Optimisation. Lecture 3

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Willis Ethan Fowler
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1 Optimisation Lecture 3

2 Objectives: Lecture 3 At the end of this lecture you should: 1. Understand the use of Petzval curvature to balance lens components 2. Know how different aberrations depend on field angle or pupil zone 3. Understand the basics of the Zemax merit function and the Zemax operands 4. Be able to progressively optimise a complex lens system to achieve the final performance requirements March 10, 2015 Optical Systems Design 2

3 Petzval Surface & Petzval Curvature Theoretical best image surface which exhibits no astigmatism φ Petzval sum P = n2 n1 where φ = n is the 1 n 2 r optical power of each surface For simple lenses P = n where φ is the power of each lens (reciprocal of focal length) and n is the refractive index Minimizing Petzval curvature produces a flat, anastigmatic image plane φ March 10, 2015 Optical Systems Design 3

4 Aberration Dependance on Aperture and Field Aperture Exponent Field Exponent Longitudinal colour 1 0 Lateral colour 0 1 Spherical aberration 3 0 Coma 2 1 Astigmatism 1 2 Field curvature 1 2 Distortion 0 3 Stopping down a lens can make a big difference on spherical aberration Stopping down a lens won t improve the distortion For wide-angle lenses, astigmatism is harder to control than coma Symmetrical systems (about stop) minimise lateral colour, coma & distortion March 10, 2015 Optical Systems Design 4

5 Optimisation Process Enter a starting lens configuration Allow Zemax to change lens parameters to improve performance Requires a measure of performance merit function (error function) Optimisation tries to minimise merit function (gradient search or Hammer) March 10, 2015 Optical Systems Design 5

6 Constituents of Merit Function Measures of: 1. How well first-order properties are satisfied (e.g. paraxial focus, locations of pupils and images) 2. How well special constraints are satisfied (e.g. element centre or edge thickness, curvatures, glass properties) 3. How well aberrations are controlled (e.g. image sharpness and distortion) March 10, 2015 Optical Systems Design 6

7 Image Sharpness metrics 1. Spot size measured by ray-intercept errors in image plane 2. Wavefront imperfections measured by optical path difference (OPD) errors in the exit pupil 3. Modulation transfer function (MTF) in the image plane (Start with [1], moving to [2] or [3] only in final optimisation stages) March 10, 2015 Optical Systems Design 7

8 Optimization Operands Individual components of the merit function which are assigned a target value and weights Number of operands often greatly exceeds the number of independent lens variables Apply iterative least squares optimisation to minimise the (weighted) deviations between operands and their target values March 10, 2015 Optical Systems Design 8

9 Zemax Operands March 10, 2015 Optical Systems Design 9

10 Zemax Operands Zemax has over 300 user-selectable operands (see OpticStudio manual, p. 259) Mostly used to supplement a default merit function (now called Sequential Merit Function) Weights = 0 ignored, weights < 0 treated as a Lagrangian multiplier ( weight) OptimizationWizard adds the default merit function Can also have user-defined operands (ZPL) Spherical Coma Astigmatism Field Curvature Distortion Long. Colour Lateral Colour SPHA, REAY COMA, TRAY ASTI, TRAX,TRAY FCUR DIMX, DIST AXCL LACL March 10, 2015 Optical Systems Design 10

11 Optimisation Techniques Choose starting design carefully (e.g. scale from existing lens catalogue) Develop optimisation approach that is systematic & rationale Sheperd design in direction intended Do continuous sanity checks Discard poor solutions as they arise March 10, 2015 Optical Systems Design 11

12 Optimisation Wizard March 10, 2015 Optical Systems Design 12

13 Early Optimisations Reduce number of independent variables Freeze glass types and use pickup solves to symmetrise configurations Replace large RoC surfaces with planes Include first order (paraxial) properties and boundary conditions (e.g. back focal length) in merit function March 10, 2015 Optical Systems Design 13

14 Intermediate Optimisations Start to control on-axis and off-axis aberrations Chromatic aberrations using only two extreme wavelengths Monochromatic aberrations using single central wavelength Typically: longitudinal & lateral colour, spherical & distortion Keep image plane at paraxial focus March 10, 2015 Optical Systems Design 14

15 Final Optimisations Shrink polychromatic spots for all field angles Use several wavelengths across the band Re-optimise using wavefront OPDs in exit pupil rather than transverse ray errors (spots) on image surface Allow small amount of paraxial defocussing Include any deliberate mechanical vignetting Take a critical look at the final lens & its performance March 10, 2015 Optical Systems Design 15

16 Potential Problem Areas Avoid systems which attempt to balance lenses with large amounts of positive and negative power Avoid highly curved surfaces and grazing rays Look out for designs which have individual elements which stand out as either very strong (split) or very weak (eliminate) Watch for variables that are only weakly effective Avoid aspherics unless really necessary Avoid glasses with undesirable properties (e.g. low transmission, softness) March 10, 2015 Optical Systems Design 16

17 Example: Cooke Triplet (1983) One of 1st fast, wide-field photographic lenses. Consists of two positive singlets and one negative singlet (all thin lenses) Negative element located about halfway between positive elements to maintain a large amount of symmetry 8 major variables (6 radii, 2 spacings). 10/03/2015 Optical Systems Design 17

18 Early Optimisation 10/03/2015 Optical Systems Design 18

19 Intermediate Optimisation 10/03/2015 Optical Systems Design 19

20 Final Optimisation 10/03/2015 Optical Systems Design 20

21 Balancing Aberrations Analyse > Aberrations > Seidel Diagram 10/03/2015 Optical Systems Design 21

22 Summary: Lecture 3 Minimising the Petzval sum can give a good starting point for lens optimisation Proper use of the Zemax optimisation tools is the key to successful lens design Optmisation using spot size (ray intercept errors) is more stable than OPD errors and should normally be used first Whilst the Zemax default merit function gives a good starting point, in many cases it will need supplementing with individual user-selected operands to achieve the desired constraints March 10, 2015 Optical Systems Design 22

23 Exercises: Lecture 3 Repeat the analysis of a Cooke triplet to work at F/3.5 which has a 52mm focal length, starting from COOKE-LECT3-EARLY.ZMX on course www page (Lecture 3). Assume wavelengths of 0.45,0.50,0.55,0.60 & 0.65 µm and field angles of 0 o,9 o,16 o & 22 o Place the aperture stop between the 2 nd and 3 rd lenses and use LaFN21 & SF53 for the glass types Optimize the performance on the paraxial focal plane, so that the lens still performs well when stopped down March 10, 2015 Optical Systems Design 23

Sequential Ray Tracing. Lecture 2

Sequential Ray Tracing. Lecture 2 Sequential Ray Tracing Lecture 2 Sequential Ray Tracing Rays are traced through a pre-defined sequence of surfaces while travelling from the object surface to the image surface. Rays hit each surface once