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Medical Photonics Lecture 1.2Optical Engineering

Lecture 8: Instruments I

2019-06-05

Michael Kempe

Winter term 2017

2

Contents

No Subject Ref Date Detailed Content

1 Introduction Zhong 10.04. Materials, dispersion, ray picture, geometrical approach, paraxial approximation

2 Geometrical optics Zhong 17.04. Ray tracing, matrix approach, aberrations, imaging, Lagrange invariant

3 Diffraction Zhong 24.04. Basic phenomena, wave optics, interference, diffraction calculation, point spread function, transfer function4 Components Kempe 08.05. Lenses, micro-optics, mirrors, prisms, gratings

5 Optical systems Zhong 15.05. Field, aperture, pupil, magnification, infinity cases, lens makers formula, etendue, vignetting6 Aberrations Zhong 22.05. Introduction, primary aberrations, miscellaneous7 Image quality Zhong 29.05. Spot, ray aberration curves, PSF and MTF, criteria

8 Instruments I Kempe 05.06. Human eye, loupe, eyepieces, photographic lenses, zoom lenses, telescopes

9 Instruments II Kempe 12.06. Microscopic systems, micro objectives, illumination, scanning microscopes, contrasts

10 Instruments III Kempe 19.06. Medical optical systems, endoscopes, ophthalmic devices, surgical microscopes

11 Photometry Zhong 26.06. Notations, fundamental laws, Lambert source, radiative transfer, photometry of optical systems, color theory

12 Illumination systems Gross 03.07. Light sources, basic systems, quality criteria, nonsequential raytrace13 Metrology Gross 10.07. Measurement of basic parameters, quality measurements

The Human Eye

Ref: Wikipedia

The Eye of Owl, Cat, Gecko, Insects

Ref: Wikipedia

The Human Eye

cornea

pupil

iris

tear liquid

front chamber

conjunctiva

conjunctiva

lens vitreous body

macula(yellow)

retina

blind spot

rear chamber

muscle

muscle

nerve

fibres

fibres

outer skin

choroidmembrane

The Human Field of View

Ref: Wikipedia

< 10°: central< 30°: near-peripheral< 60°: mid-peripheral

The Human Vision

Optical Data of the Eye

Property relaxed accomodatedRefractive power 58.63 dptr 70.57 dptrFocal length in air 17.1 mm 14.2 mmPower of the crystalline lens 19 dptr 33 dptrPupil diameter, smallest value for high brightness 1.5 mmPupil diameter, largest value for night vision 8.0 mmAbbe number (approx.) 50.23Petzval radius -17.58 mmLocation of entrance pupil -3.047 mmField of view maximum (vertical) 108°Field of view maximum (horizontal) 200°Field of foveated seeing 5°Diameter eye ball 24 mmDistance rotation point from cornea vertex 13.5 mmNodal point location 7.33 mmPrincipal plane location 1.6 mm

Eye Data - Overview

Terms Sizes and lengths

retina

fovea

cornea

iris

optical discblind spotcrystalline lens

lens capsule

anteriorchamber

posteriorchamber

vitreoushumor

temporal

nasal

0.5 mm3.6 mm

3.6 mm

F'

F

24.4 mm15.7 mm

NN'PP'

1.6 mm

7.33 mm

C

13.5 mm

1.8 mm

4 mm

1.8 mm

2.5 mm

Refractive Index

Distribution of the indexalong z

Smooth index variationof crystalline lens

z[mm]

n

0 5 10 15 20 251

1.05

1.1

1.15

1.2

1.25

1.3

1.35

1.4

1.45

1.5

cornea crystallinelens

lenscapsule retina

vitreous humoranterior

chamber

n

z[mm]0 0.5 1 1.5 2 2.5 3 3.5 4 4.51.3

1.32

1.34

1.36

1.38

1.4

1.42

Gullstrand Model Eye

Six media Crystalline lens with shell Data for relaxed and accomodated eye Simple version : single crystalline lens

Relaxed Accomodated Parameter Notation Value Value

Focal length object sided f [mm] 17.055 14.169 Focal length image sided f' [mm] 22.785 18.930 Refractive power F [dpt] 58.636 70.57 Location entrance pupil p [mm] 3.045 2.667 Location exit pupil p' [mm] 3.664 3.211 Principal point object sided P [mm] 1.348 1.772 Principal point image sided P' [mm] 1.602 2.086 Nodal point object sided N [mm] 7.078 6.533 Nodal point image sided N' [mm] 7.332 6.847 Length L [mm] 24.387

30°

10°

0°

0°

486 nm 587 nm 656 nm

10°

20°

Spectral Transmission of the Eye

Absorption of the eye media prevents retina damage Special truncation of UV and IR contributions

3000

20

40

60

80

100

500400 800600 1000 1400 2000λ [nm]

T [%]visible

after corneabefore lensafter lensat retina

Receptors, rods and cones

Cones : Fovea, bright light, color Rods : Peripheral, dim light, no color

Source:http://news.feinberg.northwestern.edu/2012/04/retina_research/

Property cones rods Location in the fovea outside the fovea Field of view small, 5° large, 108° Resolution and visual acuity large small Brightness sensitivity small, for daylight vision large, vision at night Colour sensitivity yes no Total number of elements 5 million 120 million Limiting brightness 683 lm / W 1699 lm / W Spectral maximum 555 nm 507 nm

14

Fundus

Range Diameter [mm]

Cones Rods

Foveola 0.35 number :3500

density 190000/mm2 pitch 2.3 µm

no rods

Fovea 1.85 density : 100000/mm2

pitch : 3.2 µm a few rods

Prafovea 2.85

Macula lutea

Perifovea 5.85 density : 160000/mm2

pitch : 2.5 µm

Periphery density : 5000/mm2

pitch : 14.0 µm density : 50000/mm2

pitch : 4.5 µm

Papille, blind spot 4 mm off axis nasal 1.8 no cones no rods

Source: ZEISS

Source: ZEISS

Spectral Sensitivity of the Eye

Spectral sensitivity of the eye: depends on brightness

Daylight / high brightness: cones (blue, green, red), peak sensitivity at 550 nm

At night/ low brightness: rods, peak sensitivity at 507 nm, no color distinction

Absolute sensitivity: 5-15 photons (1 photon per rod) corresponds to 50-150 photons at cornea

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

V(λ)

λ

nightscotopic

rods

dayphotopic

cones

cyan green

400 450 500 550 600 650 700 750

Source: Wikipedia

Accommodation

Change of accommodation range with age

age inyears

∆D [dpt]

16

12

8

4

00 20 40 60

maximum

minimum

mean

dpt

0 20 40 8060age

[years]

relaxedeye

strongestaccomodation

immobilepoint

4

0

-4

-8

-12

Adaptation

Aging effect on adaptation range and on adaptation speed

8

6

4

2

00 20 40 60 age in

years

pupil diameter[mm]

cones

rodsLog Ithresh

[a.u.]

2

3

10 20 30 40

4

5

6

7

8

time[min]

80 years

50 years

30 years17 years

7

kink ofHelmholtz

rod mono-chromate

nightblindness

Adaptation Range

Smallest Stimulus Adaptation

Resolution of the Eye

Resolution of the eye dependson the object shape

The quantitative measure isgiven as angle

Rough measure :2𝛼𝛼𝑐𝑐 = 0.017° ≈ 1′

Least distance of (comfortable) distinct vision: 250 mm

∆x'c = 75 µm

so = 250 mm

L = 22 mm

αc

∆x

distancecones

a) letter5'

b) grating2'

c) two points1'

d) nonius10''

e) binocular 5''

L=23 mm

34 µm

Visual Acuity

Subjective recognition of simple geometricalshapes :

1. Landolt ring with gap2. Letter 'E'

a)

5a

a

a

3a

3a

a

3a

b)

distance 6.096 m

blockletter

E 8.9mmimageheight25 µm eye

Acuity measures

a=1’ at 6 m

𝑉𝑉𝑆𝑆 =𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑑𝑑𝑡𝑡𝑡𝑡𝑡𝑡𝑑𝑑𝑡𝑡𝑑𝑑𝑡𝑡 [𝑚𝑚]

𝑑𝑑𝑡𝑡𝑡𝑡𝑡𝑡𝑑𝑑𝑡𝑡𝑑𝑑𝑡𝑡 𝑚𝑚 𝑑𝑑𝑡𝑡 𝑤𝑤𝑤𝑡𝑡𝑑𝑑𝑤 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑙𝑙𝑡𝑡𝑡𝑡𝑡𝑡 𝑙𝑙𝑡𝑡𝑡𝑡𝑡𝑡 𝑙𝑙𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑙𝑙 𝑡𝑡𝑠𝑠𝑠𝑠𝑡𝑡𝑡𝑡𝑡𝑡𝑑𝑑𝑡𝑡 5′

𝑉𝑉 =1

𝑚𝑚𝑡𝑡𝑡𝑡𝑡𝑡𝑚𝑚𝑠𝑠𝑚𝑚 𝑑𝑑𝑡𝑡𝑡𝑡𝑙𝑙𝑡𝑡 𝑜𝑜𝑜𝑜 𝑙𝑙𝑡𝑡𝑡𝑡𝑜𝑜𝑙𝑙𝑠𝑠𝑡𝑡𝑡𝑡𝑜𝑜𝑡𝑡 [𝑑𝑑𝑙𝑙𝑑𝑑𝑚𝑚𝑡𝑡𝑡𝑡] V=0.020-2.5 (normal: V=1)

Normal: 6/6 (20/20 in inch)

Snellen Testchart

Used for subjectivemeasurement ofvisual acuity

20

EF P

T O ZL P E DP E C F DE D F C F D

F E L O P Z DD E F P O T E C

L E F O D P C T

F D P L T C E O

P E Z O L C F T D

Group Snellen Acuity

1 20/200 (6/60)

2 10/100 (6/30)

3 20/70 (6/21)

4 20/50 (6/15)

5 20/40 (6/12)

6 20/30 (6/9)

7 20/25 (6/7)

8 20/20 (6/6)

9 20/15 (6/4.5)

10 20/13 (6/4)

11 20/10 (6/3)

Eye Diseases

Four major defects

a) refraction error b) glaucom

c) retina defects d) cataract

original

Spectacles

Correction of refraction error by spectacle lenses

1. Myopia (short-sightedness) : negative lens

2. Hyperopia (far-sightedness) : positive lens

eye binocular

∞

eye binocular

∞

Lens close to the eyeReference distance so = 250 mmrelaxed eye Lens at focal distance to eye:

Nominal magnification

Angle magnification

Loupe Magnifier

s = 250 mmo

f lens

y

y'lens

eye

y

lens

eye

object

so

wo wm

fL

Lmag f

s0=Γ∞

L

o

o

L

o

mw f

s

syfy

wwm ===

tantan

fL

General case :Linse at distance d from the eye

Magnification

Loupe Magnifier

yy'

lens

eye

ss' d

objectvirtualimage𝑚𝑚𝑤𝑤 =

𝑜𝑜𝐿𝐿(𝑡𝑡′ + 𝑑𝑑)𝑑𝑑(𝑜𝑜𝐿𝐿 + 𝑡𝑡) − 𝑜𝑜𝐿𝐿 � 𝑡𝑡

d (mm)

mw

fL=50mms’=250mm

0

1

2

3

4

5

6

7

8

9

10

4 0 4 5 5 0 5 5 6 0 6 5 7 0 7 5 8 0 8 5

Eyepiece: Basic Setup

Eyepieces images a finite image of an instrument to infinity Viewing with a relaxed eye Magnification

Objective exit pupil = entrance pupil of eyepiece Eyepiece exit pupil = eye pupil (size: 2-8 mm) Eye relief : distance between last lens surface and eye cornea

- required : 15 mm- with eyeglasses : 20 mm- typ.: 22 mm

Objectiveexit pupil

intermediatefocus

Eyepiece

Eye pupil

tube length

eyepiecefmm250

=Γ

Pupil mismatch Eye relief, spherical aberration, eye movement

26

Mismatch of Eyepieces

Ref: Smith, Ceragioli, Berry, Telescopes, Eyepieces, Astrographs, Willman-Bell, 2012

Evolution of Eyepiece Designs

Monocentric

Plössl

Erfle

Von-Hofe

Erfle diffractive

Wild

Erfle type(Zeiss)

BerteleScidmore

Loupe

Erfletype

Bertele

Kellner

Ramsden

Huygens

Kerber

König

Nagler 1

Nagler 2

Bertele

Aspheric

Dilworth

Huygens Eyepiece

Distance

Lateral color corrected paraxially Intermediate image between

lenses, not corrected

Virtual object(image plane of objective)

Exit pupil(eye position)

d

221 ffd +=

-1.000 0.000 1.000

0.250

0.500

0.750

1.000

LONGITUDINALSPHERICAl ABER.

DIOPTER-3.000 0.000 3.000

2.125

4.250

6.375

8.500

tan sag

ASTIGMATICFIELD CURVES

DIOPTER-20.00 0.00 20.00

2.125

4.250

6.375

8.500

DISTORTION

Distortion (%)

0°

10°

20°

20 a

rcm

in

Kellner Eyepiece

Corresponds to Ramsden type Intermediate image accessible Eye lens achromatized over larger field

-1.000 0.000 1.000

0.250

0.500

0.750

1.000

LONGITUDINALSPHERICAl ABER.

DIOPTER-3.000 0.000 3.000

2.625

5.250

7.875

10.500

tan sag

ASTIGMATICFIELD CURVES

DIOPTER-20.00 0.00 20.00

2.625

5.250

7.875

10.500

DISTORTION

Distortion (%)

0°

10°

20°

24°

20 a

rcm

in

Photographic Lenses

• Photographic lenses image a certain field on a sensor• Most important characteristics:

- field angle ((for a given image format also characterized by focal length)- aperture (given as f-number)

• Applications of this lens type:- photographic lenses- video lenses- photogrammetry - projections

f# =𝑜𝑜𝐷𝐷

Image sensor (e.g. full frame 24mm x 36mm corresponds to 35-mm film)

Typical Photographic Lens Types

Type focal

length in mm

Typical f-number

Field of view (full diagonal)

in degrees

Lens type element number

Fisheye 6 - 10 4 - 2.8 220 - 180 Fisheye 7 - 12

quasi-fisheye 10 - 16 3.5 180 - 100 Fisheye 6 - 10

extreme wide-angle 13 - 18 3.5 120 - 100 retrofocus 9 - 13 very large angle 20 - 24 2.8 - 2 94 - 84 retrofocus 8 - 10

wide-angle 28 - 35 2 - 1.4 75 - 62 Double Gauss, retrofocus 6 - 9

standard 40 - 55 1.4 - 1 56 - 43 Triplet, Tessar, Sonnar, Double Gauss 3 - 7 short telephoto 75 - 105 2.8 - 1.4 37 - 23 Double Gauss, telephoto 5

medium telephoto 120 - 200 4 - 2 21 - 12 Tessar, telephoto 4 - 6

long telephoto 300 - 500 8 - 2.8 8 - 5 telephoto 4 - 7 extreme telephoto 600 - 1200 11 - 5.6 4 - 2 telephoto 2 - 5

Requirements of Photo Objective Lenses

Large field of view- correction of coma, astigmatism, distortion an field curvature

Color correction Resolution

- typically small F-number- usually the sensor is limiting, no diffraction limited correction

Smart system, small and light weight- short length- plastic components

Additional functionalities- zoom option- focussing- autofocus function- large field viewer

Tessar

Double Gauss

Super Angulon

Photographic Lenses

Distagon

Tele system

Wide angleFish-eye

Example lensfisheye

Fish-Eye-Lens

0°

50°

100°

71°

486 nm 587 nm 656 nma)

ν[mm-1]

tansag

0 20 40 60 80 1000

0.2

0.4

0.6

0.8

1

ideal0°50°71°100°

b)

0 50°

fieldangle

solid: tandashed: sag

100°

40 cyc/mm60 cyc/mm

10 cyc/mm20 cyc/mm

0

0.2

0.4

0.6

0.8

1c)

100%

y

-100% 0

Handy Phone Objective lenses

Examples

Ref: T. Steinich

US 7643225L = 4.2 mm , F'=2.8 , f = 3.67 mm , 2w=2x34°

US 6844989L = 6.0 mm , F'=2.8 , f = 4.0 mm , 2w=2x31°

EP 1357414L = 5.37 mm , F'=2.88 , f = 3.32 mm , 2w=2x33.9°

Olympus 2L = 7.5 mm , F'=2.8 , f = 4.57 mm , 2w=2x33°

1. Sampling of the field pixel by pixelSignal digitized in the time domain

2. Active: Flying spot scanningPoint wise scanning of illumination, often by laser beamApplications: - bar code reader

- confocal microscopy- laser radar (e.g. optical coherence tomography)

3. Passive: Remote sensingDecomposition of object signal into pixelsApplications: - night Vision

- monitoring, surveying- missile tracking

Scan Systems

Source: http://www.zamisel.com/SSpostavka2.html

Confocal

Wide Field

Objectiveexit pupil

intermediatefocus

Eyepiece

Eye pupil

tube length

Scan lens

Beam deflecting element

Scan Systems: Introduction

Scan resolution:Number of resolvable points in the field of view(scan length over diffraction limited spot size)

Information capacity:1. Resolvable points2. Speed of scanning

Etendue: product of scan range andscanner area

λθ⋅⋅

== max2 ExP

Airy

DD

LN

log ∆θ

log v

angleresolution

scan speed

growing scancapacity

acoustic optical modulator

polygonmirror

galvoscanner

holographicscanner

electroopticalmodulator

resonantgalvoscanner

maxθθ ⋅=⋅ ExPMirMir DD

Deflecting Components

Different types of deflecting elements

Scanning

Non-Mechanical Deflection

Electro-optic EOD

Acousto-optic AOD

Mechanical

Oszillation

Galvanometric Galvoscanner

Holographic Holographic Scanner

Electrostatic MEMS Scanner

Rotation

Polygon Polygon-scanner

Rotating Prisms Dove Prism

Translation Lenses and lens arrays

Galvanometer and Electrostatic Scanner

Galvo scanner MEMS-Scanner

Source: scanlab.de Source: researchgate.net

Scanner Lenses

Ideal scanner lens (F-θ lens): h = f θ Flat-field corrected lens: h = f tanθ

nonlinear displacement: distortion correction needed

• In addition telecentricityensures minimum beam distortions

44

Source: thorlabs.com

Example: Scanner Lens

Scan angle 2x30° Monochromatic

diffraction limited F-θ-corrected

0° 5° 10°

20°

15°

24° 28° 30.4°

USP 4436382:

45

Ref: B. Böhme

Medical Photonics Lecture 1.2�Optical Engineering�Contents�The Human Eye�The Eye of Owl, Cat, Gecko, Insects�The Human Eye�The Human Field of View�The Human Vision �Optical Data of the Eye�Eye Data - Overview�Refractive Index�Gullstrand Model Eye�Spectral Transmission of the Eye�Receptors, rods and conesFoliennummer 14�Spectral Sensitivity of the Eye�Accommodation�Adaptation�Resolution of the Eye�Visual Acuity�Snellen Testchart�Eye Diseases�Spectacles�Loupe Magnifier�Loupe Magnifier�Eyepiece: Basic Setup�Mismatch of Eyepieces�Evolution of Eyepiece Designs�Huygens Eyepiece�Kellner Eyepiece�Photographic Lenses�Typical Photographic Lens Types�Requirements of Photo Objective LensesPhotographic Lenses�Fish-Eye-LensHandy Phone Objective lenses �Scan Systems�Scan Systems: Introduction�Deflecting Components�Galvanometer and Electrostatic Scanner�Scanner Lenses �Example: Scanner Lens