-rearrangement method, respectively. This result indicates that the intensity was homogenized by our address-rearrangement process, which leads to a narrower shift pitch with single pulse recording, as shown in later experiments.

3.3. Experimental results

On the basis of the signal design, we evaluated the pattern performance using the evaluation function similarity ratio (SR), which is defined as SR = 10 log(S_ac/S_cc) (dB), where S_ac and S_cc denote autocorrelation and cross-correlation, respectively. To evaluate the random address arrangement, we used 4 signal patterns, which have p = 1, 2, 5, and 10. These values were detected as the optical intensity in the optical correlation experiment using 26 images with a shift pitch of 4.6 µm. Figure 5 shows the experimental results obtained using the images whose block size p values are 1, 2, 5, and 10. The highest SR is obtained for the image with p = 2. From this result, we decide to use the image which is divided the 2 × 2 pixels and random address rearrangement. This means that the high-frequency component is increased and the Fourier power spectrum is spread uniformly by the random address rearrangement method. It seems that the interference area with signal and reference patterns are broad and uniform, and the grating is generated uniformly by achieving a homogenizing intensity distribution in the recording medium. Note that it is also possible to combine other phase-device approaches^14,18) with our method, which should further improve the recording density of the volume holographic optical correlator.

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After implementing all previously mentioned techniques, we estimated the achievable shift selectivity and further experimentally evaluated it. First, we measured the profile of the autocorrelation signal and found that the 1/e² width of the autocorrelation profile is approximately 2.39 µm, as shown in Fig. 6(a). A shift selectivity of 2.39 µm is sufficiently large for disk position control of servo techniques, and small enough for multiplexing holograms to realize high recording density. Then, we verified the shift selectivity by measuring similarity ratio while changing the shift pitch to 2.3 and 5.4 µm. To obtain the experimental SR, all 15 correlation signals, of which 5 were autocorrelation and 10 were cross correlation signals, were used. We also measured the write energy and similarity ratio dependence, so as to estimate the optimum write energy. We set the disk rotation speed to 600 rpm. In Fig. 6(b), the horizontal axis indicates the write energy (equal to the number of pulses) and the vertical axis indicates the similarity ratio. When the shift pitch was 5.4 µm, the SR with more than 0.5 pulses exceeded the SR of the calculation, while, when the shift pitch was 2.3 µm, the SR with more than a single pulse also exceeded the SR of the calculation. On the basis on these results, we used single-pulse recording and a shift pitch greater than 2.3 µm in this experiment.

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Assuming that such a correlation system can be applied to video identification, we measured the correlation 900 times, incorporating 30 reference images in a holographic optical disk and 30 input images taken from a movie that was pre-processed into images of 180 × 240 pixels in size. The experiment was performed using the developed system with a shift pitch of 2.45 µm, singlepulse recording, and a revolution speed of 900 rpm. To decide an optimum threshold of image identification, we used the equal error rate (EER). Figure 7 shows the intersection of the areas representing the EER (when the threshold is chosen optimally). In this experiment, an EER of 0% was achieved. FRR stands for false reject rate and FAR for false acceptance rate. EER is an error rate when the FRR is equal to the FAR. The error rates below and above a threshold divided by the total number of registered images are given by the FRR and FAR, respectively. We determined the optimum threshold that yields the lowest error rate, which is equal to the EER in this experiment. Using this threshold, we performed shift multiplex recordings of data element #1 for 100 recording trials under the following conditions: a disk radius of 48.0 mm, a rotation speed of 900 rpm, and a shift pitch of 2.45 µm. The multiplexed recording sequences used in the experiment are shown in Figs. 8(a) and 8(c).²¹⁾ In the experiment, 300 data pages were recorded with a 2.45 µm circumferential shift pitch using multiple recordings. Figures 8(b) and 8(d) show the 100 correlation signals that correlate with an input and the 100 data pages, respectively. The 100 data pages are at the center of the 300 data pages that were recorded on a holographic disk. When the same data element (code #1) was entered [Fig. 8(a)], 100 autocorrelation signals were detected [Fig. 8(b)]. Figure 8(d) presents the correlation signals for data #1 to #100 [Fig. 8(c)] and code #30. In Figs. 8(b) and 8(d), we note that our ultrafast optical correlation calculations yielded a peak interval of 542 ns, which corresponds to 1.846 × 10⁶ frames per second and 79.8 Gbps. Assuming that 210 × 280 pixels is the image size within the lens aperture, we calculated a correlation speed of more than 124 Gbps for the outermost track.

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We have demonstrated an ultra-high-speed optical correlation by introducing a newly designed signal pattern and a custom designed actuator. We also optimized the recording conditions with a single pulse for high-speed recording. These results suggest that our ultrafast optical correlator can contribute significantly to the development of optical correlation systems in holography.

The authors acknowledge Professor K. Kodate at Photonic System Solutions Inc. for valuable discussions throughout this work. The authors also acknowledge Nippon Steel & Sumikin Chemical Corporation for providing the holographic material.