Advanced Lens Design

Transcription

1 Advanced Lens Design Lecture 3: Optimization II Herbert Gross Winter term

2 2 Preliminary Schedule Introduction Paraxial optics, ideal lenses, optical systems, raytrace, Zemax handling Optimization I Basic principles, paraxial layout, thin lenses, transition to thick lenses, scaling, Delano diagram, bending Optimization II merit function requirements, effectiveness of variables Optimization III complex formulations, solves, hard and soft constraints Structural modifications zero operands, lens splitting, aspherization, cementing, lens addition, lens removal Aberrations and performance Geometrical aberrations, wave aberrations, PSF, OTF, sine condition, aplanatism, isoplanatism Aspheres and freeforms spherical correction with aspheres, Forbes approach, distortion correction, freeform surfaces, optimal location of aspheres, several aspheres Field flattening thick meniscus, plus-minus pairs, field lenses Chromatical correction Achromatization, apochromatic correction, dialyt, Schupman principle, axial versus transversal, glass selection rules, burried surfaces Special topics symmetry, sensitivity, anamorphotic lenses Higher order aberrations high NA systems, broken achromates, Merte surfaces, AC meniscus lenses Advanced optimization local optimization, control of iteration, global approaches, strategies growing requirements, AC-approach of Shafer Mirror systems special aspects, bending of ray paths, catadioptric systems Diffractive elements color correction, straylight suppression, third order aberrations Tolerancing and adjustment tolerances, procedure, adjustment, compensators

3 3 Contents 1. Merit function in optical design 2. Effectiveness of variables 3. Optimization in Zemax

4 4 Optimization Merit Function in Optical Design Goal of optimization: Find the system layout which meets the required performance targets according of the specification Formulation of performance criteria must be done for: - Apertur rays - Field points - Wavelengths - Optional several zoom or scan positions Selection of performance criteria depends on the application: - Ray aberrations - Spot diameter - Wavefornt description by Zernike coefficients, rms value - Strehl ratio, Point spread function - Contrast values for selected spatial frequencies - Uniformity of illumination Usual scenario: Number of requirements and targets quite larger than degrees od freedom, Therefore only solution with compromize possible

5 5 Parameter of Optical Systems Characterization and description of the system delivers free variable parameters of the system: - Radii - Thickness of lenses, air distances - Tilt and decenter - Free diameter of components - Material parameter, refractive indices and dispersion - Aspherical coefficients - Parameter of diffractive components - Coefficients of gradient media General experience: - Radii as parameter very effective - Benefit of thickness and distances only weak - Material parameter can only be changes discrete

6 6 Optimization in Optics Typical in optics: Twisted valleys in the topology Selection of local minima LM 1 LM 2 LM 5 LM 4 LM 3

7 7 Optimization Landscape of an Achromate Typical merit function of an achromate Three solutions, only two are useful r 2 aperture reduced r 1 good solution

8 Optimierung nominal w=10 w=10000 w= Merit function of an achromate weight w of chromatic aberration M=1 M=6 M=9 conjugation parameter M BK7 / SF5 LLF1 / SF5 FK54 / SF5 crown glass choice BK7 / SF5 BK7 / SF58 BK7/ / SK4 flint glass choice

9 9 Optimization of Achromatic Glasses Perfect aplanatic line of corresponding glasses For one given flint a line indicates the usefull crown glasses and vice versa n n fixed flint glass line of minimal spherical aberration line of minimal spherical aberration fixed crown glass

10 Optimization: Achromate Bending of an achromate : spherical aberration 3 Parameters : n, X, M A s 1 32n( n 1) f 3 3 n n 1 1 X n n 1 n n 1 2 n 2 M n 2 M 2 Merit function relief n A s min > 0 n A s = 0 n A s = M = n 3 X M = n 3 X M = n 3 X M = X M = X M = X

11 Effectiveness of Variables Effectiveness of variables Change of variables x cause a change in the error a J x The change vector a causes a component, which directly influences the error f The direction is given by f 2 f a cos error f 2 f Since the orthogonal components must be compensated too, also non-effective components help effective parallel component a change vector of error due to one variable f 1 a perpendicular non-effective component

12 12 Effectiveness of Variables Single lens Effect of radius and thickness change on spherical aberration Nearly no effect of thickness

13 13 Quick Focus Option In the menue TOOLS DESIGN QUICK FOCUS we have the opportunity to adjust the image location according to the criteria 1. Spot diameter 2. Wavefront rms 3. Angle radius IN principle, this option is a simplified optimization Example: find the best image plane of a single lens Spot before and after performing the optimal focussing

14 14 Quick Adjust Option In the menue TOOLS DESIGN QUICK ADJUST we have the opportunity to adjust 1. one thickness 2. one radius similar to the quick focus function some where in the system. But: the effect is iterative, in case of nonlinearities, some calls are necessary Special application: adjust the air distance before a collimation lens to get the best collimation As criteria, wavefroint, spot diameter of angular radius ar possible Example: Move a lens in between a system to focus the image Spots before and after thew adjustment

15 Merit Function in Zemax Default merit function 1. Criterion 2. Ray sampling (high NA, aspheres,...) 3. Boundary values on thickness of center and edge for glass / air 4. Special options Add individual operands Editor: settings, weight, target actual value relative contribution to sum of squares Several wavelengths, field points, aperture points, configurations: many requirements Sorted result: merit function listing 15

16 Merit function in Zemax If the number of field points, wavelengths or configurations is changed: the merit function must be updated explicitly Help function in Zemax: many operands 16

17 Merit Function in Zemax Classical definition of the merit function in Zemax: Special merit function options: individual operands can be composed: - sum, diff, prod, divi,... of lines, which have a zero weight itself - mathematical functions sin, sqrt, max... - less than, larger than (one-sided intervals as targets) Negative weights: requirement is considered as a Lagrange multiplier and is fulfilled exact Optimization operands with derivatives: building a system insensitive for small changes (wide tolerances) Further possibilities for user-defined operands: construction with macro language (ZPLM) General outline: - use sinple operands in a rough optimization phase - use more complex, application-related operands in the final fine-tuning phase 17

18 Variables in Zemax Defining variables: indicated by V in lens data editor toggle: CNTR z or right mouse click Auxiliary command: remove all variables, all radii variable, all distances variable If the initial value of a variable is quite bad and a ray failure occurs, the optimization can not run and the merit function not be computed 18

19 Variable Glass in Zemax Modell glass: characterized by index, Abbe number and relative dispersion Individual choice of variables Glass moves in Glass map Restriction of useful area in glass map is desirable (RGLA = regular glass area) Re-substitution of real glass: next neighbor in n-n-diagram Choice of allowed glass catalogs can be controlled in General-menu Other possibility to reset real glasses: direct substitution 19

20 Optimization Methods Available in Zemax General optimization methods - local - global Easy-one-dimensional optimizations - focus - adjustment - slider, for visual control Special aspects: - solves - aspheres - glass substitutes 20

21 Methods Available in Zemax Classical local derivative: - DLS optimization (Marquardt) - orthogonal descent Hammer: - Algorithm not known - Useful after convergence - needs long time - must be explicitely stopped Global: - global search, followed by local optimization - Save of best systems - must be explicitely stopped 21

22 Conventional DLS-Optimization in Zemax Optimization window: Choice of number of steps / cycles Automatic update of all windows possible for every cycle (run time slows down) After run: change of merit function is seen Changes only in higher decimals: stagnation Window must be closed (exit) explictly 22

23 Merit Function in Zemax Default merit function 1. Criterion 2. Ray sampling (high NA, aspheres,...) 3. Boundary values on thickness of center and edge for glass / air 4. Special options Add individual operands Editor: settings, weight, target actual value relative contribution to sum of squares Several wavelengths, field points, aperture points, configurations: many requirements Sorted result: merit function listing 23

24 Merit function in Zemax If the number of field points, wavelengths or configurations is changed: the merit function must be updated explicitly Help function in Zemax: many operands 24

25 Merit Function in Zemax Classical definition of the merit function in Zemax: Special merit function options: individual operands can be composed: - sum, diff, prod, divi,... of lines, which have a zero weight itself - mathematical functions sin, sqrt, max... - less than, larger than (one-sided intervals as targets) Negative weights: requirement is considered as a Lagrange multiplier and is fulfilled exact Optimization operands with derivatives: building a system insensitive for small changes (wide tolerances) Further possibilities for user-defined operands: construction with macro language (ZPLM) General outline: - use sinple operands in a rough optimization phase - use more complex, application-related operands in the final fine-tuning phase 25

26 Variables in Zemax Defining variables: indicated by V in lens data editor toggle: CNTR z or right mouse click Auxiliary command: remove all variables, all radii variable, all distances variable If the initial value of a variable is quite bad and a ray failure occurs, the optimization can not run and the merit function not be computed 26

27 Variable Glass in Zemax Modell glass: characterized by index, Abbe number and relative dispersion Individual choice of variables Glass moves in Glass map Restriction of useful area in glass map is desirable (RGLA = regular glass area) Re-substitution of real glass: next neighbor in n-n-diagram Choice of allowed glass catalogs can be controlled in General-menu Other possibility to reset real glasses: direct substitution 27

28 Optimization Methods Available in Zemax General optimization methods - local - global Easy-one-dimensional optimizations - focus - adjustment - slider, for visual control Special aspects: - solves - aspheres - glass substitutes 28

29 Methods Available in Zemax Classical local derivative: - DLS optimization (Marquardt) - orthogonal descent Hammer: - Algorithm not known - Useful after convergence - needs long time - must be explicitely stopped Global: - global search, followed by local optimization - Save of best systems - must be explicitely stopped 29

30 Conventional DLS-Optimization in Zemax Optimization window: Choice of number of steps / cycles Automatic update of all windows possible for every cycle (run time slows down) After run: change of merit function is seen Changes only in higher decimals: stagnation Window must be closed (exit) explictly 30