课程第一本印刷day2os

1、Optical System Design Using ZemaxOptimization 2 - 2 OptimizationuSo far we have analyzed the performance of optical systems Optimization is the design part! uOptimization is the process by which a lens is designed to meet (usually exceed) its intended specificationuWhat do we need: A specification o

2、f the intended performance, in a format referred to as a merit function A starting design that is traceable, with some parameters set to be variableu Zemax can then change the values of the variable parameters so as to reduce the value of the merit function A zero-valued merit function means we are

3、getting exactly what we asked for Any deviation produces a positive merit function2 - 3 Todays ObjectivesuTo use a singlet lens example to demonstrate optimizationuTo explain the use of the optimization features in ZemaxuHow merit functions are builtuThe local (DLS) optimizeruWhat optimization opera

4、nds areuHow Zemax optimizesuTo touch upon global optimization We will spend the whole of day 2 on optimization!Optical System Design Using ZemaxIntroduction to Optimization- A Singlet Lens Example2 - 5 ObjectiveuThis section builds a simple example that is used as the basis of more advanced work A s

5、inglet lensuWe will cover in this section: Entering design requirements Using a solve to enforce a constraint Using the Optimization Wizard Local optimization The need for other constraints2 - 6 Statement of the ProblemuDesign a singlet lens with the following specifications: Light comes from infini

6、ty, with a 5 degree semi-field of view, and a single wavelength (d-line, .587 mm) Collimated input light is to be focused to smallest RMS spot size, averaged across the field of view F/10, EPD 40 mm Made from N-BK7, a common “workhorse” optical glass Stop is a separate surface, and is free to move2

7、- 7 PreviewuThis is what the final design will look like:2 - 8 ApproachuDefine the system apertureuDefine the field uDefine the wavelength uInsert the correct number of surfacesuDefine the glass type and other starting valuesuDefine a solve to control EFL (F/# = 10)uUse Optimize.Quick Focus to bring

8、 into focusuDefine a merit function uDefine the variables One radius, three thicknessesInitial SetupuIn the System Explorer, expand the Aperture and add a value of 40uNote “Lens Units” are mm unless we specify otherwise2 - 9 Initial SetupuIn the System Explorer, expand the FieldsuClick on “Add Field

9、” and tick “Enable” and add a field point at 5 degrees.uSince the system is rotationally symmetric, we only need to specify the field in +y, since -y and +x are implicitly the same2 - 10 Initial SetupuAlternatively double click on Fields to bring up a dialog box to enter the fields:2 - 11 Initial Se

10、tupuNow expand the Wavelengths in the System ExploreruCommon wavelengths are built in Find the d-line in the drop-down Click “Select Preset ” to use ituWe have now defined the incoming light completely: Aperture of beam Field of view WavelengthuNext well specify the basic optical system2 - 12 2 - 13

11、 Initial SetupuAlternatively you can double click Wavelengths to bring up a dialog box2 - 14 Initial SetupuClick on the solve box next to the radius of surface 3 and select F number solveInitial SetupuChoose the Optimise ribbon and Quick Focus to bring into focus2 - 15 2 - 16 Starting DesignuHere is

12、 the initial design (from the Analyze ribbon, choose Cross Section and RMSRMS vs Field)uWhat are the aberrations?2 - 17 CommentsuNote F/# solve enforces the constraint that the lens be F/10 Try changing the radius of surface 2, and note how the radius of surface 3 automatically updates to keep the l

13、ens F/10uNow this is definitely an F/10 lens, but is it the best possible F/10 lens?uWe have four parameters that we can adjust One radius, three thicknessesuWhat is the best combination of these four parameters that yields the smallest spot?2 - 18 OptimizationuSet variables (ctrl-Z in the solve box

14、, or select variable from the drop down list) on front radius, stop, lens and back focal thicknessesOptimizationuGo to the Optimize ribbon, select Merit Function Editor, expand Wizards and Operands and click Optimization WizarduSelect RMS spot radius, reference centroiduJust set this up as shown for

15、 now: we will discuss in full soon!2 - 19 2 - 20 OptimizationuFrom the Optimize ribbon choose Optimize Press StartuZemax will use all the cores in your machine to optimize very quickly2 - 21 Optimize!uDesign has much smaller spot size, but is very thickuWhat are the aberrations?2 - 22 Why So Thick?u

16、Remember the equation from yesterday, on the power of a thin lens:uSince the f terms are 1, the product f1f22uBut theres no operand for shape factor! So the next page shows an example of how to write one in your merit functionXCCCC12122 - 83 Complex OperanduNote use of zero weightsZemax computes the

17、se operands but they dont affect the value of the merit functionuThis MF prevents the lens from being meniscusOptical System Design Using ZemaxDesign Rules for Merit Functions2 - 85 Can the Singlet be Improved?uReopen the saved singlet and rebuild the original merit function for the singletuOn axis,

18、 the limiting aberration is spherical. Can we get a better design by eliminating the spherical?uTry adding an SPHA constraint. SPHA computes the third-order spherical aberration in waves.uSPHA starts at 3 waves. Optimize!uSPHA drops to 1.08 waves. The MF drops, but RMS spot size goes way up! It incr

19、eased from 33,48 microns to 61,108 microns 2 - 86 Why Cant We “Fix” the Spherical?uWhich variable controls spherical? Stop position is irrelevant, spherical appears on-axis Back focus is irrelevant: focus and spherical are independent Lens thickness is a weak variable and at its limit anyway Leaves

20、just the front radius, which must compensate on and off axis aberrationsuRequirement for minimum RMS spot and minimum spherical contradict, as focus and spherical balance for minimum spot sizeuCONCLUSION: Some variables are ineffective at reducing certain aberrations, and so reduces effective degree

21、s of freedom Aberration reduction and spot-size reduction often conflict Aberration balancing is key2 - 87 Optimizing for ComauIf we optimized for spherical, and got a worse solution, why bother with coma?uTry it: Use COMA instead of SPHA Coma drops to virtually zero! Almost identical to unconstrain

22、ed solutionuDo the same for astigmatism (ASTI). What happens? Why?uSpherical and field curvature remain, and are the limiting aberrations Spherical cannot be eliminated for a singlet made of BK7 Petzval term cannot be eliminated eithernP2 - 88 Moral of the StoryuZemax always finds a lower merit func

23、tion, but the merit function must represent what you really care about!uLower merit functions are only “better” by the criteria they define!uOptimizing for specific aberrations is not usually desirableuZemax uses physically significant merit functions Build a merit function that describes how your l

24、ens is used or tested2 - 89 Further ImprovementuLimiting aberration is field curvature Let image plane curve2 - 90 Residual AberrationuOnce a design is well optimized (see global optimization section, coming up), what were left with is the residual aberration of the designuCannot improve design by a

25、dding more constraints in the merit function “Toothpaste tube syndrome”uIn order to improve design further, need to Loosen constraints (not add!) Add further degrees of freedom Extra surface, asphere, glass choice2 - 91 SolvesuWhenever we have a constraint on the optical design, we have two choices:

26、 Make everything variable, then add boundary constraints in the merit function Use solves to enforce the constraints, eliminating useless variablesuThe second choice is vastly superior!uAlways eliminate variables where possible When we know how to compute a parameter exactly, why use the optimizer?

27、Boundary constraints slow execution of the merit function Optimization time is proportional to (# operands)2 More variables = greater chance of stagnation2 - 92 F/# SolveuSince the marginal ray determines effective focal length, we used a marginal ray angle solve on the last curve to control the EFL

28、 constraintuWhen a solve is placed on a curve, Zemax automatically adjusts it so that the required constraint is achieved:q = -1/(2*F/#)uFor F/10, q = -0.05; can specify either the MRA or F/#uSolves are useful in many applications, but this is the most common useuGeneral rule: If a parameters value

29、can be computed exactly from raytrace or LDE data, and a solve exists to compute it, use the solve instead of variable + operand(s) You can write your own solves using the ZPL macro language, but this is outside the scope of this classSolvesuThere are many solves available, see the In-Line Help for

30、more2 - 93 2 - 94 Building Your Merit FunctionuImportant decisions What optical performance criteria is appropriate? RMS spot size RMS wavefront error MTF Encircled Energy What are the constraints? Min/Max length, edge thickness, center thickness Max weight Max cost (# of elements, aspheres, materia

31、l) What other properties should the system have? EFL, F/#, FOV, Vignetting, etc Can I use a solve?2 - 95 Determining the GoalsuPerformance criteria: RMS spot size Best for systems with more than 2 waves of aberration Fastest RMS wavefront error Best for systems with less than 2 waves of aberration N

32、early as fast as spot size MTF, encircled energy Gives results similar to wavefront error Slower Best used when the design is maturing or close to finished PTV spot, wavefront Minimizes circle of least confusion2 - 96 Overall WeightuWhen switching between different default merit function types in th

33、e Optimization Wizard, such as RMS spot radius and RMS wavefront error, the numerical magnitude of the default merit function can change dramatically uThis may make it tedious to manually adjust the weights of operands that are not part of the default merit function uThe “Overall Weight” is simply a

34、 factor that scales all the weights in the default merit function uUnder most circumstances, this weight may be left simply at one2 - 97 Spot X + YuSpot X and Spot Y are used for cylindrical optics which produce line fociuSpot X+Y considers the x and y components separately, and both are optimized t

35、ogether This is similar to spot radius, except the signs of the aberrations are retained, which yields better derivatives if the system contains different power in x and yuThe relative X weight is an additional weighting placed on the X component of the transverse aberrations If the relative X weigh

36、t is less than unity, then the Y components are weighted more heavily If the relative X weight is greater than unity, then the X components are weighted more heavily If left at the default value (1), then the components are equally weighteduThis control is useful for systems which intentionally form

37、 slit images, such as spectrometers2 - 98 Angular RadiiuThere are angular equivalents of all spot merit functions Intended for afocal systems like beam expanders, eyepieces We will discuss this later, but usage is straightforward Optical System Design Using ZemaxGlobal Optimization2 - 100 There is A

38、nother Solution!uEven a singlet lens has more than one solutionuIf you change the stop position to the other side of the lens, there is an inferior solution thereuWhich solution DLS finds is a strong function of where it starts. This is a characteristic of optimization algorithms which operate in a

39、complex solution space.uThis touches on the concept of “local” and “global” optimauThe local optimum is the best solution which can be reached from the starting point whilst continuously moving “downhill”uThe global optimum is the solution with the lowest merit function. Once a good solution is foun

40、d, it is impossible to know if a better one exists or not!2 - 101 Brute Force & IgnoranceuWhy use an algorithm? Just try all possible solutions!uAssume a three element design 3 fields, 3 wavelengths, 63 targets 6 radii, 6 spacings Assume 1 radii and one spacing fixed 10 variables Each variable h

41、as 100 values (coarse sampling) 100 to 10th power is 1020 total permutations of our tripletuAssume ray-tracing of 100,000,000 RSS Evaluate about 2.5 million systems per second (nice!) Takes 4 1014 secondsabout a billion yearsuThe sheer scale of most optical design problems precludes simple number-cr

42、unching2 - 102 Local MinimauThe primary optimizer is the DLS algorithmuIt uses gradients to find lower MFsuPrimary problem: Starts by assuming we want to go downhill Starting point determines solutionuGood starting point required Problem: how do we get the good starting point? Experience Physical in

43、sight Design database Luck.2 - 103 Global TechniquesuZemax approach Two algorithms: Global and Hammer Optimization Global used for seeking possible design forms Hammer used to exhaustively improve designuBoth Zemax global optimization algorithms are genetic with DLS; the difference between them is t

44、he scope of the searchuZemax has an alternative local optimizer, the Orthogonal Descent optimizer Of most use in non-sequential work, we will cover it on day 42 - 104 Global OptimizationuBasic concept to global search: Find series of candidate solutions by genetic competition Optimize; see if design

45、 is better than any of the 10 (by default) best so far Sort and reject worst design; keeps top 10 designs Repeat until user presses “Stop” Top 10 are saved as GLOPT_01 to GLOPT_10 in current folderuAdvantage: Global Optimization works with any user defined MF! Works without extra user input - just c

46、lick a different menu item! Best left overnight or longer for most problemsuApplication: Helps find alternate design forms2 - 105 HammeruBasic concept to hammer optimization: Start with a lens file Generate variations via genetic optimization Optimize promising designs to see if they have lower MFs!

47、 Continue until user presses “Stop” Changes original file to design with lowest MFuAdvantage: Fast enough to escape local minimauApplication Finds similar designs with lower merit functionsuHammer is now used extensively by users. The name implies a designer “hammering away at a problem” until it ge

48、ts solved!2 - 106 Which to Use?uHammer starts from your existing design and “spirals out” in parameter space to find improvements on what you haveuGlobal optimization searches over all regions of parameter space to find regions of interest for you to explore furtheruThe usual workflow is: Global opt

49、imization Local optimization Hammer optimization with the merit function being refined at each stepuIn this class, we will not do any example complex enough to require the global search phase, and we wont cover it any further this weekuHammer can and should always be used2 - 107 Things to NoteuThe g

50、lobal optimisers may not ever find the global optimum to any particular problem And you couldnt prove it, if they did!uThey are very good at finding alternative design forms that would have been tedious to discover by hand uThey are very powerful tools to add to your toolbox, but not a substitute fo

51、r optical design skillsuThe global algorithms have a strong random component, and therefore no two runs will yield the exact same solutions every time Sometimes the solutions will be worse, sometimes better, but usually they are simply different for runs of similar duration2 - 108 Section SummaryuWe

52、 have covered: The use of a singlet lens example to demonstrate optimization The use of the optimization features in Zemax How merit functions are built The local (DLS) optimizer What optimization operands are How Zemax optimizes Global optimizationOptical System Design Using ZemaxPrivate Study Exer

53、cise- The Singlet Lens2 - 110 The Singlet Lens uEarlier we saw that the singlet lens example has 2 solutionsuWe had the stop in front of the lens, could have had it after the lensuNow you can build the other solution2 - 111 Statement of the ProblemuDesign a singlet lens with the following specificat

54、ions: Light comes from infinity, with a 5 degree semi-field of view, and a single wavelength (d-line, .587 mm) Collimated input light is to be focused to smallest RMS spot size, averaged across the field of view F/10, EPD 40 mm Made from N-BK7, a common “workhorse” optical glass Stop is a separate s

55、urface, and is free to move but comes after the lens Lens should have 2 mm semi-diameter margin for mounting Lens should be at least 3, and no more than 15 mm thick at center Lens should have a minimum edge thickness of 3 mm, and air gaps should be a minimum of 0.5 mm2 - 112 Preview2 - 113 Solve or

56、Operand?uSince the lens is before the stop, we cannot use the F/# solve We dont know which ray is the marginal ray until it has hit the edge of the stopuThis means we must use the other option and insert an operand in the merit function Use the EFFL operand in addition to your RMS spot default merit

57、 function Just add an extra line at the top, target the EFL to 400mm Remember to add a weight of 12 - 114 Start uYour starting point could look something like thisuGet started; please ask if you have any problems2 - 115 ComparisonuHow does the performance of the two designs compare?uWhat aberrations

58、 dominate?Optical System Design Using ZemaxDoublet Lens Design2 - 117 Objectives of this SectionuTo design a more complex systemuTo investigate chromatic effectsuTo investigate the benefits of extra surfaces versus aspheric surfacesuTo get more practice in using the optimizeruTo optimize for glass c

59、hoice2 - 118 Doublet Lens DesignuThe doublet is an extremely important design exercise Almost all optical designs are really collections of doublets! Many designs are improved by splitting singlets into doubletsuDoublets have the following degrees of freedom: Three radii, four if air-spaced Three sp

60、acings, four if air spaced Index, dispersion differences between glasses Stop locationu8-13 DOF, depending on how you count!2 - 119 Doublet ExampleuStatement of Problem: Collimated light focused to smallest RMS spot Use F,d,C lines Entrance pupil diameter of 50 mm F/8 10 degree full field of view Minimum edge