www.iap.uni-jena.de

Lens Design I

Lecture 2: Properties of optical systems I

2018-04-19

Herbert Gross

Summer term 2018

2

Preliminary Schedule - Lens Design I 2018

1 12.04. BasicsIntroduction, Zemax interface, menues, file handling, preferences, Editors, updates,

windows, coordinates, System description, 3D geometry, aperture, field, wavelength

2 19.04. Properties of optical systems IDiameters, stop and pupil, vignetting, Layouts, Materials, Glass catalogs, Raytrace,

Ray fans and sampling, Footprints

3 26.04. Properties of optical systems II

Types of surfaces, cardinal elements, lens properties, Imaging, magnification,

paraxial approximation and modelling, telecentricity, infinity object distance and

afocal image, local/global coordinates

4 03.05. Properties of optical systems IIIComponent reversal, system insertion, scaling of systems, aspheres, gratings and

diffractive surfaces, gradient media, solves

5 17.05. Advanced handling I Miscellaneous, fold mirror, universal plot, slider, multiconfiguration, lens catalogs

6 24.05. Aberrations IRepresentation of geometrical aberrations, Spot diagram, Transverse aberration

diagrams, Aberration expansions, Primary aberrations

7 31.05. Aberrations II Wave aberrations, Zernike polynomials, measurement of quality

8 07.06. Aberrations III Point spread function, Optical transfer function

9 14.06. Optimization IPrinciples of nonlinear optimization, Optimization in optical design, general process,

optimization in Zemax

10 21.06. Optimization II (subs/shift)Initial systems, special issues, sensitivity of variables in optical systems, global

optimization methods

11 28.06. Advanced handling IISystem merging, ray aiming, moving stop, double pass, IO of data, stock lens

matching

12 05.07. Correction ISymmetry principle, lens bending, correcting spherical aberration, coma,

astigmatism, field curvature, chromatical correction

13 12.07. Correction IIField lenses, stop position influence, retrofocus and telephoto setup, aspheres and

higher orders, freeform systems, miscellaneous

1. Diameters

2. Stops and Pupil definition

3. Vignetting

4. Layout

5. Materials and glass catalogs

6. Raytrace

7. Ray fans and sampling

8. Footprints

3

Contents 2nd Lecture

Pupil stop defines:

1. chief ray angle w

2. aperture cone angle u

The chief ray gives the center line of the oblique ray cone of an off-axis object point

The coma rays limit the off-axis ray cone

The marginal rays limit the axial ray cone

y

y'

stop

pupil

coma ray

chief ray

marginal ray

aperture

angle

u

field anglew

object

image

Optical system stop

The physical stop defines

the aperture cone angle u

The real system may be complex

The entrance pupil fixes the

acceptance cone in the

object space

The exit pupil fixes the

acceptance cone in the

image space

uobject

image

stop

EnP

ExP

object

image

black box

details complicated

real

system

? ?

Ref: Julie Bentley

Optical system stop

Relevance of the system pupil :

Brightness of the image

Transfer of energy

Resolution of details

Information transfer

Image quality

Aberrations due to aperture

Image perspective

Perception of depth

Compound systems:

matching of pupils is necessary, location and size

Properties of the pupil

exit

pupil

upper

marginal ray

chief

ray

lower coma

raystop

field point

of image

UU'

W

lower marginal

ray

upper coma

ray

on axis

point of

image

outer field

point of

object

object

point

on axis

entrance

pupil

Entrance and exit pupil

Generalization of paraxial picture:

Principal surface works as effective location of ray bending

Paraxial approximation: plane

Real systems with corrected

sine-condition (aplanatic):

principal sphere

effektive surface of

ray bending P'

y

f'

U'

P

Principal Surface

3D-effects due to vignetting

Truncation of the at different surfaces for the upper and the lower part

of the cone

Vignetting

object lens 1 lens 2 imageaperture

stop

lower

truncation

upper

truncation

sagittal

trauncation

chief

ray

coma

rays

Truncation of the light cone

with asymmetric ray path

for off-axis field points

Intensity decrease towards

the edge of the image

Definition of the chief ray:

ray through energetic centroid

Vignetting can be used to avoid

uncorrectable coma aberrations

in the outer field

Effective free area with extrem

aspect ratio:

anamorphic resolution

projection of the

rim of the 2nd lens

projection of the

rim of the 1st lens

Projektion der

Aperturblende

free area of the

aperture

sagittal

coma rays

meridional

coma rayschief

ray

Vignetting

Important types of optical materials:

1. Glasses

2. Crystals

3. Liquids

4. Plastics, cement

5. Gases

6. Metals

Optical parameters for characterization of materials

1. Refractive index, spectral resolved n(l)

2. Spectral transmission T(l)

3. Reflectivity R

4. Absorption

5. Anisotropy, index gradient, eigenfluorescence,…

Important non-optical parameters

1. Thermal expansion coefficient

2. Hardness

3. Chemical properties (resistence,…)

Optical materials

l in [nm] Name Color Element

248.3 UV Hg

280.4 UV Hg

296.7278 UV Hg

312.5663 UV Hg

334.1478 UV Hg

365.0146 i UV Hg

404.6561 h violett Hg

435.8343 g blau Hg

479.9914 F' blau Cd

486.1327 F blau H

546.0740 e grün Hg

587.5618 d gelb He

589.2938 D gelb Na

632.8 HeNe-Laser

643.8469 C' rot Cd

656.2725 C rot H

706.5188 r rot He

852.11 s IR Cä

1013.98 t IR Hg

1060.0 Nd:YAG-Laser

Test wavelengths

refractive

index n

1.65

1.6

1.5

1.8

1.55

1.75

1.7

BK7

SF1

l0.5 0.75 1.0 1.25 1.751.5 2.0

1.45

Flint

Kron

Description of dispersion:

Abbe number

Visual range of wavelengths:

Typical range of glasses

ne = 20 ...120

Two fundamental types of glass:

Crone glasses:

n small, n large

Flint glasses

n large, n small

n ll

n

n nF C

1

' '

ne

e

F C

n

n n

1

' '

Dispersion and Abbe number

Material with different dispersion values:

- Different slope and curvature of the dispersion curve

- Stronger change of index over wavelength for large dispersion

- Inversion of index sequence at the boundaries of the spectrum possible

refractive index n

F6

SK18A

l

1.675

1.7

1.65

1.625

1.60.5 0.75 1.0 1.25 1.751.5 2.0

VIS

flint

n small

slope large

crown

n largeslope small

Dispersion

14

Schott formula

empirical

Sellmeier

Based on oscillator model

Bausch-Lomb

empirical

Herzberger

Based on oscillator model

Hartmann

Based on oscillator model

n a a a a a ao

1

2

2

2

3

4

4

6

5

8l l l l l

n A B C( )ll

l l

l

l l

2

212

2

222

n A B CD E

Fo

o

( )

( )

l l ll

l

l ll

l l

2 4

2

2

2 22

2 2

mmit

aaaan

o

oo

o

l

llllll

168.0

)(222

3

22

22

1

lll

5

4

3

1)(a

a

a

aan o

Dispersion formulas

Relative partial dispersion :

Change of dispersion slope with l

Definition of local slope for selected

wavelengths relative to secondary

colors

Special selections for characteristic

ranges of the visible spectrum

l = 656 / 1014 nm far IR

l = 656 / 852 nm near IR

l = 486 / 546 nm blue edge of VIS

l = 435 / 486 nm near UV

l = 365 / 435 nm far UV

P

n n

n nF C

l l

l l

1 2

1 2

' '

l

n

400 600 800 1000700500 900 1100

e : 546 nm

main color

F' : 480 nm

1. secondary

color

g : 435 nmUV edge

C' : 644 nm

s : 852 nm

IR edge

t : 1014 nm

IR edge

C : 656 nmF : 486 nm

d : 588 nm

i : 365 nm

UV edge

i - g

F - C

C - s

C - t

F - e

g - F

2. secondary

color

1.48

1.49

1.5

1.51

1.52

1.53

1.54

n(l)

Relative partial dispersion

Usual representation of

glasses:

diagram of refractive index

vs dispersion n(n)

Left to right:

Increasing dispersion

decreasing Abbe number

Glass diagram

zoptical

axis

y j

u'j-1

ij

dj-1

ds j-1

ds j

i'j

u'j

n j

nj-1

mediummedium

surface j-1

surface j

ray

dj

vertex distance

oblique thickness

rr

Ray: straight line between two intersection points

System: sequence of spherical surfaces

Data: - radii, curvature c=1/r

- vertex distances

- refractive indices

- transverse diameter

Surfaces of 2nd order:

Calculation of intersection points

analytically possible: fast

computation

18

Scheme of raytrace

yj

z

Pj+1

sj

xj

yj+1

xj+1

Pj

surface

No j

surface

No j+1

dj sj+1

intersection

point

ej

normal

vector

ej+1

ray

distance

intersection

point

normal

vector

General 3D geometry

Tilt and decenter of surfaces

General shaped free form surfaces

Full description with 3 components

Global and local coordinate systems

19

Vectorial raytrace

r D R F R D rH H V V'

Single surface:

- tilt and decenter before refraction

- decenter and tilt after refraction

General setup for position and orientation in 3D

z

x

y

z

xF

yF

zF

j-1

j+1global

coordinates

surface

No j

VV

VH

KV

KH

shift before

shift after

tilt after

tilt before

20

Surfaces in 3D

Vignetting/truncation of ray at finite sized diameter:

can or can not considered (optional)

No physical intersection point of ray with surface

Total internal reflection

Negative edge thickness of lenses

Negative thickness without mirror-reflection

Diffraction at boundaries

index

j

index

j+1

axis

negative

un-physical

regular

irregular

axis

no intersection

point

axis

intersection:

- mathematical possible

- physical not realized

axis

total

internal

reflection

Raytrace errors

Meridional rays:

in main cross section plane

Sagittal rays:

perpendicular to main cross

section plane

Coma rays:

Going through field point

and edge of pupil

Oblique rays:

without symmetry

Special rays in 3D

axis

y

x

p

p

pupil plane

object plane

x

y

axissagittal ray

meridional marginal ray

skew raychief ray

sagittal coma ray

upper meridional coma ray

lower meridional coma ray

field point

axis point

Off-axis object point:

1. Meridional plane / tangential plane / main cross section plane

contains object point and optical axis

2. Sagittal plane:

perpendicular to meridional plane through object point

x

y

x'

y'

z

lens

meridional

plane

sagittal

plane

object

planeimage

plane

Tangential and sagittal plane

Pupil sampling for calculation of transverse aberrations:

all rays from one object point to all pupil points on x- and y-axis

Two planes with 1-dimensional ray fans

No complete information: no skew rays

y'p

x'p

yp

xp x'

y'

z

yo

xo

object

plane

entrance

pupil

exit

pupil

image

plane

tangential

sagittal

Pupil sampling

Pupil sampling in 3D for spot diagram:

all rays from one object point through all pupil points in 2D

Light cone completly filled with rays

y'p

x'p

yp

xp x'

y'

z

yo

xo

object

plane

entrance

pupil

exit

pupil

image

plane

Sampling of pupil area

Pupil Sampling

26

polar grid cartesian isoenergetic circular

hexagonal statistical pseudo-statistical (Halton)

Fibonacci spirals

Criteria:1. iso energetic rays2. good boundary description3. good spatial resolution

Artefacts due to regular gridding of the pupil of the spot in the image plane

In reality a smooth density of the spot is true

The line structures are discretization effects of the sampling

hexagonal statisticalcartesian

Artefacts of pupil sampling

Selection of glass catalogs in

- system Explorer / Material catalogs

- use your own catalog

Viewing of glass properties in

Material analyses

Glasses in Zemax

28

Viewing the glass map

Glasses in Zemax

29

Optional 4 glasses in comparison

30

Glass Dispersion

Optional 4 glasses in comparison

31

Glass Transmission

Optional 4 glasses in comparison

32

Spectral Dispersion

For optimization

Definition of a glass as a variable

point in the glass map

model glass

Establish own glass catalogs with

additional glasses

preferred choices

as an individual library

Glasses in Zemax

33Ref.: B. Böhme

Selection of 2 points on the ray on object and entrance pupil plane

Real and paraxial rays are tabulated

Coordinate reference can be selected to be local or global

34

Raytrace in Zemax

Definition of a single ray by two points

First point in object plane:

relative normalized coordinates: Hx, Hy

Second point in entrance pupil plane:

relative normalized coordinates Px, Py

Single Ray Selection

axis

x p

pupil plane

object plane

x

y

first point

yp

second point

HyHx

Py

Px

Raytrace Errors

Vignetting/truncation of ray at finite sized diameter:

can or can not considered (optional)

No physical intersection point of ray with surface

Total internal reflection

Negative edge thickness of lenses

Negative thickness without mirror-reflection

Diffraction at boundaries

index

j

index

j+1

axis

negative

un-physical

regular

irregular

axis

no intersection

point

axis

intersection:

- mathematical possible

- physical not realized

axis

total

internal

reflection

Different possible options for specification of the aperture in Zemax:

1. Entrance pupil diameter

2. Image space F#

3. Object space NA

4. Paraxial working F#

5. Object cone angle

6. Floating by stop size

Stop location:

1. Fixes the chief ray intersection point

2. input not necessary for telecentric object space

3. is used for aperture determination in case of aiming

Special cases:

1. Object in infinity (NA, cone angle input impossible)

2. Image in infinity (afocal)

3. Object space telecentric

Aperture data in Zemax

There are several different types of

diameters in Zemax:

1. Surface stop

- defines the axis intersection of the chief

ray

- usually no influence on aperture size

- only one stop in the system

- is indicated in the Lens Data Editor

by STO

- if the initial aperture is defined, the size

of the stop semi-diameter is determined

by marginal raytrace

38

Diameters in Zemax

2. Userdefined diameter at a surface in

the Lens Data Editor (U)

- serves also as drawing size in the

layout (for nice layouts)

- if the diameter in the stop plane is

fixed, the initial aperture can be

computed automatically by

General / Aperture Type /

Float by Stop Size

This corresponds to a ray aiming

3. Individual diameter of perhaps

complicated shape at every surface

(‚apertures‘)

- no impact on the drawing

- is indicated in the Lens Data Editor

by a star

- the drawing of vignetted rays can

by switched on/off

39

Diameters in Zemax

4. Individual aperture sizes for every field point can be set by

the vignetting factors of the Field menu

- real diameters at surfaces must be set

- reduces light cones are drawn in the layout

VDX, VDY: relative decenter of light cone in x, y

VCX, VCY: compressian factors in x, y

VAN: azimuthal rotation angle of light cone

- If limiting diameters are set in the system, the corresponding

factors can be calculated by the Set Vig command

40

Diameters and stop sizes

In the Tools-menue, the diameters

and apertures can be converted

automatically

41

Diameters in Zemax

Graphical control of system

and ray path

Principal options in Zemax:

1. 2D section for circular symmetry

2. 3D general drawing

Several options in settings

Zooming with mouse

42

Layout options

Different options for 3D case

Multiconfiguration plot possible

Rayfan can be chosen

43

Layout options

44

Layout options

Professional graphic

Many layout options

Rotation with mouse or arrow buttons

45

Layout options

Several options for representations

46

Spot Diagrams in Zemax

Looking for the ray bundle cross sections

Equivalent to spot diagram

47

Footprints