2015-09-14

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GEOMETRICALOPTICSI

Lecture1

Biophotonics

JaeGwan Kim

jaekim@gist.ac.kr ,X2220

SchoolofInformationandCommunicationEngineering

Gwangju InstituteofSciencesandTechnology

SomeCourseNotes

LectureNoteswillbeprovidedontheweborsentbyemail

OfficeHourswillbeanytimeaslongasI’matoffice

Emailforappointment:jaekim@gist.ac.kr

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ModuleGoal

• Learnenoughbasicopticstocommunicatehowtocouplelight frompointAtopointB

camera

lasercouplelaserintoafiber

PMT

opticalfiber

pictureafluorescingcell

collectlightfromatissue

?

?

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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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LENSEQUATION

Refraction

n=1.33 n=1.51

n=1.0

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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

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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)

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HomeWork

• Derive usingthefollowingfigure

Center of lens

Optical axis

image

object