成像培訓print系統(tǒng)day

1、2 - 1 Zemax 成像設(shè)計培訓成像設(shè)計培訓-Day 2Table of Contents: Day 2u1. MTF and image quality evaluation (p2-315)u2. Double gauss lens design and optimization (p2-1638)u3. Image simulation (p2-3951)u4. Coordinate system in Zemax (p2-5253)u5. Coordinate break surface and tips (p2-5484)u6.Prism model in sequential

2、mode (p2-8594)u7.Scan mirror example (p2-95113)u8. Khler Illumination example (p2-114145)u9.Black box system (p2-146151)2 - 2 2 - 3 u MTF and image quality evaluationOptical & Modulation Transfer FunctionsuThe OTF is a complex relationship of the ratio of the amplitude of a given spatial frequency i

3、n image space to that of the same spatial frequency component in object spaceuThe MTF (modulation transfer function) is the modulus of the OTF. It is a measure of the contrast in the image of a sinusoidal intensity distribution.minmaxminmaxIIIIMTF2 - 4 Spatial FrequencyuSpatial frequency, measured i

4、n cycles/mm, is a convenient way to describe the fineness of detail in an imageuImagine imaging a sinusoidal or bar-chart pattern through an optical systemuThe frequency of the pattern is its spatial frequencyuWe refer to the number of cycles/mm in the image plane, not object plane2 - 5 Modulation T

5、ransfer FunctionuA modulation of 100% indicates perfect contrast. If the maximum modulation is lower than 100% (which also means a minimum modulation greater than 0% ), the fringes are less sharp.uThese plots show the resolution of a system with a square-wave pattern at 11 cycles/mm and 58 cycles/mm

6、2 - 6 The MTF Plot uThe MTF plot shows all spatial frequencies at once2 - 7 MTF PlotuThe effects of diffraction limit the maximum spatial resolution to the value given by:uF/# is the working F-number. This expression shows that faster lenses can resolve (ignoring aberrations) a finer sinusoidal imag

7、e than a slower lens.uEven if an optical system has no aberrations, the resolution is still limited by the final F/#uThe MTF falls off as a function of spatial frequencymax/#1F2 - 8 MTF PlotuThe normalized value for the MTF is a maximum, M = 1.0, at zero spatial frequency; M drops to zero at nmax, t

8、he cutoff frequency. The drop off for a diffraction-limited system is not quite linear:2 - 9 Adding AberrationsuWhat happens as you start to add aberrations to a diffraction limited optical system?uSystem performance gets closer and closer to that predicted by pure ray tracinguDiffraction calculatio

9、ns are only needed once the ray tracing predicts better imaging than you could actually seeuBecause diffraction introduces an uncorrectable bluruHow close do you need to be?2 - 10 Strehl RatiouThe Strehl ratio is a method of relating the quality of an aberrated image to that of an unaberrated image

10、formed by an optical system with the same F/#:uAn approximation to the Strehl ratio based on the wavefront error is:uThis approximation is valid for systems having Strehl ratios greater than 0.1u is the wavefront errorF/# same with PSF free aberration ofIntensity Peak PSF real theofIntensity Peak SS

11、e()214222 2 - 11 MTF and Wavefront ErroruThe MTF improves as the RMS wavefront error decreases. The MTF is closely related to the Strehl ratio, since both are functions of the PSF. The Strehl ratio is related to the wavefront error: uAs with the Strehl ratio, the MTF approaches its maximum value ind

12、icating full contrast as the wavefront error approaches 0uGenerally, a system is considered to be near diffraction-limited ifuThe peak-to valley OPD is less than 1/4 of a waveuThe Strehl Ratio is greater than 0.8SR = 1422 2 - 12 MTF Plots in Zemax1. FFT MTF2. Huygens MTF3. Geometric MTF2 - 13 Domain

13、s of ValidityuSo if diffraction computations are more accurate, why not use them all the time?uTwo very good reasons:uDiffraction equivalents are slower, sometimes dramatically so. Some computations, such as MTF optimization, are 10 to 500 times slower than geometric equivalents, and not fundamental

14、ly better!uDiffraction effects require the discrete sampling of the phase in the exit pupil. For systems with modest to large amounts of aberration, say 2-20 waves, this requires a lot of sample points to meet the Nyquist criterion. Large sampling grids are slow and consume huge amounts of memory.uN

15、o real gain because the geometric computations are perfectly accurate in this domain2 - 14 SummaryuDiffraction imposes a fundamental limitation on the imaging properties of a lens, even if it suffers no aberrations at alluThe point spread function shows the uncorrectable blur caused by the finite ap

16、erture of the lensuFraunhofer diffraction theory shows there is a Fourier relationship between the wavefront produced in the exit pupil, and the image formeduSpatial frequencies describe the “fineness of detail” in an imageuModulation transfer function (MTF) shows how image contrast varies with spat

17、ial frequency2 - 15 2 - 16 u Double gauss lens design and optimizationDouble GaussuThe double Gauss is a traditional SLR-type camera lensuWe will design one, and specifically discuss how to optimize for the required MTFuHere is a preview of what the final design will look like:2 - 17 Design GoalsuF/

18、3, 75 mm focal length, F,d,CuDesign for 35 mm film: a 24x36 formatuSet image height to 21.6 mmuDistortion less than 1%u2 mm edge/center minimum, 12 mm maximum glass thicknessuBack focus distance at least 40 mm for mirror clearance24mm36mm43.2mmThe field is defined by a circle whose diameter is the d

19、iagonal of a single frame of film2 - 18 MTF GoalsuMTF 80% at 30 cy/mm, 60% at 50 cy/mm. This is about the response of professional-grade film.uNote that 20% is about the limit at which humans can distinguish contrast by eye, so you should rarely ever be required to design to a target less than thisu

20、Off axis may be worse, but “best obtainable”uLets say performance may drop to 50% at 30 cy/mm, 40% at 50 cy/mmuThis kind of camera is typically used with the subject in the center of the field, so requiring best performance there makes most sense2 - 19 Starting PointuLoad SamplesShort coursesc_dbga1

21、.zmx2 - 20 Why Start With a Sample?uThe double Gauss is a well known design variant, and we do not want to “reinvent the wheel”uThe goal of this exercise is really to address MTF optimization, and some other system performance issues, rather than starting from flat pieces of glassuSo we have generat

22、ed a starting point that cuts out some workuLook at the fileu12 surfaces, 6 lenses comprising of 2 doublets and 2 singletsuThe stop is on a surface in the centeruEPD is 25mmuSurface 11 has a F/3 solve to constrain the EFL2 - 21 Add Fields and WavelengthsuAdd three fields of paraxial image height 0,

23、15.1, 21.6uAdd F, d, C wavelengths2 - 22 Edge Thickness MarginsuRequire the semi-diameters to be at least 1 mm larger than required to pass the rays, so there is a mounting area2 - 23 Starting PointuUse Optimize Quick Focus2 - 24 Merit Function ConstructionuIt is way too early in the design process

24、to target MTFuMTF improves as the wavefront error decreases, so our initial optimization should be for wavefront erroruIt is difficult to optimize for MTF if the desired frequencies lie beyond the first minimum of the MTF, as the MTF has to get worse before it can get better2 - 25 Merit FunctionuSin

25、ce we want great MTF, we will use an RMS wavefront default merit function with reasonable glass and air thickness constraints. Go to Optimize and select the Optimization Wizard.2 - 26 Merit FunctionuAdd DIMX on field point 3, target = 1% to control distortionuAdd CTGT surface = 11 target = 40 uThis

26、targets the back focal length to be greater than 40 mmuVariablesuAll remaining radii (except STOp surface) and all thicknessesuStarting MF is hugeuOptimize!2 - 27 Initial DesignuMF reduces to around 0.4!uThe first cut looks pretty good!2 - 28 AnalysisuWhat are limiting aberrations? Check boundary co

27、nditions to ensure not in violation. Check distortion, field curvature, & Seidel coefficients.2 - 29 Before You Do Anything ElseuRun the Hammer optimizeruHammer is the best tool available for moderate to complex optimizationuNever change the design until it has hammered for some time2 - 30 MTF Optim

28、izationuWe are close enough to the desired performance to start optimizing for MTF explicitlyuWe will use MTF operands, with zero weight, so that the MTF is computed, but not used for the optimizationuWe will then use OPGT operands so that if the MTF is within specification, it does not contribute t

29、he to merit functionuThis is a smart move with any constraint, because when the constraint is satisfied it disappears, and it only appears if there is a problem!uBecause we want a margin of error for tolerancing, we target a more demanding performance than the users specificationuHow much of a margi

30、n for error depends strongly on the application2 - 31 MTF Optimization2 - 32 MTF Operand NotesuOn-axis in a rotationally symmetric system, the sagittal and tangential MTFs are the same, so we only need to optimize oneuOff-axis we will optimize the average of the S and T valuesuThe “Grid” argument us

31、es autocorrelation to compute the MTF only at the requested frequency, and is generally much faster than the full FFT MTF calculation that computes the MTF at all spatial frequencies at onceuThe OPGT operands allow only the out-of-specification values to affect the optimizationuJust like the DIMX, C

32、TGT, and glass/air boundary thicknessesuNote weight of 10 as these are critical specifications uOPTIMIZE!2 - 33 Not QuiteuThe design improves, but is still not quite within spec on the on-axis MTFuAlthough it is actually within the original specification, its just slightly out of our tightened speci

33、ficationuWe can improve the design in several ways:uChange glassuAdd elementsuAdd aspheric surfacesuBut note we are in-spec with respect to the customers specification, were out of spec with regard to our tightened specuIncrease weight again to 100 on out-of-spec valuesuUse the Hammer optimizer 2 -

34、34 After OptimizinguJust leaving it to Hammer optimize gives a great result2 - 35 PerformanceuHeres what we got:uOn axis:u30 cy/mm: 84.5% (our tightened target 85%, customer target 80%)u50 cy/mm: 68.1% (our tightened target 65%, customer target 60%)uOff-axisu30 cy/mm: 55.7% (our tightened target 55%

35、, customer target 50%)u50 cy/mm: 44.5% (our tightened target 45%, customer target 40%)uDistortion 1% maximum, we achieved 1.021% maximumuWe never tightened this spec, maybe we should?uBack focal distance 41.728 mm, specification 40 mm minimum2 - 36 Glass SubstitutionuUsing Glass Substitution to get

36、better glass choice gives a design completely within our tightened specificationuOpen SamplesShort CourseAdvanced_SC_doubleGauss_final.zmx if we dont have time to generate it2 - 37 Key PointsuMTF improves as wavefront error goes to zero, so optimizing on wavefront error is the best way to get good M

37、TFuTo some extent, adding MTF operands just moves the residual arounduWhen you have a constraint, use a boundary operand or the OPGT operand as we did hereuWhen the specification is met, the boundary operand adds nothing to the merit functionuTrying to get the “best possible” merit function often re

38、sults in highly sensitive designs, and what we usually want is designs that meet, or exceed by a small amount, the customers specification2 - 38 2 - 39 u Image simulationImage SimulationuOptical engineers may know what OPD, PSF, MTF, etc. are, but their customers and managers often dontuThe Image Si

39、mulation feature in Zemax quickly and accurately predicts the appearance of any scene as imaged by the lens systemuThis is one of the best ways to explain the benefits of one design over anotheruWell use the file SamplesShort course Advanced_SC_doubleGauss_final.zmx to illustrate use of this feature

40、uFirst of all, we have to prepare the Zemax model a little to better represent the experimental arrangement2 - 40 Experimental ArrangementuThis is how the lens will be tested2 - 41 Design AdjustmentsuFix the lens byuRemoving all variablesuRemove the F/# solve on the last surfaceuLens Data EditorAper

41、turesConvert Semi-Diameters to Circular Apertures to lock the lens diametersuFor the most accurate treatment of relative illumination, set the semi-diameters to the unobscured, mounted diameter uChange the Aperture definition from “Entrance Pupil Diameter” to “Float by Stop”2 - 42 Float by StopuThe

42、light entering the lens does not magically “know” it should have an entrance pupil diameter of 25 mmuInstead, the EPD is really set by magnification of the optics in front of the stop, and the real stop diameteruBUT, the optics also introduce aberrationsuAs a result, the marginal rays selected do no

43、t exactly touch the edge of the stop2 - 43 Ray AiminguZemax has a ray aiming feature that aims rays at the stop surface instead of the entrance pupiluSystem ExplorerRay AiminguMarginal rays now hit exactlyon the stop surface semi-diameter2 - 44 Test ChartuThis system images points at infinity, so to

44、 use it with a test chart we must use an auxiliary collimating opticuWe will use a paraxial surface to represent the collimating optic, although the real collimating optic could be used if preferreduEnter a new surface at surface 1, and make it a paraxial surfaceuSet the object thickness to be 100 m

45、m, and the paraxial surface thickness to be 10 mm 2 - 45 Test SetupuThe object distance should be whatever is used experimentally, we just use 100 mm here as its a conveniently round number2 - 46 Field of ViewuNow change the field of view to object height, and set the values like so:2 - 47 Experimen

46、tal ArrangementuThis version of the lens is identical to our earlier version, except everything is fixeduNo F/# solves, image height field definitions, etc.uEverything is set mechanicallyuObject height and distance, iris diaphragm, etc.uTest with the merit function or analysis features that all the

47、performance characteristics are unchangeduThis is an important step, because sometimes using image height as a field definition can trick youuZemax always finds a ray that meets the requirements, but that might not be a ray launched from a real object a real distance away2 - 48 Image SimulationuImag

48、e Simulation works by placing a BMP or JPG image on the object surfaceuIt then computes an array of PSFs across the field of view of the lensuThe output image is formed by convolving the source bitmap with the array of PSFsuIncludes the effects ofuDiffractionuAberrationsuRelative illuminationuImage

49、orientationuDistortionuPolarizationuThe feature is also fully multi-threaded to use all the CPUs in u your computer2 - 49 Image SimulationuSet up like so:2 - 50 Result2 - 51 2 - 52 u Coordinate system in Zemax3-D SystemsuSo far, our examples have been fairly simple, rotationally symmetric systemsuAn

50、d many systems fall into that categoryuWe will now move on to consider fully 3-dimensional systems, systems with apertures, systems in which some components move or changeuWe will also look at the choice of coordinate system. So far, we have used the “l(fā)ocal coordinate system” in which each surface i

51、s located a thickness away from the previous surface, but we can be more general than that.Sequential ray tracing use local coordinate system often,Sometimes we need to change to global coordinate system!2 - 53 2 - 54 u Coordinate break surface and tipsCoordinate BreaksuCoordinate breaks (CB) are sp

52、ecial dummy surfaces that are used to define a new coordinate system in terms of the current oneuCBs have 7 degrees of freedomuDecenter in X,YuTilt about X,Y,ZuThickness (decenter in z)uThe Order flaguEach decenter and tilt is performed in the above order, UNLESS the order flag is non-zero. In this

53、case, the tilts and decenters are performed in reverse order, from bottom to top.uThickness is always last, regardless of the order flag2 - 55 Why the Order Flag?uThe order matters! This is the hardest part of using coordinate breaks!uIf you tilt about X, you get “new” Y & Z axesuA positive x-tilt m

54、oves the y-axis (thumb) towards the z-axis (first finger),and the z-axis points to the floor uSo tilting X, Y, Z is different to tiltingZ, Y, X2 - 56 ExampleuLoad the file SamplesSequentialObjectivesCooke 40 degree field.zmxuTo simplify the numbers, make the following changesuSet the thickness of th

55、e last lens to 3uSet the thickness of the last surface to 42uThis just gives us round numbers to talk aboutuRemove all variablesuOptimize Remove All VariablesuOur goal is to tilt and decenter the last lens as much as we want, but to leave the image plane where it isuWe will do this the hard way (by

56、hand), and then do it the easy way (let OpticStudio do it)!2 - 57 Good DisciplineuWe want to tilt & decenter the last lens, but keep the image plane at a constant locationuConstant with respect to what?uWhere is it located anyway?uGo to Analyze ReportsPrescription DatauLook at global vertex datauSho

57、ws the position & orientation of the vertex of each surface with respect to the global coordinate reference surfaceuSurface 1 by defaultuSet comments in the lens data editor to identify surfaces easily2 - 58 Global Vertex DataThe Image surface 60.02mm to the right of surface 1, this matches the tota

58、l track (TOTR) in the status bar2 - 59 Reference SurfaceuAny surface can be the global coordinate reference surfaceuWe will discuss global coordinates in more detail later, but it is a datum against which all other surfaces can be measureduWe can also report ray data in global coordinates (e.g Ray T

59、race)2 - 60 Rotation MatrixuThe global vertex report gives the rotation matrix and position of the vertex of each surface, relative to the global coordinate reference surfaceuLets note where the image plane is for future reference:2 - 61 Now Decenter the LensuAnalyzeSystem Viewer3D VieweruDecenter t

60、he last element by +2 mm in YuInsert a dummy surface before surface 5uMake it a coordinate break uOn surface 5, set decenter Y to 2mmuThats all folks!2 - 62 Decentered Lens2 - 63 Anything Wrong?uLook at global vertex reportuAll surfaces after the CB are decentereduNeed a second CB after the first to