Modeling And Simulation Methodology For Digital Optical Computing Systems
Modeling and simulation methodologyfor digital optical computing systemsAhmed Louri and Jongwhoa NaA modeling and simulation methodology for digital optical computing systems is introduced in thispaper. The methodology predicts maximum performance of a given optical computing architecture andevaluates its feasibility. As an application example, we apply this methodology to evaluate the feasibilityand performance of the optical content-addressable parallel processor proposed in Appl. Opt. 31, 3241(1992). The approach consists of two major phases. The first phase involves analytical studies of theeffects of design parameters such as cross talk, diffraction-limited beam spot diameter, and pitch onsystem performance parameters such as signal packing density and skew time. In the second phase, asimulation model and a simulator are introduced by the use of GLAD (General Laser Analysis and Design,an optical software package developed by Applied Optics Research) to evaluate the combined effects ofbit-error rate, bit rate, optical power efficiency, available source power, and signal contrast on theperformance parameters such as signal packing density, misalignment tolerance, and distance betweendevices. The methodology presented here investigates the model, not on a component-by-componentbasis, but as a whole, which produces a more realistic representation of the actual laboratoryprototype. The proposed methodology is intended to reduce the optical computing system design time aswell as the design risk associated with building a prototype system.Key words: Digital optical computing, diffraction analysis, modeling and simulation, optical contentaddressable parallel processor.1. IntroductionIn recent years, several optical computing architectures and systems have been proposed. 1 -6 Thesesystems are designed to exploit the advantages ofoptics such as noninterference between signals, inherent parallelism, and high spatial and temporal bandwidth. Although some of the proposed systems present results of laboratory prototypes and some reportresults based on first-order analysis, the systematicor automated modeling and simulation methodologies have not yet been presented. Without the aid ofa general-purpose simulation model, the developmentperiods from an initial concept of an actual prototypehave been too long, and the accompanying costs havebeen too high. One study showed that the conceptual design, engineering design, fabrication, and testing of an optical system typically takes 3-5 years. 7Moreover, problems arise when the target systemThe authors are with the Department of Electrical and Computer Engineering, University of Arizona, Tucson, Arizona 85721.Received 20 May 1993; revised manuscript received 20 September 1993.0003-6935/94/081549-10 06.00/0. 1994 Optical Society of America.becomes so complex that there are simply too manyparameters to be considered. As the optical computing and networking systems gain popularity, futuresystems will become increasingly complicated.Therefore it is necessary to have automated opticalsystem design and analysis tools.In optical system research fields other than opticalcomputing, the importance of these automated toolsis already recognized. For example, an optical diskstorage system that utilizes a laser diode head and anoptical disk has been modeled and simulated. 8 Anintegrated design tool called SCOPE (supercompactoptoelectronic simulator) has been proposed 9 for microwave optoelectronic systems that handle laserdiodes, light-emitting diodes, and photodetectors.In the optical interconnection network field, severalresearchers have reported the modeling and simulation study of optical interconnects.10 11 For opticalcomputing systems, up until now, there have been nomodeling and simulation tools for verifying the properfunctionality of an optical computing system as wellas its physical realizability. We should note thatsome efforts have been made to design computeraided designs (CAD's) for optical computing systems, 1 2 13 but these efforts have been limited to onlythe functional aspects of systems.10 March 1994 / Vol. 33, No. 8 / APPLIED OPTICS1549
In this paper we propose a modeling and simulationmethodology for digital optical computing systemsthat not only evaluates the feasibility of the systembut also tests its functionality and predicts its performance. As an application example, we apply theproposed methodology to the optical content-addressable parallel processor' 4 (OCAPP). The approachconsists of two major phases. In the first phase,analytical studies are performed to investigate theeffects of design parameters such as cross talk (including power dissipation and noise), diffraction-limitedbeam spot diameter, and pitch on signal packingdensity, skew time (execution time), and systemvolume. In the second phase a simulation model anda simulator are introduced to evaluate the combinedeffects of bit-error rate (BER), bit rate (BR), opticalpower efficiency, and available source power on theperformance parameters such as maximum signalpacking density, misalignment tolerance, and maximum distance between devices. The simulator isdesigned by the use of GLAD (General Laser Analysisand Design, an optical simulation software packagedeveloped by Applied Optics Researchl 5 ). GLAD permits detailed modeling of each system component ofsystems such as spatial light modulators (SLM's) inaddition to simulating the propagation of an opticalwave front passing through them. The proposedapproach enables a more complete evaluation of theconceptual design, which will eventually result infaster prototype development.The rest of this paper is organized as follows:Section 2 presents a brief description of the OCAPPand GLAD. Section 3 proposed a modeling and simulation methodology for the OCAPP. Section 4 characterizes the performance of the diffraction-limitedOCAPP. Section 5 describes how GLAD is used tosimulate the OCAPP and the values of the parameters considered. Section 6 summarizes the simulation work, and Section 7 concludes the paper.2.BackgroundA.Modeling and SimulationIn this subsection we briefly discuss the underlyingconcepts of modeling and simulation. Modeling andsimulation of a system is a technique that acts as abridge between a conceptual design and a laboratoryprototype. In an abstract sense, modeling meanscollecting all possible information about a system.This information collection process may be accomplished either by coding the structure and the behavior of the optical system by the use of conventionalprogramming languages such as C or PASCAL or by theuse of optical system analysis software packages suchas CODE V, OSLO, or GLAD. 16'17Simulation may be defined as an experiment performed on a model. In computer system simulation,two aspects can be noted, namely the functional andthe physical aspects. The simulation of functionality means verifying the functions or algorithms thatare going to be performed on the system. It istypically done by using conventional programming1550APPLIED OPTICS / Vol. 33, No. 8 / 10 March 1994Fig. 1.Architecture of the OCAPP.languages or simulation packages such as DEVS (Discrete EVent-based Simulation) or SIMSCRIPT.18 ,1 9The simulation of the physical aspect of a computersystem means verifying the physical realizability ofthe conceptual design. This can be done by simulating each component of the computer system by theuse of an optics simulation or a ray-tracing softwarepackage.B. Optical Content-Addressable Parallel ProcessorIn Ref. 14, a parallel architecture called the OCAPPhas been introduced for the fast and efficient implementation of symbolic computing tasks such as searching, sorting, information retrieval and databaseknowledge-base processing. Figure 1 is a schematicdiagram of the OCAPP. The architecture is composed of a selection unit, a match/compare unit, aresponse unit, an output unit, and a control unit, thewords stored in the storage array. A detailed explanation and implementation of each unit of the OCAPPand the algorithms implemented on the OCAPP arepresented in Ref. 14.This architecture is under construction in theOptical Computing and Parallel Processing Laboratory at the University of Arizona. A laboratorysetup is shown in Fig. 2. The optical system iscomposed of three SLM's, a beam splitter, sphericaland cylindrical lens elements, spatial filtering assemblies, mirrors, and two linear CCD (charge-coupleddevice) arrays. The OCAPP uses a collimated laserLaserSF SLl SLM1 SL2 SF SL3CCDI CLi SL7SF*2 S 6 P2 CCD2 CL2 SL9 SFSLM2SLM3SSLSL4BSIL1P1 -- 5 SLegendSF - Spatial FilterSL1,SL6,SL8 - Spherical Lens(f 500nm)SL2,SL3, - Spherical Lenas(f l50mm)SL4,SL5 - Spherical Lens (f 300mn)SLM - Spatial Light ModulatorMlM2,M3 - MrorBS I -Beam SplitterPP2- PolarizerCL,CL2 - Cylindrical Lens (f lOm1m) CCD1,CCD2 - Charge Coupled DeviceFig. 2. Physical laboratory setup for implementing the firstversion of the OCAPP.
beam as an input source and two linear CCD arrays asthe output detection unit. The operations of thematch/compare unit are performed by SLM1 andSLM2. SLM1 and SLM2 are used to hold two wordsor two bit slices to be matched or compared withrespect to each other, depending on the algorithmemployed. The selection unit is mapped into SLM3,which is used to enable/disable words and/or bitslices of the two-dimensional (2-D) optical data arrayfrom SLM2. The response unit is omitted in thislayout because the first version of the OCAPP isconfigured as a relational database machine, whichdoes not use ordering between the matched words.The optical layout for OCAPP architecture is further simplified into a simulation model, shown in Fig.3. This model is more suitable for the simulationstudy without loss of functionality of the originalOCAPP described in Ref. 14. The simulation modelof Fig. 3 constitutes the major optical path of thesystem of Fig. 2 that consumes most of the power.For clarity, the spatial filtering assembly and mirrorsare not considered in the simulation model as theycontribute little power loss in our application. Thismodified OCAPP model is studied with the simulation methodology described in Section 3.C. General Laser Analysis and DesignThere are two types of commercial software packagefor the analysis and design of optical systems. Oneis a geometric code (such as CODE V16 or OSLO1 7 that isbased on ray-tracing optics, and the other is a physicaloptics code (such as GLAD) 20 that is based on diffraction propagation of wave fronts. Although geometric codes may be useful in analyzing the given systemto some extent, the physical optics code is able toprovide a more accurate and powerful tool by utilizingfast Fourier transforms.21 The physical optics codeprovides detailed beam intensity and phase profiles,whereas the geometric code is limited to providingsimple intensity profiles such as a constant or Gaussian profile.21 Moreover, the geometric code limitsthe diffraction propagation to strictly near field or farfield, whereas the physical code can handle any kindof diffraction propagation. For the above reasons,we chose to use GLAD for our purpose.A1A--\J .l 1-DSLM3 Cylindrical detectorILensFig. 3.arraySimplified model of the OCAPP.3. Modeling and Simulation of the OpticalContent-Addressable Parallel ProcessorIn this section, a two-phase modeling and simulationmethodology for digital optical computing systems isproposed, and the simulation results are explained.The main objectives of the methodology are findingmaximum values of performance parameters of agiven optical computing system as well as providing alaboratory prototype model for fast prototype development. Performance parameters considered here include signal packing density, misalignment tolerances, distance between components, power efficiency,and skew time.2 2 23 Maximum values can be foundby manipulating cross talk, BER, BR, and opticalpower efficiency of a given system. During the firstphase, a theoretical analysis of the system is performed. During the second phase, GLAD is used for adetailed simulation and evaluation of the system.In what follows, we describe each phase in detail.A. Phase 1: Diffraction Analysis of the OpticalContent-Addressable Parallel ProcessorIn the first phase, a preliminary analysis is performedto narrow down the range of values of parametersused in the simulation. The analysis provides upperbounds of performance parameters such as diffractionlimited signal packing density, skew time, and crosstalk. Knowing these bounds would enable one toavoid unnecessary simulation experiments and tohave a better understanding of the overall simulationwork. Another point to note is that some parameters identified at the preliminary analysis phase canbe used in the second phase. For example, skewtime, which is estimated in the first phase, is used inthe calculation of the BR that is used in evaluatingthe required optical input power. A summary ofparameters and definitions used in this paper is givenin Table 1.In the first phase, the pitch, signal power, noisepower, cross talk, and diffraction-limited beam spotdiameter are used as design parameters that can bemanipulated whereas the signal packing density isused as a performance parameter. First, the diffraction-limited signal packing density is calculated byobtaining the minimum pitch for a given system crosstalk. The cross talk is expressed in terms of thepitch. This is possible because the cross talk is theratio of the noise power to the signal power, and thenoise power can be expressed in terms of pitch. Thenoise power is obtained by integrating the outputintensity distribution over the neighboring detectorapertures. The neighboring detector aperture canbe expressed in terms of the diffraction-limited beamspot diameter and pitch. The skew time is obtainedby calculating the difference between the maximumand the minimum optical path lengths. The skewtime is then used to estimate the cycle time andmaximum bit rate of the OCAPP. Finally, the volume of the OCAPP and optical power dissipationlimited signal packing density are calculated. In10 March 1994 / Vol. 33, No. 8 / APPLIED OPTICS1551
Table 1.List of the Parameters UsedSymboladDnppDefinitionLength of a pixel of a SLMDiffraction-limited beam spot diameterNumber of pixels per row (or column)Pitch: center-to-center distance between twoadjacent pixelsSignal packing density: number of pixels per1 cm2,qtdfSystem optical power efficiencyDistance between SLM'sCylindrical lens focal lengthXOptical wavelengthILNLength of the SLMLength of the systemSystem fanoutNfFresnel numberTskewSkew time: propagation time difference frominput to output among the various opticalVVolume of the systemBit error rateBit ratepathsBERBRXPi.Psi gnalPnoiseQrUPCross talk: ratio of noise power to signal powerRequired optical power per beamCollected optical power at the designated detectorelementCollected optical power at the detectors otherthan the designated detector elementRatio of the rms signal voltage to the total rmscross-talk voltageRatio of current to the detector in the OFF stateover the ON statePower dissipation density (in watts per squarecentimeter)what follows, the parameters in Phase 1 are calculated based on the architecture shown in Fig. 3.1. Diffraction-LimitedBeam Spot DiameterThe diffraction-limited beam spot diameter dD for agiven system configuration is calculated here. dDwill be used below for the optical signal power calculation. In order to check the extreme case, we assumethat the SLM's, beam splitter, and cylindrical lens arein contact. In the case of square input aperture, dDis given bydDXa(1)where a is the length of a pixel of the SLM, f is thefocal length of the cylindrical lens, and Xis the laserwavelength (refer to Fig. 3). For simplicity, weassume that the lengths of the pixel on the SLM andthat of a detector have the same value, which is a.Then dD becomesdD a Xf.(2)2. Diffraction-LimitedSignal Packing DensityThe signal packing density p is one of the mostimportant performance parameters as it limits the1552APPLIED OPTICS / Vol. 33, No. 8 / 10 March 1994maximum number of pixels in the optical data plane.In order to determine the maximum signal packingdensity PM, the individual pixels must be packed astightly as possible. Therefore PM is obtained byfinding the minimum pitch pm of the 2-D array.The pitch p can be related to the cross talk Xcalculation because the cross-talk calculation requires the evaluation of the collected noise powerPnoise, which uses p as an integration parameter. Inother words, to calculate Pnoise, the intensity distribution must be integrated over the neighboring detectoraperture, which has a diameter of dD, and separatedfrom the designated detector aperture by multiples ofp. 2 4 ,25 Therefore, by setting Xto some value, we cancalculate Pm of the array. Once pm is known, we candirectly calculate PM and the maximum number ofpixels in the array.To calculate X,we calculate the field distribution atthe output plane u 2(x, y) of a pixel located at thecenter of the input plane (SLM1 of Fig. 3) for a giveninput field distribution ul(x, y). As we have a collimated laser beam as a source, u1 (x, y) can be approximated as a normally incident unit amplitude planewave. Assuming a square aperture for the SLMpixel, the field distribution immediately after thesquare pixel of dimension a is given byul(x,y) rect(x/a,y/a) rect(x/a)rect(y/a).(3)Because the rect function is separable and the powerof the lens exists only along the y axis, the outputdistribution at they axis will be a Fraunhofer diffraction pattern that can be expressed asU2(Y) exp(jkz)exp(jkx 2/2z) aayja sct - -(4)The output field distribution u 2(x) along the x axiswill be a Fresnel diffraction pattern as there is nofocal power in the x direction in the cylindrical lens:exp(jkz)U12(X)-jXzCa/2exp[J/2- (X1- x)2ldxl(5)Now we check the Fresnel number Nf, which isdefined to be a2 /Xf, to study u2(x). For the followingestimation, we assume that we have 633 nm andf 0.1 m. For the given and f, with Eq. (2), abecomes 356 Rim. With the above data, Nf becomes- 2. This number implies that the diffraction pattern of u2(x) will be neither a geometric projection ofaperture function nor the Fraunhofer diffractionpattern. Figure 4 shows the intensity distributionof the diffraction pattern of u 2(x), which we calculatedby solving Fresnel integrals at the cylindrical lensfocal plane. Next we calculate Xbetween channels.Figure 5 shows the geometry used in the signal andnoise power calculation. The parameter X can bedefined asIPnoisosignal(6)
1.00--6.00-8.00mY -10.000.800.20 i -12.00U -14.000.00 i-200600 -400-0200400-16.00600400 500 600 700Pitch (m)x axisFig. 4. Intensity distribution of the Fresnel diffraction pattern ofa square aperture of a SLM. The dimension of apixel is 356 tom x356 pm.where Pjgnal is the power collected over the centerpixel (pixel A of Fig. 5) of the detector (assuming pixelA is the intended destination). The signal powercollected at pixel A isPsignal IdD/2dD/2-dD/2-dD/2J JI(x,y)dxdy.(7)On the other hand, Pnoise is the power collected bythe neighboring detector elements around the intended detector element. For simplicity, if we include only two neighboring detector elements (pixel Band pixel C of Fig. 5) in our calculation, Pnoise is givenbyI Pnoise2PnlX(8)where P is the power obtained from the closestneighboring pixel and can be calculated as(dD/2Pnl rp dD/2I(x,y)dxdy,J-dD/2Fig. 6. Cross talk for various pitches of the SLM array in thediffraction-limited OCAPP. Diffraction-limited beam spot diameter is set to 356 pm.From Fermat's principle, light takes the shortestpath between two points. As the OCAPP has a 3-Dstructure, there are inherent path-length differencesbetween pixels of the input and the output opticaldata planes. This path-length difference generates aclock skew problem that can affect the accuracy aswell as the operating speed of the optical computingsystem. This problem will be aggravated in systemsin which the output signals are designed to be fedback to the input stage. Therefore, to calculate theoperating speed of the OCAPP and avoid the aboveproblems, we must identify the skew time of thesystem and the longest signal path to satisfy thesynchronization requirement. 2 6In Fig. 3, the three SLM's perform imaging operations. Assuming that the length of the OCAPP is L(from SLM1 to the detectors) and that is the lengthof an SLM, the time taken to travel the shortest pathof the system, if the switching time of the SLM's isignored, is given by(9)Tmin p-dD/2wherep represents the pitch between pixels. For Pn1calculation, I(x) (the Fresnel diffraction pattern) isintegrated over the integration interval p dD/2along the x axis at the cylindrical lens focal plane.Figure 6 shows the calculated cross talk for variouspitches when dD is fixed at 356 [im, 633 nm, andf 0.1 m. Once the pitch is found, as shown in Fig.7, the signal packing density can be estimated withthe following relation 2 5 :On the other hand, the time taken to travel thelongest path is given byTp 1/p . f ]1/-.r-.,Tmin 800700 t600500400300uzpPixel CFig. 7.(12)Tkew is[(1/2)2 f 2 ]1/ 2Tm.2C-fKI III2cC(10)Fig. 5. Model of the detector aperture used for estimating thecross talk.2(L - f) [(1/2)2 Therefore the skew timeT kew 2(11)L/c.(13)IIX400 450 500 550 600Pitch (m)Diffraction-limited estimation of signal packing density ofthe SLM versus the pitch.10 March 1994 / Vol. 33, No. 8 / APPLIED OPTICS1553
It should be noted that 1 np, where n is thenumber of pixels per row (or column) of the SLM, andp is the pitch. Substituting I np into Eq. (13)yieldsTskew 2(14)2cIt can be seen that the skew time grows linearlywith the number of pixels per dimension.3. System VolumeThe volume of an optical system affects the ease ofpackaging as well as the feasibility of the system.As SLM's are connected by imaging, the length of theOCAPP L from Fig. 3 is given byL 2d 2f,(15)where d is the distance between two SLM's and f isthe focal length of the cylindrical lens. The systemvolume v is given byu L12 2(d f)12 2(d f)(np) 2 .(16)It can be seen that the volume is proportional to thesquare of the number of pixels per dimension.4. Power Dissipation-LimitedSignal PackingDensityNow we consider the effect of power dissipationdensity on the signal packing density. It is knownthat the maximum intensity of the beam is limited bythe maximum real power dissipation density up,which has a typical value of 1 W/cm 2 . 25 27 Then themaximum allowable heat dissipation per input beam,Pcrit, iSPeritp(17)As shown by Ref. 25, it is p that limits signalpacking density more severely than diffraction effects.Even for low threshold lasers currently available, athreshold current of 1 mA is required for minimaloperation. Assuming that laser operation requires- 3 mW per beam, then, for oup 1 W/cm 2 , p becomes333 pixels/cm 2 . For an SLM of 2 cm x 2 cm activearea, the maximum number of pixels available on theSLM becomes 1332 pixels. Table 2 summarizes theresults obtained from the analysis phase.B. Phase 2: Modeling and Simulation of the OpticalContent-Addressable Parallel Processor by the Use of GLADThe second phase consists of modeling and simulating OCAPP. The main objective here is to provide arealistic evaluation of the system by providing thecombined effects of design parameters on performance.Specifically, we would like to determine the maximum signal packing density, maximum misalign-ment tolerance, and maximum distance betweendevices for a given operating BR, BER, and optical1554APPLIED OPTICS / Vol. 33, No. 8 / 10 March 1994Table 2.Summary of Parameters Studied in the Analysis rValueCylindrical lensfocal length f10 cmDiffractionlimited spotdiameter dD356 .mLength of SLM1.6 cmMinimum pitch410 pLmIPmSystem crosstalk X-10 dBDiffractionlimited signal packingdensity pWavelength X633 nmPower dissipation densityJ1p1 W/cm 2Power dissipation densitylimited pSkew time594 pixels/cm 2333 pixels/cm 226.67 psTskewLight propagation timeTpropVolume v1.360 ns25.6 cm 3power efficiency. As the GLAD model can provide arealistic representation of the model and simulatediffraction propagation of wave fronts by using 220observation points of the model, it is expected togenerate the closest data to the prototype being built.1. Modeling the Optical Content-AddressableParallelProcessorby the Use of GLADGLAD employs a modular-building-block approach tomodel each component in sequence as the beampropagates through the system.1 5 The buildingblock approach permits a beam train of any configuration to be modeled by assembling blocks in the correctorder. To design a simulation model for OCAPP, wemust first model its components. Among the components of OCAPP, as shown in Fig. 3, the SLM is themost complicated component in the system. Tomodel an SLM, we generate a prototype mask of aspecific number of pixels, pixel size, pixel pitch, andphysical dimension. Simulations are performed forsystems that contain SLM's of varying signal packingdensities. In order to maintain consistency amongthese various OCAPP models, the aggregate SLMdimension is held at a constant 1.6 cm x 1.6 cm size.For example, one of the models was a pixelated SLMconsisting of 8 pixels x 8 pixels in a matrix configuration. This 8 x 8 SLM model determined the aggregate 1.6 cm x 1.6 cm dimension as the pixel pitch was0.2 cm (i.e., the pixel size and the interpixel gap areboth 0.1 cm). Then, for each specific bit pattern ofthe optical data plane of the SLM, the desired targetpattern is overlaid on the prototype mask pattern.GLAD contains many commands to model componentssuch as mirrors, lenses, apertures, etc. An initialfield distribution for the beam by the use of geometricdata such as the beam center, coordinates, waist size,and location can be defined with a command likeGAUSSIAN. Once the optical configuration and theinitial optical beam distribution are available, the
(PROPagation) command is used to simulatediffraction propagation.PROP2. Simulation of the Optical Content-AddressableParallelProcessorby the Use of GLADa. Signal Packing Density. The simulation algorithm is illustrated in Fig. 8. Part-(A) of Fig. 8describes the procedure for the maximum signalpacking density PM. The maximum signal packingdensity is obtained by simulating the model to obtainoptical signal and noise power and calculating therequired optical input power Pin. Once Pin is calculated, we compare it with the available optical sourcepower. If the calculated Pin with a given signalpacking density p is greater (less) than the availableoptical power, the model with a decreased (increased)p is prepared for the next simulation experiment.In the following calculations, we set BER 10-7.23The BER can be represented as27, exp(BER /22)(18)where Q is the ratio of the rms signal voltage to thetotal rms cross-talk voltage. For a given BER 10-17, Q 8.5. For this given Q, the required opticalinput power Pin can be calculated as2 8Pin (1r)P( -r)Q AXeiNA2)/2(19)'l.w.i{LAFind maximum signal packing densityISet jP (signal packingDecrease. pl'[density) to an initial value]Increase p.Determine output intensity distribution, calculate contrast ratio,calculate required optical ower.OpticalPswer(ROP)to AvailsbleROPAOPtial Powm(AROP.O.O P.ROP AOP AOP.1---.-I Ideal model with maximum signal packing density Ient tolerance. .F d inax n n n. sa.igumApply initial mnisalignmentDetermine output intensity distributionDecreasemisalignment. calculatere utredratio,ot tical wer.calculate contrastPAROPCompare ROPROP AOP. Alowhere r is the ratio of current to the detector in thelow illumination state relative to the high illumination state, N is the system fan-out, nt is the product ofthe quantum efficiency of the detector and the efficiency of the optical system, and (iNA 2 )1/2 is the rmscurrent noise generated by the detector and preamplifier circuit.Finally, to calculate Pin, we should determine theparameter r. As r represents the ratio of currents atthe high illumination state to low illumination state,we obtain it by comparing the power incident uponthe detector aperture at high and low illumination.The power for the two states is obtained by simulating the OCAPP model with a given SLM pixel pattern.To obtain power at the high illumination state, thedesired pixel of each SLM is made transparent whileothers are set to opaque. Similarly, to obtain thepower at the low illumination state, we set the pixelsat the same column to opaque and make all the otherpixels transparent. The whole column is cleared toavoid the effect of the cylindrical lens in the OCAPP.The factor (iNA 2), which is expressed in terms of theBR, is calculated based on the data presented in Ref.10, and N is set to 1 because of the one-to-one imagingbetween SLM's in the OCAPP. 't is set to -0.051by considering a 50% ON-state power transmissionefficiency for an ON-state pixel of the SLM, 50% powerdivision at the beam splitter, and 4% reflection lossper surface (5 optical surfaces).Once Pin is available, the number of pixels allowedper SLM can be obtained by comparing the requiredoptical input power with the available source power.As shown in Part-(A) of Fig. 8, if the calculated poweris less than (or greater than) the available power, amodel with an increased (or decreased) number ofpixels on the SLM plane is simulated. The maximum number of pixels is determined when the required optical input power is less than or equal to theavailable source power. The available optical powermust be less than the actual power as there are othersources of power losses such as component misalignment and aberrations.Figure 9 shows the optical p
3. Modeling and Simulation of the Optical Content-Addressable Parallel Processor In this section, a two-phase modeling and simulation methodology for digital optical computing systems is proposed, and the simulation results are explained. The main objectives of the methodology are finding maximum values of performance parameters of a
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