In this paper, we proposed a parallel phase-only lensless optical correlator based on two pieces of Liquid Crystal on Silicon Spatial Light Modulators. Phase Fresnel Lens Array and specialized grating are implemented to realize multi-channel and multiplexed LOC. Experimental results of Chinese characters’ recognitions are given as demonstration of proposed technique. High uniformity of processing channels has been verified by autocorrelation process of four same Chinese characters. The technique is programmable and adjustment of optical path could be realized without changing of optical setup. The implementations could be performed on the same configuration as single channel optical correlator without mechanical alternation.
© 2011 OSA
Pattern recognition technology has traditionally been utilized in military and commercial applications. Existing techniques can be primary categorized as electric or optical processing. The optical correlator is perhaps the most common use of optical processing, which has a unique superiority in complex image recognition over electric pattern recognition. With the development of information technology, massive information requires a fast, real-time system for information processing. For an optical pattern recognition system, single channel optical correlator cannot meet the demands of information processing and parallel optical correlator for multi-targets recognition was put forward. Several approaches have been proposed in previous literatures to achieve parallel optical information processing, such as exploiting multidiffraction grating [1,2], holographic lenses [3–5] and wavelength-multiplexed method [6,7]. Some of the configurations can realize position, rotation and scale invariant recognition [1,8,9], or some of the architectures could process massive optical correlation up to 75 channels , others exhibited the advantages on discriminability of similar objects . However, the former parallel implementations often short of flexible alignment of optics and the uniformity of processing channels is poor which limits their applications for commercial products. Particularly, in a VanderLugt type optical correlatior, the misalignment between the Fourier transform image of input pattern and filter pattern leads to a sharp decline of the correlation signal. Moreover, with the increase of channel number in parallel optical processing system, the position misalignment becomes severer as fabrication tolerance increases, which decreases the uniformity of optical processing.
In previous paper , we proposed a Lensless Optical Correlator (LOC) based on two phase-only Spatial Light Modulators (SLMs), which enabled easy lateral and axial adjustment of the optical path by using programmable lenses. Furthermore, a more compact LOC based on one SLM was proposed recently . Here, in this paper, we developed the LOC for parallel phase recognition. Two techniques were introduced, denoted as muti-channel and multiplexed LOC. And especially in multiplexed LOC, two multiplexing methods were presented by utilizing different diffraction gratings. In these implementations, programmable phase type Fresnel Lens Array (FLA) was employed to accomplish parallel Fourier Transform. Compared with earlier proposed parallel optical correlators, parallel LOC could achieve satisfactory uniformity in correlation channels by adjusting the phase patterns on SLMs. Furthermore, our configuration is universally applicable for both single channel and parallel optical recognition, which means, no hardware adjustment is needed when improving from single to parallel processing.
In the next section, the basic principle and basic configuration of parallel LOC is given. Section 3 contains experimental results and discussions of proposed architectures. Section 4 gives the conclusions and future plans of our research.
2. Principle and configuration
The architecture of parallel LOC for optical processing is illustrated in Fig. 1 which is same as that in reference 11. Two reflective type SLMs are parallel arranged. A collimated beam is incident obliquely on SLM1 and reflected to SLM2 along a zigzag path. The input and filter patterns are displayed on SLM1 and SLM2, correspondingly. A camera is placed at the focal plane of the system to record the correlation results. Figure 1(a) illustrates the optical path of a multichannel LOC. The processing channels are spatial arranged on the different positions of SLM. The input beam is divided into several small beams after reflecting from SLM1 and incident on the SLM2 individually. While for a multiplexed LOC, each channel is frequency multiplexed, the incident beam is split after reflecting from SLM1, as shown in Fig. 1(b).
To realize spatial multiplexing in multichannel LOC, a FLA pattern, which are consisted of Fresnel Lens Patterns (FLPs) located on different positions of SLM, are employed to realize parallel correlation calculations between input and reference targets. Figure 2 shows the procedures to create the input pattern of multichannel LOC. Detailed descriptions are as follows.
- 1. Input targets to be identified are arranged into a array pattern, and the elementary unit located are denoted as (i, j = 0, 1, 2 … N). Each is phase encoded, and the total size of should be smaller than liquid crystal size of SLM.
- 2. A phase type FLA composed of FLPs is programmed to realize multichannel Fourier Transform. The focal length of each FLP is identical to each other and designed by the strategy proposed previously . Moreover, the size and center position of each FLP should be same as that of input targets, correspondingly.
- 3. Add the FLA with the input targets and wrap the phase within .
Filter pattern generation procedures of multichannel LOC are analogous to that of constructing input pattern, and the concept is illustrated in Fig. 3 . The reference targets, represented as (i, j = 0, 1, 2, … N), are constructed and arranged as input targets. Fourier transform is performed on each reference target to form phase-only filter array denoted by (i, j = 0, 1, 2, … N), respectively. After that, another FLA is superimposed on filter array to create filter pattern of multichannel LOC.
In multichannel LOC, the input channel number is limited by the liquid crystal chip size of SLM. In order to increase the input channels, multiplexed LOC is proposed. Compared with multichannel LOC, the input targets are loaded on different spatial frequency carriers to achieve parallel processing. The procedure of generating filter pattern of multiplexed LOC is the same as that of multichannel LOC. Yet the approaches utilized of yielding input pattern are different. Two methods were explored in multiplexed LOC, denoted as Type I and Type II. Type I multiplexed LOC is constructed as follows, which is illustrated in Fig. 4 .
- 1. Input targets are phase-encoded and denoted as (k = 0, 1, 2, … N). Also, the size of each should be smaller than that of liquid crystal on SLM.
- 2. Different frequency carriers (k = 0, 1, 2, … N) are applied to shift the spectrum of input targets to different channels on SLM2. In order to reduce high frequency components, is added with in complex value and the phase image of the superposition results is exported and denoted as (k = 0, 1, 2, … N).
- 3. Make a summation of the phase image (k = 0, 1, 2, … N) and denoted the phase pattern as , additionally, a FLP is added with to obtain the input pattern of multiplexed LOC.
Through this technique, the Fourier Transform of different input targets are loaded on different spatial frequencies and split to different positions of SLM2. The multiplexed LOC could corporate many input targets into one hologram regardless of the liquid crystal size of SLM. But this approach is not suitable to process complex phase targets with several features to be classified. The reason is that the above multiplexed technique needs to add the same input targets with different frequency carriers, which will generate high frequency components in input pattern. Hence, Type II multiplexed LOC technique is introduced. As shown in Fig. 5 , the phase target to be recognized is represented as T. Similarly in this case, a specific designed high frequency carrier G, which duplicates the input targets into two dimension array, is added with T in complex value. Likewise, the phase image of the summation results is exported as I and overlapped with a FLP. Compared with Type I multiplexed LOC, this method is more suitable and easier for the input target with sophisticated features to be classified.
For a multichannel LOC, the correlation signal is stronger than multiplexed LOC. On the contrary, the multiplexed LOC could carry more information without the limitation of liquid crystal size of SLM.
The capability decrease on single channel when extending to parallel processing can be theoretically indicated by the Space-Bandwidth Product (SBP). Furthermore, the SBP affects the optical processing performance of LOC. For a SLM, the SBP is expressed as
Based on the Nyquist sampling criteria, the maximum spatial frequencies are determined by the pixel pitch and is given asEq. (2) and Eq. (3) following relationship is apparentEqs. (2), (3), (4), and (5) into Eq. (1), the SBP of SLM can be rewritten asEquation (6) directly shows that in a LOC, the SBP is proportionate to the pixel number, which means, for a specified SLM, when the channel number of a multichannel LOC is increased, the SBP of each channel is decreased and the performance of each processing channel is degraded correspondingly.
In a channel LOC implementation, FLA restricts the performance of SLM as it taks the high frequency band of the system, and the smaller the focal length of FLP, the higher the frequency band is required. The focal length of FLP on the input targets is determined by the pixel pitch of SLM. The Fourier Transform image width of the input targets can be expressed asEq. (7) and Eq. (8), the focal length of FLP on the input targets can be deduced and given asEq. (9), it can be concluded that the focal length of FLP on each channel of LOC is inversely proportional to N.
Additionally, in reference , we reported the minimum focal length of FLP restricted by the sampling frequency of SLM, which isEq. (10). Therefore, Eq. (10) can be written asEq. (12) into Eq. (11) and the minimum focal length is deduced byEquation (13) shows that, when the channel number in multichannel implementation is increased, although, from Eq. (9) the required focal length of FLP should be decreased, the minimum focal length can be reached on each channel is decreased This indicates that with the increment of channel number, the bandwidth taken by FLP will not change.
While, for multiplexed implementation, the input targets are multiplexed in frequency domain and the SBP is shared among each channel. Analysis for multiplexed SBP is just like the situation in multichannel implementation, with the difference that the interested plane is the frequency plane (SLM2). As the filter patterns of each channel are arranged independently on SLM2, the input channel of multiplexed LOC is limited by the filter number displayed on SLM2. Furthermore, multiplexed LOC suffers from the low diffraction efficiency of the grating structures. With the increment of channel number, the input pattern would be more complex and the diffraction efficiency will be reduced.
From the above discussion, with the increment of channel number in parallel LOC, the performance of each channel is reduced due to changes of channel’s SBP, yet the bandwidth required by FLP of each channel is decreased accordingly. The maximum channel number is expected to be demonstrated in the future experiment.
3. Experimental results and discussions
In this section, results of experimental applications of this parallel LOC are given to verify the proposed techniques. Optical Characters Recognition (OCR) is the translation of images of characters into machine-editable text, which plays an important part in pattern recognition, computer vision and artificial intelligence. Thus, verification of parallel LOC is performed by Chinese characters recognition.
The SLM used in parallel LOC is phase-only reflective type Liquid Crystal On Silicon Spatial Light Modulator (LCOS-SLM, Hamamatsu Photonics K.K. X10468 series), which is characterized by pure, linear and precise phase control. The liquid crystal chip of LCOS-SLM is consisted of 792 × 600 square pixels, where the pixel size is 20μm. The light utilization efficiency and the fill factor is approximately 90% and 95%, respectively. The SLM is addressed with 256 gray-scale levels, and the phase modulation capability at the wavelength of 633 nm is 0 to 2π corresponding to a gray range from 0 to 255. The input and filter pattern are displayed on SLM1 and SLM2 with a size of 512 × 512 pixels, 10.24 × 10.24 mm on SLMs. A He-Ne laser with the wavelength of 633 nm is utilized as the light source. The beam is collimated and obliquely incident on SLM1 with an angle less than 10°. In addition, the size of input beam is shaped to approximately 10.24 × 10.24 mm to keep consistent with input pattern.
As ordinary Chinese characters are composed by elementary parts, therefore, it’s reasonable to recognize characters’ radicals to accomplish Chinese characters identification. The experiment is designed under the principle that if reference radicals are parts of input characters, strong correlation peak will appear. During this process, the feasibility, and even efficiency can be verified and evaluated. The input target is composed of four same Chinese characters patterns, as shown in Fig. 6(a) . Each pattern is consist of 256 × 256 pixels, with the center located at (127, 127), (127, 383), (383, 127), (383, 383), respectively, where we define the top left corner of the input target pattern as (0, 0) and the right bottom corner as (511, 511). Each pattern has a Chinese character with gray value of 127 and the other part is 0. A 2 × 2 FLA with focal length of 648 mm is superimposed with input targets. The size and center of each FLP is coincident with the individual character pattern. Figure 6(b) gives the reference pattern that is consisted of four different Chinese character parts of 256 × 256 pixels denoted as 1, 2, 3, 4. The part 1, 2, 3 are intercepted from the input target, while the 4th reference target is not. The filter pattern is programmed from the reference pattern and overlapped with a FLA following the procedures presented in section 2. The FLA written onto the phase-only filter possesses a focal length of 324 mm. The input and filter patterns are displayed on the center of SLM1 and SLM2, respectively. At the focal plane of the system, approximately 648 mm from SLM2, a CCD camera is placed to capture the correlation signal. Figure 6(c) provides the correlation signals intensity between input and reference targets. The results shows that at the top-left, bottom-left and top-right of correlation plane, three correlation peaks are observed that correspond to the reference pattern 1, 2 and 3. However, at the position of the bottom-right that is represented as 4, no obvious correlation peak is detected, which means that there has no relationship between the input targets and reference target in the 4th correlation channel. This proves that four-channel LOC is feasible for parallel Chinese characters parts recognition.
Demonstration for multiplexed LOC is performed in a similar manner. As Fig. 7(a) shows, the left column represents four different Chinese characters are chosen as input targets, each has a size of 512 × 512 pixels. Then, the input targets will be superimposed with appropriate frequency carriers for the purpose of shifting them into separate channels, as shown in the center column of Fig. 7(a). Precise frequency carrier patterns are constructed by Iterative Fourier Transform Algorithm (IFTA) such as G-S algorithm  from object intensity patterns. In this implementation, spot patterns, as the object intensity patterns, adopted for G-S algorithm are shown in the right column of Fig. 7(a). Correspondingly generated phase patterns are shown in the middle column of Fig. 7(a). Each spot pattern is consisted of 512 × 512 pixels with only one pixel has gray value 255. The bright spots locate sequentially at (127, 127), (383, 127), (127, 383) and (383, 383) in the row 1, 2, 3 and 4, which are identical to channel center on the filter pattern. After the procedure in Fig. 7(a), a FLP with a focal length at 648mm is overlapped on SLM1 to Fourier transform the input targets. Four identical Chinese characters, which are same as the input characters at line 2 in Fig. 7(a), are utilized as reference targets (as shown in Fig. 7(b)). The reference pattern is composed of 512 × 512 pixels and the filter pattern is constructed from this reference pattern. Likewise, a FLP with a focal length of 324mm is used in filter pattern. And CCD camera was placed at the system focal plane for correlation signal as shown in Fig. 7(c). An obvious correlation peak is appeared on the top-right of correlation plane, while no apparent signal is seen on the other area. This result indicates that the input target at row 2 in Fig. 7(a) is successfully identified and the Type I multiplexed correlation technique is feasible based on two SLMs.
Verification for type II multiplexed LOC shares the same configuration as multichannel LOC. Input target is one Chinese character that is identical to the character in Fig. 6(a) yet the image size is 512 × 512 pixels. While in this application, the frequency carrier (the middle column in Fig. 8(a) ) is retrieved from the 4-spots pattern (the right image in Fig. 8(a)). To be specific, the spot pattern is composed of 512 × 512 pixels and at the position of (127, 127), (383, 127), (127, 383) and (383, 383), the gray value is 255. To realize Fourier Transform, FLPs are implemented on SLM1 and SLM2 just as Type I multiplexed LOC. Resulting correlation signal is given in Fig. 8(b). The correlation plane is divided into four parts which are represented as 1, 2, 3, 4 correspond to four processing channels. At the part 1, 2 and 3 of correlation plane, three correlation peaks are emerged from background. In contrast, at the 4th part, no sharp correlation signal appears. From the results, it can be demonstrated that the technique in Type II multiplexed LOC is suitable for character recognition. Moreover, by comparing the correlation results between Fig. 6(c) and Fig. 8(b), it also can be observed that the correlation peaks of multiplexed LOC are weaker than that of multichannel LOC. The reason is that the input pattern of multiplexed LOC contains more high frequency components than that of multichannel LOC, which will influence the performance of SLM.
Channel uniformity is a key factor in parallel optical processing which affects the discriminability of each channel. To evaluate the degree of uniformity of parallel LOC, identical Chinese characters are utilized as input and reference targets, resulting in autocorrelation in all the channels. The intensity of correlation signal is further measured by a photodiode, and uniformity can be evaluated by ratio between minimum intensity and maximum intensity. Uniformity evaluation has been done both on multichannel configuration and Type II multiplexed configuration. We use the input targets as in Fig. 6(a). Figure 9(a) shows the experimental results of four-channel LOC. On the correlation plane, four apparent correlation peaks denoted as 1, 2, 3 and 4 are observed at corresponding positions. Table 1 shows the results of normalized correlation signal intensity of each processing channel. From the results we can conclude that the difference among four-channel LOC is less than 10%. While, autocorrelation results for Type II multiplexed LOC is illustrated in Fig. 9(b).
Similarly, normalized intensity for 1 to 4 channels are measured and reported in Table 2 . Under this circumstance, we can obtain that the minimum intensity versus maximum intensity is 0.92, which implies that the uniformity of multiplexed and divergence LOC is acceptable.
In this paper, we presented a theoretical and experimental study of the parallel LOC concept based on two phase-only LCOS-SLMs. Employing the approach of adding FLA with input targets and filter pattern, multi-channel LOC for Chinese characters’ parts recognition is realized. Through multiplexing algorithm, multiplexed LOC is described and demonstrated for characters recognition applications. Uniformity of four-channel parallel LOC is verified and performance differences within 10% are achieved through experimental results.
In summary, one of the major advantages of this new approach is that various LOCs are able to be performed in the same optical setups without hardware alignment or alternation. This technique will lead to developing a compact, multifunctional, universal system, which could be used in digital image processing, optical neural networks, and furthermore, optical computer. Currently, the processing channel numbers of parallel LOC is mainly limited by the liquid crystal area of LCOS-SLM. The development of SLM technique will expand the processing capability of parallel LOC. Further research through associating methods from traditional optimization algorithms could be applied to improve the performances (SDF, SNR etc.) of our system.
This work was supported by Hamamatsu Photonics K. K., State Key Laboratory of Mordern Optical Instrumentation, Zhejiang University, and the National Natural Science Foundation of China (NSFC) 60877008. The authors are grateful to T. Hiruma, Y. Suzuki and T. Hara for their encouragement and H. Toyoda and N. Matsumoto for their useful discussions.
References and links
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