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Introduction• Past Homework solutions

• Optimization

• Test Plate fitting

• Tolerance routine

• Homework

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OptimizationOptimization 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.

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OptimizationThe most common optimization algorithm is Damped Least Squares (DLS)

Assume a “Merit Function” that can be defined as follows:

There are n targets and each target can be described by

Xi=Vi-Ti

Where V is the current value and T is the target

The very best Merit Function (MF) is when MF=0

222

21 ... nXXXX ++=

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OptimizationDLS 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

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OperandsOperands are individual targets with a unique number assigned in the order/line they are defined in the Merit function Editor

Examples could be

EFFL - Effective Focal Length

SPHA - 3rd Order Spherical Aberration

TTHI - Total Thickness from Sx to Sy

CONS - 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

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Operands - Example

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OptimizationDegrees 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

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OptimizationOptimization 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.

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Example of a Cemented DoubletAn 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

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OptimizationDefine 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

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OptimizationOne 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.

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TolerancingTest 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.

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Test Plate fitting routine

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Test Plate fitting results

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TolerancingError 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

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TolerancingError 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

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Tolerance limits

Quality Level Wavefront Thickness Radius Index V-number Homog Decenter Tilt Spherical IrregularityResidual (mm) (%) (%) mm arc sec # Fringes # Fringes

Commercial 0.25 RMS 0.1 1 0.001 1 0.0001 0.1 60 2 12 P-V

Precision 0.1 RMS 0.01 0.1 0.0001 0.1 0.00001 0.01 10 1 0.250.5 P-V

High Precision <0.07 RMS 0.001 0.01 0.00001 0.01 0.000002 0.001 1 0.25 <0.10.25 P-V

From Professor's Shannon’s BookThe Art and Science of Optical Design

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Error BudgetRequired 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.

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Real Budgeting Example

M1 Radius0.5 mm

M2 Radius0.5 mm

M1 Spherical0.0791 microns

(1/8 Wave P-V Surface error)

M2 Spherical0.06328 microns

(0.1 Wave P-V Surface error)

M1 Conic Constant0.5% of K=-1.204627

(Residual on Conic Constant)

M2 Conic Constant0.5% of K=-5.951308

(Residual on Conic Constant)

M1 Astigmatism0.1582 microns

(1/4 Wave P-V Surface error)

M2 Astigmatism0.06328 microns

(0.1 Wave P-V Surface error)

Mgf2 Det Window CT+/-0.100 mm

Aspheric Radius+/-8000 mm

MgF2 Det Window Radius S1+/- 10 mm

Aspheric Coeff R4-5.0E-11/9.0E-11

Mgf2 Det Window Fringes S2+/- 1.0 Fringe (HeNe)

Aspheric Coeff R6-1.75E-14/4.0E-14

TIR (Wedge) Det Window Mgf2 0.050 mm

Aspheric Coeff R8-8.0E-18/1.70E017

Refractive Index Var MgF20.0001

Imaging window S1 Radius+/- 500 mm

Mgf2 Filter S1+/- 1 Fringe (HeNe)

Imaging window S2+/-5 fringes(HeNe)

Mgf2 Filter S2+/- 1 Fringe (HeNe)

Imaging window CT0.200 mm

See spec for part

Mgf2 Filter CT+/- 0.100 mm

Refractive Index Var Caf20.0001

TIR (Wedge) Filter Mgf20.050 mm

TIR (wedge) Imaging window0.006 mm

Fabrication

Primary Tilt10 arcsec

Primary Decenter50 microns

Secondary Despace0.25 mm

Secondary Tilt40 arcsec

Secondary Decenter50 microns

Imaging Window Decenter0.5 mm

Imaging Window Tilt12 Arcmin

Detector Window Dec0.5 mm

Detector Window Tilt12 arcmin

Aspheric Tilt1 arcmin

Aspheric Decenter0.2 mm

TA Decenter0.5 mm

TA Tilt5 arcminutes

Despace Caf2 to Asp0.25 mm

Alignment

Fabrication/Alignment8.267 microns

M1 Tilt8 arcsec

M1 Decenter5 microns

M2 Despace10 microns

M2 Tilt8 arcsec

M2 Decenter5 microns

Imaging Window Decenter0.75 mm

Imaging Window Tilt12 Arcmin

Filter Dec1.0 mm

Filter Tilt30 arc minutes

Aspheric Tilt30 arcsec

Aspheric Decenter50 microns

TSP to Imaging window10 microns

Imaging Win to Aspheric20 microns

Alignment

M1 Radius15 microns

M2 Radius20 microns

TA to TSP Decenter0.005 mm

TA to TSP Tilt8 arc seconds

BFA to TSP Decenter0.05 mm

BFA to TSP tilt8 arc seconds

Radius/Figure

Ground to Orbit6.907 microns

Nominal Design5.723 microns

Total RMS Spot Radius13.381 microns

(80% EE=2.3 arcsec)

Margin5.499 microns

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Tolerancing the doublet

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Use the Following values

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Tolerance data editor

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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

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Tolerancing Procedure

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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

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Output - I

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Output -II

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Output - III

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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!

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Practice ExampleOptimize, 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