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1、Lighting & Illumination Design Using ZemaxIllumination Systems2 - 2 Illumination SystemsIllumination systems can include designs such as projection systems, microscopes, lighting systems, headlamps, etc.In systems where a source illuminates an object to be projected onto a screen or other device, it

2、 is necessary to maintain a high level of efficiency and uniformityMost real sources require specialized optics to ensure the required light distribution2 - 3 Light PipesOne of the simplest methods of homogenizing the energy from a source is the light pipeCan build light pipes of different geometrie

3、s in Zemax:Rectangular, Cylindrical: using native objectsPolygonal (e.g. triangular, pentagonal, hexagonal): using POB objectWill learn more about POB objects later2 - 4 Complex Reflector DesignsOther common reflector geometries that are used in illumination systems include:Parabolic (for collimated

4、 input or output)CPC (for angle-mapping)Polynomial/Freeform (general solution for arbitrary output)Zemax can also model reflectors generated from a list of facet positions (with either radial or toroidal symmetry)2 - 5 Some Reflectors Are More Flexible“Disadvantage” of a faceted reflector:Fixed geom

5、etry in Zemax; cannot be optimizedWell focus our attention on reflector designs that can be optimized as a part of design, specifically:ParabolicCPCFreeform ZMore information on the other reflector types is available in the Zemax Users GuideLighting & Illumination Design Using ZemaxParabolic Reflect

6、ors2 - 7 Parabolic ReflectorsParabolic reflectors are often used in illumination systems for directing light to the desired locationA point source placed at the reflector focus will generate a perfectly collimated beamRays emitted from the source which dont hit the parabola but hit the detector spre

7、ad energy at the detector2 - 8 Parabolic ReflectorsReal sources have finite extent, causing greater spreading of lightThe extent of the reflector as well as the position of the source is selected to generate the desired energy distributionCollimated output does not produce uniform irradiance (left)M

8、oving the source away from focus uses aberration to spread the energy (right)2 - 9 Parabolic Reflector ExampleLets design a parabolic reflector to provide a uniform irradiance outputStart with a point source, then increase source model complexityGood rule of thumb for many NSC designsOpen up a new Z

9、emax file and switch to non-sequential modeAdd 3-4 lines in the NSCEObject #1: Source Point# Layout Rays = 25# Analysis Rays = 100,000Cone Angle = 120 degrees2 - 10 Parameter SpecificationsObject #2: Standard SurfaceZ position = 10Material = MIRRORRadius = -20Conic = -1 (parabolic)Max Aper = 20Objec

10、t #3: Detector RectangleZ position = -60Material = ABSORBX, Y Half Widths = 50#X, Y Pixels = 1002 - 11 Initial ResultsOpen up a Detector Viewer, and then trace rays using the Ray Trace/Detector Control: 2 - 12 How Do We Quantify Uniformity?We can see that this initial system does not provide uniform

11、 irradiancePoint source launches power uniformly in angle, not spaceHow is this observation quantified?Using the merit function!The merit function can then be used to optimize system performance based on the desired spec(s)2 - 13 Optimization in NSCAs in sequential mode, optimization in NSC proceeds

12、 by defining an optimization criterion (merit function) and system variablesIn NSC, the Default Merit Function cannot be used to construct the optimization criterionMust build merit function manuallyTwo operands are primarily used for defining the merit function:NSTR: Executes a non-sequential ray t

13、raceNSDD: Reads out detector data from ray traceData may either be from a specific pixel or averaged over all pixels on the detector2 - 14 NSTRNSTR initiates a Non-Sequential Tracing of RaysInput parameters:Surf: Surface numberIn pure NSC, this is always 1In mixed mode, this is the number of the sur

14、face on which the non-sequential group is defined in the Lens Data EditorSrc#: Row number for the source to be tracedIf 0, rays are traced from all sources defined in the NSCEControls for splitting (Splt?), scattering (Scat?), polarization (Pol?), and ignore errors (IgEr?)A value of 0 turns the asso

15、ciated feature off, a value of 1 turns the associated feature on 2 - 15 Ray Sets Used During OptimizationNSTR does not return any value to the MFOptimization uses derivatives to compute change vectorProblem: When tracing a finite number of rays in a Monte Carlo fashion, the detected energy fluctuate

16、sDid system performance change as a result of changing system variables, or due to random nature of ray trace?Solution: NSTR always traces the same rays each timeRay set is random, but is the same random ray set each timeSystem performance will only change because system variables changeA (reasonabl

17、y) large number of rays are needed to ensure optimization ray set is valid“Randomization” is improved with Sobol sampling (more later)2 - 16 NSDDUsed to obtain Non-Sequential Detector DataInput parameters:Surf: Surface numberSame as for NSTRDet#: Detector numberSpecifies the object number of the det

18、ector for which data should be readMultiple NSDD operands can be used to read out data from multiple detectors in the same systemSet the Det# to 0 to clear all detectorsSet the Det# to -n to clear detector n only2 - 17 NSDDPix#: Pixel numberIf 0, the sum of all data on the detector is returnedIf pos

19、itive, data are returned from the specified pixelIf negative, various averages over the detector are returned e.g. Pix# = -5 yields mean value of all non-zero pixel dataMore information in the Zemax Users Guide (Chapter 12)Data: Data typeData = 0 returns pixel fluxData = 1 returns pixel flux/unit ar

20、eaData = 2 returns pixel flux/solid angle2 - 18 Other Detector OperandsNSDD is used to obtain incoherent data from the Detector Rectangle, Surface, or Volume objects, or objects used as a detectorCoherent data from the Detector Rectangle may be obtained with NSDCData from the Detector Color may be o

21、btained with NSDEData from the Detector Polar may be obtained with NSDP2 - 19 General Merit Function ConstructionIn NSC, the merit function will have this basic structure:1 NSDD operand to clear the detectors1 NSTR operand to ray trace (with various optional controls)Multiple NSDD operands to obtain

22、 detector data from ray-traceAdditional operands to provide boundary constraints on the optimization variablesFor example, NPLT and NPGT (Non-sequential Parameter Less Than, Non-sequential Parameter Greater Than) operands can be used to constrain values for object parameters2 - 20 Back to ExampleA m

23、erit function for evaluating our initial parabolic reflector design is:Using NSDD with Pix# = -4 provides standard deviation of all non-zero pixel data on detectorUsing NSDD with Pix# = 0 provides total power on detector2 - 21 Initial Results QuantifiedThe merit function shows a standard deviation o

24、f 2.6E-04 W/cm2 (operand #6) and a total power of 0.665 W (operand #8)Improve (via optimization) by changing Z position for the source, Max Aper for the mirrorSet Weight on each NSDD operand to 1.0 Except for first NSDD operand used to clear the detectorSet Target on operand #6 to 0.0, Target on ope

25、rand #8 to 1.0 Add boundary operands to the merit function to constrain possible values for optimization variablesNPGT, NPLT used to constrain Max Aper between 10 and 50 mmMax Aper is parameter #3 for the objectNPZL used to constrain Z position to 10 mm2 - 22 Merit Function for OptimizationNew merit

26、 function with targets, weights, and constraints:File is SamplesShort coursesc_parabolic1.ZMX2 - 23 Optimize!Define the Z position of the source and the Max Aper on the mirror to be variables:Optimize using damped least squares (DLS) optimizer:2 - 24 Optimized ResultsFile is SamplesShort coursesc_pa

27、rabolic2.ZMXNew Z position is 2 mm, Max Aper 33 mmUniformity improves by a factor of 2, efficiency is 100% (i.e. all launched power hits detector)Most improvement observed on power criterion, as this was “further out of spec” in initial designCould have increased weight on standard deviation operand

28、 to give it more importance during optimizationCould also “create” a slightly different operand to characterize uniformity: standard deviation/power (=noise/signal)Use DIVI to take ratio of two operandsJust as in sequential mode, need to make sure that the merit function accurately describes what we

29、 want!2 - 25 Far-Field UniformityGenerally we are looking for uniformity in the far-field of the mirrorRemove “ABSORB” property from Detector Rectangle object #3Use either SPACE or ESC key with cell highlightedAdd another Detector Rectangle at object #4Z position = -1000Material = ABSORBX, Y Half Wi

30、dths = 250#X, Y Pixels = 100Change weight on NSDD operand #6 (uniformity) from 1.0 to 10.0Re-optimize system for far-field detector (change Det# input to NSDD operands from 3 to 4)2 - 26 Near vs. Far-FieldFile is SamplesShort coursesc_parabolic3.ZMXResults look fairly good in both near (left) and fa

31、r-field (right)Plots shown in Log -5 scale:2 - 27 Real SourcesThe real source wont be an ideal pointUse measured data for an LED source from OsramChange object #1 to a Source File object:Data File = RAYFILE_LB_T67C_100K_190608_Zemax.DATZ position = 2# Layout Rays = 25# Analysis Rays = 100,000Re-opti

32、mize system using DLS2 - 28 Results From LED SourceFile is SamplesShort coursesc_parabolic4.ZMXUniformity improves in both the near- and far-field for the real sourceFinite source size contributes to energy spreading2 - 29 Notes on NSC OptimizationBecause a ray either lands or does not land on a det

33、ector when an optimization variable is perturbed, there are some consequences:Large numbers of rays needed to smooth-out discontinuitiesImproved by using “Pixel Interpolation” on detectorOptimization may stagnate because a small perturbation does not make any change on a detector where a larger one

34、doesAs a result:OD, Global optimization are often more useful than DLS in non-trivial systemsAutomatic data collection via macros is often useful to “scope out” interesting areas of the merit functionMore information on macros in our course entitled “Programming Zemax”Lighting & Illumination Design

35、Using ZemaxCompound Parabolic Concentrator (CPC)2 - 31 CPCThe compound parabolic concentrator (CPC) is a non-imaging concentrator that provides maximum concentration ratio and almost ideal angle-area tradeoffOften used with solar cells, in wireless communication, or in any application requiring a di

36、vergent light source to be condensedThe CPC is constructed by overlapping two offset, truncated parabolic mirrorsImage take from 2 - 32 CPC ParametersThe CPC is defined by the input angle qi and the output radial size aThe maximum length of the CPC is:The focal length of the CPC is:The radial size o

37、f the input aperture is:2 - 33 CPC PerformanceAll rays incident into the CPC at angles less than the input angle will pass (left)Rays beyond the collection angle are rejected (right)2 - 34 CPC ExampleLets look at an example using the CPC object to achieve collimation from an LED sourceStarting point

38、: SamplesNon-sequentialSourcessimple LXHL-BD01 LED model.ZMXModel of a LumiLeds LED using the Source Radial objectSobol sampling used for efficient randomizationInsert a new object #2, between the source and the detectorMake this object a CPC2 - 35 CPC SpecsParameters for the CPC object:Z position =

39、 1Radial Aperture = 4Angle = 10Length = 10Is Volume = 1 (so it is a solid object and not a shell)Material = PMMA2 - 36 Position the DetectorLets say the detector should always be 1 mm behind the output of the CPC, but that the length of the CPC may change during optimizationHow can this be done? Usi

40、ng a pickup solve!This is an occasion when the order of components in the NSCE mattersSince the detector comes after the CPC, it can be positioned relative to the CPC2 - 37 Pickup Solve on Detector PositionSet the “Ref Object” flag to “2” (i.e. the CPC) for the detectorThe length of the CPC is param

41、eter 3 for this objectOn the Z position of the detector, use a pickup solve:The detector will always be 1 mm behind the CPC output face!2 - 38 Define the VariablesSet the X, Y Half Width for the detector to 20Define the Angle, Length parameters for the CPC to be variables:The Radial Aperture of the

42、CPC is fixed, to ensure full collection from the emitting surface2 - 39 Construct the Merit FunctionWant to optimize for collimation of the LED sourceUse NSDD with Pix# = -9, Data = 2 (angular RMS radius)As this goes to zero, the beam es more collimatedAlso need to make sure sufficient power hits th

43、e detectorNSDD with Pix# = 0, Data = 0 gives total powerUse OPGT (Operand Greater Than) to constrain powerShould also constrain minimum, maximum values for optimization variables:CPC angle between 10 and 50 degreesCPC length 0.8*input power (27 lumens)Remember to set the “IgEr?” flag to 1 for the NS

44、TR operand2 - 41 Ready to OptimizeSet # Analysis rays = 10,000 for initial runCurrent RMS angular radius is about 40 degrees, peak luminous intensity is about 2.4 Lumens/steradianUse DLS optimizerGo!2 - 42 Initial ResultsAngular radius is about 15 degrees after DLS optimizationPeak luminous intensit

45、y is 170 Lumens/steradianAlmost all of the input power has been collected2 - 43 Length Boundary ViolatedThe CPC length is a bit longer than our spec (46 mm)Not unusual for a boundary operand to be violated during optimizationIndicates that Zemax wants this parameter to be as long as possibleIf this

46、is a problem, then:Increase weight on boundary operandORSimply fix length at maximum allowable valueIn other cases the increased performance may justify changing the specification2 - 44 Next StepsRepeat with more raysProbably wont affect results significantly, but will yield better statisticsIncreas

47、e angular resolution of detector by decreasing X Angle Min, X Angle Max, Y Angle Min, Y Angle MaxYields more accurate RMS radius valueUse Orthogonal Descent and Hammer OptimizationUse different object:CPC Rectangular (rectangular rather than radial symmetry)Annular aspheric lensFresnel lens with gro

48、oves that can be individual setFreeform Z Lighting & Illumination Design Using ZemaxFreeform Z2 - 46 Freeform OpticsA freeform surface is defined by discrete points on the surface through which a function is fitUsually no analytic representation for the surfaceFitting functions are generally smooth:

49、Cubic splinesBezier curvesNURBSSplines provide limited accuracy in high precision imaging systemsCannot maintain continuity of higher order derivatives across segment boundariesSplines are very useful in non-imaging (e.g. illumination) designs, as they allow optical power to be added “where needed”2

50、 - 47 Freeform ZThe Freeform Z object defines a rotationally symmetric surface or volume by:Fitting a cubic spline curve through a series of defined points in the YZ planeRotating this curve about the Z axisSplines are formed by a piece-wise concatenation of curved segmentsWithin each segment, the c

51、urve is defined by a third order polynomialPolynomial coefficients are determined by requirements that:The curve goes through the defined pointsThe first and second derivatives are continuous across segment boundaries2 - 48 Freeform Z ExampleWell design a Freeform Z light pipe to provide collimated

52、output from an LED source while also providing maximum powerOpen up a new Zemax and switch to non-sequential modeInsert 4-5 objects in the NSCESwitch Source Units to Lumens and Analysis Units to Lumens per M2:Set Wavelength to 0.465 microns:2 - 49 Source SetupObject #2: Source FileSelect RAYFILE_LB_

53、T67C_100K_190608_Zemax.DATOSRAM LED model with 100K rays# Layout Rays = 100# Analysis Rays = 100,000Power = 1.0 (Lumens)Randomize? = 1Different (random) rays will be used only when the layout plot is updated (full ray-set is being used for analysis)2 - 50 LED HousingObject #1: Imported objectUsed to

54、 define LED housingSelect LB_T67C_190608_GEOMETRY.STEP:We will discuss CAD import/export tomorrow2 - 51 Freeform Z DefinitionObject #3: Freeform ZZ position = 1# Points = 5 (can define up to 124)Is Volume? = 1 (volume rather than surface)Material = PMMANeed to define initial points in YZ plane:Z5 =

55、40.0; Y5 = 2.0Z4 = 30.0; Y4 = 2.0Z3 = 20.0; Y3 = 2.0Z2 = 10.0; Y2 = 2.0Z1 = 0 (always); Y1 = 2.0Initial definition represents a cylindrical pipe2 - 52 Detector SetupObject #4: Detector RectangleRef Object = 3 (reference relative to Freeform Z)# X, Y pixels = 101Z Position has pickup solve based on l

56、ength of Freeform Z:X, Y Half Widths have pickup solves based on exit height of Freeform Z:2 - 53 Merit Function ConstructionThe merit function will look very similar to previous examples:NSDD with Det# = 0 to clear the detectorNSTR to trace rays (set “IgEr?” flag to 1 to ignore errors)NSDD with Pix

57、# = -9, Data = 2 for RMS angular radiusNSDD with Pix# = 0, Data = 0 for total powerHowever, new boundary operands are needed to constrain possible solutions for the spline curveUsing NPLT and NPGT to constrain values for input points is not sufficientCould get strange behavior of the spline between

58、points!Need to constrain shape of the spline over the full curve2 - 54 FREZ OperandThe FREZ optimization operand is used to constrain the shape of the Freeform Z object at all points along the surfaceNot just at the input pointsInput points can be optimized in both Y and ZFREZ can be used to control

59、:Min and Max Y valuesMax Z value (Min Z value = 0 always)Min and Max Y and Z increments (difference between input points)Min and Max slopeMonotonic deviation (to control ringing)Object volumeFull details in the Zemax Users Guide (Chp. 14)2 - 55 ConstraintsFreeform constraints to use:Maximum length o

60、f light pipe 50 mmMaximum height of pipe 2 mmFREZ can be used directly as a boundary constraint operand through use of the “Mode” input (set to 2 for greater than, 3 for less than)Will also target maximum power on the detector by specifying that the reciprocal of the power should be zeroUse RECI ope