- Email: [email protected]
Holographic optical disk correlator
Optics Communications North-Holland
99 (1993)
320-324
OPTICS COMMUNICATIONS
Holographic optical disk correlator Francis T.S. Yu, Aris Tanone Department of Electrical and Computer Engineering, The Pennsylvania State University. University Park, PA 16802, USA
and Suganda Jutamulia Kowa Company, Ltd., Silicon Valley Office, 100 Homeland Court, Suite 302, San Jose, CA 95112. USA Received
24 November
1992; revised manuscript
received
A novel optical joint transform correlator architecture the proposed system are high speed random accessibility
1993
using a holographic optical disk is described. The main advantages of and high storage capacity. A proof-of-concept demonstration is given.
1. Introduction Optical disks (ODs) have found numerous applications in the past decade. An OD is a storage medium in which information is stored using a string of pits on the surface of the disk. Usually, the information is retrieved by sequential reading using a laser spot of 1 pm size and spinning the disk. When an OD is employed in an optical processor and illuminated with a plane wave (not a spot), it can be considered a spatial light modulator (SLM), because it modulates the incident reading beam [ 11. Also, it can be considered a memory device, because it provides the required two-dimensional memory.
2. Background and concept Various optical disk correlators have been proposed. Psaltis et al. [2] and Yu et al. [3] demonstrated the recording of the reference pattern on the disk. Psaltis et al. used Vander Lugt architecture, while Yu et al. used joint transform architecture. Yatagai et al. [4] demonstrated the recording of the computer generated hologram (CGH) of the reference pattern on the disk. Also, an OD can be used for storing an interconnection pattern in a neural net 320
8 February
0030-4018/93/%
as shown by Lu et al. [ 5 1. In this paper, we describe a new architecture that is based on the joint transform correlator (JTC) but the reference image is stored as the Fourier hologram on the disk. In the optical disk JTC [ 3 1, the reference image is directly stored on the disk. During the recognition process, the reference image from the OD and the input image displayed by an electronically addressed SLM are correlated. The format of an electronically addressed SLM is in a grid structure, thus the input image is sampled in Cartesian coordinates. On the other hand, the OD consists of pits on concentric tracks, and the reference is sampled in polar coordinates. It is obvious that the input and reference images will not be correlated before the sampling functions are removed. The sampling function removal can be done by low-pass filtering. However, in order to discriminate different classes, high-pass filtering is preferred. To alleviate this contradiction, we store the Fourier hologram of the reference instead of the reference image itself. When the reference is recalled for correlation with an input image, the reference image will be reconstructed free from the sampling polar coordinate. Furthermore, we may control the linear dynamic range of the hologram recording process, such that the edge-enhanced image can be reconstructed 06.00 0 1993 Elsevier
Science Publishers
B.V. All rights reserved.
Volume 99, number 5,6
OPTICS COMMUNICATIONS
for better discrimination between different classes. The hologram will also solve the problem of magnification [6]. Since the resolution of an electronically SLM is typically 100 urn and an OD is 1 pm, to fully utilize the storage capacity of the OD, a magnification lens should be used if the reference image is stored on the disk. The hologram recorded on the disk can be directly used as a complex matched spatial filter in a Vander Lugt correlator. However, in our architecture, we reconstruct the hologram and then use the reconstructed image as the reference in a JTC. The reason is as follows. The main difficulty of a Vander Lugt correlator is the alignment of the matched filter [ 71. Since the resolution of an OD is in the order of 1 urn, the alignment is very crucial. And it becomes even worse because of the jitter of spinning of the disk. In principle, the misalignment in the Vander Lugt correlator may cause severe diminution of the correlation peak, while the same degree of misalignment in the JTC only shifts and slightly degrades the correlation peak.
15 June 1993
3. Architecture and simulation The proposed architecture is schematically depicted in fig. 1. We may employ an OD that is a copy of the specially made disk master as used by Yatagai [ 41, or a write-once-read-manytimes (WORM) OD as used by Psaltis [ 21. However, we may not be able to employ an erasable magneto-optic (MO) disk, since the contrast of the image may be too low. The MO layer of the disk rotates light polarization less than 1”. Although the detected sequential signals from an MO disk can be amplified by several stages of differential amplifier, the same method is difficult to apply to parallel image reading of an OD. Nevertheless, there is a possibility of coating a photographic emulsion or photorefractive film on a transparent disk substrate. So that a transmission type OD with variable format or continuous layer can be employed in the system [ 3,5]. A linearly polarized laser (horizontal polarization) is used as the light source for two-dimensional optical processing. To save the light energy, we employ the common optical pick up system of an OD. The read beam is directed toward the OD by a polarizing beam splitter PBSl. Then the beam passes through a quarter-wave plate, and becomes circular
OSLMZ
Fig. 1. Schematic diagram of the holographic optical disk joint transform correlator. OD: optical disk, PBS: polarizing beam splitter, BS: beam splitter, FL: Fourier transform lens, IL: imaging lens, OSLM: optically addressed SLM, ESLM: electronically addressed SLM, LD: laser diode.
321
Volume 99, number
5,6
OPTICS
COMMUNICATIONS
polarized. The reflected beam is circular polarized in the counter direction, and is linearly polarized in vertical direction after passing through the quarterwave plate. The reflected beam is Fourier transformed by the lens FL1 forming the reference image on the optically addressed SLM (OSLM 1) after passing through PBS2. The input image is displayed on the electrically addressed SLM (ESLM) and imaged by the imaging lens IL onto OSLMl through PBS2. Since the beam from OD is vertically polarized and the beam from ESLM is horizontally polarized, they can be combined by PBS2 without loss. The OSLMl functions as the input plane of the wellknown JTC [ 81. The operation of the rest is described in detail in the literature [ 9 1. In fig. 1, the OSLM2 converts the joint transform power spectra into an amplitude distribution. Needless to say, a combination of CCD and liquid crystal television (LCTV) or photorefractive crystal can also be used as a real-time square law detector [ 9 1. The CCD finally detects the optical correlation output and feeds the electronic signals into the computer which is the system manager. At the upper part of the OD in the figure, there is an optical system independent of the correlator part that performs the OD tracking tasks. A laboratory experiment was performed to show an advantage of the proposed concept. To simulate the system of ref. [ 31, a reference object (tall bottle) was correlated with itself and a short bottle in a JTC. Figure 2a shows the input plane of the JTC, where the left object is the reference and the right two objects are the input objects. The optical correlation output was detected by a CCD camera and digitized by a computer. The detected output is plotted in fig. 2b, in which two correlation peaks are clearly shown at both sides. Note that the center of the output plane was blocked to exclude the dc from fig. 2b and fig. 3b. The correlator could not distinguish between two objects: tall bottle and short bottle. To simulate the system proposed in this paper, first we optically recorded the Fourier hologram of the reference (tall bottle) on a holographic film (Kodak SO-253). The power spectrum of the reference was not uniform but it had the maximum intensity at the center (low frequency zone) and gradually decreased at the edge (high frequency zone). The film 322
15 June 1993
I a
bb Fig. 2. (a) Objects shown in the input plane of JTC. The bottle in left hand side is the reference. (b) Output of the JTC (dc is blocked).
had a limited linear range [ lo]. If the exposure is under the lower limit or toe, it is under exposed and nothing will be recorded. On the other hand, if the exposure is over the upper limit or shoulder, it is overexposed and the film will be blackened. Both underexposed and over-exposed parts do not contribute to the reconstructed image. If we make the low frequency zone over-exposed and at the same time adjust the exposure of the high frequency zone in the linear range, the reconstructed image will consist of high frequency only. Thus, by selecting proper exposure we were able to reconstruct the edge-enhanced reference as shown in the left hand side of fig. 3a. In the experiment, we recorded a number of holograms with various exposures. The hologram that gave us the desired reconstructed image (fig. 3a) was selected. The reconstructed reference was photographed and used as the reference in the JTC as shown in fig. 3a. As it was expected, the correlation
Volume 99,
number 5,6
OPTICS
COMMUNICATIONS
15 June 1993
shown by the experiment
reported
here.
4. Discussion
a
Fig. 3. (a) Objects shown in the input plane of JTC. The edgeenhanced bottle is the optically reconstructed image from the hologram simulating OD. (b ) Output of the JTC (dc is blocked).
output contained only one correlation peak (at both sides) as shown in fig. 3b. The size of the hologram could be very small as compared with the size of the object. Thus, we may consider that the hologram is recorded on OD, the input objects are displayed by an electronically addressed SLM, and the JTC input (fig. 2a and fig. 3a) is given by an optically addressed SLM. It is wellknown that the edge-enhanced reference provides better discrimination in pattern recognition. The simulation experiment shows that the proposed architecture can perform inherently edge enhancement and thus provide better discrimination. However, the features of the proposed architecture are not limited to this demonstration. The features include the elimination of non-compatibility between OD format and SLM format which is not
The general merits of the OD based JTC are [ 31: (i) high operation speed, (ii) large information capacity, (iii) shift invariant correlation, and (iv) relaxed in optical alignment. The proposed architecture will present additional merits: (v) no format distortion and (vi) no magnification aberration in storing and retrieving the memory, However, there are some problems which need to be addressed. A disadvantage of holographic memory is that it consumes more space of the OD. For example, a Lohmann type CGH requires a one hundred times space-bandwidth product of the image itself [ 2 1. Therefore a new algorithm for a binary CGH that consumes less space of an OD is needed. The trade-off of using a hologram is, however, worthwhile. When the object is directly recorded on the disk with 1 pm resolution or higher density, even a small dust particle or scratch on the disk-covering plastic may result in fatal misreading. However, when using holograms for high density recording, a small damage on the disk will not change the information, but merely causes a slight increase in the noise on the reconstructed image, so that no particular portion of the image is lost [ 111. The standard capacity of the currently available 120 mm CD-ROM (compact disk read only memory) used for multimedia that stores text, sound, and video images for personal computer is 600 MB (megabytes) which is 4800x lo6 bits. Using this standard format, 4800 Lohmann type CHGs of 100 X lOO-pixels image can be stored in the CDROM. Since the area of the 120 mm OD is about 1O4 mm2, by using a proprietary format such that 1 mm2 area can store one Lohmann type CGH of 100 x 100 pixels image, the OD can potentially store more than lo4 reference images. Of course, the references can also be recorded optically.
References [ 1] F.T.S. Yu and S. Jutamulia, computing, sec. 5.8.
and neural networks
Optical signal processing, (Wiley, New York, 1992)
323
Volume 99, number
5,6
OPTICS
COMMUNICATIONS
[2] D. Psaltis, M.A. Neifeld and A. Yamamura, Optics Lett. 14 (1989) 429. [3]F.T.S. Yu, E.C. Tam, T.W. Lu, E. Nishihara and T. Nishikawa, Appl. Optics 30 ( 199 1) 9 15. [4] T. Yatagai, J.G. Camacho-Basilio and H. Onda, Appl. Optics 28 (1989) 1042. [ 51 T. Lu, K. Choi, S. Wu, X. Xu and F.T.S. Yu, Appl. Optics 28 (1989) 4722. [6] F.K. Hsu, Optical disk-based joint transform correlators: System analysis and design, Ph.D. Thesis, The Pensylvania State University, Dec. 1992.
324
15 June I993
[7] D. Casasent and A. Furman, Appl. Optics 16 (1977) 1652. [8] C.S. Weaver and J.W. Goodman, Appl. Optics 5 (1966) 1248. [ 9) See, for example, F.T.S. Yu and S. Jutamulia, Optical signal processing, computing, and neural networks (Wiley, New York, 1992) chs. 6,7. [ lo] See, for example, F.T.S. Yu and S. Jutamulia, Optical signal processing, computing, and neural networks (Wiley, New York, 1992) ch. 5. [ 111 K. Iizuka, Engineering optics (Springer, Berlin, 1985) sec. 8.8.
99 (1993)
320-324
OPTICS COMMUNICATIONS
Holographic optical disk correlator Francis T.S. Yu, Aris Tanone Department of Electrical and Computer Engineering, The Pennsylvania State University. University Park, PA 16802, USA
and Suganda Jutamulia Kowa Company, Ltd., Silicon Valley Office, 100 Homeland Court, Suite 302, San Jose, CA 95112. USA Received
24 November
1992; revised manuscript
received
A novel optical joint transform correlator architecture the proposed system are high speed random accessibility
1993
using a holographic optical disk is described. The main advantages of and high storage capacity. A proof-of-concept demonstration is given.
1. Introduction Optical disks (ODs) have found numerous applications in the past decade. An OD is a storage medium in which information is stored using a string of pits on the surface of the disk. Usually, the information is retrieved by sequential reading using a laser spot of 1 pm size and spinning the disk. When an OD is employed in an optical processor and illuminated with a plane wave (not a spot), it can be considered a spatial light modulator (SLM), because it modulates the incident reading beam [ 11. Also, it can be considered a memory device, because it provides the required two-dimensional memory.
2. Background and concept Various optical disk correlators have been proposed. Psaltis et al. [2] and Yu et al. [3] demonstrated the recording of the reference pattern on the disk. Psaltis et al. used Vander Lugt architecture, while Yu et al. used joint transform architecture. Yatagai et al. [4] demonstrated the recording of the computer generated hologram (CGH) of the reference pattern on the disk. Also, an OD can be used for storing an interconnection pattern in a neural net 320
8 February
0030-4018/93/%
as shown by Lu et al. [ 5 1. In this paper, we describe a new architecture that is based on the joint transform correlator (JTC) but the reference image is stored as the Fourier hologram on the disk. In the optical disk JTC [ 3 1, the reference image is directly stored on the disk. During the recognition process, the reference image from the OD and the input image displayed by an electronically addressed SLM are correlated. The format of an electronically addressed SLM is in a grid structure, thus the input image is sampled in Cartesian coordinates. On the other hand, the OD consists of pits on concentric tracks, and the reference is sampled in polar coordinates. It is obvious that the input and reference images will not be correlated before the sampling functions are removed. The sampling function removal can be done by low-pass filtering. However, in order to discriminate different classes, high-pass filtering is preferred. To alleviate this contradiction, we store the Fourier hologram of the reference instead of the reference image itself. When the reference is recalled for correlation with an input image, the reference image will be reconstructed free from the sampling polar coordinate. Furthermore, we may control the linear dynamic range of the hologram recording process, such that the edge-enhanced image can be reconstructed 06.00 0 1993 Elsevier
Science Publishers
B.V. All rights reserved.
Volume 99, number 5,6
OPTICS COMMUNICATIONS
for better discrimination between different classes. The hologram will also solve the problem of magnification [6]. Since the resolution of an electronically SLM is typically 100 urn and an OD is 1 pm, to fully utilize the storage capacity of the OD, a magnification lens should be used if the reference image is stored on the disk. The hologram recorded on the disk can be directly used as a complex matched spatial filter in a Vander Lugt correlator. However, in our architecture, we reconstruct the hologram and then use the reconstructed image as the reference in a JTC. The reason is as follows. The main difficulty of a Vander Lugt correlator is the alignment of the matched filter [ 71. Since the resolution of an OD is in the order of 1 urn, the alignment is very crucial. And it becomes even worse because of the jitter of spinning of the disk. In principle, the misalignment in the Vander Lugt correlator may cause severe diminution of the correlation peak, while the same degree of misalignment in the JTC only shifts and slightly degrades the correlation peak.
15 June 1993
3. Architecture and simulation The proposed architecture is schematically depicted in fig. 1. We may employ an OD that is a copy of the specially made disk master as used by Yatagai [ 41, or a write-once-read-manytimes (WORM) OD as used by Psaltis [ 21. However, we may not be able to employ an erasable magneto-optic (MO) disk, since the contrast of the image may be too low. The MO layer of the disk rotates light polarization less than 1”. Although the detected sequential signals from an MO disk can be amplified by several stages of differential amplifier, the same method is difficult to apply to parallel image reading of an OD. Nevertheless, there is a possibility of coating a photographic emulsion or photorefractive film on a transparent disk substrate. So that a transmission type OD with variable format or continuous layer can be employed in the system [ 3,5]. A linearly polarized laser (horizontal polarization) is used as the light source for two-dimensional optical processing. To save the light energy, we employ the common optical pick up system of an OD. The read beam is directed toward the OD by a polarizing beam splitter PBSl. Then the beam passes through a quarter-wave plate, and becomes circular
OSLMZ
Fig. 1. Schematic diagram of the holographic optical disk joint transform correlator. OD: optical disk, PBS: polarizing beam splitter, BS: beam splitter, FL: Fourier transform lens, IL: imaging lens, OSLM: optically addressed SLM, ESLM: electronically addressed SLM, LD: laser diode.
321
Volume 99, number
5,6
OPTICS
COMMUNICATIONS
polarized. The reflected beam is circular polarized in the counter direction, and is linearly polarized in vertical direction after passing through the quarterwave plate. The reflected beam is Fourier transformed by the lens FL1 forming the reference image on the optically addressed SLM (OSLM 1) after passing through PBS2. The input image is displayed on the electrically addressed SLM (ESLM) and imaged by the imaging lens IL onto OSLMl through PBS2. Since the beam from OD is vertically polarized and the beam from ESLM is horizontally polarized, they can be combined by PBS2 without loss. The OSLMl functions as the input plane of the wellknown JTC [ 81. The operation of the rest is described in detail in the literature [ 9 1. In fig. 1, the OSLM2 converts the joint transform power spectra into an amplitude distribution. Needless to say, a combination of CCD and liquid crystal television (LCTV) or photorefractive crystal can also be used as a real-time square law detector [ 9 1. The CCD finally detects the optical correlation output and feeds the electronic signals into the computer which is the system manager. At the upper part of the OD in the figure, there is an optical system independent of the correlator part that performs the OD tracking tasks. A laboratory experiment was performed to show an advantage of the proposed concept. To simulate the system of ref. [ 31, a reference object (tall bottle) was correlated with itself and a short bottle in a JTC. Figure 2a shows the input plane of the JTC, where the left object is the reference and the right two objects are the input objects. The optical correlation output was detected by a CCD camera and digitized by a computer. The detected output is plotted in fig. 2b, in which two correlation peaks are clearly shown at both sides. Note that the center of the output plane was blocked to exclude the dc from fig. 2b and fig. 3b. The correlator could not distinguish between two objects: tall bottle and short bottle. To simulate the system proposed in this paper, first we optically recorded the Fourier hologram of the reference (tall bottle) on a holographic film (Kodak SO-253). The power spectrum of the reference was not uniform but it had the maximum intensity at the center (low frequency zone) and gradually decreased at the edge (high frequency zone). The film 322
15 June 1993
I a
bb Fig. 2. (a) Objects shown in the input plane of JTC. The bottle in left hand side is the reference. (b) Output of the JTC (dc is blocked).
had a limited linear range [ lo]. If the exposure is under the lower limit or toe, it is under exposed and nothing will be recorded. On the other hand, if the exposure is over the upper limit or shoulder, it is overexposed and the film will be blackened. Both underexposed and over-exposed parts do not contribute to the reconstructed image. If we make the low frequency zone over-exposed and at the same time adjust the exposure of the high frequency zone in the linear range, the reconstructed image will consist of high frequency only. Thus, by selecting proper exposure we were able to reconstruct the edge-enhanced reference as shown in the left hand side of fig. 3a. In the experiment, we recorded a number of holograms with various exposures. The hologram that gave us the desired reconstructed image (fig. 3a) was selected. The reconstructed reference was photographed and used as the reference in the JTC as shown in fig. 3a. As it was expected, the correlation
Volume 99,
number 5,6
OPTICS
COMMUNICATIONS
15 June 1993
shown by the experiment
reported
here.
4. Discussion
a
Fig. 3. (a) Objects shown in the input plane of JTC. The edgeenhanced bottle is the optically reconstructed image from the hologram simulating OD. (b ) Output of the JTC (dc is blocked).
output contained only one correlation peak (at both sides) as shown in fig. 3b. The size of the hologram could be very small as compared with the size of the object. Thus, we may consider that the hologram is recorded on OD, the input objects are displayed by an electronically addressed SLM, and the JTC input (fig. 2a and fig. 3a) is given by an optically addressed SLM. It is wellknown that the edge-enhanced reference provides better discrimination in pattern recognition. The simulation experiment shows that the proposed architecture can perform inherently edge enhancement and thus provide better discrimination. However, the features of the proposed architecture are not limited to this demonstration. The features include the elimination of non-compatibility between OD format and SLM format which is not
The general merits of the OD based JTC are [ 31: (i) high operation speed, (ii) large information capacity, (iii) shift invariant correlation, and (iv) relaxed in optical alignment. The proposed architecture will present additional merits: (v) no format distortion and (vi) no magnification aberration in storing and retrieving the memory, However, there are some problems which need to be addressed. A disadvantage of holographic memory is that it consumes more space of the OD. For example, a Lohmann type CGH requires a one hundred times space-bandwidth product of the image itself [ 2 1. Therefore a new algorithm for a binary CGH that consumes less space of an OD is needed. The trade-off of using a hologram is, however, worthwhile. When the object is directly recorded on the disk with 1 pm resolution or higher density, even a small dust particle or scratch on the disk-covering plastic may result in fatal misreading. However, when using holograms for high density recording, a small damage on the disk will not change the information, but merely causes a slight increase in the noise on the reconstructed image, so that no particular portion of the image is lost [ 111. The standard capacity of the currently available 120 mm CD-ROM (compact disk read only memory) used for multimedia that stores text, sound, and video images for personal computer is 600 MB (megabytes) which is 4800x lo6 bits. Using this standard format, 4800 Lohmann type CHGs of 100 X lOO-pixels image can be stored in the CDROM. Since the area of the 120 mm OD is about 1O4 mm2, by using a proprietary format such that 1 mm2 area can store one Lohmann type CGH of 100 x 100 pixels image, the OD can potentially store more than lo4 reference images. Of course, the references can also be recorded optically.
References [ 1] F.T.S. Yu and S. Jutamulia, computing, sec. 5.8.
and neural networks
Optical signal processing, (Wiley, New York, 1992)
323
Volume 99, number
5,6
OPTICS
COMMUNICATIONS
[2] D. Psaltis, M.A. Neifeld and A. Yamamura, Optics Lett. 14 (1989) 429. [3]F.T.S. Yu, E.C. Tam, T.W. Lu, E. Nishihara and T. Nishikawa, Appl. Optics 30 ( 199 1) 9 15. [4] T. Yatagai, J.G. Camacho-Basilio and H. Onda, Appl. Optics 28 (1989) 1042. [ 51 T. Lu, K. Choi, S. Wu, X. Xu and F.T.S. Yu, Appl. Optics 28 (1989) 4722. [6] F.K. Hsu, Optical disk-based joint transform correlators: System analysis and design, Ph.D. Thesis, The Pensylvania State University, Dec. 1992.
324
15 June I993
[7] D. Casasent and A. Furman, Appl. Optics 16 (1977) 1652. [8] C.S. Weaver and J.W. Goodman, Appl. Optics 5 (1966) 1248. [ 9) See, for example, F.T.S. Yu and S. Jutamulia, Optical signal processing, computing, and neural networks (Wiley, New York, 1992) chs. 6,7. [ lo] See, for example, F.T.S. Yu and S. Jutamulia, Optical signal processing, computing, and neural networks (Wiley, New York, 1992) ch. 5. [ 111 K. Iizuka, Engineering optics (Springer, Berlin, 1985) sec. 8.8.