2015-09-14
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GEOMETRICALOPTICSI
Lecture1
Biophotonics
JaeGwan Kim
[email protected] ,X2220
SchoolofInformationandCommunicationEngineering
Gwangju InstituteofSciencesandTechnology
SomeCourseNotes
LectureNoteswillbeprovidedontheweborsentbyemail
OfficeHourswillbeanytimeaslongasI’matoffice
Emailforappointment:[email protected]
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ModuleGoal
• Learnenoughbasicopticstocommunicatehowtocouplelight frompointAtopointB
camera
lasercouplelaserintoafiber
PMT
opticalfiber
pictureafluorescingcell
collectlightfromatissue
?
?
?
ItemsYouWillLearn
1. Lensbasics–Conventions–typesoflenses–useoflensequations
2. Keycouplingconcepts–“f‐number”(f/#)–numericalaperture(NA)–aperturestops
3. FiberOptics–workingprinciples–typesoffibers– limitations
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OutlineforLenses
• Snell’sLawandrefraction
• ThinLenses
• LensConventions
• ATrueOpticsProblem
• CollectionEfficiency(f/# andNA)
• ExampleleadingtotheApertureStop
• FocusingConcerns
PRELIMINARY:REFRACTION&THETHINLENS
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ASimpleExample
• HowcanIcouplelightfroma1mmfilamentlampintoa0.1mmdiameteropticalfiber?
• Ofcourse,wemayusealens,buthowdowecalculate?
CONVENTIONS
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Conventions:LightIncidentonLeft
• Beforewecancalculatethegoodstuff,wewillneedtoadoptsomeconventionsconcerningournewfoundfriends.
• Conventionsneededfor:
1) objectdistance(so)2) imagedistance(si)3) radiusofcurvature(R)4) focalpoint(f)
(1)ObjectConventions
so
object is REALwhen rays diverge from object:
so > 0
object is VIRTUAL when rays converge to object:
so < 0
usually only with lens combinations
so
principal rays
+ ‐0
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(2)ImageConventions
si
image is REALwhen rays converge :
si > 0
image is VIRTUAL when rays diverge :
si < 0
rays project back to the imagesi
rays focus on the image‐ +0
(3)R Conventions
R1
R2
R1
R2
R > 0 when line lands on right R < 0 when line lands on left
R1 > 0
R2 < 0
R1 < 0
R2 >0
‐ +0
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(4)f Conventions
f
lens is CONVERGINGwhen rays converge:
f > 0
lens is DIVERGINGwhen rays diverge:
f < 0
f
f f check rays from
‐ +0
Geometrical Optics
https://youtu.be/uQE659ICjqQ
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LENSTYPE
CommonLensTypes
Planar convex
f > 0f > 0
Bi-convex
• symmetric lenses cancel some aberrations
• focus or magnify light
• produce real or virtual images
ForSimulations,http://phet.colorado.edu/sims/geometric‐optics/geometric‐optics_en.html
http://physics.bu.edu/~duffy/java/Opticsa1.html
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RayTracing
• Converginglens
http://upload.wikimedia.org/wikipedia/commons/8/82/Large_convex_lens.jpg
CommonLensTypes
Bi-concave
f < 0f < 0
Planar concave
• increase f of systems
• symmetric lenses cancel some aberrations
• light expanders
• produce real or virtual images
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RayTracing
• DivergingLens
http://en.wikipedia.org/wiki/File:Concave_lens.jpg
EyeAnatomy
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HumanLensFar distance Short distance
LensesMommyNeverMentioned
Meniscus (convex and concave)
f > 0 or f < 0
• used to change f or light collection in system
• aplanatic: won’t introduce spherical abbs
• BFL: back focal length• EFL: effective focal length,
for a thick lens or imaging system composed of multiple lenses/mirrors
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LensesMommyNeverMentioned
Cylindrical
• Used when magnification needed in only one dimension (slits, etc)
• Focus into a line instead of a point
f > 0 or f < 0
LensesMommyNeverMentioned
f > 0
Ball
f > 0
Gradient index (GRIN)
•collimate high-angle outputs (diode lasers, fibers)
• easy alignment, high coupling efficiencies
• easy to correct aberrations
• used in laser diode coupling
n=1.406
n=1.386
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TheFundamentalLaw
2211 sinsin nn
1
2
n1 n2
taken wrt normal
for n2 > n1:ray bends towardsnormal
Snell’s Law
=
Snell’sLawSimulator
http://interactagram.com/physics/optics/refraction/
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ThePowerofSnell’sLaw
h = 0.7 mm
d = 1 mm
• Snell’s Law can calculate the focal spot of the glass sphere.
• Glass spheres are used to couple light into and from optical fibers. Use Snell’s law and that is all!
note: these rays are NOT paraxial
Paraxial: a ray makes a small angle to the optical axis of the system
LensMaker’sEquation
• Thefocallengthofathicklensin aircanbecalculatedfromthisequation.
Wheref isthefocaldistancefromlensnlens istherefractiveindexofthelensmaterial,R1 istheradiusofcurvatureofthelenssurfaceclosesttothelightsource,R2 istheradiusofcurvatureofthelenssurfacefarthestfromthelightsource,andd isthethicknessofthelens(thedistancealongthelensaxisbetweenthetwosurfacevertices).
11
1
1
1
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Thin LensEquation
• Ifd issmallcomparedtoR1 andR2,thenthethinlens approximationcanbemade.
• Ex)thinplanar‐convexlens,radius=50mm,=1.5,whatisf?
1.5 1
or 1.5 1 ,
=100mm
11
1
1
R1
R2
GaussianLensFormula
• Withtheparaxialapproximation,Gaussianlensformulaisasfollows
•
– iftheobjectdistanceSo becomesinfinity,thenSi becomesf.
– Whatare if isat600,200,150,100,and50mm?
–∗ 120 ,200,300,∞,and‐100mm
• Magnification Gaussian Lens Formula, For simulations, http://graphics.stanford.edu/courses/cs178-10/applets/gaussian.html
So is the distance to an object from lensSi is the distance from lens to image
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ThinLensEquationSign
So Si f
+ + +
+ ‐ +
+ ‐ ‐
1 1 1
Coupling:LamptoFiber
Goal: couple as much light as possible from this lamp into the fiber
Solution: f = 10 mm, D = 5 mm planar convex lens (cheap)