MicroscopyField Guide toTomasz S. TkaczykSPIE Field GuidesVolume FG13John E. Greivenkamp, Series EditorBellingham, WashingtonUSALibrary of Congress Cataloging-in-Publication Data Tkaczyk, Tomasz S. Field guide to microscopy / Tomasz S. Tkaczyk. p. cm. --(The field guide series) Includes bibliographical references and index. ISBN 978-0-8194-7246-5 1.Microscopy--Handbooks, manuals, etc.I. Title.QH205.2.T53 2009 502.8'2--dc22 2009049648 Published by SPIE P.O. Box 10Bellingham, Washington98227-0010 USA Phone: +1 360.676.3290 Fax: +1 360.647.1445 Email:spie@spie.org Web:http://spie.org Copyright2010TheSocietyofPhoto-OpticalInstrumentation Engineers (SPIE) All rights reserved. No part of this publication may be reproduced or distributed in any form or by any means without written permission of the publisher. The content of this book reflects the work and thought of the author. Everyefforthasbeenmadetopublishreliableandaccurate informationherein,butthepublisherisnotresponsibleforthe validityoftheinformationorforanyoutcomesresultingfrom reliance thereon. Printed in the United States of America. Introduction to the Series WelcometotheSPIEFieldGuidesaseriesof publications written directly for the practicing engineer or scientist.Manytextbooksandprofessionalreference bookscoveropticalprinciplesandtechniquesindepth. TheaimoftheSPIEFieldGuidesistodistillthis information,providingreaderswithahandydeskor briefcasereferencethatprovidesbasic,essential informationaboutopticalprinciples,techniques,or phenomena,includingdefinitionsanddescriptions,key equations,illustrations,applicationexamples,design considerations,andadditionalresources.Asignificant effortwillbemadetoprovideaconsistentnotationand style between volumes in the series. EachSPIE FieldGuide addressesa majorfieldofoptical science and technology. The concept of these Field Guides isaformat-intensivepresentationbasedonfiguresand equations supplemented by concise explanations. In most cases,thismodularapproachplacesasingletopicona page, and provides full coverage of that topic on that page. Highlights,insights,andrulesofthumbaredisplayedin sidebarstothemaintext.Theappendicesattheendof eachFieldGuideprovideadditionalinformationsuchas relatedmaterialoutsidethemainscopeofthevolume, key mathematical relationships, and alternative methods. While complete in their coverage, the concise presentation may not be appropriate for those new to the field. TheSPIEFieldGuidesareintendedtobeliving documents.Themodularpage-basedpresentationformat allowsthemtobeeasilyupdatedandexpanded.Weare interested in your suggestions for new Field Guide topics as well as what material should be added to an individual volumetomaketheseFieldGuidesmoreusefultoyou. Please contact us at fieldguides@SPIE.org. John E. Greivenkamp, Series Editor College of Optical Sciences The University of Arizona The Field Guide Series Keepinformationatyourfingertipswithallofthetitles in the Field Guide series: Field Guide to Geometrical Optics, John E. Greivenkamp (FG01) Field Guide to Atmospheric Optics, Larry C. Andrews (FG02) Field Guide to Adaptive Optics, Robert K. Tyson & Benjamin W. Frazier (FG03) Field Guide to Visual and Ophthalmic Optics, Jim Schwiegerling (FG04) Field Guide to Polarization, Edward Collett (FG05) Field Guide to Optical Lithography, Chris A. Mack (FG06) Field Guide to Optical Thin Films, Ronald R. Willey (FG07) Field Guide to Spectroscopy, David W. Ball (FG08) Field Guide to Infrared Systems, Arnold Daniels (FG09) Field Guide to Interferometric Optical Testing, Eric P. Goodwin & James C. Wyant (FG10) Field Guide to Illumination, Angelo V. Arecchi; Tahar Messadi; R. John Koshel (FG11) Field Guide to Lasers, Rdiger Paschotta (FG12) Field Guide to Microscopy, Tomasz Tkaczyk (FG13) Field Guide to Laser Pulse Generation, Rdiger Paschotta (FG14) Field Guide to Infrared Systems, Detectors, and FPAs, Second Edition, Arnold Daniels (FG15) Field Guide to Optical Fiber Technology, Rdiger Paschotta (FG16) Preface to the Field Guide to Microscopy Inthe17thcenturyRobertHookedevelopedacompound microscope, launching a wonderful journey. The impact of his inventionwasimmediate;inthesamecenturymicroscopy gavenametocellsandimagedlivingbacteria.Sincethen microscopyhasbeenthewitnessandsubjectofnumerous scientificdiscoveries,servingasaconstantcompanionin humans quest to understand life and the world at the small end of the universes scale. Microscopyisoneofthemostexcitingfieldsinoptics,asits varietyappliesprinciplesofinterference,diffraction,and polarization. It persists in pushing the boundaries of imaging limits.Forexample,lifesciencesinneedofnanometer resolutionrecentlybrokethediffractionlimit.Thesenew super-resolutiontechniqueshelpednamemicroscopythe method of the year by Nature Methods in 2008.

Microscopywillcriticallychangeoverthenextfewdecades. Historically,microscopywasdesignedforvisualimaging; however,enormousrecentprogress(indetectors,light sources,actuators,etc.)allowstheeasingofvisual constrains,providingnewopportunities.Iamexcitedto witnessmicroscopyspathtowardbothintegrated,digital systems and nanoscopy. ThisFieldGuidehasthreemajoraims:(1)togiveabrief overview of concepts used in microscopy; (2) to present major microscopyprinciplesandimplementations;and(3)topoint tosomerecentmicroscopytrends.Whilemanypresented topicsdeserveamuchbroaderdescription,thehopeisthat thisFieldGuidewillbeausefulreferenceineveryday microscopy work and a starting point for further study. Iwouldliketoexpressmyspecialthankstomycolleague hereatRiceUniversity,MarkPierce,forhiscrucialadvice throughoutthewritingprocessandhistremendoushelpin acquiring microscopy images. This Field Guide is dedicated to my family: my wife, Dorota, and my daughters, Antonina and Karolina. Tomasz TkaczykRice University vii Table of Contents Glossary of Symbolsxi

Basics Concepts1Nature of Light1 The Spectrum of Microscopy2Wave Equations3 Wavefront Propagation4 Optical Path Length (OPL)5 Laws of Reflection and Refraction6 Total Internal Reflection7Evanescent Wave in Total Internal Reflection8 Propagation of Light in Anisotropic Media9Polarization of Light and Polarization States10 Coherence and Monochromatic Light11 Interference12 Contrast vs Spatial and TemporalCoherence13 Contrast of Fringes (Polarizationand Amplitude Ratio)15Multiple Wave Interference16 Interferometers17 Diffraction18 Diffraction Grating 19 Useful Definitions from Geometrical Optics21 Image Formation22 Magnification23 Stops and Rays in an Optical System24 Aberrations25 Chromatic Aberrations26 Spherical Aberration and Coma27 Astigmatism, Field Curvature, and Distortion28 Performance Metrics29 Microscope Construction31 The Compound Microscope31The Eye32 Upright and Inverted Microscopes33 The Finite Tube Length Microscope34 viii Table of Contents Infinity-Corrected Systems35 Telecentricity of a Microscope36 Magnification of a Microscope37 Numerical Aperture38 Resolution Limit39 Useful Magnification40 Depth of Field and Depth of Focus41 Magnification and Frequency vs Depthof Field42 Khler Illumination43 Alignment of Khler Illumination45 Critical Illumination46 Stereo Microscopes47 Eyepieces48 Nomenclature and Marking of Objectives50 Objective Designs51 Special Objectives and Features53 Special Lens Components55 Cover Glass and Immersion56 Common Light Sources for Microscopy58 LED Light Sources59 Filters60 Polarizers and Polarization Prisms61 Specialized Techniques63 Amplitude and Phase Objects63 The Selection of a Microscopy Technique64 Image Comparison65 Phase Contrast66 Visibility in Phase Contrast69 The Phase Contrast Microscope70 Characteristic Features of Phase Contrast71Amplitude Contrast72 Oblique Illumination73 Modulation Contrast74 Hoffman Contrast75 Dark Field Microscopy76 Optical Staining: Rheinberg Illumination77 ix Table of Contents Optical Staining: Dispersion Staining78 Shearing Interferometry: The Basis for DIC79 DIC Microscope Design80Appearance of DIC Images81 Reflectance DIC82 Polarization Microscopy83 Images Obtained with Polarization Microscopes84 Compensators85 Confocal Microscopy86 Scanning Approaches87 Images from a Confocal Microscope89 Fluorescence90 Configuration of a Fluorescence Microscope91 Images from Fluorescence Microscopy93 Properties of Fluorophores94 Single vs Multi-Photon Excitation95 Light Sources for Scanning Microscopy96 Practical Considerations in LSM97 Interference Microscopy98 Optical Coherence Tomography/Microscopy99 Optical Profiling Techniques100 Optical Profilometry: System Design101 Phase-Shifting Algorithms102 Resolution Enhancement Techniques103 Structured Illumination: Axial Sectioning103 Structured Illumination: ResolutionEnhancement104 TIRF Microscopy105 Solid Immersion106 Stimulated Emission Depletion107 STORM108 4Pi Microscopy109 The Limits of Light Microscopy110 Other Special Techniques111 Raman and CARS Microscopy111 SPIM112 x Table of Contents Array Microscopy113 Digital Microscopy and CCD Detectors114 Digital Microscopy114 Principles of CCD Operation115 CCD Architectures116 CCD Noise118 Signal-to-Noise Ratio and the Digitizationof CCD119 CCD Sampling120 Equation Summary122 Bibliography128 Index133 xi Glossary of Symbols a(x, y), b(x, y)Background and fringe amplitude AOVector of light passing through amplitudeObject AR, ASAmplitudes of reference and sample beamsb Fringe period cVelocity of lightCContrast, visibility Cac Visibility of amplitude contrast Cph Visibility of phase contrast Cph-min Minimum detectable visibility of phase contrast dAiry disk dimension dDecay distance of evanescent wave dDiameter of the diffractive object dGrating constant dResolution limit DDiopters DNumber of pixels in the x and y directions (Nx and Ny, respectively) DAVector of light diffracted at the amplitudeobject DOFDepth of focus DPVector of light diffracted at phase object DpinholePinhole diameter dxy, dzSpatial and axial resolution of confocal microscope EElectric field EEnergy gap Ex and EyComponents of electric field F Coefficient of finesse F Fluorescent emission fFocal length fC, fFFocal length for lines C and F feEffective focal length FOVField of view FWHMFull width at half maximum h Plancks constant h, h' Object and image height HMagnetic field I Intensity of light i, j Pixel coordinates Io Intensity of incident light xii Glossary of Symbols (cont.) Imax, Imin Maximum and minimum intensity in the image I, It, Ir Irradiances of incident, transmitted, and reflected light I1, I2, I3 Intensity of successive images 0I , 2/ 3I t, 4/ 3I t Intensities for the image point and three consecutive grid positions k Number of events k Wave numberL Distance lc Coherence length m Diffraction order M MagnificationMmin Minimum microscope magnification MP Magnifying power MTF Modulation transfer function Mu Angular magnification n Refractive index of the dielectric median Step number N Expected value N Intensity decrease coefficient N Total number of grating linesnaProbability of two-photon excitationNANumerical aperture ne Refractive index for propagation velocity of extraordinary wave nm, nr Refractive indices of the media surrounding the phase ring and the ring itself noRefractive index for propagation velocity of ordinary wave n1Refractive index of media 1 n2Refractive index of media 2o, eOrdinary and extraordinary beams ODOptical density OPDOptical path differenceOPLOptical path length OTF Optical transfer function OTL Optical tube length PProbability Pavg Average powerPOVector of light passing through phase object xiii Glossary of Symbols (cont.) PSFPoint spread function Q Fluorophore quantum yield r Radius r Reflection coefficients r, m, and oRelative, media, or vacuum rAS Radius of aperture stop rPR Radius of phase ringr Radius of filter for wavelength s, s' Shear between wavefront object and image spaceSPinhole/slit separation s Lateral shift in TIR perpendicular component of electromagnetic vector s Lateral shift in TIR for parallel component of electromagnetic vector SFD Factor depending on specific Fraunhofer approximation SMVector of light passing through surrounding media SNR Signal-to-noise ratio SR Strehl ratio t Lens separation t Thickness t Time tTransmission coefficient T Time required to pass the distance between wave oscillations T Throughput of a confocal microscopetc Coherence time u, u' Object, image aperture angleVd, Ve Abbe number as defined for lines d, F, C or e, F', C' Vm Velocity of light in mediaw Width of the slit x, y CoordinateszDistance along the direction of propagationzFraunhofer diffraction distancez, z'Object and image distances zm, zoImaged sample depth, length of referencepath xiv Glossary of Symbols (cont.) o Angle between vectors of interfering waves o Birefringent prism angle o Grating incidence angle in plane perpendicular to grating plane os Visual stereo resolving power | Grating diffraction angle in plane perpendicular to grating plane Angle of fringe localization plane Convergence angle of a stereo microscope Incidence / diffraction angle from the plane perpendicular to grating plane I Retardation o Birefringence o Excitation cross section of dyeozDepth perception Ab Axial phase delay Af Variation in focal length AkPhase mismatch Az, Az' Object and image separations A Wavelength bandwidth A Frequency bandwidth A Phase delay A Phase difference A Phase shift Amin Minimum perceived phase difference c Angle between interfering beams c Dielectric constant, i.e., medium permittivityq Quantum efficiencyu' Refraction angle ucr Critical angle ui Incidence angle ur Reflection angle Wavelength of lightp Peak wavelength for the mth interference order Magnetic permeability v Frequency of lightv Repetition frequency Propagation direction Spatial frequency o Molecular absorption cross section xv Glossary of Symbols (cont.) odarkDark noise ophotonPhoton noise oreadRead noise t Integration time t Length of a pulse t Transmittance Incident photon flux Optical power Phase difference generated by a thin film o Initial phaseo Phase delay through the objectp Phase delay in a phase plate TFPhase difference generated by a thin film e Angular frequencye Bandgap frequency and Perpendicular and parallel components of the light vector Microscopy: Basic Concepts 1 Nature of Light Opticsusestwoapproaches,termedtheparticleandwave models,todescribethenatureoflight.Theformerarises from atomic structure, where the transitions between energy levelsarequantized.Electronscanbeexcitedintohigher energylevelsviaexternalprocesseswiththereleaseofa discrete quantum of energy (aphoton) upon their decay toa lower level.Thewavemodelcomplementsthiscorpusculartheoryand explains optical effects involving diffraction and interference. Thewaveandparticlemodelscanberelatedthroughthe frequencyofoscillations,withtherelationshipbetween quanta of energy and frequency given byE h [in eV or J], whereh=4.1356671015[eVs]=6.6260681034[Js]is Plancksconstant,andisthefrequencyoflight[Hz]. The frequency of a wave is the reciprocal of its period T [s]: 1T. The period T [s] corresponds to one cycle of a wave or, if defined in terms of the distance required to performone full oscillation, describes the wavelength of light [m]. The velocityoflightinfreespaceis2.99792108m/sandis definedasthedistancetraveledinoneperiod()dividedby the time taken (T):c T. Note that wavelength is often measured indirectly as time T required to pass the distance between wave oscillations.The relationship for the velocity of light c can be rewritten in terms of wavelength and frequency asc .TTime (t)Distance (z) Microscopy: Basic Concepts 2 The Spectrum of Microscopy Therangeofelectromagneticradiationiscalledthe electromagnetic spectrum. Various microscopy techniques employwavelengthsspanningfromx-rayradiationand ultravioletradiation(UV)throughthevisiblespectrum (VIS)toinfraredradiation(IR).Thewavelengthin combination with the microscope parameters determines the resolutionlimitofthemicroscope(0.61/NA).Thesmallest featureresolvedusinglightmicroscopyanddeterminedby diffraction is approximately 200 nm for UV light with a high numerical aperture (for more details, see Resolution Limit on page39).However,recentlyemergingsuper-resolution techniquesovercomethisbarrier,andfeaturesare observable in the 2050 nm range. 0.1 nm1.0 nm10.0 nm100.0 nm1.0 m10.0 m100.0 m gamma rays( ~ 3X1024 Hz)X rays( ~ 3X1016 Hz)Ultraviolet( ~ 8X1014 Hz)Visible( ~ 6X1014 Hz)Infrared( ~ 3X1012 Hz)Resolution Limit of Human EyeLimit of Classical Light MicroscopyLimit of Light Microscopy with superresolution techniquesLimit of Electron MicroscopyEphithelial CellsRed Blood CellsBacteriaVirusesProteinsDNA / RNAAtomsFrequency /Wavelength/Object Type380.0 nm750.0 nm

Microscopy: Basic Concepts 3 Wave Equations Maxwellsequationsdescribethepropagationofan electromagneticwave.Forhomogenousandisotropicmedia, magnetic(H)andelectric(E)componentsofan electromagnetic field can be described by the wave equations derived from Maxwells equations:22m m2 0EEt 22m m2 0HHt , whereisadielectricconstant,i.e.,medium permittivity while is a magnetic permeability:m o r m o r = Indicesr,m,andostandforrelative,media,orvacuum, respectively. Theaboveequationsindicatethatthetimevariationofthe electricfieldandthecurrentdensitycreatesatime-varying magneticfield.Variationsinthemagneticfieldinducea time-varyingelectricfield.Bothfieldsdependoneachother and compose an electromagnetic wave. Magnetic and electric components can be separated. H FieldE Field Theelectriccomponentofanelectromagneticwavehas primarysignificanceforthephenomenonoflight.Thisis becausethemagneticcomponentcannotbemeasuredwith optical detectors. Therefore, the magnetic component is most oftenneglected,andtheelectricvectorEiscalledalight vector. Microscopy: Basic Concepts 4 Wavefront Propagation Lightpropagatingthroughisotropicmediaconformstothe equation ( )osin E A t kz = e + , wheretistime,zisdistancealongthedirectionof propagation, and e is an angular frequency given by m2 2 VTt te= =. Thetermkziscalledthephaseoflight,whileoisan initialphase.Inaddition,krepresentsthewavenumber (equal to 2t/) and Vm is the velocity of light in media: 2kz nz =Theabovepropagationequationpertainstothespecialcase when the electric field vector varies only in one plane.The refractive index of the dielectric media n describes the relationshipbetweenthespeedoflightinavacuumandin media. It ismcnV= , where c is the speed of light in vacuum. An alternative way to describe the propagation of an electric field is with an exponential (complex) representation: ( )oexp E A i t kz = e + ( . This form allows the easy separation of phase components of an electromagnetic wave.ztEAo/ko/n Microscopy: Basic Concepts 5 Optical Path Length (OPL) FermatsprinciplestatesthatThepathtraveledbya lightwavefromapointtoanotherpointisstationarywith respecttovariationsofthispath.Inpracticalterms,this means that light travels along the minimum time path. Opticalpathlength(OPL)isrelatedtothetimerequired forlighttotravelfrompointP1topointP2.Itaccountsfor the media density through the refractive index:t 1cndsP1P2 or OPL n dsP1P2, where ds2 dx2 dy2 dz2. Opticalpathlengthcanalsobediscussedinthecontextof thenumberofperiodsrequiredtopropagateacertain distanceL. In a mediumwith refractive index n, light slows down and more wave cycles are needed. Therefore, OPL is an equivalentpathforlighttravelingwiththesamenumberof periods in a vacuum: nL OPL . Opticalpathdifference (OPD)isthedifference betweenopticalpathlengths traversed by two light waves:2 2 1 1L n L n OPD . OPD can also be expressed as a phase difference: 2OPD . Ln = 1nm > 1 Microscopy: Basic Concepts 6 Laws of Reflection and Refraction Light rays incident on an interface between different dielectric media experience reflection and refraction as shown. ReflectionLaw:Anglesofincidenceandreflectionare related by i r . RefractionLaw(SnellsLaw):Incidentandrefracted angles are related to each other and to the refractive indices of the two media by Snells Law:

isin sin n n' ' . Fresnelreflection:Thedivisionoflightatadielectric boundary into transmitted and reflected rays is described for nonlossy, nonmagnetic media by the Fresnel equations: Reflectance coefficients Transmission Coefficients 2ir2isinsin'IrI ' 2r|| i|| 2|| itantanI 'rI ' 2 2t i2i4sin cossinI 'tI ' 2 2t||i|| 2 2|| i i4sin cossin cosI'tI ' ' tand raretransmissionandreflectioncoefficients, respectively.I,It,andIraretheirradiancesofincident, transmitted, and reflected light, respectively. and denote perpendicularandparallelcomponentsofthelightvector withrespecttotheplaneofincidence.iandinthetable aretheanglesofincidenceandreflection/refraction, respectively.Atanormalincidence(=i=0deg),the Fresnel equations reduce to 2||2n nr r rn n and

||24nnt t tn n . irIncident Light Reflected LightRefracted Lightnn > nMicroscopy: Basic Concepts 7 Total Internal Reflection Whenlightpassesfromonemediumtoamediumwitha higher refractive index, the angle of the light in the medium bendstowardthenormal,accordingtoSnellsLaw. Conversely, when light passes from one medium to a medium withalowerrefractiveindex,theangleofthelightinthe second medium bends away from the normal. If the angle of refraction is greater than 90 deg, the light cannot escape the densermedium,anditreflectsinsteadofrefracting.This effectisknownastotal internalreflection(TIR). TIRoccursonlyfor illuminationwithanangle largerthanthecritical angle, defined as 1cr2arcsinnn . Itappears,however,thatlightcanpropagatethrough(ata limitedrange)tothelower-densitymaterialasan evanescentwave (a nearly standing wave occurring at the materialboundary),evenifilluminatedunderanangle largerthancr.Suchaphenomenoniscalledfrustrated totalinternalreflection.FrustratedTIRisused,for example,withthinfilms(TF)tobuildbeamsplitters.The properselectionofthefilmthicknessprovidesthedesired beam ratio (see the figure below for various split ratios). Note thatthemaximumfilmthicknessmustbeapproximatelya singlewavelengthorless,otherwiselightdecaysentirely. Theeffectofanevanescentwavepropagatinginthelower-densitymaterialunderTIRconditionsisalsousedintotal internal reflection fluorescence (TIRF) microscopy. 0 20 40 60 80 100 0.00.51.0 n1R > crn2 < n1 TransmittanceReflectanceTransmittanceReflectanceOpticalThicknessofthinfilm(TF)inunitsofwavelength Microscopy: Basic Concepts 8 Evanescent Wave in Total Internal Reflection A beam reflected at the dielectric interface during total internal reflection is subject to a small lateral shift, also known as the Goos-Hnchen effect. The shift is different for the parallel and perpendicular components of the electromagnetic vector. Lateral shift in TIR Parallel* componentof e/m vector 1||22 22ctansin sinnsn Perpendicular*component of e/m vector 2 21ctansin sinsn * to the plane of incidence Theintensityoftheilluminatingbeamdecaysexponentially with distance y in the direction perpendicular to the material boundary: o exp / I I y d . Note that d denotes the distance at which the intensity of the illuminating light Io drops by e. The decay distance is smallerthanawavelength.Itisalsoinversely proportional to the illumination angle. Decay distance (d) of evanescent wave Decay distance as a function of incidence and critical angles 2 21c14sin sindn Decay distance as a function of incidenceangleandrefractive indices of media d 41n12sin2 n22 n2 < n1n1 > crdyzI=Ioexp(-y/d)sI=IoMicroscopy: Basic Concepts 9 Propagation of Light in Anisotropic Media Inanisotropicmediathevelocityoflightdependsonthe directionofpropagation.Commonanisotropicandoptically transparentmaterialsincludeuniaxialcrystals.Such crystalsexhibitonedirectionoftravelwithasingle propagationvelocity.Thesinglevelocitydirectioniscalled theopticaxisofthecrystal.Foranyotherdirection,there are two velocities of propagation.Thewaveinbirefringentcrystalscanbedividedintotwo components:ordinaryandextraordinary.Anordinary wavehasauniformvelocityinalldirections,whilethe velocityofanextraordinarywavevarieswithorientation. Theextremevalueofanextraordinarywavesvelocityis perpendiculartotheopticaxis.Bothwavesarelinearly polarized,whichmeansthattheelectricvectoroscillatesin oneplane.Thevibrationplanesofextraordinaryand ordinaryvectorsareperpendicular.Refractiveindices correspondingto the direction of the opticaxisand perpendicularto theopticaxisare no=c/Voandne= c/Ve respectively.Uniaxialcrystals can be positive or negative (see table). The refractive index n() for velocities between the two extreme (no and ne) values is 2 22 2 2o e1 cos sinn n n . Notethatthepropagationdirection(withregardtothe opticaxis)isslightlyofffromtheraydirection,whichis defined by the Poynting (energy) vector. Uniaxial CrystalRefractive index Abbe Number Wavelength Range [m] Quartzno = 1.54424 ne = 1.55335 70 69 0.184.0 Calciteno = 1.65835 ne = 1.48640 50 68 0.22.0 The refractive index is given for the D spectral line (589.2 nm). (Adapted from Pluta, 1988)Positive Birefringence Ve Vo Negative BirefringenceVe Vo Positive BirefringencenoneOptic AxisNegative BirefringencenoneOptic Axis Microscopy: Basic Concepts 10 3D ViewFront Top PolarizationAmplitudesCircular11/2Linear110Linear010Elliptical11/4Polarization of Light and Polarization States Theorientationcharacteristicofalightvectorvibratingin timeandspaceiscalledthepolarizationoflight.For example,ifthevectorofanelectricwavevibratesinone plane,thestateofpolarizationislinear.Avectorvibrating with a random orientation represents unpolarized light.The wave vector E consists of two components Ex and Ey.( ),x yE z t E E = +( )expx x xE A i t kz = e + ( ( )exp .y y yE A i t kz (= e + Theelectricvectorrotatesperiodically(theperiodicity correspondstowavelength)intheplaneperpendicularto thepropagationaxis(z)andgenerallyformsanelliptical shape. The specific shape depends on the Ax and Ay ratios and thephasedelaybetweentheExandEycomponents,defined as A = x y. Linearlypolarizedlightisobtainedwhenoneofthe componentsExorEyiszero,orwhenAiszeroort. Circularly polarized light is obtained when Ex = Ey and A = t/2. The light is called right circularly polarized (RCP) if it rotatesinaclockwisedirectionorleftcircularlypolarized (LCP)ifitrotatescounterclockwisewhenlookingatthe oncoming beam. Microscopy: Basic Concepts 11 Coherence and Monochromatic Light An ideal light wave that extends in space at any instance to and has only one wavelength (or frequency ) is said to bemonochromatic.Iftherangeofwavelengthsor frequenciesisverysmall(around o or o ,respectively), thewaveisquasi-monochromatic.Suchawavepacketis usually called a wave group.Notethatformonochromaticandquasi-monochromatic waves, no phase relationship is required, and the intensity of lightcanbecalculatedasasimplesummationofintensities fromdifferentwaves;phasechangesareveryfastand random, so only the average intensity can be recorded.If multiple waves have a common phase relation dependence, theyarecoherentorpartiallycoherent.Thesecases correspond to full- and partial-phase correlation respectively. A common source of a coherent wave is a laser where waves mustbeinresonanceandthereforeinphase.Theaverage lengthofthewavepacket(group)iscalledthecoherence length, while the time required topass this lengthis called coherence time. Both values are linked by the equations c c1 Vt l where coherence length is2cl. Thecoherencelengthlcandtemporalcoherencetcare inverselyproportionaltothebandwidthofthelight source.Spatialcoherenceisatermrelatedtothecoherenceof light with regard to the extent of the light source. The fringe contrast varies for interference of any two spatially different source points. Light is partially coherent if its coherence is limited by the source bandwidth, dimension, temperature, or other effects. Microscopy: Basic Concepts 12 Interference Interferenceisaprocessofsuperpositionoftwocoherent (correlated) or partially coherent waves. Waves interact with eachother,andtheresultingintensityisdescribedby summing the complex amplitudes (electric fields) E1 and E2 of both wavefronts: E1 = A1 exp i et kz + 1( )

( and E2 = A2 exp i et kz + 2( )

(. The resultant field is E = E1 + E2. Therefore,theinterferenceof the two beams can be written as*, I EE =( )2 21 2 1 22 cos , I A A A A = + + A( )1 2 1 22 cos , I I I I I = + + A*1 1 1, I E E =*2 2 2, I E E =and 2 1, A = where*denotesaconjugatefunction,Iistheintensityof light,Aisanamplitudeofanelectricfield,andAisthe phasedifferencebetweenthetwointerferingbeams. ContrastC(calledalsovisibility)oftheinterference fringes can be expressed as max minmax min.I ICI I=+ Thefringeexistenceandvisibilitydependsonseveral conditions. To obtain the interference effect, -Interferingbeamsmustoriginatefromthesamelight source and be temporally and spatially coherent; -The polarization of interfering beams must be aligned;-To maximize the contrast, interfering beams should have equal or similar amplitudes. Conversely,iftwononcorrelated,randomwavesareinthe sameregionofspace,thesumofintensities(irradiances)of these waves gives a total intensity in that region: 1 2. I I I = +E1E2IPropagating WavefrontsMicroscopy: Basic Concepts13 Contrast vs Spatial and Temporal Coherence Theresultofinterferenceisaperiodicintensitychangein space,whichcreatesfringeswhenincidentonascreenor detector. Spatial coherence relates to the contrast of these fringesdependingontheextentofthesourceandisnota functionofthephasedifference(orOPD)betweenbeams. The intensity of interfering fringes is given byII1 I2 2CSource Extent I1I2 cos 'M, where C is a constant, depending on the extent of the source. C = 1 C = 0.5 Thespatialcoherencecanbeimprovedthroughspatial filtering. For example, light can be focused on the pinhole (or coupledintothefiber)byusingamicroscopeobjective.In microscopy,spatialcoherencecanbeadjustedbychanging the diaphragm size in the conjugate plane of the light source. Microscopy: Basic Concepts 14 Contrast vs Spatial and Temporal Coherence (cont.) TheintensityofthefringesdependsontheOPDandthe temporalcoherenceofthesource.Thefringecontrast trendstowardzeroastheOPDincreasesbeyondthe coherence length: II1 I2 2 I1I2COPDcos 'M. The spatial width of a fringe pattern envelope decreases with shortertemporalcoherence.Thelocationoftheenvelopes peak (with respect to the reference) and narrow width can be efficientlyusedasagatingmechanisminbothimagingand metrology. For example, it is used in interference microscopy foropticalprofiling(whitelightinterferometry)andfor imagingusingopticalcoherencetomography.Examplesof shortcoherencesourcesincludewhitelightsources, luminescent diodes, and broadband lasers. Longcoherencelengthisbeneficialinapplicationsthatdo notnaturallyprovidenear-zeroOPD,e.g.,insurface measurementswithaFizeauinterferometer.Microscopy: Basic Concepts15 Contrast of Fringes (Polarization and Amplitude Ratio) The contrast of fringes depends on the polarization orientation of the electric vectors. For linearly polarized beams, it can be described asCcosD , where D represents the angle between polarization states.Angle between Electric Vectors of Interfering Beams 0S/6S/3S/2 Interference Fringes Fringecontrastalsodependsontheinterferingbeams amplituderatio.Theintensityofthefringesissimply calculatedbyusingthemaininterferenceequation.The contrastismaximumforequalbeamintensitiesandforthe interferencepattern, defined as 1 2 1 22 cos , I I I I I'M it isC 2 I1I2I1 I2. Ratio between Amplitudes of Interfering Beams 10.50.250.1 Interference Fringes Microscopy: Basic Concepts 16 Multiple Wave Interference Iflightreflectsinsideathinfilm,itsintensitygradually decreases and multiple beam interference occurs. The intensity of reflected light is ( )( )2r i 2sin / 21 sin / 2FI IF=+ , and for transmitted light is ( )t i 211 sin / 2I IF=+ . The coefficient of finesse F of such a resonator is F =4r1 r ( )2. Becausephasedependsonthewavelength,itispossibleto designselectiveinterferencefilters.Inthiscase,a dielectricthinfilmiscoatedwithmetalliclayers.Thepeak wavelength for the mth interference order of the filter can be defined as pTF2 cos2nt 'mu =| | |t\ . , where TF is the phase difference generated by a thin film of thickness t and a specific incidence angle. The interference order relates to the phase difference in multiples of 2t. Interference filters usually operate for illumination with flat wavefrontsatanormalincidenceangle.Therefore,the equation simplifies as p2ntm = . Thehalfbandwidth (HBW) of the filter for normal incidence is p1[m]rHBWm= t. The peak intensity transmission is usually at 20% to 50%, or upto90%oftheincidentlightformetal-dielectricormulti-dielectric filters respectively. 0 1 0Reflected LightTransmitted Light4 3 2 Microscopy: Basic Concepts 17 Interferometers Duetothehighfrequencyoflight,itisnot possible to detect the phase of the light wave directly. To acquire the phase, interferometry techniques may be used. There are two major classesofinterferometers,basedon amplitudesplittingandwavefront splitting. Fromthepointofviewoffringepattern interpretation,interferometerscanalsobe divided into those that deliver fringes, which directly correspond to the phase distribution, andthoseprovidingaderivativeofthephasemap(also calledshearinginterferometers). Thefirsttypeisrealizedby obtainingtheinterferencebetween thetestbeamandareference beam. An example of such a system istheMichelsoninterfero-meter.Shearinginterfero-metersprovidetheintereference of two shifted object wavefronts.Thereare numerouswaysofintroducingshear (linear,radial,etc.).Examplesof shearinginterferometersincludethe parallelorwedgeplate,thegrating interferometer,theSagnac,and polarizationinterferometers(commonlyusedinmicroscopy). TheMach-Zehnderinterferometercanbeconfiguredfor directanddifferentialfringes,dependingonthepositionof the sample. ObjectMirrorBeam SplitterMach Zehnder Interferometer(Direct Fringes)Beam SplitterMirror Amplitude SplitWavefront SplitObjectMirrorBeam SplitterMach Zehnder Interferometer(Differential Fringes)Beam SplitterMirrorObjectReference MirrorBeam SplitterMichelson InterferometerTested WavefrontShearing Plate Microscopy: Basic Concepts 18 Diffraction Thebendingofwavesbyaperturesandobjectsiscalled diffractionoflight.Wavesdiffractedinsidetheoptical systeminterfere(forpathdifferenceswithinthecoherence lengthofthesource)witheachotherandcreatediffraction patterns in the image of an object. Destructive InterferenceDestructive InterferenceConstructive InterferenceConstructive InterferenceSmall Aperture StopLarge Aperture StopPoint Object Therearetwocommonapproximationsofdiffraction phenomena:Fresneldiffraction(near-field)and Fraunhoferdiffraction(far-field).Bothdiffractiontypes complementeachotherbutarenotsharplydivideddueto variousdefinitionsoftheirregions.Fraunhoferdiffraction occurswhenonecanassumethatpropagatingwavefronts are flat (collimated), while the Fresnel diffraction is the near-field case. Thus, Fraunhofer diffraction (distance z) for a free-spacecaseisinfinity,butinpracticeitcanbedefinedfora region 2FD dz S , where d is the diameter of the diffractive object, and SFD is a factor depending on approximation. A conservative definition oftheFraunhoferregionisSFD=1,whileformostpractical cases it can be assumed to be 10 times smaller (SFD = 0.1). Diffractioneffectsinfluencetheresolutionofanimaging systemandareareasonforfringes(ringpatterns)inthe imageofapoint.Specifically,Fraunhoferfringesappearin theconjugateimageplane.Thisisduetothefactthatthe imageislocatedintheFraunhoferdiffractingregionofan optical systems aperture stop.Microscopy: Basic Concepts 19 Diffraction Grating Diffractiongratingsareopticalcomponentsconsistingof periodic linear structures that provide organized diffraction oflight.Inpracticalterms,thismeansthatforspecific angles(dependingonilluminationandgratingparameters), it is possible to obtain constructive (2t phase difference) and destructive(tphasedifference)interferenceatspecific directions.Theanglesofconstructiveinterferenceare definedbythediffractiongratingequationandcalled diffraction orders (m). Gratings can be classified as transmission or reflection (mode ofoperation),amplitude(periodicamplitudechanges)or phase(periodicphasechanges),orruledorholographic (methodoffabrication).Ruledgratingsaremechanicallycut and usually have a triangular profile (each facet can thereby promoteselectdiffractionangles).Holographicgratingsare made using interference (sinusoidal profiles). Diffractionanglesdependontheratiobetweenthegrating constantandwavelengthsovariouswavelengthscanbe separated.Thismakesthemapplicableforspectroscopic detection or spectral imaging. The grating equation ism= d cos (sin | sin o) Microscopy: Basic Concepts 20 Diffraction Grating (cont.) The sign inthe diffraction gratingequation definesthe type ofgrating:Atransmissiongratingisidentifiedwitha minus sign (), and a reflective grating is identified with a plus sign (+). Foragratingilluminatedintheplaneperpendiculartothe grating, its equation simplifies and is m = d sin| sin o ( ). Incident Light0th order(Specular Reflection)GratingNormal -1st-2ndReflective Grating g = 0-3rd+1st +2nd+3rd+4th+- For normal illumination, the grating equation becomes sin . m d = | Thechromaticresolvingpowerofagratingdependson itssize(totalnumberoflinesN).Ifthegratinghasmore lines,thediffractionordersarenarrower,andtheresolving power increases:. mN =A Thefreespec-tralrangeAof thegratingisthe bandwidthinthe mthorderwithout overlappingother orders.Itdefines usefulbandwidth forspectroscopic detection as11 11.mm m +A = =Incident Light0th order(non-diffracted light)GratingNormal -1st-2ndTransmission Grating-3rd+1st +2nd+3rd+4th+-+-Microscopy: Basic Concepts21Useful Definitions from Geometrical Optics All optical systems consist of refractive or reflective interfaces (surfaces) changing the propagation angles of optical rays. Rays define the propagation trajectory and always travel perpendicular to the wavefronts. They are used to describe imaging in the regime of geometrical optics and to perform optical design. Thereare two optical spaces correspondingtoeachoptical system: object space and image space. Both spaces extend fromfto+fandaredividedintorealandvirtualparts. Abilitytoaccesstheimageorobjectdefinestherealpartof the optical space. Paraxialopticsisanapproximationassumingsmallray angles and is used to determine first-order parameters of the optical system (image location, magnification etc.). Thinlensesareopticalcomponentsreducedtozero thickness and are used to perform first-order optical designs (see next page). Thefocalpointofanopticalsystemisalocationthat collimatedbeamsconvergetoordivergefrom.Planes perpendicular to the optical axis at the focal points are called focal planes. Focal length is the distance between the lens (specifically, its principal plane) and the focal plane. For thin lenses, principal planes overlap with the lens. SignConvention:Thecommonsignconventionassigns positivevaluestodistancestracedfromlefttoright(the direction of propagation) and to the top. Angles are positive if theyaremeasured counterclockwisefrom normaltothesurfaceor opticalaxis.Iflight travelsfromrighttoleft, therefractiveindexis negative.Thesurface radiusismeasuredfrom itsvertextoitscenterof curvature. FFf f Microscopy: Basic Concepts 22 Image Formation Asimplemodeldescribingimagingthroughanoptical systemisbasedonthinlensrelationships.Arealimageis formed at the point where rays converge. Object Plane Image PlaneF Ff fz zReal Image Real ImageObjecthhx xn n Avirtualimageisformedatthepointfromwhichrays appear to diverge. For a lens made of glass, surrounded on both sides by air (n = n=1),theimagingrelationshipisdescribedbythe Newtonian equation xx' ff ' or2xx' f ' . Note that Newtonian equations refer to the distance from the focal planes so, in practice, they are used with thin lenses. Imaging can also be described by the Gaussian imaging equation 1f f 'z z' . The effective focal length of the system is e1 f f 'fn n' , where is the optical power expressed in diopters D [m1].Therefore,e1 n' nz' z f . For air, when n and n' are equal to 1, the imaging relation is e1 1 1z' z f .

Object PlaneImage PlaneF Ff fzzVirtual Imagen nMicroscopy: Basic Concepts23 Magnification Transversemagnification(alsocalledlateral magnification)ofanopticalsystemisdefinedastheratio oftheimageandobjectsizemeasuredinthedirection perpendicular to the optical axis: ( )z' f 'h' x' f z' fMh f ' x z z f f ' = = = = = =. Longitudinalmagnificationdefinestheratioofdistances for a pair of conjugate planes: 1 2z' f 'M Mz f| | A= |A\ ., where Az = z2 z1 2 1z' z ' z ' A = and 111h'Mh=222h 'Mh= . Angular magnification is the ratio of angular image size to angular object size and can be calculated with uu' zMu z'= = . Object PlaneImage PlaneF Ff fzzhhx xnnuh1 h2z1z2z2z1h2h1zuz Microscopy: Basic Concepts 24 Stops and Rays in an Optical System Theprimarystopsinanyopticalsystemaretheaperture stop(whichlimitslight)andfieldstop(whichlimitsthe extent of the imaged object or the field of view). The aperture stopalsodefinestheresolutionoftheopticalsystem.To determinetheaperturestop,allsystemdiaphragms includingthelensmountsshouldbeimagedtoeitherthe image or the object space of the system. The aperture stop is determinedasthesmallestdiaphragmordiaphragmimage (intermsofangle)asseenfromtheon-axisobject/image point in the same optical space.Note that there are two important conjugates of the aperture stop in object and image space. They are called the entrance pupil and exit pupil, respectively.The physical stop limiting the extent of the field is called the field stop. To find a field stop, all of the diaphragms should beimagedtotheobjectorimagespace,withthesmallest diaphragmdefiningtheactualfieldstop,asseenfromthe entrance/exit pupil. Conjugates of the field stop in the object and image space are called the entrance window and exit window, respectively.Twomajorraysthatpassthroughthesystemarethe marginalrayandthechiefray.Themarginalraycrosses the optical axis at the conjugate of the field stop (and object) and the edge of the aperture stop. The chief ray goes through theedgeofthefieldandcrossestheopticalaxisatthe aperture stop plane. Object PlaneImage PlaneChief RayMarginal RayApertureStopFieldStopEntrancePupilExitPupilEntranceWindowExitWindowIntermediateImage Plane Microscopy: Basic Concepts 25 Aberrations Individualsphericallensescannotdeliverperfectimaging becausetheyexhibiterrorscalledaberrations.All aberrationscanbeconsideredeitherchromaticor monochromatic. To correct for aberrations, optical systems usemultipleelements,asphericalsurfaces,andavarietyof optical materials. Chromaticaberrationsareaconsequenceofthedispersion of optical materials, which is a change in the refractive index asafunctionofwavelength.Theparameter-characterizing dispersion of any material is called the Abbe number and is defined as ddF C1 nVn n. Alternatively,the followingequation mightbeusedfor other wavelengths: eeF C1' 'nVn n. Ingeneral,Vcanbedefinedbyusingrefractiveindicesat anythreewavelengths,whichshouldbespecifiedfor materialcharacteristics.Indicesintheequationsdenote spectral lines. If V does not have an index, Vd is assumed. Geometricalaberrationsoccurwhenopticalraysdonot meet at a single point. There are longitudinal and transverse rayaberrationsdescribingtheaxialandlateraldeviations fromtheparaxialimageofapoint(alongtheaxisand perpendicular to the axis in the image plane), respectively. Waveaberrationsdescribeadeviationofthewavefront fromaperfectsphere.Theyaredefinedasadistance(the opticalpathdifference)betweenthewavefrontandthe reference sphere along the optical ray. [nm]SymbolSpectral Line 656Cred hydrogen 644Cred cadmium 588dyellow helium 546egreen mercury 486Fblue hydrogen 480Fblue cadmium Microscopy: Basic Concepts 26 Chromatic Aberrations Chromaticaberrationsoccurduetothedispersionof opticalmaterialsusedforlensfabrication.Thismeansthat therefractiveindexisdifferentfordifferentwavelengths; consequently, various wavelengths are refracted differently. Object Planen nBlueGreenRed Chromaticaberrationsincludeaxial(longitudinal)or transverse(lateral)aberrations.Axialchromatic aberrationarisesfromthefactthatvariouswavelengths arefocusedatdifferentdistancesbehindtheopticalsystem. It is described as a variation in focal length: F C1 f f ff f V . BlueGreenRedObject Planenn Transversechromaticaberrationisanoff-axisimaging of colors at different locations on the image plane.To compensate for chromatic aberrations, materials with low andhighAbbenumbersareused(suchasflintandcrown glass).Correctingchromaticaberrationsiscrucialformost microscopyapplications,butitisespeciallyimportantfor multi-photonmicroscopy.Obtainingmulti-photonexcitation requireshighlaserpowerandismosteffectiveusingshort pulselasers.Suchalightsourcehasabroadspectrum,and chromatic aberrations may cause pulse broadening. Microscopy: Basic Concepts 27 Spherical Aberration and Coma Themostimportantwaveaberrationsarespherical,coma, astigmatism, field curvature, and distortion. Spherical aberration (on-axis) is a consequence of building anopticalsystemwithcomponentswithsphericalsurfaces. Itoccurswhenraysfromdifferentheightsinthepupilare focused at different planes along the optical axis. This results inanaxialblur.Themostcommonapproachforcorrecting sphericalaberrationusesacombinationofnegativeand positivelenses.Systemsthatcorrectsphericalaberration heavilydependonimagingconditions.Forexample,in microscopy a cover glass must be of an appropriate thickness and refractive index in order to work with an objective. Also, the media between the objective and the sample (such as air, oil, or water) must be taken into account. Spherical AberrationObject Plane Best Focus Plane Coma(off-axis)canbedefinedasavariationof magnificationwithaperturelocation.Thismeansthatrays passingthroughadifferentazimuthofthelensare magnifieddifferently.Thenamecomawasinspiredbythe aberrationsappearance,becauseitresemblesacometstail as it emanates from the focus spot. It is usually stronger for lenseswithalargerfield,anditscorrectionrequires accommodation of the field diameter. Coma Object Plane Microscopy: Basic Concepts 28 Astigmatism, Field Curvature, and Distortion Astigmatism(off-axis)isresponsiblefordifferent magnificationsalongorthogonalmeridiansinanoptical system.Itmanifestsaselliptical,elongatedspotsforthe horizontalandverticaldirectionsonoppositesidesofthe bestfocalplane.Itismorepronouncedforanobjectfarther fromtheaxisandisadirectconsequenceofimproperlens mounting or an asymmetric fabrication process. Field curvature (off-axis) resultsina non-flatimage plane.The imageplanecreatedisaconcavesurfaceasseenfromthe objective; therefore, various zones of the image can be seen in focusaftermovingtheobjectalongtheopticalaxis.This aberration is corrected by an objective design combined with a tube lens or eyepiece. Distortion is a radial variationof magnificationthat will image a square as apincushionor barrel.Itiscorrected inthesamemanner asfieldcurvature.If precededwithsystemcalibration,itcanalsobecorrected numerically after image acquisition. Object PlaneImage PlaneField CurvatureAstigmatism Object PlaneBarrel Distortion Pincushion DistortionMicroscopy: Basic Concepts29 Performance Metrics Themajormetricsdescribingtheperformanceofanoptical systemarethemodulationtransferfunction(MTF),the point spread function (PSF), and the Strehl ratio (SR).TheMTFisthemodulusoftheopticaltransferfunction described by exp OTF MTF i UU M U , where the complex term in the equation relates to the phase transferfunction.TheMTFisacontrastdistributioninthe imageinrelationtocontrastintheobjectasafunctionof spatial frequency U (for sinusoidal object harmonics) and can be defined as imageobjectCMTFCUU U. The PSF is the intensity distribution at the image of a point object.ThismeansthatthePSFisametricdirectlyrelated to the image, while the MTF corresponds to spatial frequency distributionsinthepupil.TheMTFandPSFareclosely relatedandcomprehensivelydescribethequalityofthe opticalsystem.Infact,theamplitudeoftheFourier transform of the PSF results in the MTF. TheMTFcanbecalculatedastheautocorrelationofthe pupilfunction.Thepupilfunctiondescribesthefield distributionofanopticalwaveinthepupilplaneofthe optical system. In the case of a uniform pupils transmission, it directly relates to the field overlap of two mutually shifted pupils where the shift corresponds to spatial frequency. Microscopy: Basic Concepts 30 Performance Metrics (cont.) Themodulationtransferfunctionhasdifferentresults forcoherentandincoherentillumination.Forincoherent illumination,thephasecomponentofthefieldisneglected sinceitisanaverageofrandomfieldspropagatingunder random angles.Forcoherentillumination,thecontrastoftransferring harmonicsofthefieldisconstantandequalto1untilthe location of the spatial frequency in the pupil reaches its edge. Forhigherfrequencies,thecontrastsharplydropstozero since they cannot pass the optical system. Note that contrast for the coherent case is equal to 1 for the entire MTF range. The cutoff frequency for an incoherent system is two times thecutofffrequencyoftheequivalentaperturecoherent system and defines the Sparrow resolution limit. The Strehl ratio is a parametric measurement that defines thequalityoftheopticalsysteminasinglenumber.Itis definedastheratioofirradiancewithinthetheoretical dimensionofadiffraction-limitedspottotheentire irradianceintheimageofthepoint.Onesimplemethodto estimate the Strehl ratio is to divide the field below the MTF curve of a tested system by the field of the diffraction-limited system of the same numerical aperture. For practical optical design consideration it is usually assumed that the system is diffractionlimitediftheStrehlratioisequaltoorlarger than 0.8. Microscopy: Microscope Construction 31 The Compound Microscope Theprimarygoalofmicroscopyistoprovidetheabilityto resolve the small details of an object. Historically, microscopy wasdevelopedforvisualobservationand,therefore,wasset uptoworkinconjunctionwiththehumaneye.Aneffective high-resolutionopticalsystemmusthaveresolvingability andbeabletodeliverpropermagnificationforthedetector. In the case of visual observations, the detectors are the cones and rods of the retina. A basic microscope can be built with a single-element, short-focal-lengthlens(magnifier).Theobjectislocatedinthe focalplaneofthelensandisimagedtoinfinity.Theeye creates a final image of the object on the retina. The system stop is the eyes pupil.Toobtainhigherresolutionforvisualobservation,the compoundmicroscopewasfirstbuiltinthe17thcentury byRobertHooke.Itconsistsoftwomajorcomponents:the objectiveandtheeyepiece.Theshort-focal-lengthlens (objective)isplacedclosetotheobjectunderexamination and creates a real image of an object at the focal plane of the secondlens.Theeyepiece(similartothemagnifier)throws animagetoinfinity,andthehumaneyecreatesthefinal image. An important function of the eyepiece is to match the eyes pupil with the system stop, which is located in the back focal plane of the microscope objective. Microscope Objective OcularAperture StopEyeObjectPlaneEyes PupilConjugate PlanesEyes Lens Microscopy: Microscope Construction 32 The Eye LensCorneaIrisPupilRetinaMacula and FoveaBlind SpotOptic NerveCiliary MuscleVisual AxisOptical AxisZonules Theeyewasthefirstandforalongtime,theonlyreal-time detector used in microscopy. Therefore, the design of the microscopehadtoincorporateparametersrespondingtothe needs of visual observation.Corneathetransparentportionofthesclera(thewhite portionofthehumaneye),whichisarigidtissuethatgives the eyeball its shape. The cornea is responsible for two thirds of the eyes refractive power. Lensthelensisresponsibleforonethirdoftheeyes power.Ciliarymusclescanchangethelensspower (accommodation) within the range of 1530 diopters. Iriscontrols the diameter of the pupil (1.58 mm). Retinaalayerwithtwotypesofphotoreceptors:rodsand cones. Cones (about 7 million) are in the area of the macula (~3 mm in diameter) andfovea (~1.5 mm in diameter,with thehighestconedensity),andtheyaredesignedforbright visionandcolordetection.Therearethreetypesofcones (red, green, and blue sensitive), and the spectral range of the eyeisapproximately400750nm.Rodsareresponsiblefor night/low-lightvision,andthereareabout130million located outside the fovea region. Itisarbitrarilyassumedthattheeyecanprovidesharp imagesforobjectsbetween250mmandinfinity.A250-mm distanceiscalledtheminimumfocusdistanceornear point.Themaximumeyeresolutionforbrightillumination is 1 arc minute. Microscopy: Microscope Construction 33 Upright and Inverted Microscopes Thetwomajormicroscopegeometriesareuprightand inverted.Bothsystemscanoperateinreflectanceand transmittance modes. ObjectiveEyepiece (Ocular)Binocular and Optical Path Split TubeRevolving NosepieceStandFine and CoarseFocusing KnobsLight Source - Trans-illuminationBaseCondensers FocusingKnobCondenser andCondensers DiaphragmSample StageSource PositionAdjustmentAperture DiaphragmCCD CameraEyeLight Source - Epi-illuminationField DiaphragmFilter HoldersField Diaphragm Theinvertedmicroscopeisprimarilydesignedtoworkwith samplesincellculturedishesandtoprovidespace(witha long-workingdistancecondenser)forsamplemanipulation (for example, with patch pipettes in electrophysiology). ObjectiveEyepiece (Ocular)Binocular and Optical Path Split TubeRevolving NosepieceTrans-illuminationSample StageCCD CameraEyeEpi-illuminationFilter and Beam Splitter Cube Upright Inverted Microscopy: Microscope Construction 34 The Finite Tube Length Microscope M, NA, WDTypeuMicroscope SlideGlass Cover SlipAperture AngleRefractive Index - nMicroscope ObjectiveWD - Working DistanceBack Focal PlaneParfocal DistanceEyepieceOptical Tube LengthMechanical Tube LengthEye ReliefEyes PupilField StopField Number[mm]Exit Pupil Historically,microscopeswerebuiltwithafinitetube length. With this geometry, the microscope objective images the object into the tube end. This intermediate image is then relayedtotheobserverbyaneyepiece.Dependingonthe manufacturer,differentopticaltubelengthsarepossible (for example, the standard tube length for Zeiss is 160 mm). Theuseofastandardtubelengthbyeachmanufacturer unifies the optomechanical design of the microscope.Aconstantparfocaldistanceformicroscopeobjectives enablesswitchingbetweendifferentmagnificationswithout defocusing. The field number, corresponding to the physical dimension(inmillimeters)ofthefieldstopinsidethe eyepiece,allowsthemicroscopesfieldofview(FOV)tobe determined according to objectivemmFieldNumberFOVM . Microscopy: Microscope Construction 35 Infinity-Corrected Systems Microscope objectives can be corrected for a conjugate located at infinity, which means that the microscope objective images an object into infinity. An infinite conjugate is useful for introducing beam splitters or filters that should work with small incidence angles. Also, an infinity-corrected system accommodates additional components like DICprisms, polarizers.etc.Thecollimatedbeamisfocusedtocreate anintermediateimagewithadditionaloptics,calleda tube lens. The tube lens either creates an image directly ontoaCCDchiporanintermediateimage,whichis further reimaged with an eyepiece. Additionally, the tube lensmightbeusedforsystemcorrection.Forexample, Zeisscorrectsaberrationsinitsmicroscopeswitha combination objective-tube lens. Inthecaseofaninfinity-correctedobjective,the transversemagnificationcanonlybedefinedinthe presenceofatubelensthatwillformarealimage.Itis given by the ratio between the tube lenss focal length and thefocallengthofthe microscope objective. ManufacturerFocal Length of Tube Lens Zeiss164.5 mm Olympus180.0 mm Nikon200.0 mm Leica200.0 mm M, NA, WDTypeuMicroscope SlideGlass Cover SlipAperture AngleRefractive Index - nMicroscope ObjectiveWD - Working DistanceBack Focal PlaneParfocal DistanceEyepieceMechanical Tube LengthEye ReliefEyes PupilField StopField Number[mm]Exit PupilTube LensTube Lens Focal Length Microscopy: Microscope Construction 36 Telecentricity of a Microscope Telecentricityisafeatureofanopticalsystemwherethe principalrayinobject,image,orbothspacesisparallelto the optical axis. This means that the object or image does not shiftlaterally,evenwithdefocus;thedistancebetweentwo object or image points is constant along the optical axis.An optical system can be telecentric inObject space, where the entrance pupil is at infinity, and the aperture stop is in the back focal plane; Imagespace,wheretheexitpupilisatinfinity,andthe aperture stop is in the front focal plane; orBoth(doublytelecentric),wheretheentranceandexit pupilsareatinfinity,andtheaperturestopisatthe centerofthesystem,inthebackfocalplaneofthe elementbeforethestopandfrontfocallengthofthe element after the stop (afocal system). Focused Object PlaneAperture StopImage PlaneSystem Telecentric in Object SpaceObject Planef Defocused Image PlaneFocused Image PlaneSystem Telecentric in Image SpacefAperture StopAperture StopFocused Object Plane Focused Image PlaneDefocused Object PlaneSystem Doubly Telecentricf1 f2 The aperture stop in a microscope is located at the back focal plane of the microscope objective. This makes the microscope objective telecentric in object space. Therefore, in microscopy, theobjectisobservedwithconstantmagnification,evenfor defocusedobjectplanes.Thisfeatureofmicroscopysystems significantlysimplifiestheiroperationandincreasesthe reliability of image analysis. Microscopy: Microscope Construction 37 Magnification of a Microscope Magnifyingpower(MP)isdefinedastheratiobetween theanglessubtendedbyanobjectwithandwithout magnification. The magnifying power (as defined for a single lens)createsanenlargedvirtualimageofanobject.The angle of an object observed with magnification is h f z'h'u'z' l f z' l . Therefore, od f z'u'MPu f z' l . The angle for an unaided eyeisdefinedfortheminimumfocusdistance(do)of10 inches or 250 mm, which is the distance that the object (real orvirtual)maybeexaminedwithoutdiscomfortforthe averagepopulation.Adistancelbetweenthelensandthe eye is often small and can be assumed to equal zero: 250mm 250mmMPf z' . Ifthevirtualimageisatinfinity(observedwitharelaxed eye), z' = , and250mmMPf . Thetotalmagnifyingpowerofthemicroscoperesultsfrom themagnificationofthemicroscopeobjectiveandthe magnifying power of the eyepiece (usually 10): objectiveobjectiveOTLMf microscope objective eyepieceobjective eyepiece250mm OTLMP M MPf f . FeyepieceFeyepieceOTL = Optical Tube LengthFobject veFobject veObjectiveEyepiece udo = 250 mmhFFuhzlf f Microscopy: Microscope Construction 38 Numerical Aperture The aperture diaphragm of the optical system determines the angleatwhichraysemergefromtheaxialobjectpointand, afterrefraction,passthroughtheopticalsystem.This acceptanceangleiscalledtheobjectspaceapertureangle. Theparameterdescribingsystemthroughputandthis acceptance angle is called the numerical aperture (NA): sin NA n u . Asseenfromtheequation, throughputoftheoptical systemmaybeincreasedby usingmediawithahigh refractiveindexn,e.g.,oilor water. This effectively decreases therefractionanglesatthe interfaces.Thedependencebetweenthe numerical aperture in the object spaceNAandthenumerical apertureintheimagespacebetweentheobjectiveandthe eyepiece NA' is calculated using the objective magnification: objectiveNA NA'M . As a result of diffraction at theapertureoftheoptical system,self-luminous pointsoftheobjectarenot imaged as points but as so-calledAirydisks.AnAiry diskisabrightdisk surroundedbyconcentric ringswithgraduallydecreasingintensities.Thedisk diameter (where the intensity reaches the first zero) is d 1.22nsinu 1.22NA. Notethattherefractiveindexin the equation is for media between the object and the optical system.MediaRefractive Index Air1 Water1.33 Oil 1.451.6(1.515 is typical) Microscopy: Microscope Construction 39 0th order +1storderDetail d not resolved0th orderDetail d resolved-1storder+1storderSample Plane Resolution Limit Thelateralresolutionofan opticalsystemcanbedefinedin termsofitsabilitytoresolve imagesoftwoadjacent,self-luminouspoints.WhentwoAiry disksaretooclose,theyforma continuousintensitydistribution andcannotbedistinguished.TheRayleighresolution limitisdefinedasoccurringwhenthepeakoftheAiry patternarisingfromonepointcoincideswiththefirst minimumoftheAirypatternarisingfromasecondpoint object. Such a distribution gives an intensity dip of 26%. The distance between the two points in this case is d 0.61nsinu 0.61NA. Theequationindicatesthattheresolutionofanoptical system improves with an increase in NA and decreases with increasing wavelength . For example, for = 450 nm (blue) andoilimmersionNA=1.4,themicroscopeobjectivecan optically resolve points separated by less than 200 nm.Thesituationinwhichtheintensitydipbetweentwo adjacentself-luminouspointsbecomeszerodefinesthe Sparrow resolution limit. In this case d = 0.5/NA. TheAbberesolutionlimitconsidersboththediffraction causedbythe objectandthe NA of the optical system.Itassumes thatifatleasttwo adjacentdiffraction ordersforpointswith spacing d are accepted by the objective, these two points can beresolved.Therefore,theresolutiondependsonboth imaging and illumination apertures and is objective condenserdNA NA. Microscopy: Microscope Construction 40 Useful Magnification Forvisualobservation,theangularresolvingpowercan bedefinedas1.5arcminutes.Forunmagnifiedobjectsata distanceof250mm(theeyesminimumfocusdistance),1.5 arcminutesconvertstodeye=0.1mm.Sincemicroscope objectivesbythemselvesdonotusuallyprovidesufficient magnification,theyarecombinedwithocularsoreyepieces. The resolving power of the microscope is theneye eyemicmin obj eyepieced ddM MM . IntheSparrowresolutionlimit,theminimummicroscope magnification is min eye2 / M d NA . Therefore,atotalminimummagnificationMmincanbe definedasapproximately250500NA(dependingon wavelength).Forlowermagnificationtheimagewillappear brighter,butimagingisperformedbelowtheoverall resolutionlimitofthemicroscope.Forlargermagnification, thecontrastdecreasesandresolutiondoesnotimprove. Whileatheoreticallyhighermagnificationshouldnot provideadditionalinformation,itisusefultoincreaseitto approximately1000NAtoprovidecomfortablesamplingof theobject.Therefore,itisassumedthattheuseful magnificationofamicroscopeisbetween500NAand 1000 NA. Usually, any magnification above 1000 NA is called emptymagnification.Theimagesizeinsuchcasesis enlarged,butnoadditionalusefulinformationisprovided. Thehighestusefulmagnificationofamicroscopeis approximately1500foranoil-immersionmicroscope objective with NA = 1.5. Similaranalysiscanbeperformedfordigitalmicroscopy, whichusesCCDorCMOScamerasasimagesensors. Camera pixels are usually small (between 2 and 30 microns), andusefulmagnificationmustbeestimatedforaparticular imagesensorratherthantheeye.Therefore,digital microscopycanworkatlowermagnification,and magnificationofthemicroscopeobjectivealoneisusually sufficient. Microscopy: Microscope Construction 41 Depth of Field and Depth of Focus Two important terms are used to define axial resolution: depth of field and depth of focus. Depth of field refers to the object thickness for which an image is in focus, while depthoffocusisthecorrespondingthicknessoftheimage plane. In the case of a diffraction-limited optical system, the depthoffocusisdetermined foranintensitydropalongthe optical axis to 80%, defined as 22 .nDOF z'NA Therelationbetweendepthof field(2z)anddepthoffocus (2z')incorporatesthe objective magnification: 2objective2 2 ,n'z' M zn wheren'andnaremediumrefractiveindexesintheobject and image space, respectively. Toquicklymeasurethedepthoffieldforaparticular microscopeobjective,thegridamplitudestructurecanbe placedonthemicroscopestageandtiltedwiththeknown angle . The depth of field is determined after measuring the grid zone w while in focus:2 tan z nw . -z z2zObject PlaneImage Plane-z z2z0.8Normalized I(z)1.0n nn nuuz Microscopy: Microscope Construction42Magnification and Frequency vs Depth of Field Depthoffieldforvisualobservationisafunctionofthe totalmicroscopemagnificationandtheNAoftheobjective, approximated as 2microscope0.5 3402 z n nNA M NAO' . Notethatestimatedvaluesdonotincludeeye accommodation.Thegraphbelowpresentsdepthoffieldfor visual observation. Refractive index n of the object space was assumed to equal 1. For other media, values from the graph must be multiplied by an appropriate n. Depthoffieldcanalsobedefinedforaspecificfrequency present in the object because imaging contrast changes for a particularobjectfrequency,asdescribedbythemodulation transfer function. The approximated equation is 0.42 =zNA, whereUis the frequency incyclesper millimeter. Microscopy: Microscope Construction 43 Khler Illumination Oneofthemostcriticalelementsinefficientmicroscope operationispropersetupoftheilluminationsystem.To assistwiththis,AugustKhlerintroducedasolutionthat providesuniformandbrightilluminationoverthefieldof view, even for light sources that are not uniform (e.g., a lamp filament).Thissystemconsistsofalightsource,afield-stop diaphragm,acondenseraperture,andcollectiveand condenserlenses.ThissolutionisnowcalledKhler illumination and is commonly used for a variety of imaging modes. Light SourceCondenser LensCollective LensIntermediateImage PlaneMicroscope ObjectiveSampleAperture StopField DiaphragmCondensers DiaphragmEyepieceEyeEyes PupilSource ConjugateSample ConjugateSample ConjugateSample ConjugateSample ConjugateSource ConjugateSource ConjugateSource ConjugateField DiaphragmSample Path Illumination Path Microscopy: Microscope Construction 44 Khler Illumination (cont.) The illumination system is configured such that an image of the light source completely fills the condenser aperture. Khlerilluminationrequiressettingupthemicroscope systemsothatthefielddiaphragm,objectplane,and intermediateimageintheeyepiecesfieldstop,retina,or CCDareinconjugateplanes.Similarly,thelampfilament, frontapertureofthecondenser,microscopeobjectivesback focal plane (aperture stop), exit pupil of the eyepiece, and the eyespupilarealsoatconjugateplanes.Khlerillumination canbesetupforboththetransmissionmode(alsocalled DIA) and the reflectance mode (also called EPI). The uniformity of the illumination is the result of having the lightsourceatinfinitywithrespecttotheilluminated sample.EPIilluminationisespeciallyusefulforthebiologicaland metallurgical imaging of thick or opaque samples. Light SourceIntermediateImage PlaneMicroscope ObjectiveSampleAperture StopField DiaphragmEyepieceEyeEyes PupilBeam SplitterSample PathIllumination Path Microscopy: Microscope Construction 45 Alignment of Khler Illumination TheprocedureforKhlerilluminationalignmentconsists of the following steps: 1.Placethesampleonthemicroscopestageandmoveitso thatthefrontsurfaceofthecondenserlensis12mm fromthemicroscopeslide.Thecondenserandcollective diaphragms should be wide open. 2.Adjustthelocationofthesourcesoilluminationfillsthe condensersdiaphragm.Thesharpimageofthelamp filamentshouldbevisibleatthecondensersdiaphragm planeandatthebackfocalplaneofthemicroscope objective.Toseethefilamentatthebackfocalplaneof theobjective,aBertrandlenscanbeapplied(alsosee SpecialLensComponentsonpage55).Thefilament shouldbecenteredintheaperturestopusingthebulbs adjustment knobs on the illuminator. 3.Foralow-powerobjective,bringthesampleintofocus. Since a microscope objective works at a parfocal distance, switchingtoahighermagnificationlateriseasyand requires few adjustments.4.Focus and center the condenser lens. Close down the field diaphragm, focus down the outline of the diaphragm, and adjust the condensers position. After adjusting thex-, y-, andz-axis,openthefielddiaphragmsoitaccommodates the entire field of view. 5.Adjustthepositionofthecondensersdiaphragmby observingthebackfocalobjectiveplanethroughthe Bertrandlens.Whentheedgesoftheapertureare sharply seen, the condensers diaphragm should be closed toapproximatelythreequartersoftheobjectives aperture.6.Tune the brightness of the lamp. This adjustment should beperformedbyregulatingthevoltageofthelamps powersupplyor,preferably,throughtheneutraldensity filtersinthebeampath.Donotadjustthebrightnessby closingthecondensersdiaphragmbecauseitaffectsthe illumination setup and the overall microscope resolution. Notethatwhilethreequartersoftheaperturestopis recommended for initial illumination, adjusting the aperture oftheilluminationsystemaffectstheresolutionofthe microscope.Therefore,thefinalsettingshouldbeadjusted after examining the images. Microscopy: Microscope Construction 46 Critical Illumination AnalternativetoKhlerilluminationiscritical illumination,whichisbasedonimagingthelightsource directly onto the sample. This type of illumination requires a highly uniform light source. Any source non-uniformities will resultinintensityvariationsacrosstheimage.Itsmajor advantage is high efficiency, since it can collect a larger solid anglethanKhlerilluminationandthereforeprovidesa higherenergydensityatthesample.Forparabolicor elliptical reflective collectors, critical illumination can utilize up to 85% of the light emitted by the source.Condenser LensIntermediateImage PlaneMicroscope ObjectiveSampleAperture StopCondensers DiaphragmEyepieceEyeEyes PupilSample ConjugateSample ConjugateSample ConjugateSample ConjugateField Diaphragm Microscopy: Microscope Construction 47 Stereo Microscopes Stereomicroscopesarebuilttoprovidedepthperception, whichisimportantforapplicationslikemicro-assemblyand biologicalandsurgicalimaging.Twoprimarystereo-microscopeapproachesinvolvebuildingtwoseparatetilted systems,orusingacommonobjectivecombinedwitha binocular system. Microscope ObjectiveFobEntrance Pupil Entrance PupildRight Eye Left EyeEyepiece EyepieceImage InvertingPrismsImage InvertingPrismsTelescope Objectives Inthelatter,theangleofconvergenceofastereo microscopedependsonthefocallengthofamicroscope objectiveandadistancedbetweenthemicroscopeobjective andtelescopeobjectives.Theentrancepupilsofthe microscopeareimagesofthestops(locatedattheplaneof the telescope objectives) through the microscope objective.Depth perception z can be defined as smicroscope250[mm],tanzM wheresisavisualstereoresolvingpower,whichfor daylight vision is approximately 510 arc seconds.Stereomicroscopeshaveaconvergenceangleintherange of 1015 deg. Note that is 15 deg for visual observation and 0forastandardmicroscope.Forexample,depthperception forthehumaneyeisapproximately0.05mm(at250mm), whileforastereomicroscopeofMmicroscope=100and=15 deg, it is z = 0.5 m. Microscopy: Microscope Construction 48 Eyepieces Theeyepiecerelaysanintermediateimageintotheeye, correctsforsomeremainingobjectiveaberrations,and providesmeasurementcapabilities.Italsoneedstorelayan exit pupil of a microscope objective onto the entrance pupil of theeye.Thelocationoftherelayedexitpupiliscalledthe eyepointandneedstobeinacomfortableobservation distancebehindtheeyepiece.Theclearancebetweenthe mechanicalmountingoftheeyepieceandtheeyepointis called eye relief. Typical eye relief is 712 mm. An eyepiece usually consists of two lenses: one (closer to the eye)whichmagnifiestheimage,andasecondworkingasa collective lens and also responsible for the location of the exit pupil of the microscope. An eyepiece contains a field stop that provides a sharp image edge. Parameterslikemagnifyingpowerofaneyepieceand fieldnumber(FN),i.e.,fieldofviewofaneyepiece,are engravedonaneyepiecesbarrel:M/FN.Fieldnumber andmagnificationofamicroscopeobjectiveallowquick calculationoftheimagedareaofasample(seealsoThe Finite Tube Length Microscope on p. 34). Field number varies with microscopy vendors and eyepiece magnification. For 10 orlowermagnificationeyepieces,itisusually2028mm whileforhighermagnification,wide-angleocularscanget down to approximately 5 mm. ThemajorityofeyepiecesareHuygens,Ramsden,or derivationsofthem.TheHuygenseyepiececonsistsoftwo plano-convexlenseswithconvexsurfacesfacingthe microscope objective: tFocFocFEye PointExit PupilField StopLens 1Lens 2FLens 2 Microscopy: Microscope Construction 49 Eyepieces (cont.) Both lenses are usually made with crown glass and allow for somecorrectionoflateralcolor,coma,andastigmatism.To correct for color, the following conditions should be met: f1 f2 and

t 1.5 f2. Forhighermagnifications,theexitpupilmovestowardthe ocular,makingobservationlessconvenient,andsothis eyepieceisusedonlyforlowmagnifications(10).In addition,Huygensocularseffectivelycorrectforchromatic aberrations,andthereforecanbemoreeffectivelyusedwith lower-end microscope objectives (e.g., achromatic). TheRamsdeneyepiececonsistsoftwoplano-convexlenses withconvexsurfacesfacingeachother.Bothfocallengths areverysimilar,andthedistancebetweenlensesissmaller than f2:tFocFocFEye PointExit PupilField Stop Thefieldstopisplacedinthefrontfocalplaneofthe eyepiece. A collective lens does not participate in creating an intermediateimage,sotheRamsdeneyepieceworksasa simple magnifier: 1 2f f and

2t f . Compensatingeyepiecesworkinconjunctionwith microscopeobjectivestocorrectforlateralcolor (apochromatic).High-eyepointocularsprovideanextendeddistance between the last mechanical surface and the exit pupil of the eyepiece. They allow users with glasses to comfortably use a microscope. The convenient high eye-point location should be 2025 mm behind the eyepiece. Microscopy: Microscope Construction 50 Nomenclature and Marking of Objectives Objective parameters include: ObjectivecorrectionsuchasAchromat,PlanAchromat, Fluor, Plan Fluor, Apochromat (Apo), and Plan Apochromat. Magnificationthe lensmagnificationfora finite tube length, or for a microscope objective in combination with a tube lens.Ininfinity-correctedsystems, magnificationdepends on the ratio between the focallengthsofatube lensandamicroscope objective.Aparticularobjectivetypeshouldbeusedonlyin combination with the proper tube lens.Applicationspecializeduseordesignofanobjective,e.g., H (bright field), D (dark field), DIC (differential interference contrast),RL(reflectedlight),PH(phasecontrast),orP (polarization). Tube lengthan infinity corrected() orfinitetube length in mm. Coverslipthethickness ofthecover slipused(inmm).0ormeansnocoverglassorthe cover slip is optional, respectively.Numericalaperture(NA)andmediumdefinessystem throughput and resolution. It depends on the media between thesampleandobjective.Themostcommonmediaareair (no marking), oil (Oil), water (W), or Glycerine. Workingdistance(WD)thedistanceinmillimeters between the surface of the front objective lens and the object. MagnificationZeiss Code 1, 1.25Black 2.5Khaki 4, 5Red 6.3Orange 10Yellow 16, 20, 25, 32 Green 25, 32Green 40, 50Light Blue 63Dark Blue > 100White MAKERPLAN Fluor40x / 1.3 OilDIC H160/0 17WD 0 20Optical Tube Length (mm)Coverslip Thickness (mm)Objective MakerObjective TypeApplicationMagnificationNumerical Apertureand MediumWorking Distance (mm)Magnification Color-Coded RingMicroscopy: Microscope Construction 51 Objective Designs Achromaticobjectives(alsocalledachromats)are correctedattwowavelengths:656nmand486nm.Also, sphericalaberrationandcomaarecorrectedforgreen(546 nm),whileastigmatismisverylow.Theirmajorproblems are a secondary spectrum and field curvature.AchromaticobjectivesareusuallybuiltwithalowerNA (below0.5)andmagnification(below40).Theyworkwell forwhitelightilluminationorsinglewavelengthuse.When corrected for field curvature, they are called plan-achromats. Object PlaneAchromatic ObjectivesNA = 0.2510xNA = 0.50 0.8020x 40xNA > 1.0> 60xImmersion LiquidAmici LensMeniscus LensLow NALow M Fluoritesorsemi-apochromatshavesimilarcolor correction as achromats; however, they correct for spherical aberrationfortwoorthreecolors.Thenamefluoriteswas assignedtothistypeofobjectiveduetothematerials originallyusedtobuildthistypeofobjective.Theycanbe applied for higher NA (e.g., 1.3) and magnifications, and used forapplicationslikeimmunofluorescence,polarization,or differential interference contrast microscopy. The most advanced microscope objectives are apochromats, whichareusuallychromaticallycorrectedforthreecolors, withsphericalaberrationcorrectionforatleasttwocolors. Theyaresimilarinconstructiontofluoritesbutwith different thicknesses and surface figures. With the correction offieldcurvature,theyarecalledplan-apochromats.They areusedinfluorescencemicroscopywithmultipledyesand canprovideveryhighNA(1.4).Therefore,theyaresuitable for low-light applications. Microscopy: Microscope Construction 52 Objective Designs (cont.) Object PlaneApochromatic ObjectivesNA = 0.310x NA = 1.4100xNA = 0.9550xImmersion LiquidAmici LensLow NALow MFluorite Glass TypeNumber of wavelengths for spherical correction Number of colors for chromatic correction Achromat12 Fluorite2323 Plan-Fluorite2424 Plan-Apochromat 2435 (Adapted from Murphy, 2001 and http://www.microscopyu.com/) Examplesoftypicalobjectiveparametersareshowninthe table below: MTypeMediumWDNAdDOF 10AchromatAir4.40.251.348.80 20AchromatAir0.530.450.752.72 40FluoriteAir0.500.750.450.98 40FluoriteOil0.201.300.260.49 60ApochromatAir0.150.950.350.61 60ApochromatOil0.091.400.240.43 100ApochromatOil0.091.400.240.43 Refractive index of oil is n = 1.515 (Adapted from Murphy, 2001) Microscopy: Microscope Construction 53 Special Objectives and Features Specialtypesofobjectivesincludelongworkingdistance objectives,ultra-low-magnificationobjectives,water-immersion objectives, and UV lenses.Long working distance objectives allow imaging through thick substrates like culture dishes. They are also developed forinterferometricapplicationsinMichelsonandMirau configurations.Alternatively,theycanallowforthe placement of instrumentation (e.g., micropipettes) between a sample and an objective. To provide a long working distance andhighNA,acommonsolutionistousereflective objectives,orextendtheworkingdistanceofastandard microscope objective by using a reflective attachment. While reflectiveobjectiveshavetheadvantageofbeingfreeof chromaticaberrations,theirseriousdrawbackisasmaller fieldofviewrelativetorefractiveobjectives.Thecentral obscuration also decreases throughput by 15%20%.LWD Refective Objective Microscopy: Microscope Construction 54 Special Objectives and Features (cont.) Lowmagnificationobjectives can achieve magnifications aslowas0.5.However,insomecasestheyarenotfully compatiblewithmicroscopysystems,andmaynotbe telecentric in the image space. They also often require special tubelensesandspecialcondenserstoprovideKhler illumination. Waterimmersionobjectivesareincreasinglycommon, especially for biological imaging, because they provide a high NAandavoidtoxicimmersionoils.Theyusuallywork without a cover slip. UVobjectivesaremadeusingUVtransparent,low-dispersion materials such asquartz. These objectives enable imagingatwavelengthsfromthenear-UVthroughthe visiblespectrum,e.g.,240700nm.Reflectiveobjectivescan also be used for the IR bands. MAKERPLAN Fluor40x / 1.3 OilDIC H160/0 17WD 0 20Refective Adapter to extend working distance WDMicroscopy: Microscope Construction 55 Special Lens Components The Bertrand lens is a focusable eyepiece telescope that can be easily placed in the light path of the microscope. This lens isusedtoviewthebackapertureoftheobjective,which simplifies microscope alignment, specifically when setting up Khler illumination.Toconstructahigh-numerical-aperturemicroscopeobjective withgoodcorrection,numerousopticaldesignsimplement theAmicilensasafirstcomponentoftheobjective.Itisa thick lens placed in close proximity tothe sample. An Amici lens usually has a plane (or nearly plane) first surface and a large-curvaturesphericalsecondsurface.Toensuregood chromaticaberrationcorrection,anachromaticlensis located closely behind the Amici lens. In such configurations, microscope objectives usually reach an NA of 0.50.7.Tofurther increasetheNA, anAmicilensis improvedby eithercementing ahigh-refractive-indexmeniscus lenstoitor placinga meniscuslens closelybehindtheAmicilens.Thismakesitpossibleto construct well-corrected high magnification (100) and high numerical aperture (NA > 1.0) oil-immersion objective lenses. Amici Lens with cemented meniscus lens

Amici Lenswith Meniscus Lensclosely behind Amici-Type microscope objectiveNA = 0.50-0.8020x - 40xAmici LensAchromatic Lens 1 Achromatic Lens 2 Microscopy: Microscope Construction 56 Cover Glass and Immersion Thecoverslipislocatedbetweentheobjectandthe microscope objective. It protects the imaged sample and is an importantelementintheopticalpathofthemicroscope. Coverglasscanreduceimagingperformanceandcause sphericalaberration,whiledifferentimagingangles experiencemovementoftheobjectpointalongtheoptical axis toward the microscope objective. The object point moves closertothe objectivewith anincreasein angle.Theimportance ofthecover glassincreases inproportionto theobjectives NA,especially inhigh-NAdry lenses.For lenseswithan NAsmaller than0.5,the typeofcoverglassmaynotbeacriticalparameter,but should always be properly used tooptimize imaging quality. Coverglassesarelikelytobeencounteredwhenimaging biologicalsamples.Notethatthepresenceofastandard-thicknesscoverglassisaccountedforinthedesignofhigh-NA objectives. The important parameters that define a cover glass are its thickness, index of refraction, and Abbe number. The ISO standards for refractive index and Abbe number are n = 1.5255 0.0015 and V = 56 2, respectively. Microscopeobjectivesareavailablethatcanaccommodatea rangeofcover-slipthicknesses.Anadjustablecollarallows theusertoadjust forcoverslip thicknessinthe rangefrom100 micronstoover 200 microns.Cover Glassn=1.525NA=0.10NA=0.25NA=0.5NA=0.75NA=0.90Airn=1.0Microscopy: Microscope Construction 57 Cover Glass and Immersion (cont.) Thetablebelowpresentsasummaryofacceptablecover glassthicknessdeviationsfrom0.17mmandtheallowed thicknesses for Zeiss air objectives with different NAs. NA of the Objective Allowed Thickness Deviations (from 0.17 mm) Allowed Thickness Range

Water,whichismorecommon,orglycerinimmersion objectivesaremainlyusedforbiologicalsamples,suchas living cells or a tissue culture. They provide a slightly lower NAthanoilobjectivesbutarefreeofthetoxicityassociated withimmersionoils.Waterimmersionisusuallyapplied withoutacoverslip.Forfluorescentapplicationsitisalso critical to use non-fluorescent oil. Microscopy: Microscope Construction 58 Common Light Sources for Microscopy Common light sources for microscopy include incandescent lamps,suchastungsten-argonandtungsten(e.g.,quartz halogen)lamps.Atungsten-argonlampisprimarilyused forbright-field,phase-contrast,andsomepolarization imaging.Halogenlampsareinexpensiveandaconvenient choice for a variety of applications that require a continuous and bright spectrum.Arclampsareusuallybrighterthanincandescentlamps. Themostcommonexamplesincludexenon(XBO)and mercury(HBO)arclamps.Arclampsprovidehigh-quality monochromaticilluminationifcombinedwiththe appropriatefilter.Arclampsaremoredifficulttoalign,are moreexpensive,andhaveashorterlifetime.Theirspectral rangestartsintheUVrangeandcontinuouslyextends throughvisibletothe infrared.About20%of theoutputisinthe visiblespectrum,while themajorityisinthe UVandIR.Theusual lifetimeis100200 hours. Another light source is the gas-arc discharge lamp, which includesmercury,xenon,andhalidelamps.Themercury lamphasseveralstronglines,whichmightbe100times brighter than the average output. About 50% is located in the UVrange,andshouldbeusedwithprotectiveglasses.For imagingbiologicalsamples,theproperselectionoffiltersis necessary to protect living cell samples and micro-organisms (e.g.,UV-blockingfilters/coldmirrors).Thexenonarclamp hasauniformspectrum,canprovideanoutputpower greaterthan100W,andisoftenusedforfluorescence imaging.However,over50%ofitspowerfallsintotheIR; therefore,IR-blockingfilters(hotmirrors)arenecessaryto prevent the overheating of samples.Metal halide lamps were recently introduced as high-power sources (over 150 W) with lifetimes several times longer than arclamps.Whileingeneralthemetal-halidelamphasa spectraloutputsimilartothatofamercuryarclamp,it extends further into longer wavelengths. Microscopy: Microscope Construction 59 LED Light Sources Light-emittingdiodes(LEDs)areanew,alternativelight sourceformicroscopyapplications.TheLEDisa semiconductordiodethatemitsphotonswheninforward-biased mode. Electrons pass through the depletion region of a p-njunctionandloseanamountofenergyequivalenttothe bandgap of the semiconductor. The characteristic features of LEDsincludealonglifetime,acompactdesign,andhigh efficiency.Theyalsoemitnarrowbandlightwithrelatively high energy. Wavelengths [nm] of High-power LEDs Commonly Used in Microscopy Total Beam Power [mW] (approximate) 455Royal Blue225450 470Blue200400 505Cyan150250 530Green100175 590Amber1525 633Red2550 435675White Light200300 An important feature of LEDs is the ability to combine them intoarraysandcustomgeometries.Also,LEDsoperateat lower temperatures than arc lamps, and due to their compact designtheycanbecooledeasilywithsimpleheatsinksand fans.The radiance of currently available LEDs is still significantly lower than that possible with arc lamps; however, LEDs can produce an acceptable fluorescent signal in bright microscopy applications.Also,thepulsedmodecanbeusedtoincrease the radiance by 20 times or more. LED Spectral Range [nm] Semiconductor 350400GaN 400550In1-xGaxN 550650Al1-x-yInyGaxP 650750Al1-xGaxAs 7501000GaAs1-xPx Microscopy: Microscope Construction 60 Filters Neutraldensity(ND)filtersareneutral(wavelengthwise) gray filters scaled in units of optical density (OD): OD = log101t|\

|.|, wheretisthe transmittance. NDfilterscanbe combinedto provideODasa sum of the ODs of theindividual filters.NDfilters areusedto changelight intensitywithout tuningthelight source, which can result in a spectral shift. Color absorption filters and interference filters (also see MultipleWaveInterferenceonpage16)isolatethedesired range of wavelengths: e.g. bandpass and edge filters. Edge filters include short-pass and long-pass filters. Short-passfiltersallowshortwavelengthstopassandstoplong wavelengths, and long-pass filters allow long wavelengths to passwhilestoppingshortwavelengths.Edgefiltersare defined for wavelengths with a 50% drop in transmission.Bandpassfiltersallowonlyaselectedspectralbandwidth to pass and are characterized with a central wavelength and full-width-half-maximum(FWHM)definingthespectral range for transmission of at least 50%. Colorabsorptionglassfiltersusuallyserveasbroad bandpassfilters.Theyarelesscostlyandlesssusceptibleto damage than interference filters.Interferencefiltersarebasedonmultiplebeaminterference inthinfilms.Theycombinebetweenthreetoover20 dielectriclayersof/2and/4,separatedbymetallic coatings.Theycanprovideasharpbandpasstransmission downtothesub-nmrangeandfull-width-half-maximumof 1020 nm. Transmission [ % ] 100500Short Pass Cut-off WavelengthHigh Pass Cut-off WavelengthShort Pass High PassCentral Wavelength FWHM(HBW)BandpassMicroscopy: Microscope Construction 61 Polarizers and Polarization Prisms Polarizersarebuiltwithbirefringentcrystalsusing polarizationatmultiplereflections,selectiveabsorption (dichroism), form birefringance, or scattering. Forexample,polarizers builtwithbirefringent crystals(Glan-Thompson prisms)usetheprinciple oftotalinternalreflection toeliminateordinaryor extraordinarycomponents (forpositiveornegative crystals). Birefringentprismsarecrucialcomponentsfornumerous microscopytechniques,e.g.,differentialinterference contrast.Themostcommonbirefringentprismisa Wollastonprism.Itsplitslightintotwobeamswith orthogonalpolarizationandpropagatesunderdifferent angles. The angle between propagating beams ise o2 tan n n c = o . Both beams produce interference with fringe period b: e o2 tanbn n = =c o. The localization plane of fringes is e o1 1 12 n n| | = + o |\ .. Optic AxisOptic AxisIllumination Light Linearly Polarized at 45OWollaston PrismOptic AxisOptic AxisExtraordinary RayOrdinary Rayunder TIRGlan-Thompson Prism Microscopy: Microscope Construction 62 Polarizers and Polarization Prisms (cont.) Thefringelocalizationplanetiltcanbecompensatedby using two symmetrical Wollaston prisms. IncidentLightTwo Wollaston Prismscompensate for tilt of fringe localization plane Wollastonprismshaveafringelocalizationplaneinsidethe prism.OneexampleofamodifiedWollastonprismisthe Nomarskiprism,whichsimplifiestheDICmicroscope setup by shifting the plane outside the prism, i.e., the prism does not need to be physically located at the condenser front focal plane or the objectives back focal plane. Microscopy: Specialized Techniques 63 Amplitude and Phase Objects Themajorobjecttypesencounteredonthemicroscopeare amplitudeandphaseobjects.Thetypeofobjectoften determinesthemicroscopy techniqueselectedfor imaging. Theamplitudeobjectis definedasonethatchanges theamplitudeandtherefore theintensityoftransmitted orreflectedlight.Such objectsareusuallyimaged with bright-field microscopes. Astainedtissuesliceisa common amplitude object.Phase objects do not affect the optical intensity; instead, they generateaphaseshiftinthetransmittedorreflectedlight. Thisphaseshiftusuallyarisesfromaninhomogeneous refractive index distribution throughout the sample, causing differencesinopticalpathlength(OPL).Mixedamplitude-phase objects are also possible (e.g., biological media), which affecttheamplitudeandphaseofilluminationindifferent proportions. Classifyingobjectsasself-luminousandnon-self-luminousisanotherwaytocategorizesamples.Self-luminousobjectsgenerallydonotdirectlyrelatetheir amplitudeandphasetotheilluminatinglight.Thismeans that while the observed intensity may be proportional to the illumination intensity, its am