南京光研成像and照明培訓(xùn)osduz32

1、Optical System Design Using ZEMAX Introduction to Optimization - A Singlet Lens Example Copyright 2014 Radiant ZEMAX Copyright 2014 Radiant ZEMAX 2 - 2 Objective uThis section builds a simple example that is used as the basis of more advanced work A singlet lens uWe will cover in this section: Enter

2、ing design requirements Using a solve to enforce a constraint Building a default merit function Local optimization The need for other constraints Copyright 2014 Radiant ZEMAX Copyright 2014 Radiant ZEMAX 2 - 3 Statement of the Problem uDesign a singlet lens with the following specifications: Light c

3、omes 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 surface, and i

4、s free to move Copyright 2014 Radiant ZEMAX Copyright 2014 Radiant ZEMAX 2 - 4 Preview uThis is what the final design will look like: Copyright 2014 Radiant ZEMAX Copyright 2014 Radiant ZEMAX 2 - 5 Approach uDefine the system aperture uDefine the field uDefine the wavelength uInsert the correct numb

5、er of surfaces uDefine the glass type and other starting values uDefine a solve to control EFL (F/# = 10) uUse ToolsMiscellaneous.Quick Focus to bring into focus uDefine a merit function uDefine the variables One radius, three thicknesses Copyright 2014 Radiant ZEMAX Copyright 2014 Radiant ZEMAX 2 -

6、 6 Initial Setup uSystemGeneral or use the “Gen” button uNote “Lens Units” are mm unless we specify otherwise Copyright 2014 Radiant ZEMAX Copyright 2014 Radiant ZEMAX 2 - 7 Initial Setup uSystemFields, or use the “Fie” button uSince the system is rotationally symmetric, we only need to specify the

7、field in +y, since -y and +x are implicitly the same Copyright 2014 Radiant ZEMAX Copyright 2014 Radiant ZEMAX 2 - 8 Initial Setup uSystemWavelength or use the “Wav” button uCommon wavelengths are built in Find the d-line in the drop-down Press “Select” to copy it into the dialog uWe have now define

8、d the incoming light completely: Aperture of beam Field of view Wavelength uNext well specify the basic optical system Copyright 2014 Radiant ZEMAX Copyright 2014 Radiant ZEMAX 2 - 9 Initial Setup uRight-click on radius of surface 3 and select F number solve uToolsMiscellaneous.Quick Focus to bring

9、into focus Copyright 2014 Radiant ZEMAX Copyright 2014 Radiant ZEMAX 2 - 10 Starting Design uHere is the initial design (AnalysisLayout2D layout or use the “Lay” button) uWhat are the aberrations? Copyright 2014 Radiant ZEMAX Copyright 2014 Radiant ZEMAX 2 - 11 Comments uNote F/# solve enforces the

10、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 lens F/10 uNow 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 thickness

11、es uWhat is the best combination of these four parameters that yields the smallest spot? Copyright 2014 Radiant ZEMAX Copyright 2014 Radiant ZEMAX 2 - 12 Optimization uSet variables (ctrl-Z) on front radius, stop, lens and back focal thicknesses uEditorsMerit FunctionTools: Build default merit funct

12、ion, RMS spot radius, reference centroid uJust set this up as shown for now: we will discuss in full soon! Copyright 2014 Radiant ZEMAX Copyright 2014 Radiant ZEMAX 2 - 13 Optimization uToolsOptimizationOptimization or press the Opt button Press Automatic uZEMAX will use all the CPUs in your machine

13、 to optimize very quickly Copyright 2014 Radiant ZEMAX Copyright 2014 Radiant ZEMAX 2 - 14 Optimize! uDesign has much smaller spot size, but is very thick uWhat are the aberrations? Copyright 2014 Radiant ZEMAX 2 - 15 Why So Thick? uRemember the equation from yesterday, on the power of a thin lens:

14、uSince the f terms are 1, the product f1f21, so t must be large to have any effect Hence we say that thickness is a weak variable It must go to extreme values to have any influence uAs a general rule, we must also build constraints into the merit function to exclude solutions that we do not want Cop

15、yright 2014 Radiant ZEMAX Copyright 2014 Radiant ZEMAX 2 - 16 A Better Design uUse F3 to undo the optimization, or just reload the file uLets set the default merit function tool up like so: This sets a range of boundary values on the center and edge thicknesses of the lens and the air thicknesses Co

16、pyright 2014 Radiant ZEMAX Copyright 2014 Radiant ZEMAX 2 - 17 Lens Semi-Diameter uNow, how has the value of the surface semi-diameters been set? We never entered any values into those cells! uZEMAX will automatically size the surfaces so that the real marginal rays pass through the lens uIt is usua

17、l to add a margin to this, so there is a small amount of “dark” glass that can be used by the mounting arrangement uSet a 2 mm aperture margin under SystemGeneralMiscellaneous Copyright 2014 Radiant ZEMAX 2 - 18 Before and After Copyright 2014 Radiant ZEMAX Copyright 2014 Radiant ZEMAX 2 - 19 Re-opt

18、imize! uHere is the design. This is the classic “l(fā)andscape lens” with the stop at the front of the lens. uWhat are the dominant aberrations? Copyright 2014 Radiant ZEMAX Copyright 2014 Radiant ZEMAX 2 - 20 Improved Design uThe field performance is good, and the spherical is balanced on and off axis

19、uSave this file for later Copyright 2014 Radiant ZEMAX Copyright 2014 Radiant ZEMAX 2 - 21 Optional Exercise uShow the original and optimized performance on the same plot, like so: Copyright 2014 Radiant ZEMAX Copyright 2014 Radiant ZEMAX 2 - 22 System Check Utility uBefore concluding singlet exampl

20、e, take a look at a basic diagnostic that should be used frequently ReportsSystem Check uFlags common system errors and gives useful warnings/alerts Errors require system modification Warnings are acceptable conditions that should be verified Trivial warnings are valid conditions flagged for your in

21、formation uAlso reports approximate amount of memory a file uses uGet in the habit of checking this in any optical system you design! Especially if you are concerned about system behavior Copyright 2014 Radiant ZEMAX Copyright 2014 Radiant ZEMAX 2 - 23 Section Summary uWhat we have done so far: Set

22、up an initial starting point F/# solve on back radius ToolsMiscellaneous.Quick Focus Defined a “merit function” Defined “optimization variables” Run the optimizer uWe will soon explain what ZEMAX does when it optimizes uFirst, we must discuss the role of sampling and reference points in optical calc

23、ulations Optical System Design Using ZEMAX Sampling and Reference Points Copyright 2014 Radiant ZEMAX Copyright 2014 Radiant ZEMAX 2 - 25 Sampling uRays are infinitely thin lines that go through the optical system uFor any given field point, we trace some finite number of rays and then perform calcu

24、lations based on that data; like RMS spot radius, OPD, etc. uLets take RMS spot size as an example The spot diagram traces some pattern of rays through the pupil, and onto the specified surface ZEMAX computes the radial landing coordinate of each ray, and then computes the RMS (root-mean-square) of

25、the ray set The “RMS spot radius” is a measure of the sharpness of the spot. As it goes to zero, the lens approaches “perfect” imaging. “Geometric radius” is just the most extreme single ray landing coordinate Copyright 2014 Radiant ZEMAX 2 - 26 RMS Spot Size Copyright 2014 Radiant ZEMAX 2 - 27 RMS

26、Spot Radius uTry varying the number of rays traced, and see what the effect on the RMS spot size is Copyright 2014 Radiant ZEMAX Copyright 2014 Radiant ZEMAX 2 - 28 Is There a Better Way? uYes! Remember the functional form of the third-order aberration coefficients is a series of polynomials uAs you

27、 take higher and higher order approximations to sinq, you get an increasingly complex set of polynomials that you cant even write down uA numerical method, known as Gaussian Quadrature allows integrals, RMS, PTV, etc., of arbitrary functions to be evaluated by fitting sampled data to a polynomial Th

28、is gives very accurate data without having to trace huge numbers of rays uThe man to thank for this insight is Greg Forbes, and his paper “Optical system assessment for design: numerical ray tracing in the Gaussian pupil”, J. Opt. Soc. Am. A, Vol. 5, No. 11, p1943 (1988), is one of the most readable

29、 and accessible papers in the optical design literature Copyright 2014 Radiant ZEMAX Copyright 2014 Radiant ZEMAX 2 - 29 Gaussian Quadrature uWorks by defining a number of rings for radial sampling and arms for angular sampling Because wavefront polynomials are functions of r and cosq pupil coordina

30、tes u Using n rings, you can compute the wavefront exactly to order r(2n-1) three rings gives control to r5, four to r7, etc. uYou can use the OPD, ray fan plots to estimate the highest radial order of aberration, add one, and use that number of rings to compute the wavefront (and hence spot, etc.)

31、exactly! uAnother reason why we do not concern ourselves with aberration coefficients, especially at orders higher than third Why bother when GQ gives you this data exactly and with fewer rays? Copyright 2014 Radiant ZEMAX Copyright 2014 Radiant ZEMAX 2 - 30 Gaussian Quadrature uCompute the whole ra

32、y fan plot (for example) using only a few data points and some knowledge of the order of polynomials and any symmetry the lens has: Copyright 2014 Radiant ZEMAX 2 - 31 Symmetry uIt gets even better if the lens has rotational symmetry! uWe define rings and arms On-axis, we only need to trace the rays

33、 along one arm, the rest are identical by symmetry! Off-axis, we have left-right symmetry, so only half the pupil of rays needs to be traced uZEMAX is extremely good at exploiting symmetry if it is available! uIf you define field points along +y only, and use only rotationally symmetric surface type

34、s, ZEMAX will automatically assume rotational symmetry uIf no symmetry exists, need to trace rings*arms for each field point Copyright 2014 Radiant ZEMAX Copyright 2014 Radiant ZEMAX 2 - 32 Reference Point uWhere is the center of this spot diagram? If we use the tip of the comatic spot (the chief ra

35、y) as the reference, the RMS radius is a circle of radius 13.6m, located at (0,0). If we use the centroid of the spot, the RMS radius is 8.6m, centered at (0, -11) m. Which is most realistic experimentally? Copyright 2014 Radiant ZEMAX Copyright 2014 Radiant ZEMAX 2 - 33 Centroid Reference uGenerall

36、y speaking, centroid references are more physically meaningful than chief ray references uHistorically chief ray references have been used for speed, but on modern machines this is not an issue any more uWe recommend that you always think about how you will measure the performance in the real world,

37、 and configure ZEMAX features to be as close to that real-world setup as possible Copyright 2014 Radiant ZEMAX Copyright 2014 Radiant ZEMAX 2 - 34 What is RMS Spot Size? uRMS spot size is a geometric assessment of image quality, based on ray landing coordinates in the image plane A set of rays is tr

38、aced from an object point to the image plane The radial distance from the reference point to the place in the image plane where the ray landed is computed, squared, averaged and the square root taken Copyright 2014 Radiant ZEMAX Copyright 2014 Radiant ZEMAX 2 - 35 What is RMS Wavefront Error? uRMS w

39、avefront error is an assessment of image quality using the deviation of the phase in the exit pupil from a reference sphere A set of rays is traced from an object point to the image plane The phase of each ray is measured with respect to the reference sphere The phase of each ray is squared and aver

40、aged The square root is taken Copyright 2014 Radiant ZEMAX Copyright 2014 Radiant ZEMAX 2 - 36 Wavefront Error uThe RMS wavefront error is usually referenced to a tilted and shifted reference sphere, chosen to minimize the RMS: Or alternatively RMS2 = avg(W2) - (avg(w)2 uThis is called the “standard

41、 deviation” in every field except optics! uZEMAX calls this “centroid reference”, which is not an exactly correct name, but is a convenient analogy to spot size Options exist for other references, but centroid is usually the most physical, and hence best Optical System Design Using ZEMAX Doublet Len

42、s Design Copyright 2014 Radiant ZEMAX Copyright 2014 Radiant ZEMAX 2 - 38 Objectives of this Section uTo design a more complex system uTo investigate chromatic effects uTo investigate the benefits of extra surfaces versus aspheric surfaces uTo get more practice in using the optimizer uTo optimize fo

43、r glass choice Copyright 2014 Radiant ZEMAX Copyright 2014 Radiant ZEMAX 2 - 39 Doublet Lens Design uThe doublet is an extremely important design exercise Almost all optical designs are really collections of doublets! Many designs are improved by splitting singlets into doublets uDoublets have the f

44、ollowing degrees of freedom: Three radii, four if air-spaced Three spacings, four if air spaced Index, dispersion differences between glasses Stop location u8-13 DOF, depending on how you count! Copyright 2014 Radiant ZEMAX Copyright 2014 Radiant ZEMAX 2 - 40 Doublet Example uStatement of Problem: C

45、ollimated 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 & center 4 mm, max center 18 mm Add 2 mm semi-diameter margin for mounting Copyright 2014 Radiant ZEMAX Copyright 2014 Radiant ZEMAX 2 - 41 Preview uThis is wha

46、t it will look like Copyright 2014 Radiant ZEMAX Copyright 2014 Radiant ZEMAX 2 - 42 Approach uDefine the system aperture uDefine fields and wavelengths (3 of each) Fields are 0, 3.5, and 5 degrees uDefine the correct number of surfaces uStart with the cemented design uAdd F/# solve uGuess at glasse

47、s N-BK7, F2 uBuild the merit function RMS spot until we have reason to change uVariables are 2 radii, 4 thicknesses uGO! Copyright 2014 Radiant ZEMAX 2 - 43 Field Definitions uIf we have an on-axis point at 0, and the most off-axis point at 5, shouldnt the intermediate field point be at 2.5? uNo! Re

48、member we are sampling a unit circle, so we want to divide it into regions of equal area, not equal radii uSo for three field points, have them at (0, 1/2, 1) times radial field uFor n field points, divide into n-1 rings of equal area: Copyright 2014 Radiant ZEMAX Copyright 2014 Radiant ZEMAX 2 - 44

49、 Setup uSystemGeneral uEnter aperture and semi-diameter margins: Copyright 2014 Radiant ZEMAX 2 - 45 Fields & Wavelengths Copyright 2014 Radiant ZEMAX Copyright 2014 Radiant ZEMAX 2 - 46 Lens Data Editor uRight-click on radius of surface 4 for F/# solve uAlso use ToolsMiscellaneous.Quick Focus Copyr

50、ight 2014 Radiant ZEMAX Copyright 2014 Radiant ZEMAX 2 - 47 Starting Design uAt least its in focus. Copyright 2014 Radiant ZEMAX Copyright 2014 Radiant ZEMAX 2 - 48 Glass Choice uN-BK7 is a workhorse crown glass uF2 is a workhorse flint uUsing N-BK7 and F2 in a doublet is a good place to start, but

51、we will refine this choice later Copyright 2014 Radiant ZEMAX Copyright 2014 Radiant ZEMAX 2 - 49 Merit Function uAs we will use an aspheric surface later, use 4 rings (r7) to be safe: Copyright 2014 Radiant ZEMAX Copyright 2014 Radiant ZEMAX 2 - 50 Optimize! uHere is the solution after local optimi

52、zation and a quick hammer (MF = 0.0174). What are the dominant aberrations? Copyright 2014 Radiant ZEMAX Copyright 2014 Radiant ZEMAX 2 - 51 Axial Color uAxial color is wavelength-dependent focus. Marginal ray lands at different location as a function of wavelength: Copyright 2014 Radiant ZEMAX Copy

53、right 2014 Radiant ZEMAX 2 - 52 Lateral Color uLateral color is wavelength-dependent magnification. The edge of the lens behaves like a prism with curved faces: Copyright 2014 Radiant ZEMAX Copyright 2014 Radiant ZEMAX 2 - 53 Lateral Color uChief ray lands at a different location as a function of wa

54、velength: Copyright 2014 Radiant ZEMAX Copyright 2014 Radiant ZEMAX 2 - 54 Analysis uImportant points: No specific chromatic targets required Default merit function provides good color correction on-axis Moving stop away from lens introduces lateral color We are hitting maximum thickness boundary uA

55、re we in a local minimum? Check by running Hammer. uNo significant change in merit function, but always run Hammer because you dont know until you try! Copyright 2014 Radiant ZEMAX Copyright 2014 Radiant ZEMAX 2 - 55 How to Improve Design? uAdd an aspheric surface Use conic constant Use even asphere

56、 surface uAdd an air space between the two elements More degrees of freedom uImprove your glass choice Copyright 2014 Radiant ZEMAX Copyright 2014 Radiant ZEMAX 2 - 56 Aspheric Surface uZEMAX has a wide range of aspheric surfaces uLook at the properties of the standard surface, you can find this in

57、the surface types section (Chp. 11) of the ZEMAX manual Copyright 2014 Radiant ZEMAX Copyright 2014 Radiant ZEMAX 2 - 57 Conic Constant uAs we discussed yesterday, k is “conic constant” uStandard surface is conic asphere Spherical surface k = 0 is special case Parabola is k = -1 Ellipse has -1 k 0 u

58、If a is the semi-major axis of ellipse, and b is the semi-minor axis, then Copyright 2014 Radiant ZEMAX Copyright 2014 Radiant ZEMAX 2 - 58 Conic Asphere uMake conic of last surface variable, optimize uMF falls to 0.0136, spots improve Copyright 2014 Radiant ZEMAX Copyright 2014 Radiant ZEMAX 2 - 59

59、 Even Asphere uReset conic to zero, remove variable and re-optimize Or use undo (F3) uMake surface 4 an even asphere surface uMake r4 term variable Dont use r2 as well since we are using the base radius (c) instead of an 1 term. Copyright 2014 Radiant ZEMAX Copyright 2014 Radiant ZEMAX 2 - 60 Even A

60、sphere uAgain, a big improvement uTry adding r6 term, small further improvement uAlways resist the temptation to make everything variable! Start with lowest order terms, and add one by one uAlthough the design improves, it becomes more sensitive Copyright 2014 Radiant ZEMAX Copyright 2014 Radiant ZE