Edited by

Ulrich Kubitscheck

Fluorescence Microscopy

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Edited by Ulrich Kubitscheck

Fluorescence Microscopy

From Principles to Biological Applications

The Editor

Prof. Dr. Ulrich KubitscheckRheinische Friedrich-Wilhelms-Universität BonnInstitute of Physical andTheoretical ChemistryWegelerstr. 1253115 BonnGermany

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V

Contents

Preface XIIIList of Contributors XVII

1 Introduction to Optics and Photophysics 1Rainer Heintzmann

1.1 Interference: Light as a Wave 21.2 Two Effects of Interference: Diffraction and Refraction 71.3 Optical Elements 141.3.1 Lenses 141.3.2 Metallic Mirror 171.3.3 Dielectric Mirror 181.3.4 Pinholes 181.3.5 Filters 191.3.6 Chromatic Reflectors 201.4 The Far-Field, Near-Field, and Evanescent Waves 201.5 Optical Aberrations 231.6 Physical Background of Fluorescence 241.7 Photons, Poisson Statistics, and AntiBunching 30

References 31

2 Principles of Light Microscopy 33Ulrich Kubitscheck

2.1 Introduction 332.2 Construction of Light Microscopes 332.2.1 Components of Light Microscopes 332.2.2 Imaging Path 342.2.3 Magnification 362.2.4 Angular and Numerical Aperture 382.2.5 Field of View 382.2.6 Illumination Beam Path 392.3 Wave Optics and Resolution 422.3.1 Wave Optical Description of the Imaging Process 43

VI Contents

2.3.2 The Airy Function 472.3.3 Point Spread Function and Optical Transfer Function 502.3.4 Lateral and Axial Resolution 522.3.5 Magnification and Resolution 592.3.6 Depth of Field and Depth of Focus 602.3.7 Over- and Under Sampling 612.4 Apertures, Pupils, and Telecentricity 612.5 Microscope Objectives 642.5.1 Objective Lens Design 642.5.2 Light Collection Efficiency and Image Brightness 682.5.3 Objective Lens Classes 732.5.4 Immersion Media 732.5.5 Special Applications 772.6 Contrast 782.6.1 Dark Field 802.6.2 Phase Contrast 812.6.3 Interference Contrast 862.6.4 Advanced Topic: Differential Interference Contrast 892.7 Summary 94

Acknowledgments 94References 95

3 Fluorescence Microscopy 97Jurek W. Dobrucki

3.1 Features of Fluorescence Microscopy 983.1.1 Image Contrast 983.1.2 Specificity of Fluorescence Labeling 1013.1.3 Sensitivity of Detection 1023.2 A Fluorescence Microscope 1033.2.1 Principle of Operation 1033.2.2 Sources of Exciting Light 1073.2.3 Optical Filters in a Fluorescence Microscope 1103.2.4 Electronic Filters 1113.2.5 Photodetectors for Fluorescence Microscopy 1123.2.6 CCD–Charge-Coupled Device 1133.2.7 Intensified CCD (ICCD) 1163.2.8 Electron-Multiplying Charge-Coupled Device (EMCCD) 1173.2.9 CMOS 1193.2.10 Scientific CMOS (sCMOS) 1203.2.11 Features of CCD and CMOS Cameras 1213.2.12 Choosing a Digital Camera for Fluorescence Microscopy 1213.2.13 Photomultiplier Tube (PMT) 1213.2.14 Avalanche Photodiode (APD) 122

Contents VII

3.3 Types of Noise in a Digital Microscopy Image 1233.4 Quantitative Fluorescence Microscopy 1273.4.1 Measurements of Fluorescence Intensity and Concentration

of the Labeled Target 1273.4.2 Ratiometric Measurements (Ca++, pH) 1303.4.3 Measurements of Dimensions in 3D Fluorescence

Microscopy 1313.4.4 Measurements of Exciting Light Intensity 1323.4.5 Technical Tips for Quantitative Fluorescence Microscopy 1323.5 Limitations of Fluorescence Microscopy 1333.5.1 Photobleaching 1333.5.2 Reversible Photobleaching under Oxidizing

or Reducing Conditions 1343.5.3 Phototoxicity 1353.5.4 Optical Resolution 1353.5.5 Misrepresentation of Small Objects 1373.6 Current Avenues of Development 139

References 139Further Reading 141Recommended Internet Resources 142Fluorescent Spectra Database 142

4 Fluorescence Labeling 143Gerd Ulrich Nienhaus and Karin Nienhaus

4.1 Introduction 1434.2 Principles of Fluorescence 1434.3 Key Properties of Fluorescent Labels 1444.4 Synthetic Fluorophores 1494.4.1 Organic Dyes 1494.4.2 Fluorescent Nanoparticles 1504.4.3 Conjugation Strategies for Synthetic Fluorophores 1524.4.4 Nonnatural Amino Acids 1554.4.5 Bringing the Fluorophore to Its Target 1564.5 Genetically Encoded Labels 1584.5.1 Phycobiliproteins 1584.5.2 GFP-Like Proteins 1594.6 Label Selection for Particular Applications 1634.6.1 FRET to Monitor Intramolecular Conformational

Dynamics 1634.6.2 Protein Expression in Cells 1674.6.3 Fluorophores as Sensors inside the Cell 1674.6.4 Live-Cell Dynamics 1684.7 Conclusions 168

References 169

VIII Contents

5 Confocal Microscopy 175Nikolaus Naredi-Rainer, Jens Prescher, Achim Hartschuh,and Don C. Lamb

5.1 Introduction 1755.1.1 Evolution and Limits of Conventional Widefield

Microscopy 1755.1.2 History and Development of Confocal Microscopy 1775.2 The Theory of Confocal Microscopy 1805.2.1 The Principle of Confocal Microscopy 1805.2.2 Radial and Axial Resolution and the Impact

of the Pinhole Size 1825.2.3 Scanning Confocal Imaging 1895.2.4 Confocal Deconvolution 1945.3 Applications of Confocal Microscopy 1965.3.1 Nonscanning Applications 1965.3.2 Advanced Correlation Techniques 2005.3.3 Scanning Applications Beyond Imaging 205

Acknowledgments 210References 210

6 Fluorescence Photobleaching and PhotoactivationTechniques 215Reiner Peters

6.1 Introduction 2156.2 Basic Concepts and Procedures 2166.2.1 Putting Photobleaching to Work 2166.2.2 Setting Up an Instrument 2196.2.3 Approaching Complexity from Bottom Up 2206.3 Fluorescence Recovery after Photobleaching (FRAP) 2216.3.1 Evaluation of Diffusion Measurements 2226.3.2 Binding 2256.3.3 Membrane Transport 2266.4 Continuous Fluorescence Microphotolysis (CFM) 2286.4.1 Theoretical Background and Data Evaluation 2296.4.2 Combination of CFM with Other Techniques 2316.4.3 CFM Variants 2326.5 Confocal Photobleaching 2336.5.1 Use of Laser Scanning Microscopes (LSMs)

in Photobleaching Experiments 2336.5.2 New Possibilities Provided by Confocal Photobleaching 2346.5.3 Artifacts and Remedies 2376.6 Fluorescence Photoactivation and Dissipation 2386.6.1 Basic Aspects 2386.6.2 Theory and Instrumentation 2396.6.3 Reversible Flux Measurements 239

Contents IX

6.7 Summary and Outlook 241References 241

7 Förster Resonance Energy Transfer and FluorescenceLifetime Imaging 245Fred S. Wouters

7.1 General Introduction 2457.2 FRET 2467.2.1 Historical Development of FRET 2467.2.2 Requirements 2547.2.3 FRET as a Molecular Ruler 2587.2.4 Special FRET Conditions 2627.3 Measuring FRET 2657.3.1 Spectral Changes 2667.3.2 Decay Kinetics 2727.4 FLIM 2807.4.1 Frequency-Domain FLIM 2827.4.2 Time-Domain FLIM 2837.5 Analysis and Pitfalls 2857.5.1 Average Lifetime, Multiple Lifetime Fitting 2857.5.2 From FRET/Lifetime to Species 286

Summary 287References 288

8 Single-Molecule Microscopy in the Life Sciences 293Markus Axmann, Josef Madl, and Gerhard J. Schütz

8.1 Encircling the Problem 2938.2 What Is the Unique Information? 2958.2.1 Kinetics Can Be Directly Resolved 2958.2.2 Full Probability Distributions Can Be Measured 2968.2.3 Structures Can Be Related to Functional States 2978.2.4 Structures Can Be Imaged at Superresolution 2988.2.5 Bioanalysis Can Be Extended Down

to the Single-Molecule Level 3008.3 Building a Single-Molecule Microscope 3018.3.1 Microscopes/Objectives 3018.3.2 Light Source 3048.3.3 Detector 3108.4 Analyzing Single-Molecule Signals: Position, Orientation,

Color, and Brightness 3168.4.1 Localizing in Two Dimensions 3168.4.2 Localizing along the Optical Axis 3188.4.3 Brightness 3208.4.4 Orientation 3218.4.5 Color 322

X Contents

8.5 Learning from Single-Molecule Signals 3238.5.1 Determination of Molecular Associations 3238.5.2 Determination of Molecular Conformations via FRET 3258.5.3 Superresolution Single-Molecule Microscopy 3298.5.4 Single-Molecule Tracking 3328.5.5 Detecting Transitions 332

Acknowledgments 334References 334

9 Super-Resolution Microscopy: Interferenceand Pattern Techniques 345Gerrit Best, Roman Amberger, and Christoph Cremer

9.1 Introduction 3459.1.1 Review: The Resolution Limit 3469.2 Structured Illumination Microscopy (SIM) 3479.2.1 Image Generation in Structured Illumination Microscopy 3499.2.2 Extracting the High-Resolution Information 3529.2.3 Optical Sectioning by SIM 3539.2.4 How the Illumination Pattern is Generated 3559.2.5 Mathematical Derivation of the Interference Pattern 3559.2.6 Examples for SIM Setups 3589.3 Spatially Modulated Illumination (SMI) Microscopy 3629.3.1 Overview 3629.3.2 SMI Setup 3639.3.3 The Optical Path 3649.3.4 Size Estimation with SMI Microscopy 3669.4 Application of Patterned Techniques 3689.5 Conclusion 3729.6 Summary 372

Acknowledgments 373References 373

10 STED Microscopy 375Travis J. Gould, Patrina A. Pellett, and Joerg Bewersdorf

10.1 Introduction 37510.2 The Concepts behind STED Microscopy 37610.2.1 Fundamental Concepts 37610.2.2 Key Parameters in STED Microscopy 38010.3 Experimental Setup 38410.3.1 Light Sources and Synchronization 38410.3.2 Scanning and Speed 38510.3.3 Multicolor STED Imaging 38610.3.4 Improving Axial Resolution in STED Microscopy 38810.4 Applications 38810.4.1 Choice of Fluorophore 388

Contents XI

10.4.2 Labeling Strategies 389Summary 390References 391

A Appendix: Practical Guide to Optical Alignment 393Rainer Heintzmann

A.1 How to Obtain a Widened Parallel Laser Beam 393A.2 Mirror Alignment 395A.3 Lens Alignment 396A.4 Autocollimation Telescope 396A.5 Aligning a Single Lens Using a Laser Beam 397A.6 How to Find the Focal Plane of a Lens 399A.7 How to Focus to the Back Focal Plane of an Objective

Lens 400

Index 403

XIII

Preface

What is this book?

This book is both a high-level textbook and a reference for researchers applyinghigh-performance microscopy. It provides a comprehensive yet compact accountof the theoretical foundations of light microscopy, the large variety of specializedmicroscopic techniques, and the quantitative utilization of light microscopy data. Itenables the user of modern microscopic equipment to fully exploit the complex in-strumental features with knowledge and skill. These diverse goals were approachedby recruiting a collective of leading scientists as authors. We applied a stringentinternal reviewing process to achieve homogeneity, readability, and a satisfyingcoverage of the field. Also, we took care to reduce redundancy as far as possible.

Why this book?

Meanwhile, there are numerous books on light microscopy on the market. At acloser look, however, many available books are written at an introductory level withregard to the physics behind the mostly demanding techniques, or they presentreview articles on advanced topics. Books introducing widespread techniquessuch as fluorescence resonance energy transfer, stimulated emission depletion, orstructured illumination microscopy together with the required basics and theoryare relatively rare. Even the basic optical theory such as the Fourier theory of opticalimaging or topics such as the sine condition are seldom introduced from scratch.With this book, we tried to fill this gap.

Is this book for you?

The book is aimed at advanced undergraduate and graduate students of thebiosciences and researchers entering the field of quantitative microscopy. Asthey are usually recruited from most natural sciences, that is, physics, biology,chemistry, and biomedicine, we addressed the book to this readership. Readerswould definitely profit from a sound knowledge of physics and math. This allowsdiving much deeper into the material than without. However, all authors areexperienced in teaching university and summer courses on light microscopy

XIV Preface

and have for many years explored the ways to present the required knowledge.Hopefully, you will find that they came upon good solutions. In case you see roomfor improvement or you encounter mistakes, please let me know.

How should you read the book?

Generally, there are two approaches. Students, who require an in-depth knowledge,should begin at their level of knowledge, either in Chapter 1 (Introduction to Opticsand Photophysics) or Chapter 2 (Principles of Light Microscopy). Beginners shouldinitially omit advanced topics, for example, the section on Differential InterferenceContrast (Section 2.6.4). Principally, the book is readable without the ‘‘boxes’’;however, they help in developing a good understanding of theory and history.Then, they should proceed through Chapter 3 (Fluorescence Microscopy), Chapter4 (Labeling Techniques), and Chapter 5 (Confocal Microscopy). Chapters 6–10 areon advanced topics and special techniques. They should be studied according tointerest and requirement.

Alternatively, readers familiar with the subject may certainly skip the introductoryChapters 1–3 and advance directly to the more specialized chapters. In order tomaintain the argumentation in these chapters, we repeated certain basic topics intheir introductions.

Website of the book

There is a Web site supporting this book (http://www.wiley-vch.de/home/fluorescence_microscopy/). Here, lecturers will find all figures in JPG format for usein courses and additional illustrative material such as movies.

Personal remarks on the history of this book

I saw one of the very first commercial laser scanning microscopes in the lab ofTom Jovin at the Max Planck Institute of Biophysical Chemistry in Göttingenduring the late 1980s and was immediately fascinated by the images of thatinstrument. In the early 1990s, confocal laser scanning microscopes began tospread over biological and biomedical labs. At that time, they usually requiredreally dedicated scientists for proper operation, filled a small laboratory, and weregoverned by computers as big as refrigerators. The required image processingdemanded substantial investments. That was when Reiner Peters and I noticedthat biologists and medical scientists needed an introduction into the physicalbackground of optics, spectroscopy, and image analysis for coping with the newtechniques. Hence, we offered a lecture series entitled ‘‘Microscopes, Lasers andComputers’’ at the Institute of Medical Physics and Biophysics of the Universityof Münster, Germany, which was very well received. We began to write a bookon microscopy containing the material we had presented, which should not be ascomprehensive as Jim Pawley’s ‘‘Handbook’’ but should offer an accessible path to

Preface XV

modern quantitative microscopy. We invested almost one year into this enterpriseproject, but then gave up . . . in view of numerous challenging research topics thatkept us busy, the insight into the dimension of this task, and the reality of careerrequirements. We realized we could not do it alone.

In 2009, Reiner Peters, now at The Rockefeller University in New York, organizeda workshop on ‘‘Watching the Cellular Nanomachinery at Work’’ and gatheredsome of the current leaders in microscopy to report on their latest technical andmethodical advances. On this occasion, he noted that the book that had been inour minds 15 years ago was still missing . . . and contacted the speakers of hismeeting. Like many years before, I was excited by the idea to create this book,and together we directly addressed the lecturers of the meeting and asked forintroductory book chapters in the fields of their respective expertise. Luckily, anumber of them responded positively and began the struggle for an introductorytext. Unfortunately, Reiner could not keep his position as an editor of the bookdue to further obligations, so I had to finish our joint project on my own. Hereis the result, and I hope very much the authors succeeded in transmitting theirongoing fascination for microscopy. To me, microscopy appears as a century-oldtree that began another phase of growth about 40 years ago, and since then hasshown almost every year a new branch with a surprising and remarkable techniqueoffering exciting and fresh scientific fruits.

Acknowledgments

I would like to thank some people who contributed directly and indirectly to thisbook. First of all, I would like to name Prof. Dr. Reiner Peters. As mentioned, heinvited me to the first steps to teach microscopy and to the first attempt to writethis book. Finally, he launched the initiative to create this book as an edited work.Furthermore, I would like to thank all the authors, who invested a lot of theirexpertise, time, and energy in writing, correcting, and finalizing their respectivechapters. All are much respected colleagues, and some of them became friendsduring this project. Also, I thank some people who were previously collaboratorsor colleagues and helped me to learn more and more about microscopy: Prof. Dr.Reinhard Schweitzer-Stenner, Dr. Donna Arndt-Jovin, Prof. Dr. Tom Jovin, Dr.Thorsten Kues, and Prof. Dr. David Grünwald. Likewise, I gratefully acknowledgeBrinda Luiz from Laserwords, India, for excellent project management, and thecommissioning editor and the project editor responsible at Wiley-VCH, Dr. GregorCicchetti and Anne du Guerny, respectively, who sincerely supported this projectand not only showed professional patience when yet another delay occurred butalso pushed when required. Last but not least, I would like to thank my collaboratorDr. Jan Peter Siebrasse and my wife Martina, who patiently listened to my concerns,when still another problem occurred.

Bonn, March 2013 Ulrich Kubitscheck

XVII

List of Contributors

Roman AmbergerHeidelberg UniversityApplied Optics and InformationProcessingKirchhoff-Institute for PhysicsIm Neuenheimer Feld 22769120 HeidelbergGermany

Markus AxmannDepartment of New Materials andBiosystemsMax Planck Institute forIntelligent SystemsHeisenbergstrasse 370569 StuttgartGermany

Gerrit BestHeidelberg UniversityApplied Optics and InformationProcessingKirchhoff-Institute for PhysicsIm Neuenheimer Feld 22769120 HeidelbergGermany

and

Heidelberg University HospitalDepartment of OphthalmologyIm Neuenheimer Feld 40069120 HeidelbergGermany

Joerg BewersdorfYale UniversityDepartment of Cell Biology333 Cedar StreetNew HavenCT 06510USA

and

Yale UniversityDepartment of BiomedicalEngineering333 Cedar StreetNew HavenCT 06510USA

and

Yale UniversityKavli Institute for Neuroscience333 Cedar StreetNew HavenCT 06510USA

XVIII List of Contributors

Christoph CremerHeidelberg UniversityApplied Optics and InformationProcessingKirchhoff-Institute for PhysicsIm Neuenheimer Feld 22769120 HeidelbergGermany

and

Heidelberg UniversityInstitute of Pharmacy andMolecular BiotechnologyIm Neuenheimer Feld 36469120 HeidelbergGermany

and

The Jackson LaboratoryInstitute for Molecular Biophysics600 Main StreetBar HarborMaine 04609USA

and

Institute of MolecularBiology gGmbH (IMB)Ackermannweg 455128 MainzGermany

Jurek W. DobruckiJagiellonian UniversityDivision of Cell BiophysicsFaculty of BiochemistryBiophysics and Biotechnologyul. Gronostajowa 730-387 KrakówPoland

Travis J. GouldYale UniversityDepartment of Cell Biology333 Cedar StreetNew HavenCT 06510USA

Achim HartschuhLudwig-Maximilians-UniversitätMünchenCenter for Nanoscience (CeNS)Physical ChemistryDepartment of ChemistryButenandtstrasse 5-13Gerhard-Ertl-Building81377 MunichGermany

Rainer HeintzmannInstitute of Physical ChemistryAbbe Center of PhotonicsFriedrich Schiller University JenaHelmholtzweg 407743 JenaGermany

and

Institute of Photonic TechnologyMicroscopy Research DepartmentAlbert-Einstein Strasse 907745 JenaGermany

and

King’s College LondonRandall Division of Cell andMolecular BiophysicsNHH, Guy’s CampusLondon SE1 1ULUK

List of Contributors XIX

Ulrich KubitscheckRheinische FriedrichWilhelms-Universität BonnInstitute for Physical andTheoretical ChemistryDepartment of BiophysicalChemistryWegeler Strasse 1253115 BonnGermany

Don C. LambLudwig-Maximilians-UniversitätMünchenCenter for Nanoscience (CeNS)Physical ChemistryDepartment of ChemistryButenandtstrasse 5-13Gerhard-Ertl-Building81377 MunichGermany

and

Ludwig-Maximilians-UniversitätMünchenMunich Center for IntegratedProtein Science (CiPSM)Butenandtstrasse 5-13D-81377 MunichGermany

and

University of Illinois atUrbana-ChampaignDepartment of Physics1110 West Green StreetUrbana, IL 61801USA

Josef MadlAlbert Ludwigs UniversityFreiburgInstitute of Biology II and Centerfor Biological Signaling Studies(BIOSS)79104 FreiburgGermany

Nikolaus Naredi-RainerLudwig-Maximilians-UniversitätMünchenCenter for Nanoscience (CeNS)Department of ChemistryPhysical ChemistryButenandtstrasse 5-13Gerhard-Ertl-Building81377 MunichGermany

Gerd Ulrich NienhausKarlsruhe Institute ofTechnology (KIT)Institute of Applied Physics andCenter for FunctionalNanostructuresWolfgang-Gaede-Strasse 1D-76131 KarlsruheGermany

and

University of Illinois atUrbana-ChampaignDepartment of Physics1110 West Green StreetUrbana, IL 61801USA

XX List of Contributors

Karin NienhausKarlsruhe Institute ofTechnology (KIT)Institute of Applied Physics andCenter for FunctionalNanostructuresWolfgang-Gaede-Street 1D-76131 KarlsruheGermany

Patrina A. PellettYale UniversityDepartment of Cell Biology333 Cedar StreetNew HavenCT 06510USA

and

Yale UniversityDepartment of Chemistry225 Prospect StreetNew HavenCT 06510USA

Reiner PetersRockefeller University1230 York AvenueNY 10065 New YorkUSA

Jens PrescherLudwig-Maximilians-UniversitätMünchenCenter for Nanoscience (CeNS)Department of ChemistryPhysical ChemistryButenandtstr. 5-13Gerhard-Ertl-Building81377 MunichGermany

Gerhard J. SchützVienna University of TechnologyInstitute of Applied PhysicsWiedner Hauptstrasse 8-101040 WienAustria

Fred S. WoutersUniversity Medicine GöttingenLaboratory for Molecular andCellular SystemsDepartment of Neuro- andSensory PhysiologyCentre IIPhysiology and PathophysiologyHumboldtallee 2337073 GöttingenGermany

1

1Introduction to Optics and PhotophysicsRainer Heintzmann

In this chapter, we first introduce the properties of light as a wave by discussinginterference, which explains the laws of refraction, reflection, and diffraction.We then discuss light in the form of rays, which leads to the laws of lensesand the ray diagrams of optical systems. Finally, the concept of light as photonsis addressed, including the statistical properties of light and the properties offluorescence.

For a long time, it was believed that light travels in straight lines, which are calledrays. With this theory, it is easy to explain brightness and darkness, and effectssuch as shadows or even the fuzzy boundary of shadows due to the extent of thesun in the sky. In the sixteenth century, it was discovered that sometimes lightcan ‘‘bend’’ around sharp edges by a phenomenon called diffraction. To explain theeffect of diffraction, light has to be described as a wave. In the beginning, this wavetheory of light – based on Christiaan Huygens’ (1629–1695) work and expanded(in 1818) by Augustin Jean Fresnel (1788–1827) – was not accepted. Poisson, ajudge for evaluating Fresnel’s work in a science competition, tried to ridicule it byshowing that Fresnel’s theory would predict a bright spot, now called the Poisson’sspot, in the middle of a round dark shadow behind a disk object, which he obviouslyconsidered wrong. Another judge, Arago, then showed that this spot is indeed seenwhen measurements are done carefully enough. This was a phenomenal successof the wave description of light. Additionally, there was also the corpuscular theoryof light (Pierre Gassendi *1592, Sir Isaac Newton *1642), which described light asparticles. With the discovery of Einstein’s photoelectric effect, the existence of theseparticles, called photons, could not be denied. It clearly showed that a minimumenergy per such particle is required as opposed to a minimum strength of anelectric field. Such photons can even directly be ‘‘seen’’ as individual spots, whenusing a camera with a very sensitive film imaging a very dim light distribution ormodern image intensified or emCCD cameras.

Since then, the description of light maintained this dual (wave and particle)nature. When it is interacting with matter, one often has to consider its quantum(particle) nature. However, the rules of propagation of these particles are describedby Maxwell’s wave equations of electrodynamics, identifying oscillating electricfields as the waves responsible for what we call light. The wave-particle duality of

Fluorescence Microscopy: From Principles to Biological Applications, First Edition. Edited by Ulrich Kubitscheck.© 2013 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2013 by Wiley-VCH Verlag GmbH & Co. KGaA.

2 1 Introduction to Optics and Photophysics

light still surprises with interesting phenomena and is an active field of research(known as quantum optics). It is expected that exploiting related phenomenawill form the basis of future devices such as quantum computers, quantumteleportation, and even microscopes based on quantum effects.

To understand the behavior of light, the concepts of waves are often required.Therefore, we start by introducing an effect that is observed only when theexperiment is designed carefully: interference.

For understanding the basic concepts as detailed below, only a minimumamount of mathematics is required. Previous knowledge of complex numbersis not required. However, for quantitative calculations, the concepts of complexnumbers will be needed.

1.1Interference: Light as a Wave

Suppose that we perform the following experiment (Figure 1.1). We place anylight source on the input side of the instrument, as illustrated in Figure 1.1.This instrument consists of only two 50% beam splitters and two ordinary fullyreflecting mirrors. However, if these are very carefully adjusted such that the pathlengths along the two different paths are exactly equal, something strange happens:all the light entering the device will leave only one of the exit ports. In the secondoutput port, we will observe absolute darkness. This is very strange indeed, asnaı̈vely one would expect 2 × 0.5 × 0.5 = 50% of the light emerging on either side.Even more surprising is what happens if one inserts a hand into one of the twobeams inside this device. Now, obviously the light will be absorbed by our hand,but nevertheless, some light (25%) will suddenly leave the top output of the device,where we previously had only darkness. As we would expect, another 25% light willleave the second output.

The explanation of this effect of interference lies in the wave nature of light:brightness and brightness can indeed yield darkness (called destructive interference),if the two superimposed electromagnetic waves are always oscillating in oppositedirections, that is, they have opposite phases (Figure 1.1b). The frequency ν isgiven as the reciprocal of time between two successive maxima of this oscillation.The amplitude of a wave is given by how much the electric field oscillates while itis passing by. The square of this amplitude is what we perceive as irradiance orbrightness (sometimes also referred to, in a slightly inaccurate way, as intensity) ofthe light. If one of the two waves is then blocked, this destructive cancellation willcease and we will get the 25% brightness, as ordinarily expected by splitting 50%of the light again in two.

Indeed, if we remove our hand and just delay one of the two waves by only half awavelength (e.g., by introducing a small amount of gas in only one of the two beampaths), the relative phase of the waves changes, which can invert the situation,that is, we observe constructive interference (on top side) where we previously haddestructive interference and darkness where previously there was light.

1.1 Interference: Light as a Wave 3

100%Constructiveinterference

50% Beam splitter

50% Beamsplitter

Mirror

Mirror

0%Destructiveinterference

Stic

k ha

nd in

here

Light source

t

E

t

E

t

E

Field 1

Field 2

Field of destructive interference

T = 1/n

Amplitude

(a)

(b)

Figure 1.1 Interference. (a) In the interfer-ometer of Mach–Zehnder type, the beamis split equally in two paths by a beamsplitter and after reflection rejoined witha second beam splitter. If the optical pathlengths of the split beams are adjusted to beexactly equal, constructive interference re-sults in the right path, whereas the lightin the other path cancels by destructive

interference. (b) Destructive interfer-ence. If the electric field of two interfer-ing light waves (top and bottom) is al-ways of opposite value (p phase shift),the waves cancel and the result is a zerovalue for the electric field and, thus, alsozero intensity. This is termed destructiveinterference.

The aforementioned device is called an interferometer of Mach–Zehnder type.Such interferometers are extremely sensitive measurement devices capable ofdetecting a sub nanometer relative delay of light waves passing the two arms ofthe interferometer, for example, caused by a very small concentration of gas inone arm.

4 1 Introduction to Optics and Photophysics

Sound is also a wave, but in this case, instead of the electromagnetic field, itis the air pressure that oscillates at a much slower rate. In the case of light, itis the electric field oscillating at a very high frequency. The electric field is alsoresponsible for hair clinging to a synthetic jumper, which has been electricallycharged by friction or walking on the wrong kind of floor with the wrong kind ofsocks and shoes. Such an electric field has a direction not only when it is static, asin the case of the jumper, but also when it is dynamic, as in the case of light. In thelatter case, the direction corresponds to the direction of polarization of the light,which is discussed later.

Waves, such as water waves, are more commonly observed in nature. Althoughthese are only a two-dimensional analogy to the electromagnetic wave, their crests(the top of each such wave) are a good visualization of what is referred to as aphase front. Thus, phase fronts in 3 dimensional electromagnetic waves refer to thesurfaces of equal phase (e.g., a local maximum of the electric field). Similar to whatis seen in water waves, such phase fronts travel along with the wave at the speed oflight. The waves we observe close to the shore can serve as a 2D analogy to what iscalled a plane wave, whereas the waves seen in a pond, when we throw a stone intothe water, are a two-dimensional analogy to a spherical wave.

When discussing the properties of light, one often omits the details aboutthe electric field being a vectorial quantity and rather talks about the scalar‘‘amplitude’’ of the wave. This is just a sloppy, but a very convenient way ofdescribing light when polarization effects do not matter for the experiment underconsideration. Light is called a transverse wave as in vacuum and homogeneousisotropic media, the electric field is always oriented perpendicular to the localdirection of propagation of the light. However, this is merely a crude analogy towaves in media, such as sound, where the particles of the medium actually move. Inthe case of light, there is really no movement of matter necessary for its descriptionas the oscillating quantity is the electric field, which can even propagate invacuum.

The frequency ν (measured in hertz, i.e., oscillations per second, see alsoFigure 1.1b), at which the electric field vibrates, defines its color. Blue light has ahigher frequency and energy hν per photon than green, yellow, red, and infraredlight. Here, h is Planck’s constant and ν is the frequency of the light. Because invacuum, the speed of light does not depend on its color, the vacuum wavelengthλ is short for blue light (∼ 450 nm) and gets longer for green (∼ 520 nm), yellow(∼ 580 nm), red (∼ 630 nm), and infrared (∼ 800 nm), respectively. In addition,note that the same wave theory of light governs all wavelength ranges of theelectromagnetic spectrum from radio waves over microwaves, terahertz waves,infrared, visible, ultraviolet, vacuum-ultraviolet, and soft and hard X-rays to gammarays.

In many cases, we deal with linear optics, where all amplitudes will have thetime dependency exp(iωt), as given above. Therefore, this time-dependent term isoften omitted, and one concentrates only on the spatial dependency while keepingin mind that each phasor always rotates with time.

1.1 Interference: Light as a Wave 5

Box 1.1 Phasor Diagrams and the Complex Wave

This box mathematically describes the concept of waves. For this, the knowledgeof complex numbers is required. However, a large part of the main text doesnot require this understanding.

For a deeper understanding of interference, it is useful to take a look at thephasor diagrams. In such a diagram, the amplitude value is pictured as a vectorin the complex plane. This complex amplitude is called a phasor. Even thoughthe electric field strength is just the real part of the phasor, the complex-valuedphasor concept makes all the calculations a lot simpler.

The rapidly oscillating wave corresponds to the phasor rotating at a constantspeed around the center of the complex plane (see Figure 1.2 for a depiction ofa rotating complex amplitude vector and its real part being the electric field overtime). Mathematically, this can be written as

A (t) = A0 ei� t

with the frequency � = 2πν, and the complex-valued amplitude A0 = |A0| exp(iϕ)depending on its strength |A0| and phase ϕ of the wave at time 0. The phaseor phase angle of a wave corresponds to the arguments of the exponentialfunctions, thus in our case ϕ + � t, whereas the strength |A0| is often simplyreferred to as amplitude, which is a bit ambiguous to use with the abovecomplex amplitude.

Real

Imag

inar

y

1−1

Imaginary partof A0

Real partof A0

0

i

t

Re[A0 eiω t ] = |A0| cos(ω t + ϕ)

Figure 1.2 The phasor in the complex plane. An electro-optical wave can be seenas the real part of a complex-valued wave (lower part) A0exp(iωt). This wave has thecomplex-valued phasor A0, which is depicted in the complex plane. It is characterizedby its length |A0| and its phase ϕ.

6 1 Introduction to Optics and Photophysics

To describe what happens if two waves interfere, we simply add the twocorresponding complex-valued phasors. Such a complex-valued addition meansto simply attach one of the vectors to the tip of the other to obtain the resultingamplitude (Figure 1.3).

Real

Imag

inar

y

1−1

i

0

A1 : Phasor of wave 1A2 : Phasor of wave 2A1 + A2 : Wave 1 interfering with wave 2

A1 + A2 A1

A2

Figure 1.3 Addition of phasors. The addition of two phasors A1 and A2 is depictedin the complex plane. As can be seen, the phasors (each being described by a phaseangle and a strength) add like vectors.

As light oscillates extremely fast, we have no way of measuring its electricfield directly, but we do have means to measure its ‘‘intensity,’’ which relatesto the energy in the wave that is proportional to the square of the absoluteamplitude (square of the length of the phasor).

This absolute square of the amplitude can be obtained by adding the squareof its real part to the square of its imaginary part, which is identical to writing(for a complex-valued amplitude A)

I = A A∗

with the asterisk denoting the complex conjugate.Waves usually propagate through space. If we assume that a wave oscillates

at a well-defined frequency � and travels with a speed c/n (the vacuum speed oflight c and the refractive index of the medium n), we can write such a travelingplane wave as

A (x, t) = A0e−i(kx−� t)

with k = 2πn/λ = �n/c being the wavenumber, which is related to the spatialfrequency k′ as k′ = k/2π . Note that both k and x are vectorial quantities ifworking in two or three dimensions, in which case their product refers to

1.2 Two Effects of Interference: Diffraction and Refraction 7

the scalar product of the vectors. The spatial frequency counts the number ofamplitude maxima per meter in the medium in which it is traveling (Figure 1.2).The spatial position x denotes the coordinate at which we are observing.

In many cases, we deal with linear optics, where all amplitudes will have thetime dependency exp(iωt) as given above. Therefore, this time-dependent termis often omitted and one concentrates only on the spatial dependency whilekeeping in mind that each phasor always rotates with time.

1.2Two Effects of Interference: Diffraction and Refraction

We now know the important effect of constructive and destructive interference oflight, explained by its wave nature. As discussed below, the wave nature of light iscapable of explaining two aspects of light: diffraction and refraction. Diffraction isa phenomenon that is seen when light interacts with a very fine (often periodic)structure such as a compact disk (CD). The emerging light will emerge underdifferent angles, dependent on its wavelengths and giving rise to the colorfulexperience when looking at light diffracted from the surface of a CD. On the otherhand, refraction refers to the effect where light rays seem to change their directionwhen the light passes from one medium to another. This is, for example, seenwhen trying to look at a scene through a glass full of water.

Even though these two effects may look very different at first glance, both of theseeffects are ultimately based on interference, as discussed here. Diffraction is mostprominent when light illuminates structures (such as a grating) of a feature size(grating constant) similar to the wavelength of light. In contrast, refraction (e.g.,the bending of light rays caused by a lens) dominates when the different media(such as at the air and glass) have constituents (molecules) that are much smallerthan the wavelength of light (homogeneous media), but these homogeneous areasare much larger in feature size (i.e., the size of a lens) than in the wavelength.

To describe diffraction, it is useful to first consider the light as emitted by apointlike source. Let us look at an idealized source, which is infinitely small andemits only a single color of light. This source would emit a spherically divergingwave. In vacuum, the energy flows outward through any surface around the sourcewithout being absorbed; thus, spherical shells at different radii must have the sameintegrated intensity. Because the surface of these shells increases with the squareof the distance to the source, the light intensity decreases with the inverse squaresuch that energy is conserved.

To describe diffraction, Christiaan Huygens had an ingenious idea: to find outhow a wave will continue on its path, we determine it at a certain border surfaceand can then place virtual point emitters everywhere at this surface, letting the lightof these emitters interfere. The resulting interference pattern will reconstitute theoriginal wave beyond that surface. This ‘‘Huygens’ principle’’ can nicely explainthat parallel waves stay parallel, as we find constructive interference only in the

8 1 Introduction to Optics and Photophysics

direction following the propagation of the wave. Strictly speaking, one would alsofind a backwards propagation wave. However, when Huygen’s idea is formulatedin a more rigorous way, the backward propagating wave is avoided. Huygens’principle is very useful when trying to predict the scenario when a wave hits astructure with feature size comparable to the wavelength of light, for example, aslit aperture or a diffraction grating. In Figure 1.4, we consider the example ofdiffraction at a grating with the lowest repetition distance D. D is designated asthe grating constant. As is seen from the figure, circular waves correspondingto Huygens’ wavelets originate at each aperture and they join to form new wavefronts, thus forming plane waves oriented in various directions. These directionsof constructive interference need to fulfill the following condition (Figure 1.4):

sin α = N λD

with N denoting the integer (number of the diffraction orders) multiples ofwavelengths λ to yield the same phase (constructive interference) at angle α withrespect to the incident direction. Note that the angle α of the diffracted wavesdepends on the wavelength and thus on the color of light. In addition, note that thecrests of the waves form connected lines (indicated as dashed-dotted line), whichare called phase fronts or wave fronts, whereas the dashed lines perpendicular to thesephase fronts can be thought of as corresponding to the light rays of geometricaloptics.

N =1

N= 2

DD sin α = Nλ

αλ

λ

First dif

fraction

order

Seco

nd d

iffra

ctio

n

orde

r

Phase fronts

Light ray

N = 0Zero order

Figure 1.4 Diffraction at a grating un-der normal incidence. The directions ofconstructive interference (where max-ima and minima of one wave interferewith the respective maxima and min-ima of the second wave) are shown for

several diffraction orders. The diffractionequation D sin α = Nλ, which isderived from the geometrical con-struction of Huygens’ wavelets, isshown.