Increasing Estimation Precision in Localization Microscopy
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INCREASING ESTIMATION PRECISION IN LOCALIZATION MICROSCOPY by Carl G. Ebeling A dissertation submitted to the faculty of The University of Utah in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Physics Department of Physics and Astronomy The University of Utah May 2015 Copyright © Carl G. Ebeling 2015 All Rights Reserved The University of Utah Graduate School STATEMENT OF DISSERTATION APPROVAL The dissertation of Carl G. Ebeling has been approved by the following supervisory committee members: Jordan M. Gerton Chair 12/05/2014 Date Approved Erik M. Jorgensen Member 12/05/2014 Date Approved Saveez Saffarian Member 12/05/2014 Date Approved Stephan Lebohec Member 12/05/2014 Date Approved Paolo Gondolo Member 12/05/2014 Date Approved and by _________________ Carleton DeTar_________________ , Chair/Dean of the Department/College/School o f _____________ Physics and Astronomy__________ and by David B. Kieda, Dean of The Graduate School. ABSTRACT This dissertation studies detection-based methods to increase the estimation pre cision of single point-source emitters in the field of localization microscopy. Localiza tion microscopy is a novel method allowing for the localization of optical point-source emitters below the Abbe diffraction limit of optical microscopy. This is accomplished by optically controlling the active, or bright, state of individual molecules within a sam ple. The use of time-multiplexing of the active state allows for the temporal and spatial isolation of single point-source emitters. Isolating individual sources within a sample allows for statistical analysis on their emission point-spread function profile, and the spatial coordinates of the point-source may be discerned below the optical response of the microscope system. Localization microscopy enables the identification of individual point-source emitter locations approximately an order of magnitude below standard, diffraction-limited optical techniques. The precision of localization microscopy methods is limited by the statistical uncer tainty in which the location of these sources may be estimated. By utilizing a detection- based interferometer, an interference pattern may be super-imposed over the emis sion signal. Theoretical analysis and Monte-Carlo simulations by means of Fisher infor mation theory demonstrate that the incorporation of a modulation structure over the emission signal allow for a more precise estimation when compared to conventional localization methods for the same number of recorded photons. These theoretical calculation and simulations are demonstrated through the use of two proof-of-concept experiments utilizing a modified Mach-Zehnder interferometer. The first methodology improves the localization precision of a single nanoparticle over the theoretical limit for an Airy-disk point-spread function by using self-interference to spatially modulate the recorded point-spread function. Experimental analysis demon strates an improvement factor of « 3 to 5 over conventional localization methods. A related method employs the phase induced onto the Fourier domain signal due to path length differences in the Mach-Zehnder interferometer to improve localization preci sion. The localization capability of a modified Fourier domain signal generated by self interference is utilized to yield a two-fold improvement in the localization precision for a given number of photons compared to a standard Gaussian intensity distribution of the corresponding point-spread function. iv To my wife Megan. To the next journey! CONTENTS ABSTRACT............................................................................................................................... iii LIST OF FIGURES................................................................................................................... ix ACKNOWLEDGMENTS.......................................................................................................... xiii CHAPTERS 1.....INTRODUCTION TO OPTICAL MICROSCOPY....................................................... 1 1.1 Motivation ................................................................................................................. 2 1.2 Types of Microscopy................................................................................................ 3 1.2.1 Optical Microscopy......................................................................................... 4 1.2.2 Fluorescence Microscopy............................................................................... 4 1.3 Microscopy, Specificity, and Resolution.............................................................. 8 1.4 Summary and Outline ........................................................................................... 9 1.5 References ................................................................................................................. 13 2. THE THEORETICAL FOUNDATIONS OF OPTICAL MICROSCOPY..................... 14 2.1 The Principle of Fluorescence............................................................................... 14 2.1.1 Fluorophore Interactions with Light........................................................... 16 2.1.2 Franck-Condon Principle............................................................................... 19 2.2 Resolution, the Point-Spread Function, and the Diffraction Limit ....................................................................................... 21 2.2.1 The Diffraction Limit ..................................................................................... 22 2.2.2 The Heisenberg Uncertainty Principle....................................................... 24 2.3 The Angular Spectrum Representation ................................................................ 26 2.3.1 Propagating and Evanescent W aves........................................................... 27 2.4 The Airy Profile and Rayleigh Criterion................................................................ 29 2.5 Summary ................................................................................................................... 33 2.6 References ................................................................................................................. 33 3. CIRCUMVENTING THE DIFFRACTION BARRIER VIA OPTICAL METHODOLOGIES ..................................................................................... 35 3.1 Super Resolution Microscopy in its Many Forms............................................... 36 3.1.1 Optical Super-Resolution - Moving Beyond Abbe’s Lim it....................... 38 3.1.2 Structured Illumination ................................................................................. 38 3.1.3 STED Microscopy........................................................................................... 39 3.2 Localization Microscopy ....................................................................................... 43 3.2.1 Information Extraction from the Point-Spread Function....................... 44 3.2.2 Isolating Single Fluorophores ...................................................................... 49 3.2.3 The Methodology of Localization Microscopy.......................................... 52 3.2.4 Biological Examples of Localization Microscopy...................................... ..55 3.3 Localization versus Resolution............................................................................ ..58 3.4 Concluding Remarks..................................................................................................62 3.5 References...................................................................................................................63 4. MODIFICATION OF THE POINT-SPREAD FUNCTION THROUGH SELF-INTERFERENCE............................................................................ 67 4.1 Theoretical Concept................................................................................................ 68 4.2 Localization Ability and the Fisher Information M atrix.................................. 69 4.2.1 Derivation of the Fisher Information M atrix............................................. 70 4.3 Monte-Carlo Simulations....................................................................................... 71 4.3.1 One-Dimensional Monte-Carlo Simulations ...............................................72 4.3.2 Effect of Rotating the Interference Fringes by 4 5 ° .................................... ..75 4.3.3 Monte-Carlo Simulations of Target Rings.....................................................76 4.4 Experimental Setup ..................................................................................................77 4.5 Experimental Results ............................................................................................. ..80 4.5.1 Particle Tracking and Wide-field Imaging................................................... 85 4.6 Conclusions .............................................................................................................. 86 4.7 References ................................................................................................................. 88 5. INCREASED LOCALIZATION PRECISION BY INTERFERENCE FRINGE ANALYSIS......................................................................................................................... 90 5.1 Motivation ................................................................................................................. 90 5.2 Theory