Medical Photonics Lecture Optical Engineering

Lecture 11: Optical Design 2017-01-12 Herbert Gross

Winter term 2016 www.iap.uni-jena.de

2 Contents

No Subject Ref Date Detailed Content Materials, dispersion, ray picture, geometrical approach, paraxial 1 Introduction Gross 20.10. approximation Ray tracing, matrix approach, aberrations, imaging, Lagrange 2 Geometrical optics Gross 03.11. invariant 3 Components Kempe 10.11. Lenses, micro-optics, mirrors, prisms, gratings Field, aperture, pupil, magnification, infinity cases, lens makers 4 Optical systems Gross 17.11. formula, etendue, vignetting 5 Aberrations Gross 24.11. Introduction, primary aberrations, miscellaneous Basic phenomena, wave optics, interference, diffraction 6 Diffraction Gross 01.12. calculation, point spread function, transfer function 7 Image quality Gross 08.12. Spot, ray aberration curves, PSF and MTF, criteria

Human eye, loupe, eyepieces, photographic lenses, zoom lenses, 8 Instruments I Kempe 15.12. telescopes Microscopic systems, micro objectives, illumination, scanning 9 Instruments II Kempe 22.12. microscopes, contrasts Medical optical systems, endoscopes, ophthalmic devices, 10 Instruments III Kempe 05.01. surgical microscopes Aberration correction, system layouts, optimization, realization 11 Optic design Gross 12.01. aspects Notations, fundamental laws, Lambert source, radiative transfer, 12 Photometry Gross 19.01. photometry of optical systems, color theory Light sources, basic systems, quality criteria, nonsequential 13 Illumination systems Gross 26.01. raytrace 14 Metrology Gross 02.02. Measurement of basic parameters, quality measurements 3 Modelling of Optical Systems

. Principal purpose of calculations: . Imaging model with levels of refinement

Paraxial model System, data of the structure (focal length, magnification, aperture,..) (radii, distances, indices,...) linear approximation Analysis imaging aberration Synthesis Analytical approximation and classification theorie lens design (aberrations,..)

Taylor Function, data of properties, expansion quality performance (spot diameter, MTF, Strehl ratio,...) Geometrical optics (transverse aberrations, wave aberration, distortion,...)

with approximation diffraction  --> 0

Wave optics (point spread function, OTF,...)

Ref: W. Richter

Classification in Field and Aperture Size

. Overview and sorting Log w

100° . Different types of systems Fisheye . Diagram of W. Smith: objective Retrofocus aperture vs field size 50° objective

. Spectral properties not concidered Tessar 20° Double- landscape Gauss objective Cooke-triplet objective 10° Petzval- objective Schmidt- 5.0° Cassegrain telescope Schmidt 3-mirror telescope telescope 2.0°

Ritchey-Cretien telescope Microscope 1.0° Cassegrain objective telescope

0.5° Paraboloid Diskobjective Achromate telescope

0.2°

0.02 0.05 0.10 0.20 0.50 1.0 Log NA

Field-Aperture-Diagram

w . Classification of systems with photographic Biogon field and aperture size 40° lithography Braat 1987 . Scheme is related to size, 36° correction goals and etendue 32° of the systems Triplet 28° Distagon . Aperture dominated: 24° Disk lenses, microscopy, Sonnar Collimator 20°

projection 16° . Field dominated: split double triplet Gauss lithography Projection lenses, 12° 2003 camera lenses, projection projection constant Gauss Petzval etendue 8° Photographic lenses micro micro micro micros- 100x0.9 10x0.4 40x0.6 copy 4° . Spectral widthz as a correction achromat diode collimator disc collimator focussing requirement is missed in this chart 0° 0 0.2 0.4 0.6 0.8 NA

Classification: -Lw-Diagram

 . Throughput as field- Photography aperture product Microscopy

. Additional dimension: spectral bandwidth

Astronomy

Interferometer metrology lens lens Lithography

Surface Contributions: Example

200

SI 0 . Seidel aberrations: Spherical Aberration representation as sum of -200 1000 surface contributions possible SII . Gives information on correction 0 Coma

of a system -1000 . Example: photographic lens 2000 SIII 0 Astigmatism

-2000 1000 SIV 0 Retrofocus F/2.8 Petzval field curvature Field: w=37° -1000 6000

SV 0 Distortion

-6000

5 10 150 3 4 2 CI 1 6 7 8 9 0 Axial color -100 600

CII 0 Lateral color -400 Surface 1 2 3 4 5 6 7 8 9 10 Sum 8 Basic Idea of Optimization

. Topology of the merit function in 2 dimensions . Iterative down climbing in the topology

start topology of meritfunction F

iteration path

x2 9 Nonlinear Optimization

Mathematical description of the problem:  . n variable parameters x   . m target values f (x)

. Jacobi system matrix of derivatives,  fi Influence of a parameter change on the Ji j  various target values,  x j sensitivity function m   2 . Scalar merit function F(x)  wi yi  f (x) i1  F . Gradient vector of topology g j   x j

 2 F . Hesse matrix of 2nd derivatives H  jk  x j x k 10 Boundary Conditions and Constraints

. Types of constraints 1. Equation, rigid coupling, pick up 2. One-sided limitation, inequality 3. Double-sided limitation, interval . Numerical realizations : 1. Lagrange multiplier 2. Penalty function 3. Barriere function 4. Regular variable, soft-constraint F(x) F(x)

p large penalty p large barrier function function P(x) B(x)

p small F (x) F0(x) p 0 small

x x permitted domain permitted domain xmin xmax 11 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 12 Optimization in Optical Design

. Merit function: 2 Weighted sum of deviations from target values ist soll    g j  f j  f j  j1,m . Formulation of target values: 1. fixed numbers 2. one-sided interval (e.g. maximum value) 3. interval

. Problems: 1. linear dependence of variables 2. internal contradiction of requirements 3. initail value far off from final solution

. Types of constraints: 1. exact condition (hard requirements) 2. soft constraints: weighted target

. Finding initial system setup: 1. modification of similar known solution 2. Literature and patents 3. Intuition and experience 13 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

14 Constraints in Optical Systems

Constraints in the optimization of optical systems:

1. Discrete standardized radii (tools, metrology) 2. Total track 3. Discrete choice of glasses 4. Edge thickness of lenses (handling) 5. Center thickness of lenses(stability) 6. Coupling of distances (zoom systems, forced symmetry,...) 7. Focal length, magnification, workling distance 8. Image location, pupil location 9. Avoiding ghost images (no concentric surfaces) 10. Use of given components (vendor catalog, availability, costs)

15 Lack of Constraints in Optimization

negative edge negative air thickness distance Illustration of not usefull results due to non-sufficient constraints

lens stability air space lens thickness to large to small to small 16 Optimization Landscape of an Achromate

. Typical merit function of an achromate . Three solutions, only two are useful

r2

aperture 2 reduced

good solution

r1 17

System Design Phases

1. Paraxial layout: - specification data, magnification, aperture, pupil position, image location - distribution of refractive powers - locations of components - system size diameter / length - mechanical constraints - choice of materials for correcting color and field curvature

2. Correction/consideration of Seidel primary aberrations of 3rd order for ideal thin lenses, fixation of number of lenses

3. Insertion of finite thickness of components with remaining ray directions

4. Check of higher order aberrations

5. Final correction, fine tuning of compromise

6. Tolerancing, manufactability, cost, sensitivity, adjustment concepts

Number of Lenses

. Approximate number of spots Number of spots monochromatic aspherical 12000 over the field as a function of monochromatic the number of lenses 10000 Linear for small number of lenses. polychromatic Depends on mono-/polychromatic 8000

design and aspherics. 6000

4000

2000

Number of 0 0 2 4 6 8 elements . Diffraction limited systems with different field size and diameter of field [mm] lenses aperture 8 10 12 14 6 8 2 4 6

2 numerical 0 aperture 0 0.2 0.4 0.6 0.8 1

Optimization: Starting Point

. Existing solution modified . Literature and patent collections . Principal layout with ideal lenses successive insertion of thin lenses and equivalent thick lenses with correction control

object pupil intermediate image image

f f f f f 1 2 3 4 5

. Approach of Shafer AC-surfaces, monochromatic, buried surfaces, aspherics . Expert system . Experience and genius 20

Optimization and Starting Point

. The initial starting point p determines the final result 2

. Only the next located solution

without hill-climbing is found D'

C' A'

A B

p 1 21

Correction Effectiveness

Aberration

. Effectiveness of correction Primary Aberration 5th Chromatic

features on aberration types

Coma Distortion

Astigmatism Curvature Petzval Order 5th Spherical Color Axial Color Lateral Spectrum Secondary Spherochromatism Aberration Spherical Lens Bending (a) (c) e (f) Power Splitting Power Combination a c f i j (k) Distances (e) k

Lens Parameters Lens Stop Position

Makes a good impact. Refractive Index (b) (d) (g) (h)

Dispersion (i) (j) (l)

Makes a smaller impact.

Relative Partial Disp. Material

Makes a negligible impact. GRIN Action

Zero influence. Cemented Surface b d g h i j l Aplanatic Surface Aspherical Surface Mirror

Special Surfaces Special Diffractive Surface

Symmetry Principle

Struc Field Lens

Ref : H. Zügge 22 Spherical Aberration: Lens Bending

. Effect of bending a lens on spherical aberration . Optimal bending: Spherical Minimize spherical aberration Aberration . Dashed: thin lens theory 60 Solid : think real lenses . Vanishing SPH for n=1.5 only for virtual imaging 40 . Correction of spherical aberration

possible for: 20

1. Larger values of the (b) (c)

magnification parameter |M| X (a) 2. Higher refractive indices -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 (d) M=0 M=-3 M=3 M=-6 M=6

Ref : H. Zügge 23 Correcting Spherical Aberration: Lens Splitting

Transverse aberration 5 mm . Correction of spherical aberration: Splitting of lenses (a)

. Distribution of ray bending on several 5 mm surfaces: Improvement (b) - smaller incidence angles reduces the (a)à(b) : 1/4 effect of nonlinearity

- decreasing of contributions at every 5 mm surface, but same sign Improvement (c) . Last example (e): one surface with (b)à(c) : 1/2 compensating effect

5 mm

Improvement (d) (c)à(d) : 1/4

0.005 mm

Improvement (e) (d)à(e) : 1/75

Ref : H. Zügge 24 Microscopic Objective Lens

microscope objective lens . Incidence angles for chief and marginal ray marginal ray

. Aperture dominant system

. Primary problem is to correct chief ray spherical aberration incidence angle

60 0 5 10 15 20 25 25 Photographic lens

Photographic lens . Incidence angles for chief and marginal ray

. Field dominant system

marginal . Primary goal is to control and correct ray field related aberrations: chief coma, astigmatism, field curvature, ray lateral color incidence angle

60 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 26 Sensitivity of a System

Representation of wave Seidel coefficients []

Double Gauss 1.4/50

surfaces Ref: H.Zügge 27 Symmetrical Dublet

. Variable focal length f = 200 mm f = 15 ...200 mm

f = 100 mm . Invariant: object size y = 10 mm numerical aperture NA = 0.1 f = 50 mm . Type of system changes: - dominant spherical for large f - dominant field for small f f = 20 mm . Data:

focal Length spherical field astigma- No length [mm] c curvature c tism c [mm] 9 4 5 1 200 808 3.37 -2.01 -2.27 f = 15 mm 2 100 408 1.65 1.19 -4.50 3 50 206 1.74 3.45 -7.34 4 20 75 0.98 3.93 2.31 5 15 59 0.20 16.7 -5.33 28

Structural Changes for Correction

. Lens bending

. Lens splitting

. Power combinations

(a) (b) (c) (d) (e)

. Distances

(a) (b)

Ref : H. Zügge 29 Lens Removal

. Removal of a lens by vanishinh of the optical effect

. For single lens and

cemented component a) Geometrical changes: radius and thickness . Problem of vanishinh index: 1) adapt second radius of curvature 2) shrink thickness to zero Generation of higher orders of aberrations

b) Physical changes: index 30 Aplanatic Surfaces

. Aplanatic surfaces: zero spherical aberration:

1. Ray through vertex s' s  0

2. concentric s' s und u  u' 3. Aplanatic e ns n's' e r r e e h h p p s hyperboloid oblate ellipsoid oblate ellipsoid s prolate ellipsoid . Condition for aplanatic + power series + power series + power series + power series surface: s' ns n's' ss' 0.1 r    aplanatic S 0 n  n' n  n' s  s' vertex concentric -0.1 . Virtual image location -0.2

. Applications: -0.3 1. Microscopic objective lens 2. Interferometer objective lens -0.4

-0.5 0 50 100 150 200 250 300 31 Aplanatic Lenses

A-A : . Aplanatic lenses parallel offset

. Combination of one concentric and one aplanatic surface: zero contribution of the whole lens to spherical aberration A-C : convergence enhanced

. Not useful: 1. aplanatic-aplanatic 2. concentric-concentric bended plane parallel plate, C-A : nearly vanishing effect on rays convergence reduced

C-C : no effect 32 Principles of Glass Selection in Optimization

. Design Rules for glass selection

. Different design goals: 1. Color correction: index n large dispersion positive lens field flattening difference desired Petzval curvature 2. Field flattening: large index difference + + desired

negative lens color correction + -

availability of glasses - - dispersion n

Ref : H. Zügge 33 Principle of Symmetry

. Perfect symmetrical system: magnification m = -1 . Stop in centre of symmetry . Symmetrical contributions of wave aberrations are doubled (spherical) . Asymmetrical contributions of wave aberration vanishes W(-x) = -W(x) . Easy correction of: coma, distortion, chromatical change of magnification

front part rear part

  2 3

 1 34 Symmetry Principle

. Application of symmetry principle: photographic lenses . Especially field dominant aberrations can be corrected . Also approximate fulfillment of symmetry condition helps Triplet Double Gauss (6 elements) significantly: quasi symmetry . Realization of quasi- symmetric setups in nearly all photographic systems

Biogon Double Gauss (7 elements)

Ref : H. Zügge 35 Petzval Theorem for Field Curvature

. Petzval theorem for field curvature: 1 nk 'nk 1. formulation for surfaces  nm ' Rptz k nk nk 'rk

1 1 2. formulation for thin lenses (in air)  Rptz j n j  f j . Important: no dependence on bending

. Natural behavior: image curved object towards system plane

. Problem: collecting systems with f > 0: If only positive lenses:

Rptz always negative R

ideal optical system real image image plane shell 36 Flattening Meniscus Lenses

. Possible lenses / lens groups for correcting field curvature . Interesting candidates: thick mensiscus shaped lenses r 2 2 1 nk 'nk 1  n 1 d d        Rptz k nk nk 'rk n f  n  r1r2 r 1

1. Hoeghs mensicus: identical radii 2 (n 1) d - Petzval sum zero F' nr 2 - remaining positive refractive power

2. Concentric meniscus, r  r  d - Petzval sum negative 2 1 - weak negative focal length 1 (n 1)d (n 1)d  F'  - refractive power for thickness d: R nr  r  d ptz 1  1  nr1(r1  d)

3. Thick meniscus without refractive power n 1 1 (n 1)2 d Relation between radii  0 r2  r1  d  n Rptz nr1 nr1  d (n 1) 37 Field Curvature

1 F . Correction of Petzval field curvature in lithographic lens  j for flat wafer R j n j

h j . Positive lenses: Green hj large F    Fj j h1 . Negative lenses : Blue hj small

. Correction principle: certain number of bulges

38 Influence of Stop Position on Performance

. Ray path of chief ray depends on stop position

stop positions spot 39 Field Lenses

. Field lens: in or near image planes . Influences only the chief ray: pupil shifted . Critical: conjugation to image plane, surface errors sharply seen

marginal ray

chief ray

field lens in intermediate original lens L image plane 2 shifted pupil pupil lens L1 40 Field Lens im Endoscope

Ref : H. Zügge

Evolution of Eyepiece Designs

Huygens

Loupe

Monocentric

Ramsden

Von-Hofe Plössl

Kellner Kerber

Erfle

Bertele König

Erfle type

Erfle diffractive Bertele Nagler 1

Erfle type (Zeiss)

Nagler 2 Aspheric

Scidmore Bertele Wild Dilworth

Classification

Special Extrem Wide Angle Quasi-Symmetrical Angle Topogon Telecentric I Fish Eye Metrogon

Telecentric II Compact . Families of photographic lenses Pleon Super-Angulon Hypergon Telephoto Catadioptric . Long history Panoramic Lens

. Not unique Wide Angle Retrofocus Pleogon Hologon Plastic Plastic Aspheric Retrofocus SLR Aspheric I II

IR Camera Lens UV Lens Flektogon Biogon Distagon

Triplets

Retrofocus II Vivitar Triplet Pentac

Singlets Heliar Hektor Less Symmetrical Achromatic Landscape Landscape Ernostar Ernostar II

Inverse Triplet

Sonnar

Petzval Symmetrical Doublets

Petzval, Portrait Petzval Dagor Rapid Projection Rectilinear Aplanat Quadruplets Petzval,Portrait flat R-Biotar Double Gauss Ultran Dagor Biotar / Planar reversed Periskop

Double Gauss II Quasi-Symmetrical Doublets Noctilux Orthostigmatic Tessar Protar

Plasmat Celor Kino-Plasmat Unar Antiplanet Angulon

43 Medium Magnification Microscopic lenses

Development of Lithographic Lenses

d) Catadioptric cube a) Early systems M systems 1 g) EUV mirror

M2 systems

b) Refractive spherical systems e) Multi-axis catadioptric systems

M 1

M 6

M 2

M 5

M M 1 8 M 3 M 4

M f) Uni-axis catadioptric 2 c) Refractive with aspheres and immersion systems M 3 M 6 M M 4 6

M 5

Modified Workflow in Instrument Development

Historical: Modern: sequential workflow complex workflow with feedback and relationships

Optical Design Optical design phys-opt Development Development Tolerancing Tolerancing Simulation

Mechanical Design Mechanical Metrology Design Manufacturing

Manufacturing Assembly Researchlab components Adjustment

Performance Control of Integration Software Check buyed Adjustment components Tests

Introduction to Tolerancing

. Specifications are usually defined for the as-built system

. Optical designer has to develop an error budget that cover all influences on performance degradation as - design imperfections - manufacturing imperfections - integration and adjustment - environmental influences

. No optical system can be manufactured perfectly (as designed) - Surface quality, scratches, digs, micro roughness - Surface figure (radius, asphericity, slope error, astigamtic contributions, waviness) - Thickness (glass thickness and air distances) - Refractive index (n-value, n-homogeneity, birefringence) - Abbe number - Homogeneity of material (bubbles and inclusions) - Centering (orientation of components, wedge of lenses, angles of prisms, position of

components) - Size of components (diameter of lenses, length of prism sides) - Special: gradient media deviations, diffractive elements, segmented surfaces,...

. Tolerancing and development of alignment concepts are essential parts of the optical design process Ref: K. Uhlendorf 46

Data Sheet

Tolerances: Typical Values

10...20 20...30 Diameter Tolerance Unit <10 mm mm mm Center thickness mm 0.02 0.03 0.03 Centering Tilt angle sek 60 60 60 Decenter/offset m 15 15 15 Roughness nm 15 10 10 Spherical/radius spherical rings 3 4 5 astigmatism rings .5 1 1 Asphericity Global deviation m 1 1.2 1.5 Global asphericity m 0.25 0.45 0.60 Local deviation m 0.025 0.05 0.075 Slope error rad 0.0005 0.0005 0.0005

49 Adjustment and Compensation

. Example Microscopic lens

. Adjusting: 1. Axial shifting lens : focus 2. Clocking: astigmatism 3. Lateral shifting lens: coma

. Ideal : Strehl DS = 99.62 %

With tolerances : DS = 0.1 %

After adjusting : DS = 99.3 %

Ref.: M. Peschka 50 Adjustment and Compensation

. Sucessive steps of improvements

Ref.: M. Peschka

Drawing of Microscopic Lens with Housing