Introduction Past Homework solutions Optimization Test Plate fitting Tolerance routine Homework 1
Optimization Optimization is one of the most important features in Zemax. We use optimization to be able to find a better design than the one we start with. A starting design can be 1. One that we created using Third Aberration Theory. 2. A previous similar design that can be modified, scaled, change Field of View, or change the wavelength range to fit the specifications of the optical system. Zemax uses two main optimization techniques. Local and Global optimization Local optimization finds the best design that can be reached from the starting point as defined in 1 and 2 above. Global optimization searches the whole solution space and finds the best possible design, given sufficient time. 2
Optimization The most common optimization algorithm is Damped Least Squares (DLS) Assume a Merit Function that can be defined as follows: 2 2 X = X + X 2 + 2 1... X n There are n targets and each target can be described by X i =V i -T i Where V is the current value and T is the target The very best Merit Function (MF) is when MF=0 3
Optimization DLS algorithms suffer from two main problems 1. Solutions can be trapped in local minima. These are places in the n dimensional solution space where movement in any direction increases the merit function. Though there may be a better solution somewhere in the solution space the optimization cannot and will not proceed. 2. Stagnation can occur when the targets are not defined correctly and therefore the algorithm cannot find a direction to move and find a solution. Default Merit Functions There are about a little over 20 different default merit functions that can be defined in Zemax. These include RMS or Peak-to-Valley Wavefront, spot Radius, spot X, spot Y, and many more Reference to Centroid or Chief Ray You can have any combination of the above What is important for this course are RMS spot Size and RMS Wavefront Error 4
Operands Operands are individual targets with a unique number assigned in the order/line they are defined in the Merit function Editor Examples could be EFFL SPHA TTHI CONS - Effective Focal Length - 3 rd Order Spherical Aberration - Total Thickness from S x to S y - Constant numerical value There is a huge number of operands and you can also create your own by manipulating algebraically any number of them. Boundary operands Thickness of surface 5 is < 5mm and > 0 CTGT 5 > 0 CTLT 5 < 5 5
Operands - Example 6
Optimization Degrees of freedom is the number of independent variables For example Radii, thicknesses, Air Spaces, Glass Do not over constraint the problem. Number of constraints should be equal or less to independent variables. Determine what are the goals of the design Lenses must be inexpensive to manufacture Edge and center thickness have to POSITIVE! Use the smallest number of elements in the system Use material that do not stain and are easy to polish 7
Optimization Optimization Tips Use area balanced field points Use Solves wherever you can Exploit symmetry wherever you can Allow for defocus Allow for glass substitution For starting points either Use aberration theory to create starting points, or Use prior art from Patents Use default merit functions for RMS Spot or RMS WFE. From my experience they work 99.99% of the time without having to do anything else. 8
Example of a Cemented Doublet An Achromatic cemented doublet has the following degrees of Freedom Three Radii Three spacings 2 Refractive indices, 2 Dispersions Stop Location Total of 11 Degrees of Freedom. Specifications Use F,d,C Visible EPD of 50 mm F/8 10 degrees Full FOV Min edge/center thickness 5 mm, Max Center thickness of 20 mm Allow for change of glasses 9
Optimization Define the number of surfaces in the lens editor Define 3 Field points Define the system aperture Pick up a Crown and a Flint glass such as BK7, F2 (Common choice for Doublet) Build Merit Function using RMS spot size Add constraints for air spaces and glasses Variables 2 radii 4 thicknesses Optimize 10
Optimization One can change glasses and try different combinations such as : N-BK7 & F2 or N-BK7 & SF2 or N-BK7 & SF5 or Any other combination as you become more proficient in optical design. If lenses tend to get too thick or too thin you need to constrain them in the merit function. 11
Tolerancing Test Plate Fitting Test plate fitting is a Zemax utility to redesign a lens to fit vendors tooling Primary reason is to reduce fabrication cost and delivery time, as each test plate has to be manufactured as a pair and that involves cost and time. 12
Test Plate fitting routine 13
Test Plate fitting results 14
Tolerancing Error Sources Errors in Fabrication Incorrect Radius of Curvature Incorrect Thickness of lenses (On the high side of tolerance) Incorrect shape Irregularity Incorrect edging (optical center not coincident with mechanical center) Error in Materials Index accuracy Index homogeneity Abbe number 15
Tolerancing Error Sources Errors in Assembly Decenter of Elements Tilt of Elements Error in air spaces All or some of the above errors can happen in a single element or group or elements Errors due to environment Mechanical errors due to thermal effects Optical errors due to change of refractive index of materials Atmospheric pressure and humidity Space optics Residual Design Errors - Margin 16
Tolerance limits Quality Level Wavefront Thickness Radius Index V-number Homog Decenter Tilt Spherical Irregularity Residual (mm) (%) (%) mm arc sec # Fringes # Fringes Commercial 0.25 RMS 0.1 1 0.001 1 0.0001 0.1 60 2 1 2 P-V Precision 0.1 RMS 0.01 0.1 0.0001 0.1 0.00001 0.01 10 1 0.25 0.5 P-V High Precision <0.07 RMS 0.001 0.01 0.00001 0.01 0.000002 0.001 1 0.25 <0.1 0.25 P-V From Professor's Shannon s Book The Art and Science of Optical Design 17
Error Budget Required Performance RMS,MTF, WFE, Encircled Energy, etc Design Fabrication Assembly Environment Margin An error budget should account for all possible errors that would contribute to the performance degradation in the optical system First step is to select the appropriate performance specification such as RMS, MTF, WFE, Encircled Energy, etc. Calculate all the possible errors and their contributions to the system using the RSS method. 18
Real Budgeting Example Total RMS Spot Radius 13.381 microns (80% EE=2.3 arcsec) Margin 5.499 microns Fabrication/Alignment 8.267 microns Ground to Orbit 6.907 microns Nominal Design 5.723 microns Fabrication Alignment Alignment Radius/Figure M1 Radius 0.5 mm M2 Radius 0.5 mm Primary Tilt 10 arcsec M1 Tilt 8 arcsec M1 Radius 15 microns M1 Spherical 0.0791 microns (1/8 Wave P-V Surface error) M2 Spherical 0.06328 microns (0.1 Wave P-V Surface error) Primary Decenter 50 microns M1 Decenter 5 microns M2 Radius 20 microns M1 Conic Constant 0.5% of K=-1.204627 (Residual on Conic Constant) M2 Conic Constant 0.5% of K=-5.951308 (Residual on Conic Constant) Secondary Despace 0.25 mm M2 Despace 10 microns TA to TSP Decenter 0.005 mm M1 Astigmatism 0.1582 microns (1/4 Wave P-V Surface error) M2 Astigmatism 0.06328 microns (0.1 Wave P-V Surface error) Secondary Tilt 40 arcsec M2 Tilt 8 arcsec TA to TSP Tilt 8 arc seconds Mgf2 Det Window CT +/-0.100 mm Aspheric Radius +/-8000 mm Secondary Decenter 50 microns M2 Decenter 5 microns BFA to TSP Decenter 0.05 mm MgF2 Det Window Radius S1 +/- 10 mm Aspheric Coeff R4-5.0E-11/9.0E-11 Imaging Window Decenter 0.5 mm Imaging Window Decenter 0.75 mm BFA to TSP tilt 8 arc seconds Mgf2 Det Window Fringes S2 +/- 1.0 Fringe (HeNe) Aspheric Coeff R6-1.75E-14/4.0E-14 Imaging Window Tilt 12 Arcmin Imaging Window Tilt 12 Arcmin TIR (Wedge) Det Window Mgf2 0.050 mm Aspheric Coeff R8-8.0E-18/1.70E017 Detector Window Dec 0.5 mm Filter Dec 1.0 mm Refractive Index Var MgF2 0.0001 Imaging window S1 Radius +/- 500 mm Detector Window Tilt 12 arcmin Filter Tilt 30 arc minutes Mgf2 Filter S1 +/- 1 Fringe (HeNe) Imaging window S2 +/-5 fringes(hene) Aspheric Tilt 1 arcmin Aspheric Tilt 30 arcsec Mgf2 Filter S2 +/- 1 Fringe (HeNe) Imaging window CT 0.200 mm See spec for part Aspheric Decenter 0.2 mm Aspheric Decenter 50 microns Mgf2 Filter CT +/- 0.100 mm Refractive Index Var Caf2 0.0001 TA Decenter 0.5 mm TSP to Imaging window 10 microns TIR (Wedge) Filter Mgf2 0.050 mm TIR (wedge) Imaging window 0.006 mm TA Tilt 5 arcminutes Imaging Win to Aspheric 20 microns Despace Caf2 to Asp 0.25 mm 19
Tolerancing the doublet 20
Use the Following values 21
Tolerance data editor 22
Optimization Browse through the Tolerance Editor and alter what you think is necessary. For example The default test wavelength is 632.8 nm You may change it 550 nm You may want to change the tolerance on the thicknesses on certain lenses, if the manufacturer can do better in that one thickness You may want to add more compensators. You may want to add group tilts and/or decenters 23
Tolerancing Procedure 24
Monte Carlo Analysis The Monte Carlo procedure generates lenses picking up random tolerance values within the range specified in the tolerance table. Each parameter is perturbed randomly within the appropriate statistical distribution Normal (Gaussian) Uniform Parabolic User Defined 25
Output - I 26
Output -II 27
Output - III 28
Summary Get performance criteria from customer for the as build system Criteria could be Spot Radius, WFE, MTF, Boresight, etc. Design Optical system with better performance given Consult manufacturers for their capabilities, and choose fab house for capabilities, delivery, and price. Tolerance Optical System and allow for all possible errors, and choose carefully your compensators Decouple errors by RSS method & allow for margin If RSS errors exceed specs then either tighten tolerances, i.e change fab house or start from scratch the redesign process. If RSS errors meet specs then you are ALMOST done. Talk with the various disciplines (mechanical, thermal, stray light, the person who will do the assembly & alignment) and get them to agree on the tolerances you have derived. If not, negotiate the tolerances and run the tolerance routine again When all engineers have agreed in writing then you are done! 29
Practice Example Optimize, test plate fit to any manufacturer in Zemax and Tolerance the following singlet lens EFL 75 mm F/# 7.5 WL 550 nm FOV 0 deg Glass N-BK7 Tolerance of a single lens What could possibly go wrong? 2 errors in radii 1 error in glass thickness 2 errors in surface irregularities 2 errors in decenter and tilt 1 error in wedge 1 error in index Use default values in tolerance editor. Use RMS Spot size as the criteria and compare performance before and after tolerance 30