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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