OPTOELECTRONIC IMPLEMENTATIONS OF PULSE-COUPLED NEURAL
NETWORKS: CHALLENGES AND LIMITATIONS by
Raydiance Wise
B.S. Electrical Engineering, Tufts University, 1998
Submitted to the Department of Electrical Engineering and Computer
Science in partial fulfillment of the requirements for the degree of
Master of Science in Electrical Engineering and Computer Science at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
June 2007
© 2007 MASSACHUSETTS INSTITUTE OF TECHNOLOGY. All rights reserved.
Author ..................................
Certified by ... . . . . . .........
...........
..........- -........................................
Raydiance Wise
Department of Electrical Engineering and Computer Science
May 29, 2007
........................ .....................................
Cardinal Warde r of Electrical Engineering and Computer Science
... Thesis Supervisor
Accepted by ...................
.6; t-.......
.
.
... .. .....
Arthur .Smith
Chairman, Department Committee on Graduate Theses
OF TECHNOLOGY
AUG 1 6 2007

2

OPTOELECTRONIC IMPLEMENTATIONS OF PULSE-COUPLED NEURAL
NETWORKS: CHALLENGES AND LIMITATIONS
by Raydiance Wise
Submitted to the Department of Electrical Engineering and Computer Science on May 11, 2007 in Partial Fulfillment of the
Requirements for the Degree of Master of Science in
Electrical Engineering and Computer Science
Abstract
This thesis examines Pulse Coupled Neural Networks (PCNNs) and their applications, and the feasibility of a compact, rugged, cost-efficient optoelectronic implementation. Simulation results are presented.
Proposed optical architectures are discussed and analyzed. A new optoelectronic PCNN architecture is also presented. Tradeoffs of optical versus electronic implementations of PCNNs are discussed. This work combines concepts from optical information processing and pulse-coupled neural networks to examine the challenges, limitations, and opportunities of developing an optoelectronic pulse coupled neural network. The analysis finds that, despite advances in optoelectronic technology, fully electronic implementations will still outperform today's proposed optoelectronic implementations in cost, size, flexibility, and ease of implementation.
Thesis Supervisor: Cardinal Warde
Title: Professor
3

ACKNOWLEDGMENTS
I wish to first thank God for His many blessings. I would like to thank my advisor, Dr. Cardinal Warde, for his guidance, time, wisdom, and knowledge.
I am very grateful for your continuous assistance and support. In addition, I thank Marilyn Pierce for her dedicated support.
I am also grateful to Marko Slusarczuk of OIDA for sharing his knowledge of optoelectronics and connecting me with experts in the commercial world.
During my first year at MIT, I was a recipient of a Rosenblith Fellowship. I am very thankful for that financial support.
I would like to thank the Photonic Systems Group including Gerhard Schick,
Ravi Ramkissoon, Milos Komarcevic, Ben Ruedlinger, Don Kim, Marta Ruiz-
Llata, Jose Rodrigo Serrano, and David Dunmeyer. Thank you for your advice and support. Working with you has been a pleasure.
Finally, I am especially grateful to my beloved mother and family, for their love, support, encouragement, and prayers!
4

Table of Contents
Chapter 1: Introduction....................................................................................................10
1.1 Motivation for Study of Pulse Coupled Neural Networks .............................................
1.2 Pulse Coupled Neural Networks .........................................................................................
10
13
1.2.1 General Background...................................................................................... 13
1.2.2 Software and Electronic Implementations of PCNNs......................................... 19
1.2.3 Prior Proposed Optical PCNN Architectures ............................................................ 19
1.2.4 Multi-layered PCNN Architectures...............................................................................22
1.2.5 Current Issues in PCNNs .........................................................................................
Chapter 2: Simulation of a PCNN ...................................................................................................
2.1 Simulation of an 8 x 8 PCNN ............................................................................................
2.2 Simulation of a 76 x 76 PCNN............................................................................................
23
25
25
33
Chapter 3: A New Look at an Optoelectronic Architecture of a PCNN.................................. 39
3.1 Optical Emulation of PCNN Behavior.................................................................................. 39
3.2 Proposed Optoelectronic PCNN Architecture...............................................................
3.2.1 Input Image Light Source..........................................................................................
3.2.2 Two-dimensional Convolution.................................................................................
3.2.3 Linking Channel................................................................................................................45
42
43
43
3.2.4 Feeding C hannel ...............................................................................................................
3.2.5 Array Multiplication ....................................................................................................
3.2.6 T hresholding......................................................................................................................
3.2.7 System Feedback...............................................................................................................
3.2.8 System Output using a Charge-Coupled Device........................................................ 49
C hapter 4: C onclusions............................................................................................................................50
4.1 Sum m ary ....................................................................................................................................... 50
4.2 Challenges and Opportunities of Optoelectronic Implementations of PCNNs........ 51
4.3 Future W ork................................................................................................................................. 52
46
46
47
48
5

Appendix A
-
Matlab Simulation of an N x M PCNN .................................................................... 54
Appendix B Current Optical Component Technology Useful for PCNN Implementation .57
B.1 Spatial Light Modulators..................................................................................................... 57
B.2 Beam splitters, Microlens Arrays, and Photodetector Arrays................ 58
B .3 Light-em itting diodes ............................................................................................................... 59
B .4 V C SE L s ...................................................................................................................................... 59
Appendix C Datasheets of Optical Components Useful for PCNN Implementation...........64
C.1 Transmissive Spatial Light Modulator (Meadowlark Optics, Inc.)............................... 64
C.2 Micromechanical Spatial Light Modulator (Texas Instruments).................................. 68
C.3 VCSEL Array (Finisar).......................................................................................................
C.4 VCSEL Array (Lasermate Group, Inc.)............................................................................71
G L O SSA R Y ..............................................................................................................................................
B IBL IO G R A PH Y ...................................................................................................................................
70
75
76
6

LIST OF FIGURES
Figure 1. Pulse coupled neuron m odel......................................................................................... 15
Figure 2. Optical implementation of the PCNN proposed by Kirsch, et al. [6].................20
Figure 3. Optical PCNN-like computational system proposed by Johnson [94].........21
Figure 4. Compact Optoelectronic Integrated Neural (COIN) Coprocessor.....................23
Figure 5. Input image, S, and PCNN output, Y, at select iterations.......................................27
Figure 6. Input image, S, and output, Y. Additional iterations demonstrate
28 periodic PCN N behavior..............................................................................................
Figure 7. Time signal, also known as the intensity function, shown for 100 iterations for 8 x 8 PCN N ........................................................................................... 29
Figure 8. Time signal for 200 iterations on 8 x 8 PCNN. .......................................................
Figure 9. Parameter states for neuron (ij) =(3,3).....................................................................
29
30
Figure 10. Parameter states for neuron (i,j) = (3,3) (shown separately).................................. 31
Figure 11. Rotated 8 x 8 input image, 5, and PCNN output, Y, at select iterations............. 31
Figure 12. Rotated input image, S, and output, Y. Additional iterations demonstrate periodic PCNN behavior..................................................................... 32
Figure 13. Parameter states for neuron (i,j) = (3,3) for rotated 8x8 input image................... 32
Figure 14. Time signals, G[n], for the original 8x8 input (left) and the rotated 8x8 input (right) are identical.............................................................................................. 33
Figure 15. Input stimulus, S, and outputs, Y, for the first five iterations. .............................. 34
Figure 16. Input stimulus, S, and PCNN parameter states for neuron (i,j) = (4,4)............... 36
Figure 17. Input stimulus, S, and PCNN parameter states for neuron (i,j) =
(20,40)....................................................................................................................................36
Figure 18. Input stimulus, S, and PCNN parameter states for neuron (ij) = (4,4) where VT = 10----------....--------------------------.... .
----------................................................ 37
Figure 19. Input stimulus, S, and PCNN parameter states for neuron (ij) = (20,40) w here V T = 10.................................................................................................................... 38
Figure 20. Block diagram of PCNN algorithm................................................................................. 39
Figure 21. Optoelectronic Pulse-coupled Neural Network Processor Architecture............. 42
7

Figure 22. Optical convolution of the prior state output, Y, and the kernel, K.................... 44
Figure 23. All-optical pulse generator based on optical bistability devices............................ 47
Figure 24. Example of an edge-emitting laser structure [23]......................................................60
Figure 25. Example of a simple VCSEL structure [23]..............................................................60
Figure 26. A single VCSEL in a T046 package.........................................................................
Figure 27. A 16x32 VCSEL array comprised of eight 8x8 VCSEL arrays.............................62
61
8

LIST OF TABLES
Table 1. PCNN Parameter settings..........................................................................................
Table 2.
Table 3.
PCNN Kernel Matrix .................................................................................................
Sub-section of 76 x 76 neural network. Pixel (4,4) (highlighted) and neighboring pixel intensities (256 grayscale).........................................................
Table 4. Sub-section of 76 x 76 neural network. Pixel (20,40) (highlighted) and neighboring pixel intensities (256 grayscale).........................................................
35
35
25
26
9

This chapter will address the question, "Why study Pulse-coupled neural networks (PCNNs)?" A general background of PCNNs is provided. Implementations and current issues in the area of study are discussed.
1.1 Motivation for Study of Pulse Coupled Neural Networks
There seems to be no processor greater than any biological processors for complex tasks like pattern recognition and control applications. The human mind serves as an incomparable parallel processor, solving complex problems very quickly. Scientists and engineers in the fields of cognitive sciences and artificial intelligence strive to emulate the human ability to quickly process massive amounts of information to make decisions [1].
It makes sense to emulate biological processes with the purpose of solving computationally complex problems in parallel. In some circles, one might say, "fake it till you make it." By emulating the biological processors, the field of artificial neural networks was born. According to
Zurada, artificial neural systems, or neural networks, are physical cellular systems which can acquire, store, and utilize experiential knowledge [2].
10

According to Haykin, a neural network is a massively parallel distributed processor that has a natural propensity for storing experiential knowledge and making it available for use [3]. It resembles the brain in two respects:
1. Knowledge is acquired by the network through a learning process.
2. Interneuron connection strengths known as synaptic weights are used to store the knowledge.
Pulse coupled neural networks (PCNNs) are a class of neural networks that has emerged fairly recently. PCNNs defy many written definitions of neural networks in that they require virtually no learning or training! PCNN applications span a wide range of industries from military to medical fields. Applications include:
" Sensor fusion [4]
" Image processing [5]
* Blood cell identification [5]
* Post-processor for optical correlators [6]
" Target detection [7]
* Mammogram classification [5, 8]
PCNN connectivity requirements are low; lending itself to weakly and moderately connected neural network implementations. The intent of this project is to combine the fields of optical information processing, weakly connected neural networks (WCNNs), and PCNNs to develop a
PCNN processor using an optical architecture.
Neural networks can be implemented completely electronically. However, optics may be able to provide an important benefit to neural interconnections. While VLSI progress may eventually be
11

hindered by crosstalk between electronic signals, light beams can pass through each other without interaction, thereby eliminating crosstalk problems. This allows many interconnections to be made in the same volume.
With current optics technology, implementing fully connected neural networks can be quite difficult and expensive. The ultimate goal of this line of research is to develop a novel, inexpensive, compact optical neural network processor. One way to accomplish this feat may be to implement application-specific WCNN processors. Nearest-neighbor and next-nearest neighbor networks are more easily and inexpensively implemented optically than fully connected networks.
There has not been a study that comprehensively evaluates different neural network connectivities and algorithms to find the optimal combination for optical implementation. This information would be very helpful for future works in the field of optical information processing.
Louri and Na [9] stress the importance of systematic modeling and simulation methodologies in the development of digital optical computing systems.
A significant problem hampering the field of optoelectronic processing is that while many optical computing architectures and systems are proposed, few are thoroughly simulated and tested before implementation. This results in longer development periods (from concept to prototype) and higher costs [9].
One of the purposes of this project is to design and critically examine one possible implementation of an optoelectronic pulse coupled neural network architecture.
12

1.2 Pulse Coupled Neural Networks
1.2.1 General Backgrund
Pulse-coupled neural networks are a recently developing class of neural networks. PCNNs are primarily used for image processing. In image processing, the objective is to make a decision on the content of an image. The ultimate goal in this field is to produce a machine that can perform image processing as well as humans.
The visual cortex is the part of the brain that receives information from the eye. It is specialized for information processing of stationary and moving objects and performs pattern recognition functions. The eye sends a processed image to the cortex. In turn, the cortex converts the image into a string of pulses.
In 1989, Eckhorn et al studied the cat's visual cortex and developed a neuron model capturing some biological cortex features [10]. The resulting model is the pulse-coupled neuron. The
PCNN is sometimes referred to as a computer-modeled cortex. There are three components in a pulse-coupled neuron: the feeding modulation, linking modulation, and pulse generator. The pulse coupled neural network is a two-dimensional array of neurons, typically with only a single layer. The size of the PCNN is the same size as the input image, S.
The PCNN is mathematically modeled for the i-th, j-th neuron by the following equations [15].
The feeding input, Fij, is computed by the addition of the input image intensity at pixel (ij), the weighted contributions of other neurons from the prior iteration, and the feeding input of the prior iteration scaled by a decaying constant as shown in Equation 1.
eFF [n-1] + Sj +VF MjkYk[n-1] ki
EQ1
13

The linking input, I,, shown in Equation 2, is represented by the addition of its prior state and the weighted contributions of other neurons from the prior iteration.
Llj[n] = e'LL
0
-1]+VI WklYkl[n -1] kI
EQ 2
The internal activity, U
1
, is gained by multiplying the feeding input with the output of the linking channel as shown in Equation 3.
U i = F[n]{l+3Lj[n]} EQ 3
The output of the neuron, Yij, equals one if the internal activity of the neuron, Ujj, exceeds the dynamic threshold,
Yj[]=1 <- ifUjj[n] > Eij[n - 1]
Y,[n]=EQ4
0 <- otherwise
Q
The dynamic threshold is computed by adding the scaled neuron output, Yjj, to the prior threshold value multiplied by a decaying constant as shown in Equation 5.
j [n]=eaeOj[n-1]+VY[n] EQ5
PCNN parameters are defined below: n iteration step
P linking strength
U = total internal activity
F = feeding input
L = linking input
W synaptic weight matrix (also, linking kernel)
M synaptic weight matrix (also, feeding kernel)
14

o
= threshold
Y = binary output
S = input stimulus (also, input image)
Ve, VL, VF, amplitude normalization constants (also, potential coefficients)
96 , LD
2F= decay constants.
Y. represents the outputs of other neurons that are feeding into neuron (i,j). The threshold, e, is dynamic. When the neuron pulses (Y>e), the threshold value spikes significantly, then decays gradually. The PCNN repeats the iterative equations above until the pre-defined number of iterations is fulfilled. The PCNN will continue to iterate unless it is stopped.
Figure 1 is a block diagram illustrating the system implementation of the equations modeled above.
Y
Linking
Channel LBa
W(+)-
Variable
Threshold
1+PL
Y Yii
Feedng U= F~ + P)
FeedingPulse
S
0Output
Pulse Generator
Figure 1. Pulse coupled neuron model.
The pulse coupled neuron contains two primary channels: the feeding and linking channels, represented by Equations 1 and 2, respectively. Along the feeding channel, the input pixel, S,, is
15

fed into the neuron and added to the output contributions from other neurons from a prior iteration as weighted by the weight matrix, M. Along the linking channel, the linking strength, P, dictates the strength of the contribution of the outputs of other neurons toward the internal activity, Ui. In the pulse-coupled neural network, synapses are modeled as leaky integrator connections, i.e. a capacitor and resistor in parallel. Properties of the PCNN can be adjusted by changing threshold levels and decay time constants of synapses [5]. For varying applications, the thresholds can be constant or decaying.
There are many advantageous qualities to pulse-coupled neural networks. PCNNs do not require training and are able to ignore noisy variation and spatial discontinuities. This is beneficial to image segmentation and image smoothing applications. PCNNs are capable of operating very fast. Hence, they serve as good preprocessors; they can help reduce time complexity due to highspeed parallel information processing. In addition, PCNNs produce invariant outputs. This quality is important in multimedia processing, especially pattern recognition. Furthermore,
PCNN connectivity requirements are loose and may be implemented with weakly connected neural networks [4]. With recent developments in PCNNs, it is becoming increasingly possible to recognize images in space regardless of scale, rotation, or translation.
When a pulse coupled neuron fires, it communicates to neighboring neurons. The number of neurons it will affect depends on the size of the convolution kernel. (Note that the latter parts of equations 1 and 2 model the convolution between the weight matrices and Ykd, the outputs of other neurons of a previous iteration.) In a physical implementation, the convolution kernel translates to the interconnection pattern.
16

For image processing applications, each neuron is tied to an image pixel or a set of neighboring image pixels. Each neuron processes signals that feed from the neighboring pixels (the feeding inputs) and that link from neighboring neurons (linking inputs). This process is repeated for a number of user-defined iterations. Each neuron generates a string of binary outputs. This string of outputs results in a pulse train. For a nearest neighbor optical implementation, the M
(feeding weights) and W (linking weights) matrices must be set appropriately. PCNN behavior can be tailored by varying several parameters. The linking strength, P, works with the weight matrices W and M, to scale the linking and feeding inputs.
The issue of noise can present problems in PCNN processing. The effects of noise can be mitigated by using a fast linking algorithm or adding a signal generator to the PCNN [5].
As previously mentioned, the output of a PCNN is a series of binary output images. It is necessary to be able to quantify the information from these many binary images. To do this, we convert the pulse images into a single vector of information by summing over all of the pixels for each frame. This vector, G, the time signal, is also referred to as the time series or the
intensityfunction. The time signal is shown in the equation below:
G[n]=
EQ6
The time signal can provide information about the input image. It can be likened to a unique signature of the image, similar to a fingerprint. J.L. Johnson studied the behavior of the time signal [11]. He found it to be invariant to translation, rotation, scale, and distortion. The time
17

signal displays harmonic behavior. The invariant and harmonic behavior of the time signal is shown in the figures below.
In a PCNN, when a neuron or group of neurons pulse, an autowave is generated from that region and propagates throughout the network. An autowave is defined as a wave that propagates and does not reflect or refract [5]. The speed at which an autowave travels throughout the network is dependent upon the connectivity of the network. The connectivity of the network is defined by the dimension of the convolution kernel, i.e. the weight matrices. For instance, for a fully connected network, the dimension would be the same size as the 2-D network array itself.
Since all neurons would be communicating with each other, an autowave would propagate quite quickly.
The speed of the autowave is directly related to the dimension of the kernel. The larger the dimension of the kernel, the farther away neurons can communicate with other neurons. Thus, the autowave can propagate farther in each iteration. One can surmise that if a PCNN was constructed with solely nearest neighbor interconnections, the autowave would advance more slowly than a network with higher connectivity, perhaps requiring more iteration to perform to demonstrate the same behaviors. An example, shown later in Chapter 2 (Figure 5 and Figure 6), demonstrates an autowave propagating through the network over time.
It is simpler to analyze the binary results of a PCNN to make a decision than it is to analyze the original image. Often, after just one iteration through a PCNN, the edges of an image are often detected. This is because parts of an image that are similar will pulse together. Given its inherent edge detection properties, the PCNN can often serve as a pre-processor in image processing, specifically for edge detection and image segmentation applications.
18

1.2.2 Software and Electronic Implementations of PCNNs
There have been numerous software implementations of the PCNN. Numerous simulation tools have been developed. Much of the research involving PCNNs has revolved around algorithm development and customizing the PCNN for specific applications. Many electronic designs have been proposed [15]. In 1997, a CMOS VLSI architecture of a PCNN was proposed
[31]. In 2006, a PCNN was implemented in a Field Programmable Gate Array (FPGA) [32].
1.2.3 Prior Proposed Optical PCNN Architectures
This section will discuss two previously proposed optical implementations of a PCNN, one of which was built. The current technology of optical processors and components is discussed.
1.2.3.4 Prior Proposed Implementation
In 2001, Kirsch et al. proposed an optical design of a PCNN that consisted of a Vertical Cavity
Surface Emitting Laser (VCSEL) array where the image is displayed, a spatial light modulator
(SLM) that would perform the thresholding, a microlens array to spread the beams from pixels that exceed the threshold to adjacent pixels, and beamsplitters to provide a feedback path [26].
Output beams are captured by a detector array. This architecture is shown in Figure 2. There is no evidence in literature that this system has ever been simulated or built.
19

VCSEL
Array
Microlens
Array
Photodetecla
Array
ELMI
Figure 2. Optical implementation of the PCNN proposed by Kirsch, et al. [61
1.2.3.5 Prior Optical Implementation
J.L. Johnson designed a system that performed PCNN-like behavior [5, 38]. This simple architecture is shown in Figure 3. Johnson used a spatial light modulator to perform the PCNN convolution operation. The PCNN thresholding was performed by a computer. An object was illuminated with incoherent white light. The resulting light was focused on a plane beyond the spatial light modulator. A charge coupled device (CCD) detector sensed the resulting image and stored it on the computer. The computer then wrote an image onto the SLM.
A transmissive SLM was used that employed two states: ON and OFF. The ON state transmitted considerably more light than the OFF state. As the off-focus image passed through the SLM, it was multiplied by the image on the SLM. Johnson maintained that the off-focus characteristics of the image performed the local interconnections between elements and this led to a convolution of the image elements with the SLM elements. This can be represented in the equation below:
FU = S V Ek MijkA
EQ 7 where S is the
20

input image, A is the SLM image, and
represents the interconnects generated by the off-focus properties of the image.
The CCD then detects the energy of the resulting image. The data is read by the computer off the CCD and then enters thresholding. The thresholding operation is shown below:
1
2
>
0 otherwise
EQ 8
This thresholding output then drives the SLM ON and OFF states. Although the mathematical computations differ from that of the PCNN, the output images were of this system were similar.
SMd
Focal
Plane
CCD
Object
Figure 3. Optical PCNN-like computational system proposed by Johnson
[94].
21

1.2.4 Multi-layered PCNN Arcitectures
A multi-layered PCNN was proposed for the segmentation and discrimination of structural and spectral image information [33]. This layered PCNN uses different coupling parameters at each layer to extract different information and enhance performance. Such an algorithm may potentially be implementable (with modifications) on an optoelectronic neural network with hidden layers such as the Compact Optoelectronic Integrated Neural (COIN) Coprocessor in development by the Photonic Systems research group at MIT [37]. This architecture is shown in
Figure 4.
22

10
0
Threshold
Bect ronics
Lasersor
FCLEDs
Bragg
Gating
Epacing
Bracket
Photodetector Array
:
3d
1
1-4
I
I
T
I
11
I
Figure 4. Compact Optoelectronic
Coprocessor.
Integrated Neural (COIN)
1.2.5 Current Issues in PCNNs
Lindblad and Kinser contend that although the PCNN is a significant step in emulating the mammalian visual system, it is still a very simplified model of a complex system. Work will continue in this area to fully understand mammalian visual processing. By emulating biological systems, it is expected that the image processing capabilities of computers will continue to advance.
23

In addition, an optical implementation that fully emulates PCNN behavior has not yet been built.
This may be a future area of opportunity in this field.
24

This chapter will present the simulation results of two pulse-coupled neural networks consisting of an array of 8 x 8 and 76 x 76 neurons, respectively.
2.1 Simulation of an 8 x 8 PCNN
A simple example of PCNN processing is provided below. An 8 x 8 bitmap image is input into an 8 x 8 neuron PCNN. The constants are defined as below [11]:
Table 1. PCNN Parameter settings.
radius Radius of linking field
TL 'ng decay term
Tr
IF
Threshold decay term
Feeding decay term
VL
V
7
VFFeeding
Linking amplitude constant
Threshd amplitude constant amplitude constant
25
1.0
20.0
0.01
3.0
1.0
10
0.001

All values of the PCNN architecture were initialized to zero (F=L=U=Y=0). The threshold was initially set to 1 (T = 1). The matrices T, F, L, U, and Y are of the same dimensions as S, an 8 x 8 array. The Matlab software used to simulate the PCNN can be found in Appendix A.
Both the feeding and linking weight matrices, M and W, can be represented by the kernel, K For this demonstration, a 1/r kernel was used where K is a square matrix of dimension 7 (dim =
2*radius+1). The distance r is the Euclidean distance from the center pixel. The center pixel equals one. The kernel, K, is shown below:
Table 2. PCNN Kernel Matrix
0.2357 0.2774 0.3162 0.3333 0.3162 0.2774 0.2357
0.2774 0.3536 0.4472 0.5 0.4472 0.3536 0.2774
0.3162 0.4472 0.7071 1 0.7071 0.4472 0.3162
0.3333 0.5 1 1
0.3162 0.4472 0.7071 1
1 0.5 0.3333
0.7071 0.4472 0.3162
0.2774 0.3536 0.4472 0.5 0.4472 0.3536 0.2774
0.2357 0.2774 0.3162 0.3333 0.3162 0.2774 0.2357
Figure 5 shows the PCNN outputs, Y, for iterations where neural activity occurred. Note that no neural pulsing occurred for iterations not shown, i.e. the matrix Y was a zero matrix. Also note that in the binary output, white represents the value 1, and black represents 0. Given the input image, S, let us refer to the square in the upper left corner as Square A, and the square in the
26

lower right corner as Square B. Figure 6 shows the periodic behavior of the PCNN. A comparison of iterations n=1..36 and n=65..100 shows that the initial network behavior was duplicated 64 iterations later.
2
2
4-:j
4680
Input Image, S
2468
2 4 6: 0.
2 n=33
.
4 b 5 n-34
Figure 5. Input image, S, and PCNN output, Y, at select iterations.
27

2 2
444
6E
2 4 68
Input Image, S
24 n=65
68 2 468a n97
6
8
2
4
2
2 4 6 8 n=98
4
6
8
2 4 n=99
6 8
6
8
2
4
2 4 n=100
6 8
Figure 6. Input image, S, and output, Y. Additional iterations demonstrate periodic PCNN behavior.
Figure 5 and Figure 6 demonstrate the autowave behavior of the PCNN. At n 34, the prior activity of neighboring neurons (neurons activated at n = 33) causes the neighboring neurons to pulse and an autowave begins to propagate from the each of the centers of Squares A and B. At n = 35, the next wave of neurons pulse. At n = 36, the final two neurons pulse, ending the autowave. This behavior repeated at n = 97. It can be observed that the autowave began at the centers of each square of the input image and then propagated outward.
The time signal, G[n], is shown in Figure 7 below. The time signal, also known as the intensity function, provides unique information about the image over time. In this case, the time signal demonstrates harmonic behavior with spectral peaks at n = 1, 34, 65, and 98. This can also be observed by noting the total number of activated neurons at these iterations in Figure 5 and
Figure 6. Figure 8 shows the time signal over 200 iterations. The periodic behavior continues over time.
28

I intensity Function G[n]
I I I l~ I
26
20
15
10
0
I
10
I
20
I
30 40 50
Iteration Number (n)
60 70 80 90 1 0
Figure 7. Time signal, also known as the intensity function, shown for 100 iterations for 8 x 8 PCNN.
Intensity Function G~n]
30
25.
-
20z
15
10
S
1
2r
4tio1
-
Number
Iteration
Nurmber (n)
120
14I
ItO
1IOU 2V0
Figure 8. Time signal for 200 iterations on 8 x 8 PCNN.
29

The state of each PCNN parameter is shown as a function of iteration in Figure 9 . The data shown is for the (i,j) = (3,3) neuron in the 8 x 8 PCNN. Figure 10 depicts these parameter states separately for completeness.
Parameter States
10
8
14
12 -
6-
4-
+
U
F
L
Y
T
0 t0 20 30 40 50
Iteration Number (n)
601 70 8 0 0
Figure 9. Parameter states for neuron (i,j) =(3,3).
30

4
2
Input Image, S
4 6
Internal Activity, U
8
2.5
2
1.5
1
0 20 40 60
Iteration
Number (n)
80 100
Feeding Input, F
1.14
1.12
1.1
1.08
1.06
1.04
1.02
11
20 40 60
Iteration Number (n)
80 1 10
1
-
Dynamic Threshold, T
-
08
0.6
0.4
0.2
0 20 40 60 80 100
Iteration Number (n)
Linking Input, L
14
12
10
8
6
4
2
0
1 20 40 60
Iteration Number (n)
80 100
Neural Output, Y
.
S
I
I
0
40
60 80 100
Iteration
Number (n)
Figure 10. Parameter states for neuron (i,j) = (3,3) (shown separately).
To demonstrate the invariant behavior of the time signal, G[n], the input image was rotated by
90* counter-clockwise and run through the PCNN. Simulation results are shown.
21
61
8 1
2
4 b 0
Input Inage, S
2 4 n=1
66
2
4
66
2 4 6 n=34
8
4
2 4 6 n=35
8
2
2 4 6 6 n=33
4 n=36 b
Figure 11. Rotated 8 x 8 input image, S, and select iterations.
PCNN output, Y, at
31

2
4
2 4 6 8
Input Image, S
2
4
6
8 ;
2 4 15 r=96
2 4 6 8 n6
6 a I
2 4' & 8 n=-99
2
S
4 6 8 n=97
.4. n=100 b 8
Figure 12. Rotated input image, S, and output, Y. Additional iterations demonstrate periodic PCNN behavior.
Input Image. S
0.1
Feeding Input, F
15
Linking Input, L
2
4
2 4 6 B
0.4
internal Activity, U
10
0 05
5
0
60
Iteration Number (n)
100
1
Dynamic Threshold, T
0
0 50 100
Iteration Number (n)
Neural Output, Y
N-
0.5
0.5
0.
0
0 50
Iteration Number (n)
100
0
0 50 100
Iteration Number (n)
0
0 50 100
Iteration Number (n)
Figure 13. Parameter states for neuron (i,j) = (3,3) for rotated 8x8 input image.
32

Figure 14 shows that time signals of the original 8 x 8 image and a rotated version are identical.
Wtendy Funcfon G Irenskiy Funfion
G(n)
26
20
16
1011
6 ft
0 10
3
3
0
406so 60. 70 lereian Number
(")
OR 90 100
.3
I
1
0 0s 3 5D W0 teratln
~M
xW (
70 90 90 100
Figure 14. Time signals, G[n], for the original 8x8 input (left) and the rotated 8x8 input (right) are identical.
2.2 Simulation of a 76 x 76 PCNN
A more complex example of the PCNN is shown below. This case simulates a 76 x 76 PCNN array for 100 iterations. The parameter settings initially remained the same as for the case above.
Figure 15 depicts the original input stimulus, S, and the output Y for the first five iterations.
33

20
40
60
20 40 60
Input Image, S
20
40
60
20 40 60 n=1
20
40
60
20 40 60 n=2
20
40
60
0]
20 40 60 h=3
20
40
60
S
20 40 60 n=4
20
40
60
9
20 40 60 n=5
Figure 15. Input stimulus, S, and outputs, Y, for the first five iterations. Pixel number is indicated on the coordinate axes.
From the original input image (76 x 76 pixels), it is apparent that the (4,4) pixel has a low intensity value and its neighboring pixels have low intensities. The nearest neighbor intensities range from a minimum of 0 to a maximum of 8, as shown in Table 3. Pixel (20,40), as highlighted in Table
4, has an intensity of 222 (on a 0:255 intensity scale). The nearest neighbor values range from 135 to 221. The intensities of neurons (4,4) and (20,40) and their neighbors are shown in Table 3 and
Table 4 below.
34

Table 3. Sub-section of 76 x 76 neural network. Pixel (4,4) (highlighted) and neighboring pixel intensities (256 grayscale).
201
208
200
204
211
193
210
193
17
0
3
5
0
0
8
0
0
3
210
0
0
201
3
8
0
6
2
208
5
0
0
3
5
0
200
0
0
6
5
0
0
2
0
0
4
204
0
3
Table 4. Sub-section of 76 x 76 neural network. Pixel (20,40) (highlighted) and neighboring pixel intensities (256 grayscale).
81
193
221
223
143
85
11
86
199
219
221
137
88
6
89
199
220
221
135
89
6
84
195
220
138
91
9
97
140
91
17
187
214
210
98
176
210
207
160
88
39
99
159
198
190
180
96
60
35

Input Image, S, Feeding Input, F Linking Input, L
2.15
2.1
15
10
2.05
5
2 zu 4U OU
8
7
6
Internal Activity, U
4
3
2
0 20 40 60
Iteration Number (n)
80 100
-
0.2
0
0.8
1
0.6
0.4
20 40 60 iteration
Number (n)
80 100
Dynamic Threshold, T
---
20 40 60
Iteration Number (n)
80 100
0
3 1 20 40 60
Iteration Number (n)
80
Neural Output, Y
1.5
1 30
0 20 40 60
Iteration Number (n)
8
100
Figure 16. Input stimulus, S, and PCNN parameter states for neuron (ij) = (4,4).
2[ it
3[
4C
5C
2000
1500
Input Image, S
20 40
Internal
Activity, U
60
Feeding Input, F
222.25
222.2
222.15
222.1
222.06
222
0 20 40 60
Iteration Number (n)
80
Dynamic Threshold, T
1 0
2
1.6
1000
500
C
0 20 40 60
Iteration Number
(n)
80 100
0.5 [
0~
0 20 40 60
Iteration Number (n)
80 100
0.5
2
2
0
35
30
Linking Input, L
1.5
5
0
0 20 40 60
Iteration Number (n)
80 100
Neural Output, Y
40 60
Iteration Number (n)
80 100
Figure 17. Input stimulus, S, and PCNN parameter states for neuron (i,j) = (20,40).
36

Figure 16 and Figure 17 show the parameter states for the (4, 4) and (20, 40) neurons, respectively. The two neurons behave quite differently. While the parameter states of neuron (4,
4) demonstrate periodic pulsing and decaying behaviors, neuron (20, 40) shows an exponential increase in all parameter states until it reaches a steady state or plateau. The states never decay.
This indicates that the neuron has become saturated. The amplitude normalization constants and decay constants can be adjusted to avoid saturation.
By adjusting the threshold amplitude constant from VT= 20 to VT= 10, we get the results shown in Figure 18 and Figure 19.
20
40
Input Image, S
0.
2
Feeding Input, F
01 5
0.
1
00
15
10
6
Linking Input L
60
20 40 60
0.
Internal Activity, U
0.6
0 60 100
Iteration Number (n)
Dynamic Threshold, T
1
0
0 50 100
Iteration Number (n)
1
Neural Output, Y
0.4
0.2
0.5 0.5
0
0 50 100
Iteration Number (n)
L
0 50 100
Iteration Number (n)
0 50 100
Iteration Number (n)
Figure 18. Input stimulus, S, and PCNN neuron (ij) = (4,4) where VT = 10.
parameter states for
37

Input Irnage. S
2.15
Feeding Input, F Linking Input L
'20,
40
601
20 40 60
I
Internal Activity, U
2.1
2.05
10
5
2
0 50
Iteration Number (n)
100
Dynamic Threshold, T
1
01
0 50 100
Iteration Number (n)
Neural Output, Y
1
6.
4
2,
0 50 100 iteration Number (n)
0
0
I-.
-___
100
Iteration Number (n)
0.5
06
0 50 100
Iteration Number (n)
Figure 19. Input stimulus, S, and PCNN parameter states for neuron (ij) = (20,40) where VT = 10.
It can be observed that the parameter states of neuron (20, 40) now vary and demonstrate the pulsing harmonic behavior of the PCNN. The neuron is no longer in a state of saturation.
38

In this chapter, an analysis of optical emulation of a PCNN is provided and a new optoelectronic
PCNN architecture is proposed.
3.1 Optical Emulation of PCNN Behavior
A block diagram of the PCNN architecture is shown in Figure 20 below.
13
VK
F
S
Figure 20. Block diagram of PCNN algorithm.
Y
39

The mathematical operations that occur in PCNN processing and can be modeled optically are as follows:
1. Convolution between Y and K
2. The output (light) then splits into two paths: a. Path 1: Scalar-matrix multiplication of A and L is performed. A +1 bias is then added to AL.
b. Path 2: The input image S is added to the beams, resulting in the matrix F.
3. The matrices of Path 1 and 2 are then multiplied to generate the following equation:
U = F(1l +L)
EQ 9
4. The internal activity, U, is compared with the dynamic threshold, T. The output Y equals one when U exceeds T.
Y =1,
U>T
10.
EQ 10
40

5. The dynamic threshold, T, is updated by its prior state scaled by its decay constant plus the output Y scaled by a constant
T = erT + VTY
EQ 11
6. The output Y is fed back into the PCNN through the linking and feeding channels and the process is reiterated.
The next section will discuss the proposed optoelectronic PCNN architecture as a means of implementing the operations detailed in the algorithm above.
41

3.2 Proposed Optoelectronic PCNN Architecture yI
4
/ - - - - - - - - - - - - - - -
LinkingChannel
LED(+1)
0
K
V
Convolution
Feeding Channel
S
SIM oBD
Figure 21. Optoelectronic
Processor Architecture
Pulse-coupled Neural Network
This new proposed optoelectronic architecture attempts to mathematically emulate the pulsecoupled neural network computations. In this architecture, beamsplitters are used for combining beams (addition) and also for providing feedback paths. Lenses are used for collimating beams where diffraction effects may dominate. It is assumed that the distances between the other elements are small enough such that diffraction effects are negligible. These elements are essentially sandwiched together.
42

3.2.1 Input Image Light Source
The input image, S, is represented by an array of light emitting diodes (LEDs). An architecture that employs an incoherent light source would be ideal for ease of use and implementation.
Incoherent light sources also tend to be significantly less expensive than coherent sources of light.
The intensities of the input image will be represented in each pixel-representative LED. There are no phase complications to consider. If coherent light were used, phase would have to be considered to avoid diffraction effects. Intended interconnects could easily be lost to diffraction effects.
3.2.2 Two-dimensional Convolution
A convolution is performed between Y of the prior state (the feedback Y) and the weight kernel,
K. The optical convolution is performed using the processor shown in Figure 22 below.
43

X,
K Fy9
-10 z
Y2
F{K
SM
=1
F(19
X
z
Y1 z=O
I z=F
ELM z=2F
F{Y} F{K}
I z=3F
Figure 22. Optical convolution of the prior state output, Y, and the kernel, L
V
X
3 z=4F
First, the Fourier transform of K and Y are each performed separately. The Fourier transform is an inherent property of a lens when centered in a 2F system, where F is the focal length of the lens, as depicted in Figure 22. The Fourier transform of K, F{K}, is written onto the SLM prior to the start of PCNN iterations. As the Fourier transform of Y, F{Y}, passes through the SLM, the product of F{Y} and F{K} is formed.
The convolution theorem (mathematics) states that for functions g(xy) and h(xy):
44

Pfq(xy) * h(xy)} = -F{9(xY))P{h(x,y)J = G(f
1
EQ 12
Hence, if given the product of the Fourier transforms, the convolution in the spatial domain can be computed by taking the inverse Fourier transform of the product as shown below: g(xy) * h(x,y) = F-{Fg(y)}F{h(xy)}= F~(G(f.,f,)H(f.,fr))
EQ 13
Similarly, given the product of F{Y} and {K}, we optically compute the inverse Fourier transform of that product to get the convolution of Y and K.
Y * K = F~'{FY)F{KI}
EQ 14
Note in Figure 22 that the coordinate system is inverted. The output of the optical processor must be read inverted since the lens cannot perform an inverse Fourier transform. It is also important to note that this portion of the PCNN architecture employs coherent light.
A beamsplitter is used to split the resulting convolution beam (Y * K) into two paths, to be used in the parallel linking and feeding channels. The output from the convolution processor is imaged onto the SLM along both the feeding and linking channels.
3.2.3 Linking Channel
A neutral density filter performs attenuation of the linking modulation, L, by a factor of P.
An ideal neutral density filter (NDF) would attenuate light of all wavelengths and colors equally.
However, in practice, neutral density filters do not attenuate all wavelengths equally [21]. A
45

number of companies offer both reflective and absorptive NDFs. Reflective NDFs are ideal for high power applications. Absorptive NDFs work well for lower power applications.! For this application, a neutral density filter of with an optical density of 0.6 might be used to perform an approximate scalar multiplication of P and the incident beam. The fraction of transmission of an
NDF can be calculated as T =
10
-OD [21]. In this case, the optical density is 0.6, which results in a fractional transmission of 0.25.
Next, the beam of an LED light source (+ 1) is added to the PL beam via a beamsplitter. The resulting beam models the linking channel output of 1 + PL.
In the feeding channel, the input image, S is added to the convolution term Y *K, to get the resulting term:
EQ 15
3.2.5 Array Muliplication
A delay is introduced to the feeding channel such that array or element-to-element multiplication is performed by a spatial light modulator which stores the incident linking modulation. As the delayed linking modulation passes through the spatial light modulator (which acts as a mask with the pixel values of Ff ), array multiplication is performed, resulting in the internal activity, U:
U = F(1 + ftL)
EQ 16
1
As indicated at the www.thorlabs.com website. Thorlabs, Inc. is a manufacturer of NDFs.
46

3.2.6 Thrsholding
Thresholding in this system could be performed in a number of ways. Optical methods include spatial light modulator thresholding (as in the Kirsch optical system) or the use of an optical bistable device. An optical bistable device (OBD) provides two stable transmission states which are determined by the input [21]. There are two types of optical bistability: absorptive and refractive. For absorptive bistability, an absorber blocks light dependent on the input. With refractive bistability, the refractive index of the internal material changes as a function of input intensity. Another thresholding alternative is to read out the CCD output and perform thresholding electronically, as in the Johnson PCNN-like system.
Wang, et al, proposed an all-optical pulse generator for pulse-coupled neurons which is based on optical bistable systems [39]. The pulse generator was demonstrated using an optical bistable device and a photorefractive crystal. This structure is shown in Figure 23 below. The system has two opposing feedback mechanisms and employs a two-wave mixing process. The nonlinear interference filters are tuned to a specific wavelength.
linput 'output
f6tered
Figure 23. All-optical pulse generator based on optical bistability devices.

One concern with using this device in an optical PCNN implementation is that it generates a string of pulses once an input intensity exceeds a threshold, not a single pulse. A solution must be considered to capture one output, Yj, per neuron per system iteration to maintain the overall synchronicity of the pulse-coupled neural network.
Another significant consideration for use is that it employs coherent light of a specific wavelength. For a system that employs this mechanism for thresholding, a light source such as
VCSELs might be used.
In addition, this optical pulse generation system transmits 2 states of light: low and high intensities. Upon detection of the output light, the neural output would have to be "translated" into the corresponding 0 or 1 binary output, a simple process that could be performed on the computer after photodetector readout. This might be another thresholding process in itself.
Thus, if computer thresholding or "translation" of the optical pulse generator output is required to generate a binary PCNN output image (to be input into an application-specific postprocessor), it may be worthwhile to simply perform the PCNN thresholding electronically, either via computer or by thresholding electronics.
3.2.7 System Feedback
Feedback of the optical PCNN output, Y, is routed back to the system input via the use of a beamsplitter, mirrors, and collimating and converging lenses. The feedback is performed by using a 4-focal-length (4F) 2-lens system to image the output of the optical bistable device (OBD) onto the input plane of the optical convolution processor. Initially, the OBD output beam diverges and passes through a lens which collimates the beam. Next, two mirrors direct the collimated beam to pass through a second converging lens which images the OBD output onto
48

the input plane of the optical convolution processor. The PCNN optical computations then repeat.
3.2.8 System Output using a Charge-Coupled Device
Charge-coupled devices (CCDs) are frequently used in digital cameras, scanners, fax machines, and video cameras [21]. Also called a Color-Capture Device, the CCD provides a convenient means for converting optical signals to electronic signals and vice versa.
For this application, a CCD can be used for the conversion of an electronic image, S, into an optical signal. The image can be captured on a CCD and read out. The serial CCD readout can be stored in computer memory upon readout. The resulting charges will drive the individual
LED intensities which will represent the image S.
In addition, the CCD interface will convert the binary output images, Y, of the optoelectronic
PCNN into an electronic format that can be stored on the computer and input into a postprocessor of choice.

This chapter will review the research conducted and will draw conclusions. It will also explore areas for future work.
4.1 Summary
The primary objective of this work was to further the development of an optoelectronic pulsecoupled neural network and to identify problems and opportunities of such an implementation.
A pulse coupled neural network was simulated. Simulation results were presented. An example of PCNN saturation was shown. The invariant properties of the time signal G[n] were also presented.
Previously proposed optical PCNN structures were presented and analyzed. An enhanced optoelectronic PCNN architecture that more closely models the mathematical PCNN behaviors was proposed. This design will perform PCNN processing on 128x128 pixel images (at a minimum) for a variety of applications ranging from medical to military purposes. This design is scalable to the network size that current technology (at the time of implementation) will permit.
If the lowest common pixel size of the chosen components is 1024 x 1024, then the system will perform PCNN processing on that size of image. The drivers of the network size include:
9 choice of light source,
50

e desired physical size of the system,
* and choice of spatial light modulator.
4.2 Challenges and Opportunities of Optoelectronic Implementations of PCNNs
Optical information processors, such as the PCNN, have been studied extensively as an arena where certain advantages of optics may exceed the capabilities of electronic processors for specific applications. Such advantages include:
" Ease of information processing in the optical domain; the ability to exploit optical Fourier
Transform capabilities
" Massively parallel interconnection capabilities and parallel processing
On the other hand, advances in electronics have been significant in past decades. The famous
Moore's Law, which states that the number of transistors on a chip doubles approximately every two years, continues to persist. Electronic processing capabilities continue to grow and the cost of these processors continues to decrease. Some advantages of electronic processors over optics include:
" Cost
" Size
* Thresholding capability
" Storage capability
Let us consider the potential cost of an optical PCNN using modem optics technology. For a compact system, one may desire to use VCSELs as a light source, and 3 spatial light modulators for performing convolution, array multiplication, and thresholding. A 128 x 128 array of
51

VCSELs, while theoretically feasible with current developments, may cost approximately $50 -
100K depending on the reusability of existing masks. Each spatial light modulator would cost roughly between $10 20K. Without considering the costs of other components, the cost of such a system for image processing purposes may range from $70-140K 2
. Such a system would need to be connected to a computer for readout of the detected optical signal, making it a hybrid system. On the other hand, for under $1K, the same computer can rapidly perform all of the
PCNN processing.
Another issue with an optical implementation is the ability to store the prior state of the PCNN.
The system may need to be duplicated to provide the prior states of the threshold, feeding, and linking modulations. The use of spatial light modulators' optical data storage capabilities may address this issue. However, storage of the prior states is not an issue for a computer processor.
Additionally, thresholding, which is difficult to perform optically, is performed quite simply on a processor.
Modern processors perform pulse-coupled neural network computations quite efficiently. Given the cost of optical components, and the complexity and scale of an optical implementation, this author recommends the use of traditional processors for PCNN applications. The challenges outweigh the benefits of an optical implementation.
4.3 Future Work
Future work can ensue in a number of areas. The implementation of the proposed optoelectronic architecture and a comparison of electronic versus optical PCNN performance would provide closure to the question of the benefit of an optical implementation.
2 Component prices based on a survey of commercial providers.
52

Multi-layered pulse coupled neural networks could potentially be implemented on the Compact
Optoelectronic Integrated Neural (COIN) Coprocessor with some modification. This is a potential area of study and could provide another area of application for the COIN.
In the arena of PCNNs, there may still be a need for the development of a novel, rugged, compact processor that could perform in harsh military arenas or in conjunction with medical equipment. Whether the implementation solution is optical, electronic, or a hybrid, commercialization of PCNN processors could meet the image processing needs of many industries.
53

Appendix A Matlab Simulation of an N x M PCNN
This Matlab code simulates an N x M Pulse-Coupled Neural Network. N and M are determined
by the size of the image that is input to the network. In other words, the size of the PCNN equals the size of the image. The core code for the PCNN is provided. Plotting functions are not included.
% PCNNSIM.M
User is prompted to enter the path and filename of the input
% image file. Size of the PCNN is the same as the size of the
% input image. A 1/r convolution kernel performs the linking and
% feeding weights. Parameter values are listed below:
% tauL = 1.0;
% tauT = 10.0;
% tau F = 0.001;
% VL = 1.0;
% VT = 20;
% VF = 0.01;
% beta = 0.2; %0.01 weak and 1.0 strong [J.L. Johnson]
% radius = 3.0; % radius of the Linking Field K
% Load input image.
file = input('Enter the path and file name including extension:
S = imread(file);
% If not 2D, make the input a 2D intensity image.
if length(size(S))==3 S=rgb2gray(S);end
S = double(S); %Make same format as other variables.
% Define constants / parameters.
tauL = 1.0; tauT = 10.0; tau F = 0.001;
VL = 1.0;
VT = 20;
VF = 0.01; beta = 0.2; %0.01 weak and 1.0 strong [J.L. Johnson] radius = 3.0; % radius of the Linking Field K alphaL = alpha_T = alphaF =
-1/tau L;
-1/tauT;
-1/tauF;
54

imgsize = size(S);
% Initialize all to zero.
F = zeros(imgsize(l), imgsize(2));
L = F;
U = F;
Y = F;
% Threshold is initially = 1.
T = ones(imgsize(l), imgsize(2));
% Both linking and feeding weight matrices can be represented by
% the kernel, K. For this demo, we will use a 1/r kernel where K
% is a square matrix of dimension 2*radius + 1. r is the
% distance from the center pixel. The center pixel equals one.
% [Ref. J.L. Johnson] dimk = 2*radius + 1; sizek = [dimk dimk];
K = zeros(sizek); kcenter = radius + 1; for ii=l:dimk for jj=l:dimk
K(ii,jj)=1/sqrt((kcenter-ii)^2 + (kcenter-jj)^2);
%Euclidean distance if ii == kcenter if
== kcenter
K(kcenter,kcenter) = 1; end end end end np = input('Enter the number of iterations:'); n=1; szY = size(Y);
YY = zeros(szY(1),szY(2),np);
GG = zeros(l,np);
TT = YY; while n <= np work = conv2(Y,K,'same');
% Convolution of Y with Kernel K; K represents both M and W
% weight matrices
L = exp(alphaL).*L + VL.*work; % Linking mechanism.
T = exp(alphaT).*T + VT.*Y; % Update threshold.
F = S + exp(alphaF).*F + VF.*work; % Feeding mechanism.
U = F.*(l+beta*L); % Internal activation.
pulsed = find(U>T);
Y = zeros(imgsize(1), imgsize(2));
55

end
% If pixel exceeds threshold, output = 1. Else, output = 0.
Y(pulsed)=1;
YY(:,:,n) = Y; % Store all Y outputs.
TT(:,:,n) = Y; % Store all T outputs.
UU(:,:,n) = U; % Store all U outputs.
LL(:,:,n) = L; % Store all U outputs.
FF(:,:,n) = F; % Store all U outputs.
g = sum(sum(Y));
GG(:,n)=g; % GG = intensity function.
n = n + 1;
% Uncomment below for Y plots for each iteration.
% figure; colormap(gray); imagesc(Y)
56

Appendix B Current Optical Component Technology Useful for PCNN
Implementation
B.1 Spatial Light Modulators
Spatial light modulators can be categorized by several characteristics [25]:
* Optically addressed (photoactivated) or electrically addressed
* Transmissive or reflective
" Phase modulation, amplitude modulation, or both.
The purpose of the SLMs in the proposed optoelectronic architecture is to serve as multiplication elements in two separate functions of the pulse-coupled neurons. SLMs can also perform thresholding and data storage. An additional potential capability of the
SLM is beam steering. One widely-known use of beam steering is the phased-array radar, where the phases of the signals supplied to individual antennae elements are modulated such that the effective radiated pattern is steered in a desired direction, with no physical movement of the antennae. Individual pixels of a phase-only SLM can be compared to the antennae elements of the phased array radar. A phase-only SLM can act as a diffractive or refractive grating. One form of a phase-only SLM is a liquid-crystal-onsilicon (LCOS) SLM. In 1995, a LCOS SLMs was demonstrated as a means of free-space optical interconnects. A 4x4 VCSEL array served as the light source which fed a 256x256
Ferroelectric liquid-crystal-on-silicon (FLCOS) SLM. The FCLOS was written with beam steering "patches" which directed the input VCSEL light to the desired detector in a 4x4 detector array [28,29].
57

In addition, SLMs are small, lightweight, and require low power. Finally, SLMs are relatively inexpensive. SLMs cost less than 8 cents per pixel in a 512x512 SLM. Some of the drawbacks of SLMs include: polarization dependence, wavelength dependence, slower response times, and reduced diffraction efficiency. However, research has demonstrated potential fixes to most of these drawbacks. In 1991, researchers at
Displaytech Inc. demonstrated that FLCOS SLMs could diffract unpolarized light [29,30].
Physical modifications to the SLM can enhance performance. For instance, adding a dielectric stack to the backplane of an SLM has been shown to increase SLM diffraction efficiencies up to 94%. New liquid crystal developments and higher voltage backplanes have resulted in sub-millisecond SLM response times [27].
Another version of SLM technology is the Digital Micromirror Device (DMD) manufactured by Texas Instruments. The DMD is a reflective spatial light modulator.
It is possible that the SLM would have more pixels than the light source array. In a case where the neural network has fewer neurons than the SLM pixels, each neuron pixel can correspond to an SLM macro-pixel. For instance, if the PCNN is 128 x 128 and the SLM is 512 x 512. The SLM can be addressed such that a 4 x 4 array of pixels would equal one macro-pixel. One SLM macro-pixel would then correspond to one neuron. The 512 x
512 SLM essentially becomes a 128 x 128 macro-pixel SLM.
B.2 Beam splitters, Microlens Arrays, and Photodetector Arrays
A beam splitter is exactly as the name implies. A beam splitter is an optical mechanism that divides a beam of light into two. In an optical architecture, it is used as a means to provide feedback.
58

Microlens arrays can be manufactured on a very small scale with properties ranging from refractive or diffractive, spherical or aspherical, to concave or convex. Microlenses can be as small as 15 Lm in diameter. In the Kirsch architecture, the microlens array is used to spread light from a pulsing neuron (i.e. pixel exceeding the threshold) to other adjacent neurons.
Photodetectors (PDs) sense light. In an optical architecture, a photodetector array is used to detect the output of the PCNN. This optical output is detected by the PD, read out, and converted into an electronic signal.
B.3 Light-emitting diodes
A light-emitting diode (LED) is a semiconductor device that serves as an incoherent light source. An LED emanates narrow-spectrum light when it is electrically biased in the forward direction of the diode p-n junction [21]. For the purpose of a 128 x 128 neuron architecture, a 128 x 128 LED array with an 8-bit driver, providing 256 gradation steps and allowing 256 levels of intensity, would suffice.
B.4 VCSELs
Vertical-Cavity Surface-Emitting Lasers (VCSELs) are small-scale semiconductor laser diodes that emit a laser beam perpendicular to the top surface. The precursor to the
VCSEL is the conventional edge-emitting semiconductor laser which emits light in a beam parallel with the top surface. Examples of edge-emitting laser diodes include
Fabry-Perot or distributed feedback lasers. An edge-emitting laser is depicted in Figure
24. The VCSEL's perpendicular light emissions allow many VCSELs to fit on a Gallium
Arsenide (GaAs) wafer. This property lends VCSELs to massive production. In addition, VCSELs can be tested throughout the production process, ensuring higher
59

quality manufacturing outputs over traditional edge-emitting lasers. VCSELs can be tested on-wafer, prior to being split into separate devices. This helps to reduce fabrication costs. Also, because VCSELs emit light perpendicularly, this allows them to be manufactured in 2-D arrays [21]. A simple VCSEL structure is depicted in Figure 25.
A single VCSEL is shown in Figure 26.
Top MeAW
Codact
Enitting Region
00"
Proton Bombarded
Semi-Insudating Barier
p+ GaAs pAGuAs
Active Region n AIGaA9 n GaAs Subsbrate
Bottor Contact
Figure 24. Example of an edge-emitting laser structure
[23].
An/Ti rwine4
41off ConW
I
Light Out
Figure 25. Example of a simple VCSEL structure [23].
60

Figure 26. A single VCSEL in a T046 package.
VCSELs require highly reflective mirrors (99.9 % reflectivity) to construct the internal laser resonator. The highly reflective mirrors used in VCSELs are called Distributed
Bragg Reflectors (DBRs). These DBRs (doped as p-type and n-type) bracket an active region, which generates the laser light, and form a diode structure. The cavity length of a
VCSEL is short, typically 1-3 wavelengths [23].
The VCSEL often employs a circular aperture which outputs a radially symmetric beam, i.e. a circular beam profile. In comparison, edge-emitting lasers output asymmetric elliptical beams. These elliptical beams require complex corrective optics for most applications. VCSELs offer lower divergence angles and higher efficiency. A review of numerous VCSEL manufacturer data sheets show that VCSEL beam divergence angles range from 7-30%, where beam divergence is defined as the total angle between the 1 /e
2 intensity points. Edge emitters have a beam divergence of 50-60' in the perpendicular plane and 10* in the parallel plane [24].
Given the characteristics of a VCSEL, it recommended as the light source of choice for optical interconnects. They offer reliability, efficiency, and mass producibility.
61

In the current VCSEL market, it is fairly easy to purchase commercial off-the-shelf
(COTS) VCSEL arrays. These typically are available as 1x4, 1x12, 4x8, and up to 8x8
VCSEL arrays. For the application of PCNN image segmentation, a larger VCSEL array is desirable. A 128x128 array would support a prototype for initial PCNN image processing efforts. A 128x128 VCSEL architecture is feasible and has been proven commercially [47]. If the system design is resilient to small variations in VCSEL threshold current, power, and reliability, a 16384-channel (128x128) can be prototyped.
Another possible approach to developing a 128x128 VCSEL array is to create an array of sub-arrays. For instance, by creating an array of 16 8x8 by 16 8x8 VCSEL arrays on a ceramic submount, a 128x128 array becomes feasible using COTS products. This architecture is conceptually depicted in Figure 27 which shows a 16x32 VCSEL array constructed from eight 8x8 VCSEL sub-arrays in a 2x4 sub-array configuration.
Figure 27. A 16x32 VCSEL array comprised of eight 8x8
VCSEL arrays.
Development costs are less prohibitive if the system design can accept 1-2 failed per 100
VCSELs as a part of the development. One way to build "insurance" into the system is to add some redundancy. This increases the overall system reliability. By adding 1-2
62

additional rows or columns to the VCSEL array, the system would have a performance backup. If one row has a bad VCSEL, the system would have the redundancy to skip that row and reference another.
63

-- - mr-
Appendix C Datasheets of Optical Components Useful for PCNN Implementation
C.1 Transmissive Spatial Light Modulator (Meadowlark Optics, Inc.) a.
481
SPATIAL LIGHT MODULATOR PRINCIPLES
MeadnarkOtae ual-insa
Spatial LIAght Phase Centrol tdoaulban (SLms) proida pseioeom ratardate camtrol
Owr SLhs cansist of liquid cysal (LC)piaze each
Spatit phase caont ro omdationis accompliieAd far snialry enying phase wiAnt SlarM the inteaity promfe a incideet bearn
LqghktibwlypobawindpwHal to teD stmnotaLay ammi indepel adya&hNead. acting a nerate v-iable LC mates is phasa mcdulated by ie voltage rder."hee SLMe a easily incorpted int optiai apliei amas indi*a pixd
An asptialpw& synum requiring progenabb imana and variable betaneo Adjavent pinha. tnahl to -e faulspna vpy, daft vtom uk-reret coputin beam waesing andwaeeftaet oecton fei woe i easily ascnapiabepd aas lona in figure 5-1 pvl senhpiqn optical
acive and nadalewsopbt
Bask eca.tlatia and cpatian of an SL is Sain to an standad LVeiabe Retalr deailbed as paps
WM-39. The gmphiclly patterted into indiveal ectms teat"g independently conmolklibl pink. Standald SLM gaatrien are sh RaPnpge 49.
arte si- ma idmining pixel spacing ia esieat to oiptime pedi'eaunew and reolhion.
Popriebsy
Aesigns ad teateniqae nable Madoarlak Optca to ofertight pates.rpivel NpSG Cutmin] powi~a' osmotins am
.s .
.-..
.........
,
Rg 5-?| Vftarsrmndtde se pdoafpcrdarcane e
Lighbt * ahuTheoewptt wiveyraeinvuKw ri
Aawptdc
Central
Spas)a Light Modnltomn -m showied hr amphiacdn contal a mdulation. ien, the SLdm adias le beo itenaity,
Nt aboipatiafly Aite= the phase paofie, which aqy b ndeawsabla. Cbesectia ismonapliehed hywaiug two yawul light Moadsilsic in Salimn The firpat rna ti nede ac y anplitede modulalaon alA introducing a phase chape
The eanodSLM reaenes &at original, at desird phase alatimsip btweanpinele.
Pelaries an qoial with an amptiatle SLd. These palseimers an&bot rtatable ai emoeabla ntew
SLM baoeein& ie. compart optizaalAis deigned So bsatmw unita am be planed bk-ti-bazk, minseaiing te datance bet"eanmdatalab Elameiral coSneitrns an ude abbe optical head hr ammAima inhiling and
Ustime.
At Meadowlatk Opios SLds oaenesointly inatace-with
ModelDM28 Comualbrdecribed. mpage 51
Mnadowlork OptiCS wwwmeadowlat.com I mlo@meadowlarkcom T303.8314333
64

I&andmk Opti 9 pkaidLthtMAdanton (LM) cast of pattamd ormyv of mdependy coatrood liqud aqW#d(1P vandab marm Our hMIg-mobuim
SlJ - elmbeanifay sansmabb md inab t Iw arMada cem
1D312 SLM Cotmllar Mandaowkt Option botlinvar andhaqgsnal pid geaomkn.
SPATIAL LIGHT MODULATORS
ShapeShier LinearArray Spadal Liht Madudatar
The SapaShin "M he a linew pizal auy gometry
Thi system an bm mad b sahar t tempos] profle of
*imGooSGacnd
1*t pubs via computer actir
Applicatics quiri*g the.. &bot pulse iclud .ayuis
andq ma aMnd of anumd aK ns optiad comemmicaticn, and biiambdcal kmgin
Thmmr
SU&s fmd m ima otdr apphsinas mahui"g aiaumi mpsetabopy% optica dafts uga sandwwvht campa'aftos
Ha Spedal LlghtMedutem
Ow two diammaial SL m mu duinpdtr adaptive optic. appliatas.A im dizammal mwiy of
LUpidQysVaush. Rstudaw mte an ms) tim lan, -sn~ phame imask a liuvw polmrized mom.
arn~s
Umutd abhando s act removed by intodmiag the opposite pham hifl th ough the Hex SLK The most emnou appliatioane iuwaevu hi mantion mqim
whban viewig dwroLgb m aboam maDivm = unamidal a-h Ek iuchdn astrosamcal magig with poundbased b lkapa. andmedical imaging thmgh body flmth. higl4maf law =ns also benefit fo saftie phano campaseton Eihtam prnfile countia, we nncino
49
45-2 Ma27p gwnmoy
*fr -uIIi-d
5-3 SImpeSA*lnrSlMpirnlgswunny tttsw- Njunardd-4 ~&a wwwmeedowtarkicorn I mloOmeadowlaritcom I
T303:14333 fWOadOWIII opiCS
65

KSI
SPATIAL LIGHT MODULATORS
KEY Bnsnn
fmsdcn
.
canwGN~aw
Ciaptalr cmnild
ORDEUNG INFORMATION jGemery adhifpl
P't humbs
Pholmianfemtblvume iip bmcwai
1028 a SSP -IMA-16
Nrx IN tmD mmn 127P
-4
1jul27
1u121
1000 g
Har-1BP-)t
5 1IA--
Nuw 1000 mm- 1BA4phmanm aouo n ookii, I-
U
U
U a
I.-
B
SP istntlr
W*Rb khisamtul
Namtklqhdd pstaI
OptSqum w uEek maudusEca
U
50
U
U
.1
I
U p
5
N a a bw..mt iimu*
Mimi lhaptidpmhdcuffrwnm
Ampladr
O.S1
OktnrtintatflRnu* smg
SurfamQuky:
Uammoniadam
O4Daad
Almmin
.nd dig rbfnmesr uw0k4j:a
Ofreau.ie~4
Opufrdqkut
7uDs1E.74h
bwmmradfhM
50WIWOC hu
C5%a74 in c PTIOnAL POLARIZERS
RE-nd
1bftwqA
Tw
Vrible 4o-? ?SDP-wS
Neuhtkmd1 775-u
NIwIk*mdZ #g-110
Part
Numr sop-Rt
SOP- IR modowli optids wwwJMadouarbtCOm
I MIotmeadoWbArLm
| T303.833A333
66

SPATIAL LIGHT MODULATOR CONTROLLER
MeadowtInk Optic Spal LqhtMdalator Continfa
Aflow fi indspetndentvoltap catol of ap to 128 liquid cryta1 cens orpinxsk The M&del is avuilabua wit 123 chanus for use wit Meadodanrk Optics Spatal Li*
Tha SLM Conzoller coanetmvia tS3 casbe to a
Wiudawvmbawud cownuniesa suapsu Sqpplicd sofware aliwa fmr siting of individal pixel ratdaca and fkr the propeainung ofrwwrdanee profile. aa apinlubd dtvio
Caostm soaft e a can be wrnfl usigt inchided
Lab-VEWmVhtual IksMet Llbsry to allow Ib
MIcpta Ageo custm appinatica
0a
0
SPECIFCATIONS
OstputvlNge: 2 klh AC square wwr digftallyadstable adAtyqde minimal DC bias
00V n
Vltap Resolutir 244rnNf(12bit
Computer Inbirface: LE
Power Requirements l-240YAC
47-0H
I cIieruinG 1W x F4
Weight r50&x25.50 in
2lb&.
ORDERING INFORMATIN tom
SLMCcbtroler
Output
Chn'els
128
Part
Nunber
D3128
0x
C
151 www.meadowlarkrcom mIoimeadowfarkxcom
T303J3334333
M odOwlaork optics
67

C.2 Micromechanical Spatial Light Modulator (Texas Instruments)
Chip Set
At the heart of tin DMD D).soveryf1100 Chp Set Is tlie
Tt
XGA DDR DI4C anopdkal semlconductor to manipe tlgltdtA*.When that allos devdopers
Intepated with lWt sane ndoptk
thf unique dere awef t rny liht patterns with spee4 predsos and effidency for surpassing that of Other spa t Mwdf Atr
The MD .7XGA 120 DDR{Do"te Da Rate) consin of a
1024x 7M army of nilko-nmmedikaml nrrs an a micrometer pitch. Eachmirror can be hdvldu* deflected at
+1-
120 about a inled dasgnet .is. Deflection poadty
(positive ornegtlve)of the mress is htlnhutwI conroled bydchsnjng the nary state af the underrolgCt4D control circuty and ndnarrestsrals,
NEDhwiwy-f1cACp* pr-ewswpeuez d
DiND
DhlCOVEr 1100 CHIP SET
(See
" newerapegsystem dagnaiJ
07XGA DM0 Spatil Light Moduator (See desatIlon
Ths ftur
DIX
14x7lnBino m
I i gkba ddveenin blodckre fash atewing or phseud reset Bfedt an deduka Input, ptika autput mumssy e thE dke.
DID Q7XGA hb pegej)
12" 1000 cntro 16 bats of
DI4D sibroa e
Discovey 1100 DRC (DAD Reset Cantler) provides user
The
Dfif isowvey 110Cip Set feauresthe
DMD40 and odes
Interface t DADIlWO with vredappig mirrer budk meset capaMhlA.(DIP 205.-O-001)
* DIscoemy 1100 HSC (Hih Speed Cmtroelr) provides suppondng deiourdhTI lDM cantrem aptitnied for projecton dbplat Ihcmveey 1100 is deOEd to support a wide varety of DMD pocations by dekedq dmum edlfty in fo.ting and sequamcingta and resultig itt petum,
D00
77 data load cmonad nterfac supporting gtlbits/sec D data load. (DIP 2954S.001)
" Discovety 1100 USaIpC (LiSB hIterfIe Conmolmr)
C7 XGA DDR DMD FElATl
* 1024 xS76 Wtmble mroos(16 banks
of 1024x 40) p-win seateas Inarflac beten S and DIP conuqnut% suiporthig up to 80 negslit/ac 0|ID dew load. (DLp 2354K094)
* +/12 d"ege. mbra tilt
*
Uip
ID 00 Iifi array rrr pattans/sec (7.7 Gbs)
* 13ten x 13
M.
* 15% optalfit factor
SVIbd, ultraviolta (UV), and options armIable. (See ne Infrared (MR) pedcage rmsere pale tmanmilason charts fordtds. U & MR not Involure pmudction at thk tbne.)
"
Cprese
FX fpurchased Sepatty) provides WI 2.0
sysim Interface.
68

Product Peview Data Sheet
TI DN 2503686
August30, 2005
T M
This data sha descibes the U-7XGA 12DDR DMD oiscowmy'.
May not be repamxhed Shout persissima m Texas Inslrummts hicorporated
Cqptg"I 2=0 Teas nimseik mwrpurtad
I of21
Ti ON2503680
69

C.3 VCSEL Array (Finisar)
FEATURES:
* S5lnmcatbode commionVEL array
* apableof
Gpsperchannel moduladon
3
SFuly tested and wned in wlh
STAMLAZETM pmss lxi and 1x12 verion
TheHFEONO13aehighrminnce WSnmVCSEL(VrticalCavitySuface-
Emitting Laser) array die piined r high-speed data cmmunktioms
The array die am fuly stAkized and tested, ideal kw uein mufactudng transceivers fbrparalelopticalinerconnects.The arrays are avalable in either
4 or 12 channelcanfguratins.
Each device Is a high radianceVCSEL designed to cnert electical cuuent into aptialpcwerthat can be ued in iber optk mmmunicadns and other appicadins As the cment variesabow threshold,theligt Intensity inaeases papoationaly
TheBHFaiO-103are designed tobe used vith ihexpenivesikon or gallium rsnide detectors, butexcelent pedomance can alsobeachiewd with some indium gallium arsenide detectors.lhe Advanced
Qtical Components compwaion array detector is the
HFDBx-103.
The hrw div crrent req*ementmakes direct drive from PECL ositiw
EntterCoupled Logic)arEtL nkterCaupled Lookgatesposbleand emes driverdesgn.
Designed to Inteface Yith M12Sand 625/ 25#m m imnode ftber, the
VCSELs produce cfrir4ay symmetri, nn-astigmad naowdivergence beams that,ith apprpcxbte lening,fiber coqple allof the emitterpowec
The topaioade) contact, Is a minimum 1pm Au for ese of Wie bonding Wire bodhig shodd be done ith minimal presise to enure the VC$E Is not damaged The backside common lCSEL cathode is also a mimnumn of 1pm
AumetalirgyThe die must be momnted wing thermaly and electical conductive medbm
The VCSEL arrays are shipped an median tack bie tape in 6 Inch gdpringt
F in isar
1
P
01IME. 1,W
W MWO",
Prt Ndw w DRc4Udaw
WE M-u 4dunWVMLtany
Ifac-M 12 dsnfVELithe "r
M '
NOW HIM M 1,
MM MEE,
5
70

C.4 VCSEL Array (Lasermate Group, Inc.)
T
Iel No. VCA-IxN-A1G (N =2, 3,....) tures:
850 nm implant VCSEL 1xN array
1 x N (N=2, 3,...) array bar with 250 pm pitch
Dimensions of 1xN array: 305pm x 250gm (N) x 100pm
Rise/Fall time 135/150 ps typical
Optimized for fiber optic applications
CTRO-OPTICAL CHARACTERISTICS:
AMETERS
-shold Current
)ut Power e Efficiency
'elength
-tral Width (FWHM)
-shold Voltage vard Voltage ikdown Voltage arnic Resistance n Divergence
/ Fall Time r p-p
:shold Current Uniformity(4)
)ut Power Uniformity (5) ration Temperature Range (6>
SYMBOL
Ith
Po
] xP
AX
Vth
VF
VBD dV/dI
0
Tr/Tf
Tj
Alth
AP
Top
MIN TYP MAX
2 5 7
0.2
2
0.3 0.5
835 845 860
0.5 1
1.45 1.55 1.65
1.7
5
2.0
10
2.5
15
20 35 50
12
135/150
-5
30
0.4
0.3
25 80
UNIT mA ps ps mA mW
C
TEST CONDITIONS
(1) mW IF=12 mA mW/mA IF =12 mA (3) nm IF=12 mA nm
V
IF-12 mA
V
V
IF=12 mA
Q IF=12 mA degree Full width at l/e
2
Within single array
IF=12 mA
71

meters are measured with chip die-bonded to a metal header.
parameters except mentioned are measured at l,-=12 mA, 250C, CW.
e efficiency is defined as AP/(12-IF) at 25*C.
ned as the difference between the maximum and minimum threshold currents measured for a given IxN array.
ned as the difference between the maximum and minimum output power measured for a given IxN array.
imum power larger than 1mW in the range of temperature
72

ILUTE MAXIMUM RATINGS:
METERS ye Temperature iting Temperature nuous Forward Current nuous Reverse Voltage
MIN
-30
-30
MAX
100
85
30
5
UNIT CONDITIONS
*C
0C mA
V
RMAL CHARACTERISTICS:
METERS rnperature Variation aperature Coefficient emperature Coefficient
SYMBOL
AIt
All/AT
A4p /AT
"NSIONS:
METERS
>er of PIN photodiode elements ength (lxN) width hickness pads
)W size
MIN TYP MAX
-1.5 1.5
-0.29 -0.1
0.06
SYMBOL
N
P
L
W t
UNIT TEST CONDITIONS mA TA
=0-70*C,
IF =
12mA
%/*C TA =0~70*C, IF =
12mnA nm/*C TA =0-70*C, IF =
12mA
MIN TYP MIN
N
250
250xN
305
100
85x150
18
UNIT
9m im jiM jm pim
Pm ie Dimensions of Single Element: (unit: mm)
Detail dimensions:
73

X=0
E
CA
A
295
4----
255
.
ofW"a0 F~A
215 pm 4rOX
182.5 pm 4 nE :1
A
E
-4 to
Cl
1 4 1
~ ft
~WAFXfl7A
-- -
,E
p
N
24
41
~L.. I.
zIr
Yr r
-n to
Cl
C,
A
2 to
Cl
1 -pm
260
f~ -: r fT r I )b9O--W
235 pm
-----* 215 pm
192.5p
m
-* 172.5 pm
160 gm
A
140..3 p t a i i i I
--
S55gm
-
I r
Y=0
125 pm 125 pm
: These specifications are subject to change without notice.
74

Al.Ga,-As
CMOS
DBR
FLCOS
OBD
OEIC
PCNN
RCLED
SLM
VCSEL
VLSI
FPGA
GaAs
HOIE
LCD
LED
LCOS
NDF
GLOSSARY
Aluminum Gallium Arsenide
Complementary metal-oxide-semiconductor
Distributed Bragg reflector
Ferroelectric liquid crystal on silicon
Field programmable gate array
Gallium Arsenide
Holographic optical interconnection element
Liquid crystal display
Light emitting diode
Liquid crystal on silicon
Neutral density filter
Optical bistable device (also, Bistable optical device)
Optoelectronic integrated circuit
Pulse coupled neural network
Resonant cavity light-emitting diode
Spatial light modulator
Vertical cavity surface-emitting laser
Very large scale integration
75

BIBLIOGRAPHY
[1] Noakes PD, Green ADP. Neural
Networks: problems and opportunities! IEEE Colloqium on
Neural Networks: Design Techniques and
Tools, pp. 1-4, March 1991.
[2] Zurada J.M. Introduction to Artificial
Neural Systems, Publisher: PWS
Publishing Company, 1992
[3] Haykin S. Neural Networks: A
Comprehensive Foundation,
Publisher: Macmillan, 1994
[4] Johnson JL, Schamschula MP,
Inguva R, Caulfield HJ. Pulse coupled neural network sensor fusion. Proceedings of SPIE the
International Sociey for Optical
Engineeng, vol.3376, 1998, pp.219-
26. USA.
[5] Lindblad T, Kinser JM. Image
Processing using Pulse-Coupled
Neural Networks. Springer 1998
[6] Kirsch
J,
Jones B, Banish M,
Ranganath H, Viviano
J.
Electrical and optical implementation of the
PCNN. SPIE-Int. Soc. Opt. Eng.
Proceedings of SPIE the International
Society for Optical Engineering, vol.4471, 2001, pp.
14 7
-
1 5 8
. USA.
[7] Banish M, Chenault DB, and
Harchanko JS. Neural network processor, Proc. SPIE, Vol. 5563, pp.
13-18, 2004)
76
[8] Hassanien AE, Ali JM. Digital mammogram segmentation algorithm using pulse coupled neural networks Proceedings. Third
International Conference on Image and Graphics, pp. 92 - 95, 2004.
[9] Louri A, Na
J.
Modeling and simulation methodology for digital optical computing systems.
Paper] Applied Optics, vol. 33, no. 8,
1994
[10] Eckhorn R, Reitboeck HJ, Arndt M, and Dicke PW. A neural network for feature linking via synchronous activity: Results from cat visual cortex and from simulations. Models
of Brain Function, RMJ Cotterill,
Editor. Cambridge University Press, pp. 255-272, 1989.
[11] Johnson JL, Padgett ML. PCNN models and applications. [Journal
Paper] IEEE Transactions on Neural
Networks, vol.10, no.3, May 1999,
pp.480-98. Publisher: IEEE, USA.
[12] Omidvar 0, Dayhoff
J.
Neural
Networks and Pattern Recognition.
Academic Press 1998
[13] Johnson JL, Sims SRF, Branch TW.
Test results for a 32*32 PCNN array.
[Conference Paper] Proceedings of
SPIE the International Society for
Optical Engineering vol.3728, 1999, pp.182-5. USA.

[14] Caulfield HJ, Kinser JM. Finding the shortest path in the shortest time using PCNN's. [ournal Paper] IEEE
no.3, May 1999, pp.
60 4
-
6
. Publisher:
IEEE, USA.
[15] Varadarajan R, Yuen G,
Bodruzzaman M, Malkani M.
Sensory fusion for intelligent navigation of mobile robot
[Conference Paper] Proceedings of
System Theog (Cat. No.98EX148).
IEEE. 1998, pp.
3 0 7
-
1 1
. New York,
NY, USA.
[16] Kinser JM, Johnson JL. Object isolation. [Uournal Paper] Optical
no.3, 1996, pp.
137
-
4 5
. Publisher:
Allerton Press, USA.
[17] Simmons P, Caulfield HJ, Johnson
JL, Schamschula M, Allen FT, Kinser
J.
Hearing shapes:auditory recognition of two-dimensional spatial patterns. [Conference Paper]
SPIE the International Society for
Optical Engineering, vol.2824, 1996, pp.84-98. USA.
[18] Johnson JL, Ritter D. Observation of periodic waves in a pulse-coupled neural network.[journal Paper] Optics
vol.18, no.15, 1 Aug. 1993, pp.1253-5. USA.
[19] H.J. Caulfield, H.I. Jeon, J.
Brown,
P. Werbos, Variable and fixed rank-
1 N 4 interconnections, Appl. Opt.
29, 2019 (1990).
[20] Z. Chen, I. Koren, Crosstalk
Minimization in Three-Layer HVH
Channel Routing, Proc. of the IEEE
International Symposium on Defect and Fault Tolerance in VLSI
Systems, pp. 38-42, Oct. 1997.
[21] Wikipedia @, http://en.wikipedia.org/wild/VCSE
L http://en.wikipedia.org/wiki/Phased array, http://en.wikipedia.org/wiki/Optica
1 bistability http://en.wikipedia.org/wiki/Neutra
1 density filter http://en.wikipedia.org/wiki/Led#L
ED technology
[22] Liu Y, Johnson K, Hibbs-Brenner M.
Chip-scale Integration of VCSEL,
Photodetector, and Microlens Arrays.
vol.4652, pp.
1 1
-
1 8
, 2002.
[23] Britney Spears Guide to
Semiconductor Physics, http://britneyspears.ac/lasers.htm
[24] Abidi T. Long-wavelength VCSELs optimize fiber coupling.
Focus
World, May 2001.
[25] Efron U. Spatial Light Modulator
Technology: Materials, Devices, and
Applications. CRC Press, 1995.
[26] Ranganath HS, Kuntimad G.
Iterative segmentation using pulse coupled neural networks.
[Conference Paper] Proceedings of
SPIE the International Society for
Optical Engineering, vol.2760, 1996, pp.543-54. USA.
77

[27] Goda M, Linnenberger A, Schmidt J,
Serati S. Spatial Light Modulators:
Liquid-crystal SLMs benefit the study of atmospheric turbulence.
Focus World, May 2006.
Laser
[28] O'Brien D.C., McKnight D.J., "A
Compact Holographically Routed
Optical Crossbar Using a
Ferroelectric Liquid-Crystal over
Silicon Spatial Light- Modulator,"
Optical Computing, vol. 139,
INSTITUTE OF PHYSICS CONF
SERIES. Bristol: IOP Publishing
Ltd, 1995, pp. 187-190.
[29] Displaytech, Inc. website.
http://www.displaytech.com/history emerging.html
[30] O'Callaghan MJ, Handschy MA.
Diffractive ferroelectric liquid-crystal shutters for unpolarized light. Optics
Vol. 16, No. 10. May 1991
[31] Ota Y, Wilamowski BM. VLSI
Architecture for Analog Bidirectional
Pulse-Coupled Neural Networks.
International Conference on Neural
Networks, IEEE. Volume: 2, pp.
964-968. June 1997
[32] Vega-Pineda J,
Chacon-Murguia MI,
Camarillo-Cisneros R. Synthesis of
Pulsed-Coupled Neural Networks in
FPGAs for Real-Time Image
Segmentation. 2006 IEEE World
Congress on Computational Intelligence
July 2006.
[33] Cooley JH, Cooley T. Segmentation and Discrimination of Structural and
Spectral Information using Multi-
Layered Pulse Coupled Neural
Networks. Geoscience and Remote
Sensing Symposium, IGARSS 1999
Proceedings, IEEE International, vol.
1, pp. 80-82, July 1999.
78
[34] Yeh P, Gu C. Landmark Papers on
Photorefractive Nonlinear Optics.
World Scientific, 1995
[35] Yeh P, Chiou AE, Hong
J,
Beckwith
P, Chang T, Khoshnevisan M.
Photorefractive nonlinear optics and optical computing, Opt. Eng., vol. 28, pp. 38-343, 1989.
[36] Thompson BJ, Malacara D.
Handbook of Optical Engineering.
pp. 588-592. CRC Press, 2001.
[37] T. Simpkins, C. Fonstad and C.
Warde, Architecture of the Compact
Optoelectronic Integrated Neural
(COIN) Coprocessor, Proceedings of the
pp 113-121, 2006.
[38] Johnson JL. Pulse-coupled neural networks: translation, rotation, scale, distortion, and intensity signal invariances for images, Appl. Opt. 33
(26), 6239-6253, 1994.
[39] Wang R, Yeh P, Chang H, Yi X,
Zhao
J.
All-optical pulse generators for pulse-coupled neurons,
SPIE, Vol. 3715, p. 46-52, March
1999.
[40] Kinser JM. Hardware Basic
Requirements for Implementation.
[Conference Paper] Proceedings of
SPIE the International Sociey
Optical Engineeing, vol.3728, 1999, pp.222-229. USA.
[41] Kinser JM. Future Projects in Pulse
Image Processing. [Conference
Paper] SPIE-Int. Soc. Opt. Eng.
Pmceedings of SPIE the International
Society for Optical Engineering, vol.3728, 1999, pp.
3 1 8
-
2 7
. USA.

[42] Clark N, Banish M, Ranganath HS.
Smart Adaptive Optic Systems Using
Spatial Light Modulators. [Journal
Paper] IEEE Transactions on Neural
Networks, vol.10, no.3, May 1999,
pp.599-603. Publisher: IEEE, USA.
[43] Hoffman N. Simulating Neural
Networks. Vieweg 1994
[44] Wilson CL, Watson CI, Paek EG.
Combined Optical and Neural
Network Fingerprint Matching. In proceedings Optical Pattern
Recognition VIII, volume 3073, pages 373-382, SPIE, Orlando,
Florida, April 1997 and Technical
Report NISTIR 5955, January 1997.
[45] Wilson CL, Watson CI, Paek EG.
Effect of Resolution and Image
Quality on Combined Optical and
Neural Network Fingerprint
Matching, Technical Report NISTIR
6184, July 1998.
[46] Goodman JW. Introduction to
Fourier Optics. McGraw-Hill, 1996.
[47] Hibbs-Brenner M, Vixar Inc.,
Personal communication, May 2007
79