Computer aided design of computer generated holograms
for electron beam fabrication
Kristopher S. Urquhart, Sing H. Lee, Clark C. Guest, Michael R. Feldman, and Hamid Farhoosh
Computer Aided Design (CAD) systems that have been developed for electrical and mechanical design tasks
are also effective tools for the process of designing Computer Generated Holograms (CGHs), particularly
when these holograms are to be fabricated using electron beam lithography. CAD workstations provide
efficient and convenient means of computing, storing, displaying, and preparing for fabrication many of the
features that are common to CGH designs. Experience gained in the process of designing CGHs with various
types of encoding methods is presented. Suggestions are made so that future workstations may further
accommodate the CGH design process.
1. Introduction
Computer generated holography (CGH) is today animportant tool in many areas of research (some ofwhich are only tangentially related to optics). It is atechnology that is finding its way into commercialoptical systems, and it is also a subject of active re-search.'-3 In all cases, the process of designing com-puter generated holograms (CGHs) is often a laboriousone. The optical system designer contemplating theuse of CGH faces not only the usual challenge of under-standing a new technology, but a bewildering array ofencoding schemes, a potentially tremendous explosionof computation and data storage requirements, andvery poorly defined procedures for translating a designinto a physical element.
This situation is similar to the one in the electronicsindustry that prompted the development of computeraided design (CAD) workstations with software tai-lored to the design of integrated circuits. The purposeof this paper is to demonstrate how these same CADworkstations can be used to overcome many of thedifficulties in the design and fabrication of CGHs. Inparticular, the interactive interface, optimized graph-ics software and hardware, the ability to efficientlymanage large graphical databases, and the ability toprovide output data formats compatible with the re-quirements of electron beam (e-beam) lithographysystems are characteristics that make CAD worksta-tions useful for CGH design and fabrication.
The authors are with University of California, San Diego, Depart-ment of Electrical & Computer Engineering, La Jolla, California92093.
In Sec. II we present the general design require-ments for CGHs to be written using e-beam lithogra-phy. In Sec. III we discuss the capabilities of theexisting CAD systems and their applicable features forCGH design. Sec. IV contains examples of e-beamwritten CGHs and explains how the CAD featuresaided in their design and fabrication. Suggested en-hancements to the CAD systems for efficient patterngeneration of e-beam CGHs are presented in Sec. V.Summary and conclusions are given in Section VI.
II. General E-Beam CGH Requirements
In this section we describe briefly the steps requiredfor CGH design and fabrication with e-beam lithogra-phy, along with some of the requirements this processimposes on the supporting equipment.
The first step in CGH fabrication is the computationof the CGH pattern. For numerical input data thiscomputation can be very intensive, while analytic in-put forms require relatively little computing power.The CGH support system should be interactive tocommunicate effectively with the user. After the com-putation, the data needs to be specified in a mannerconsistent with the chosen encoding method. Nu-merical data, depending on whether it is complex orreal, can be used as input for cell-oriented and pixel-oriented encoding methods, while analytic input isusually encoded by fringe-oriented methods. The sys-tem should automatically check the CGH for compati-bility with design requirements and fabrication tech-niques. The system should also be equipped withgraphics devices to allow the user to visually inspectthe generated CGH patterns. Once the graphical datais properly specified, a computer program must trans-late the graphical data into e-beam pattern data.Such a program should have a complete knowledge ofCGH encoding schemes and various e-beam data for-
mats, and it must be efficient in e-beam pattern gener-ation to minimize the amount of data and the e-beamwriting time. The supporting system also needs largeamounts of data storage and data transfer capabilitiesto accommodate the huge volume of data produced.
In summary, a system supporting CGH design and e-beam data generation should have the following fea-tures: computing power, user-friendly interface, com-plete knowledge of CGH encoding methods, CGHdesign rule checks, graphics capabilities, completeknowledge of various e-beam data formats, and datastorage and transfer capabilities.
111. CAD Capabilities for CGH Design
CAD systems are valuable and powerful tools in thedesign of components and systems for the fields ofelectrical, mechanical, and optical engineering, toname a few. Although these systems have not beendesigned specifically for CGH applications, the CADsystems that have been developed for VLSI design,such as CALMA, are able to satisfy the needs of CGHdesign. In this section we will discuss general capabili-ties of this type of CAD system and point out thosefeatures that can be used in e-beam pattern generationfor CGHs.
A. Computation
Designing computer generated holograms can becomputationally intensive. The input data for mostCGHs is represented either by a numerical array, or isspecified in some analytic form. The numerical speci-fication usually comes from computer manipulationsof arrays of complex numbers, (e.g. from the periodicsampling of an object), while an analytic representa-tion is usually obtained from theory or from the outputof optical design software.4 Holograms specified nu-merically will usually require substantial computingpower to carry out computationally intensive opera-tions, such as the 2-D Fast Fourier Transform (FFT)and iterative methods of computation.5 6 PowerfulCPUs and large amounts of fast memory contribute tothe computing power necessary, and dedicated hard-ware such as array processors can further increase thiscapability.
Iterative methods of computation and large FFTstypically need to be carried out on a computer that isseparate from the CAD system. CAD systems oftendo not have the computational power necessary toperform these operations efficiently. Small FFTs,modular coding (see Sec. III.C.), and computationsrelating to an analytic input representation can beperformed on the CAD system, due to the relativelylow computational load.
B. CAD Interface
The menu driven graphical interface of a CAD sys-tem is very powerful. The operator can use a mouse ora graphics tablet and stylus to enter both commandsand graphical data into the system. A CAD systemsuch as CALMA includes a library of functions to aidthe user with the placement of primitive as well as3388 APPLIED OPTICS / Vol. 28, No. 15 / 15 August 1989
complex graphical objects in a pattern. Most of thesefunctions are contained in the onscreen menu and canbe accessed using the graphics tablet or mouse. Ex-amples include primitive shapes such as lines, rectan-gles, polygons, and circles. Only the endpoints bflines, vertices of rectangles and polygons, or centersand radius of circles need to be entered. Functions toaid the designer include onscreen measuring devicesfor proper dimensioning, grids to help with placementof points or vertices, and zoom and pan capabilities.Functions like saving, referencing, labeling, and repli-cating can also be accessed onscreen. In fact, entirepatterns can be constructed with minimal use of thekeyboard.
For example, one can design optical interconnectCGHs for VLSI circuits using the interactive interface.The use of a CAD system will allow the user to specifythe holographic optical element (HOE) parameters inthe same manner he would lay out a conventionalmetal wire interconnect, i.e., the laser source positionand the corresponding detector positions are enteredinteractively with the graphics tablet or mouse. Thisinformation is then converted into the appropriatehologram.
C. Encoding
CGH encoding is a method for translating numericalor analytical information into geometric shapes thatwill make up a holographic mask to reconstruct thespecified wavefront. There are many CGH encodingmethods.7 8 Since the e-beam masks are binary, theclass of encoding methods suitable for e-beam fabrica-tion is binary also, although multiple masks can becreated to fabricate multi-level phase CGHs. Thebinary methods include cell-oriented, pixel-oriented,and fringe-oriented encodings. In cell-oriented meth-ods,7 such as Lohmann, Lee, and Binary Burch, theCAD system converts complex numerical data intorectangles with the size and location specified by theamplitude and phase data, respectively. Pixel-orient-ed methods, such as Error Diffusion9 and SimulatedAnnealing,'0 convert arrays of real binary data intosquares, and the CAD system places the squares atlocations within an array. Fringe-oriented interfero-gram methods perform a binary conversion of analyticdata, and then draw fringes to correspond to this bina-ry data. A comparison of the performance of theseencodings is given in Ref. 11, and depending on theapplication of the CGH, an encoding that best meetsthe needs of the project can be found.
The incorporation of CAD techniques into the calcu-lation and fabrication of CGHs offers additional en-coding options for the design. This is based on theCAD supported software that can be used to geometri-cally transform graphical data. This is particularlyapplicable in space-variant filters where different sec-tors of the hologram are related to each other. Forexample, the HOE for one-to-five optical interconnec-tion, to be described in Sec. IV.D., was designed byconstructing one Fresnel Zone Plate (FZP), and thenreplicating and reflecting a specific portion of the zoneplate. This reduced computation because the FZP
was calculated and generated only once, instead of fiveseparate times. Modular coding is another alternativeencoding option. For example, a wire frame model canbe specified by using geometrically transformed repli-cas of the holograms for a graphical primitive, such as asingle line or circle. Each subhologram in the finalhologram reconstructs one graphical primitive, andtogether they produce a complete reconstructed imageof the wire-frame model.
D. Design Rule Checks
The VLSI industry is responsible for the develop-ment of design rules for the design and fabrication ofcomplex circuits. Design rules are used to catch hu-man errors and account for fabrication tolerances andtechniques. This dictates the smallest allowable fea-ture size and separation in the design. Many of thesesame concepts can be transferred to the design andfabrication of CGHs, as shown in Table I. The leftcolumn shows the VLSI design considerations and theright column shows the corresponding CGH designconsiderations.
The e-beam lithography limitations include the res-olution of both the e-beam system itself and the e-beam resist. Typical resolutions of commerciallyavailable e-beam systems vary from 0.05 Atm-1.1 Aim.The resolution of the e-beam writer typically exceedsthe resolution of common e-beam resists. The resistresolution limitation is due to electron scattering, de-veloping procedures, and resist purity and uniformity.Positive resist usually gives a higher resolution thannegative resist.
For multi-level phase holograms that require etch-ing of a substrate, several variables need to be consid-ered and included in the encoding and pattern genera-tion software. The etching method chosen can affectthe final hologram quite dramatically. Dry etchingtechniques, e.g., reactive ion etching and ion milling,are typically superior to wet etching techniques forCGH fabrication. Dry etching methods generallyyield more controllable and repeatable etching rates,etch in a preferred vertical direction, produce a moreuniform etching across the entire hologram, and have a
Table 1. Design Rule Considerations for VLSI and E-Beam FabricatedCGHs
higher resolution.There are two registration tolerances that need to be
considered. The first considers the e-beam exposuresequence for large holograms. After the first segmentof stripes is written, the substrate is translated beforethe next segment is written. How accurately the seg-ments line up is called the stitching accuracy. Thesecond registration tolerance is applicable for multi-level phase where more than one mask is used. A maskaligner is used to align the masks before exposing thephotoresist, and this machine has a certain accuracy.This is an additive condition, so that the more masksthat are used, the more tolerant the design needs to be.
There are many electrical constraints in VLSI de-sign, e.g. contacts overlapping devices, conductor con-tinuity, and proximity requirements. The analogousCGH constraints need to prevent apertures from over-lapping cell boundaries in cell-oriented CGHs, and tomake sure that fringes do not intersect in fringe-ori-ented CGHs. For a designer laying out source anddetector position for an optical interconnect HOE,certain limitations must be imposed due to the capa-bilities of the interconnect CGH. Certain layoutswould require feature sizes too small for fabrication.
All of these variables and constraints need to betaken into account when writing the encoding andpattern generation software. CGHs must be eitherdesigned to fit the design rules, or a completed CGHpattern should be checked against the design rules. Ifthe design rules are not followed, the hologram will notperform as expected.
E. Graphics Capabilities
The step of producing an e-beam generated mask is acostly one (-$1000 per cm2), thus an inexpensivemeans of providing an approximate check on the resultis desirable before proceeding with fabrication. Inmany cases visual inspection of the reconstructed im-age can provide-a better measure of the CGH qualitythan numerical measures. A simulated reconstructoncan be carried out mathematically, and the resultingimage can be displayed on the CAD graphics monitor.If the reconstruction appears as it should, the fabrica-tion can take place with a greater expectation of theCGH performing properly.
It is also advantageous to be able to visually inspectthe hologram pattern during the design process. Theentire hologram, or a portion thereof, can be loadedinto memory in graphical format and displayed. Theonscreen menu can then be used to pan around tolocate a specific region to be inspected. This regioncan be magnified or demagnified many times for in-specting small details or viewing the overall appear-ance of the hologram. Every CGH described in Sec. IVwas visually inspected to ensure that the encodingalogrithms performed as expected. The CGHs canalso be visually inspected as a large paper plot, such asthose produced by a Versatec electrostatic plotter.(Such plots can also be photoreduced to produce aprototype hologram. Though such holograms do nothave nearly the quality that the e-beam mask will have,
gross errors in the encoding algorithms can be detect-ed.)
In addition to generating e-beam compatible dataoutput, a CAD system is also capable of reading in e-beam compatible data and converting it to internalgraphical data for display and manipulation. Thisfeature is particularly useful when the e-beam data isgenerated on another computer, and the user needs agraphics system for visual inspection or plotting of theCGH pattern. This feature was used for the focusingbeamsplitter to be described in Sec. IV.D. Due to thelarge size of this CGH, the data set required was solarge that the computer supporting the CAD stationcould not perform the computation satisfactorily.Thus, a mainframe computer was used to calculate theholographic patterns. Tapes with this data could thenbe read into the CAD station database for visual in-spection with the graphics equipment.
Capabilities like those mentioned above would notbe possible without the high resolution graphics moni-tors and graphics software that CAD systems areequipped with. The graphics features are also usefulfor several other display operations. In the case ofmulti-level phase holograms, alignment marks need tobe placed on each mask to facilitate accurate etching ofthe substrate. The CAD system can display the indi-vidual masks (using different colors for visibility) atthe same time and they can be moved separately.When the graphical masks are correctly aligned, thealignment marks are placed on each mask simulta-neously. After e-beam fabrication, each mask willhave alignment marks in the appropriate location, andthe etching steps can be performed accurately.
F. E-beam Fabrication
There are several traditional procedures for fabri-cating CGHs.78 After the hologram transmissionfunction is calculated by a computer, it is usuallytransferred to a mask. Traditionally, this has beenaccomplished by either plotting the hologram on ace-tate or by exposing photographic film to the light froma CRT display. In either case, photoreduction is usu-ally necessary to produce the final hologram. Morerecently e-beam lithography techniques, identical tothose used in the fabrication of electronic integratedcircuits, have been used in creating CGHs.12-18
Before the hologram can be written by e-beam lith-ography, the geometric patterns generated by the en-coding must be translated to a format that the e-beamwill accept. This process is called fracturing, and itconsists of taking arbitrary geometrical shapes andsectioning them into graphical primitives such as rect-angles and trapezoids'9 that the e-beam system willaccept.
Figure 1(a) shows the MEBES figure set, consistingof the acceptable parallelograms and trapezoids. Fig-ure 1(b) shows a sample set of fringes to be fractured.Fracturing consists of an arc-to-chord approximation,followed by the formation of acceptable trapezoids, asshown in Figure 1(c). Careful choice of fracturinglocations can result in data reduction. If the fringes
Rectangle
Trapezoid 2
Parallelogram Trapezoid 1
(a)
Trapezoid 3
(b)
(c)
Fig. 1. (a) MEBES figure set. The e-beam system will only acceptprimitive shapes with horizontal top and bottom edges. (b) Anexample set of fringes to be fractured. The dotted lines representthe stripe boundaries. (c) An arc-to-chord approximation has been
employed to fracture the fringes into acceptable trapezoids.
are fractured at the stripe boundaries, additional frac-turing, which would produce additional trapezoids,need not be performed. Also, if the fringes are frac-tured into shapes with horizontal top and bottomboundaries, additional fracturing to produce the ac-ceptable shapes is not necessay.'9
After the graphical data has been fractured, it needsto be specified in an e-beam format. One of the mostuseful features of a CAD system is its knowledge ofvarious e-beam data formats and its ability to generatethis data. Some of the existing formats are MEBES,Cambridge, and JEOL, with MEBES becoming a de-facto standard format that many e-beam systems willaccept.
In MEBES, the pattern to be written is subdividedinto address units (AU). The e-beam spot size is nu-merically equal to the distance between individual AU,which is variable from 0.05 gm to 1.1 Aim. On some e-beam systems, this spot size variation can be used tosave exposure time. If only a small portion of a CGHrequires high resolution, the spot size can be changedduring the exposure. The spot size is made smaller bydecreasing the current, and while this limits the beamspread, it also lengthens the exposure time per AU.By only using small spot sizes where absolutely neces-sary, the overall exposure time can be reduced.
In MEBES, any pattern up to 6 in. square can bewritten by subdividing the pattern into stripes andsegments. Each stripe is 32,768 AU wide, and either256, 512, or 1024 AU high. Each segment is one stripewide and is made up of as many stripes in the Y-direction as necessary to complete the pattern in the Y-direction. The pattern is then constructed with asmany segments as necessary, up to fifty, in the X-direction. The exposure sequence begins with theleftmost segment, writing the stripes from bottom to
top within this segment, and then starts at the bottomof the next segment, repeating until all segments havebeen written.
Due to the exposure sequence of the e-beam, thefractured data must be sorted geographically bystripes, so that the e-beam will receive all the trape-zoids within one stripe before receiving the trapezoidsin the next stripe. If a large hologram is being written,the stripes must also be sorted by segments. If thefracturing algorithm did not pay attention to the stripeboundaries when fracturing, additional fracturingmust be performed at the stripe and segment bound-aries. The e-beam then writes the primitive shapes ina layer of e-beam resist on top of a chrome-coated glasssubstrate. After development removes the exposedresist, the chrome in the open regions is etched fromthe substrate to form a binary mask. This mask can beused directly as a thin transmission hologram, or it canbe used to expose photoresist for etching quartz tocreate a surface relief phase hologram. Multilevelphase CGHs can be achieved using multiple masks.2 N phase levels can be achieved using N masks.
G. Data Storage and Transfer
On a CALMA system graphical data are stored as adatabase with a format called GDSII. This format isused internally for efficient storage of large amounts ofgraphical data. GDSII achieves this efficiency by us-ing referencing, whereby a large complex object isstored as a combination of smaller component objectsat specific locations. The smaller objects are thenstored as combination of even smaller objects, and thisprocess is repeated until the primitive shapes level isreached. The major drawback of this type of datastorage is the increased data access times involved.
Although this graphical data is stored for maximumefficiency, a typical CGH will still occupy several me-gabytes of storage. For this reason, CAD stations areusually equipped with high capacity hard drives. The
Table II. Cell Oriented CGH Datall120
Encoding SBWP Computer Number of Patternmethod (number used for trapezoids generation(object) of pixels) computation time
CALMA system at UCSD is equipped with a 300-megabyte removable hard disk.
After the graphical data of a CGH is translated tothe fractured data of an e-beam format, this fractureddata must be transferred to the e-beam system forfabrication. Typically, the data is transferred on 9-track tapes. Therefore, if this method is used, theCAD system must be equipped with a 9-track tapedrive to be able to download the data for transferringto the e-beam facility. If, however, the CAD systemand the e-beam system are located at the same facilityand connected electronically, e.g., using Ethernet, thetape drive can be eliminated. This also eliminatesdata transportation costs, e.g., magnetic tapes andmailing, which can be high due to the large amount ofdata. A less obvious benefit is the relaxation of memo-ry and disk space constraints for design of large SBWPholograms. A small portion of a large SBWP holo-gram can be calculated and sent to the e-beam writer,and while the e-beam is writing, another portion of thehologram can be computed. This eliminates opera-tions on large data sets, and can reduce the overallfabrication time.
IV. Examples of CGHs Designed at UCSD Using CAD
In this section we present examples of e-beam CGHsfabricated at UCSD and the CAD features used in theprocess. The computation and fabrication specifica-tions of these holograms are presented in Tables II-IV.The space bandwidth product (SBWP) is defined asthe area of the CGH divided by the unit cell size or thesmallest feature size in both the X and Y directions.This is equal to the number of cells or pixels in theCGH for cell-oriented and pixel-oriented holograms,respectively. CAD output graphics devices, i.e., thehigh-resolution CRT and the plotter, were used fordebugging and visual inspection of the patterns, andfor documentation purposes in all the examples.
A. Description of Equipment
The dataflow for a CAD workstation used for CGHdesign is illustrated in Fig. 2. The system accepts awide variety of input data formats. Standard mathe-matical transformations, such as the Fast FourierTransform (FFT), may be performed on a mainframecomputer or array processor. A VAX 8250 was used inmost cases for this purpose. Small FFT's, CGH en-coding, graphical operations, pattern display, and e-
Table Ill. Pixel Oriented CGH Data10,17
Encoding SBWP Computer Number of Patternmethod (number used for trapezoids generation(object) of pixels) computation time
ErrorDiffusion 51 2x512 CALMA 188,000 6 hr.(UCSD)
Simulated 45x45 VAXAnnealing (Replicated in 8250 256,000 1 hr.(3x3 array) an 8x8 array)
beam formatting are most efficiently done on the CADstation.
We have employed the capabilities of a CALMACAD workstation supported by a computer (Data Gen-eral Eclipse S140) utilizing the GDSII graphics pack-age. The system included 300 megabytes of disk stor-age, one-half megabyte of random access memory, a1600 bpi 9-track tape drive, a Versatec plotter, a high-resolution (800 X 1200 pixels) color graphics monitor, agraphics tablet and stylus, and a monochrome alpha-numeric monitor with keyboard. Holograms havebeen written and etched for us, up to now, by a varietyof different vendors with a variety of e-beam systems.
B. Cell-Oriented CGHs
Cell-oriented encodings are tailored to fit FFT data,i.e., arrays of complex numbers (amplitude and phase)representing Fourier coefficients. The FFT data isobtained by sampling an object to obtain amplitudeinformation (usually a random phase is added to theamplitude values to equalize the power throughout theFourier plane), and then taking the Fourier transformof the resultant complex array. Most cell-orientedencodings operate on the principles of detour phase,where apertures are positioned within cells. When thehologram is illuminated with coherent light and Fouri-er transformed with a lens, the apertures transforminto amplitude and phase information, which createsthe reconstruction of the original sampled object.
The cell-oriented design procedure using numericalinput data has been implemented for three encodingschemes:7 Lohmann, Lee, and Burch. Burch's meth-od was modified to translate gray levels to sizes ofbinary apertures. Some of the Lohmann CGHs usedan interlaced algorithm.20 Comparisons of the encod-ing methods can be found in Ref. 11. Software waswritten in GPL, a CALMA graphics programming lan-guage, for translating quantized amplitude and phasedata into the size and positions of rectangles requiredfor each of the encodings. The CALMA was responsi-ble for placing the rectangles as actual graphical ob-jects into the GDSII database. The graphics capabili-
Digital E-Beam DataHologram_ Generation (Encoded) , ,
Fig. 2. Tasks of specifying, computing, encoding, and fabricating aCGH are shown here. The design procedure must convert manyalternate types of input to an output acceptable to the e-beam
system.
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Fig. 3. (a) Portion of a Lohmann cell-oriented encoding as plottedon a Versatec plotter for visual inspection. (b) Actual reconstruc-
tion of the e-beam CGH.
ties of the workstation allowed visual inspection of thehologram both on the graphics monitor and on theVersatec plotter. The graphical data was translatedby the CALMA into the MEBES format that the e-beam writer required. The holograms were written asapertures in a chrome on glass substrate. The unex-posed substrate, photoresist coating, e-beam exposureand development, and etching of the chrome were allprovided by the e-beam lithography vendor.
A portion of a Lohmann recording, along with theresulting reconstruction, is shown in Fig. 3. Pertinentdata of several cell-oriented CGHs that have beenfabricated at UCSD is contained in Table II. Theobjects consisted of a binary image of the lettersUCSD, a grey-level image of a USC girl, and an AirForce resolution target. Some of the CGHs were toolarge to be efficiently computed on the CALMA sys-
beam data, the 45 X 45 CGH was replicated in an 8 X 8array (to reduce the signal spot size). The CALMAperformed this function efficiently and accuratelythrough its built-in functions for copying and referenc-ing. The desired transmission function for simulatedannealing is binary phase (for improved diffractionefficiency), so the binary amplitude mask obtainedfrom the e-beam system is not the final hologram.The mask is used to expose photoresist on top of asubstrate, which is then etched to form a binary phasehologram.
Two pixel-oriented holograms, as described above,have been produced at UCSD using the CALMA sys-tem. The fabrication data is shown in Table III.
Fig. 4. CGH of 45 X 45 pixels computed by simulated annealing is
plotted on the Versatec for visual inspection. The CGH was repli-cated in an 8 X 8 array before being fabricated by an e-beam system.
(b) Actual reconstruction of the e-beam CGH showing the 3 X 3array of equal intensity spots.
tem, but the CALMA was used for visual inspectionand plotting in these cases. The last two columnsshow the number of trapezoids after fracturing and thetotal time required to produce e-beam data from thedigitized input data.
C. Pixel-Oriented CGHs
Pixel-oriented CGHs differ from cell-orientedCGHs in that they do not have apertures within cells,the entire cells are turned on or off. In the error-diffusion9 and simulated annealing' 0 encoding meth-ods, the data describing the hologram transmittance isbinary. A GPL program on CALMA translates thebinary data into locations for the opaque cells. Thegraphical data would then appear similar to an irregu-lar checkerboard, as is illustrated in Fig. 4. After theinput data is encoded as graphical data, visual inspec-tion, simulated reconstruction, and plotting can thentake place in the graphical environment of the CADsystem.
A simulated annealing CGH was designed to pro-duce nine equal-amplitude spots in a 3 X 3 array. Theiterative computations were performed on the VAX8250, and the resulting numerical data was transferredto the CALMA and encoded. Before generating the e-
D. Fringe-Oriented CGHs
Two encoding schemes for fringe-oriented CGHshave been employed at UCSD with the help of CADfacilities: Fresnel zone plates (FZPs) and fringe-drawing algorithms. FZPs are used as HOEs for theparaxial approximation of a spherical lens, whilefringe-drawing algorithms are used to produce morecomplicated functions. The specific data of theFringe-oriented CGHs are contained in Table IV.
A FZP is encoded by first calculating the phasetransmittance function of the desired lens, taking themodulo 27r of this phase data to obtain a Fresnel lens,and then making a binary approximation to form thefringes. Once the fringes have been calculated by aGPL program, the FZP is constructed by drawingcircles, with a width dependent on the binary phaseapproximation, using a circle function from the CAD'slibrary of graphical functions. To perform intercon-nection of one source to five detectors, 15 a CGH con-sisting of five separate FZPs, as shown in Fig. 5, isneeded. Once the master FZP was constructed, asdescribed above, the five facet CGH could be con-structed easily on the CALMA. By using the interac-tive graphical interface, specific portions of the masterFZP were duplicated and placed in the appropriatelocations.
The fringe-drawing algorithms calculate the end-points and widths of straight segments that are used toapproximate curved fringes. The CALMA is thenused to translate this data into graphic paths which arestored in the GDSII format before being translated toe-beam format. This procedure was used to fabricatea CGH designed to interconnect sixty-four semicon-ductor sources with 256 detectors.
Two of the fringe-drawing CGHs produced at UCSDwere beam splitters with focussing capabilities, andthus appeared similar to typical binary gratings with avery slight curvature. Due to the large size of one ofthe CGH's, the data required was too large for theCALMA system to accommodate, and was fracturedon a mainframe computer. The fractured data wasthen transferred to the CALMA for visual inspection,plotting, and simulated reconstruction. The high-res-olution graphics and measuring tools of the CALMAworkstation along with its capability to read e-beamtapes into its own standard graphics database files
(b)Fig. 5. Portion of the fringe-oriented HOE for optical interconnec-tion of one semiconductor source to five detectors. The inset showswhich portion of the entire hologram is shown. (b) Actual recon-
struction of the e-beam CGH.
were very useful in debugging and perfecting the e-beam pattern generation program and provided ameans to see and measure fringe widths and positions.
V. Discussion
A. General Guidelines
The amount of necessary random access memory,disk storage, and computation time associated withCGH design on a CAD workstation depends on manyfactors. Even so, the rule-of-thumb numbers we havedeveloped may be used to guide the specification of anappropriate system. For holograms approximately 2X 2 cm, typical computation times for processes suchas encoding a hologram or reformatting data into e-beam compatible format range from 2-8 h. Interac-tive tasks, such as displaying a holographic pattern,can take from 15 sec-5 min, depending on its complex-ity. Hard disk capacity of 300 megabytes is sufficientfor system software and the data for holograms up totwo centimeters on a side. The database descriptionof a holographic pattern typically occupies 0.1-2 mega-bytes of random access memory. Though this muchmemory need not be installed in the machine, match-ing the size of installed memory to that required by thedatabase speeds operation by reducing disk access.Memory sizes up to 8 megabytes would be useful forsome data fracturing operations.
Because of the enormous information content of e-,beam holograms when designing a CGH, one should becareful to minimize the size of data as much as possible.The amount of graphical data describing a CGH de-pends on the encoding method used in the design
-algorithm. It is generally desirable to have hologrampatterns that generate the smallest Number of Primi-tive Shapes (NPS) because the amount of graphicaldata is directly proportional to the NPS. For exam-ple, when drawing interferogram fringes, the e-beamdata are typically made out of line segments approxi-mating the curved fringes. Depending on the speci-fied phase error tolerance, the pattern generation pro-gram should try to use the longest possible linesegments in order to reduce the NPS and therefore thee-beam data. Orientation of these patterns is impor-tant as well. Patterns consisting of rectangular shapesoriented along the x and y axes generate much less datathan patterns consisting of curved lines in arbitrarydirections. E-beam spot size is one of the major fac-tors affecting the amount of the necessary data; small-er spot size requires larger amounts of data for a givenwriting area.
B. Suggested ImprovementsThe efficiency and usefulness of CAD systems for
CGH design differ from one to the next. Newer ver-sions of CADs, such as the new version of GDSII imple-mented on the SUN microcomputer, are considerablymore powerful, reliable, and efficient than the olderversions. They provide high computing power and thestandard UNIX environment, along with networkingcapabilities. Combined with high-resolution graphicsdevices and other features of CAD, such a system couldbe even more useful in CGH design and e-beam datageneration for CGH uses.
High positioning accuracy, submicron resolutionand large SBWP are desirable features of e-beam lith-ography for fabrication of CGH's. The price that onehas to pay for these advantages is the potentially ex-plosive amount of data necessary to define a CGHpattern. Although useful for VLSI-type of designs,where the volume of data is considerably less than thatfor CGH patterns, the existing data fracturing pro-grams on CAD systems do not efficiently handle frac-turing of CGH data. They are general purpose innature, and are much more complicated than theyneed to be for CGH applications, where the shapes tobe fractured are quite simple. A fracturing programspecifically designed for CGH applications is neces-sary for reduction of the amount of pattern data.
A system supporting CGH design needs to be userfriendly in order to accomodate a wide cross section ofusers. People who are not familiar with the technicaldetails of CGH should still be able to design and useCGH's efficiently. This requires an intuitive inter-face, preferably menu driven, between the user and thehardware. Furthermore, the design center should re-move from the user the burden of choosing an encodingfor the application at hand. An expert system capableof translating a variety of user formats for hologramspecification into an efficiently encoded hologram inan e-beam ready format is needed.
Another desirable enhancement to CAD would be agray-scale display capability with at least thirty-twolevels. This would facilitate viewing of simulated ho-
lographic reconstructions on the high-resoluton CADmonitor.
C. Standards Development
At the present time there are no set standards in theCGH design and e-beam fabrication process. Withoutstandards, engineers in different organizations followdifferent methods of design and fabrication. Thisleads not only to an overall time inefficiency, but moreimportantly, there is no way to transport programsand/or data from one system to another without stan-dards.
Numeric and graphic data that are entered to the e-beam pattern generation program need to be standard-ized. This provides transportability of data betweendifferent systems, i.e., numerical data used by the pat-tern generation program can be produced on one sys-tem and then transported into the CAD system forpattern generation. This requires not only data struc-ture standards, but operating system compatibility aswell. The UNIX operating system is one of the mostwidely used operating system for the mini, mainframe,and some micro-computers today. Therefore, aUNIX operating system may be chosen as the operat-ing system standard.
Currently the majority of the CGHs are written onPerkin-Elmer's MEBES system. Therefore, the stan-dard e-beam data format can be that of the MEBESsystem. Tape file structure needs to be standardizedas well. For example, a MEBES tape has a file struc-ture compatible with RDOS or CDOS operating sys-tem. Therefore, independent of the operating systemunder which a MEBES tape is generated, the file struc-ture on the MEBES tape must be compatible withCDOS/RDOS.
The computer graphics industry was without stan-dards for some time, until the GKS standards wereadopted after numerous meetings and discussions.We believe that engineers actively involved with e-beam fabrication of CGHs should try to establish therequired standards before the diverse efforts becomeeven more divergent.
VI. Summary
The arduous task of designing an e-beam writtenCGH can be considerably simplified by using a CADworkstation. The workstation's interactive user in-terface, high performance graphics hardware and soft-ware, and efficient graphical database are valuableassets for CGH design. Translation of numerical datainto graphical shapes, geometrical transformations,and visual inspection of generated patterns and recon-structions are among the design tasks efficiently han-dled by the CAD workstation. Further, preparingCGH patterns for fabrication using e-beam lithogra-phy is supported by data format translation softwareavailable on the workstation.
Though existing workstations are very useful, someadditional features are needed to fully support CGHdesign. In particular, the database and pattern frac-turing software must be tuned to minimize the data
required to represent holograms with very largeSBWP. We expect that the CAD workstation willbecome a common and valuable tool for CGH design byusers with a broad range of interests, experience, andbackground.
Support of the Defense Advanced Research ProjectsAgency through the Jet Propulsion Laboratory (NASAcontract NAS7-918), the Army Research Office (con-tract DAAL03-88-K0142), and the Air Force Office ofScientific Research (contract 88-0022) is gratefully ac-knowledged.
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The Managing Editor welcomes news from any source. It should be addressed toP. R. WAKELING, WINC, 1613 Nineteenth Street N. W., Washington D. C. 20009
Mysterious waves may speed fiber optics
Edmund L. Andrews
A short survey of the possibilities of the soliton in fiber optics technology appeared in the BusinessTechnology section of The New York Times of 5 July 1989 and is reprinted here by permission. The NewYork Times Company.
A seemingly unnatural phenomenon, a wave that rollsalong almost endlessly without losing its shape, may providethe key to increasing the speed of fiber optic communicationsalmost a hundredfold. The first report of the mysteriouswave form, known as a soliton, was made in 1834, when aScottish naval architect followed a slow moving wave almosttwo miles down a canal. The waves have since been foundthroughout nature-in electricity, acoustics, ocean currentsand light-and their strange properties have fascinatedphysicists in many fields.
The most immediate commercial application of solitons islikely to be in fiber optics. In laboratory experiments lastyear, researchers at AT&T's Bell Laboratories transmittedpulses of laser light that retained their shape through fiberloops totaling 3700 miles, without the need for any electronicboost along the way. If those results can be incorporatedinto a working long-distance network, said a Bell physicist,Linn F. Mollenauer, it should be possible to relay as many as100 billion bits of information a second. In contrast, thefastest system today carries 1.7 billion bits.
Fiber optic lines are already the fastest form of communi-cation. But a quantum increase in their speed would removea large bottleneck to the significant expansion of multimediacommunications. Encyclopedia-size data bases completewith sound and video could be relayed in brief bursts of data.High powered facsimile machines would be able to exchangeglossy photographs over transmission lines, and cable sys-tems might be able to relay multiple channels of two-wayhigh definition TV. "I would hope we can solve the remain-ing problems within a few years," Mollenauer said. "I thinkit's just a matter of hard work and time." Added Steven E.Trullinger, a physicist specializing in soliton research at theUniversity of Southern California: "I think it's exciting.We now understand enough about solitons and about thebasics of their behavior to start going after commercial appli-cations."
In today's fiber optic networks, light pulses act like a highspeed Morse code. But as each bell-shaped pulse travels
down an optical fiber, it begins to spread out, a dispersionsimilar to the way a motorboat's wake widens into a V. After40 or 50 miles, light pulses in optical fibers eventually be-come so wide that they start to bump into one another andbecome garbled. To keep them clear, today's communica-tions carriers install electronic repeaters along the way.These convert the light pulses to electricity, give them aboost of extra power and convert them into freshened lightpulses for the next leg of the trip. Because the process iscumbersome, however, the repeaters themselves, becomebottlenecks that prevent the fibers from reaching anythingnear their potential speed.
Enter the soliton, once described as the one thing in naturethat comes closest to having perpetual motion qualities. Asoliton wave can occur in any medium where the wave'snatural tendency to spread is offset by some other force thatcompresses it back together. Researchers believe solitonsmay hold the key to exotic new plastics that conduct electric-ity, and perhaps also to understanding high temperaturesuperconductors. Solitons are also being explored for theiruse in optical computers that process information throughlight pulses rather than electrical switches.
As early as 1973, a Bell physicist, Akiro Hasegawa, theo-rized that optical fibers have a natural tendency to resistpulse dispersion-similar to the effect of the Scottish canalon waves of water. The key, which Mollenauer first put intopractice several years ago, is to inject a separate continuousstream of laser light into the optical fiber, which the signalpulses draw on and replenish their energy. As a result, thepulses reach their destination with exactly the same shapethey had at the start.
In addition to doing away with electronic repeaters, whichwould make a communications system simpler and quicker,solitons offer other advantages. For one thing, they could berelayed on optical fibers in use today. In addition, becausethe pulses do not spread, data could be packed into extreme-ly tight bundles of signals, each hundreds of times shorter in
