Coded Aperture Magnetic Sector Mass Spectrometry by Zachary Eugene Russell Department of Electrical and Computer Engineering Duke University Date:_______________________ Approved: ___________________________ Jeffrey T Glass, Supervisor ___________________________ Michael E Gehm ___________________________ Scott D Wolter ___________________________ Chris Dwyer ___________________________ Jungsang Kim Dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Electrical and Computer Engineering in the Graduate School of Duke University 2015 i v ABSTRACT Coded Aperture Magnetic Sector Mass Spectrometry by Zachary Eugene Russell Department of Electrical and Computer Engineering Duke University Date:_______________________ Approved: ___________________________ Jeffrey T Glass, Supervisor ___________________________ Michael E Gehm ___________________________ Scott D Wolter ___________________________ Chris Dwyer ___________________________ Jungsang Kim An abstract of a dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Electrical and Computer Engineering in the Graduate School of Duke University 2015 i v Copyright by Zachary Eugene Russell 2015 Abstract Mass spectrometry is widely considered to be the gold standard of elemental analysis techniques due to its ability to resolve atomic and molecular and biological species. Expanding the application space of mass spectrometry often requires the need for portable or hand-held systems for use in field work or harsh environments. While only requiring “sufficient” mass resolution to meet the needs of their application space, these miniaturized systems suffer from poor signal to background ratio which limits their sensitivity as well as their usefulness in field applications. Spatial aperture coding techniques have been used in optical spectroscopy to achieve large increases in signal intensity without compromising system resolution. In this work similar computational methods are used in the application of these techniques to the field of magnetic sector mass spectrometry. Gains in signal intensity of 10x and 4x were achieved for 1D and 2D coding techniques (respectively) using a simple 90 degree magnetic sector test setup. Initial compatibility with a higher mass resolution double focusing Mattauch-Herzog mass spectrograph was demonstrated experimentally and with high fidelity particle tracing simulations. A novel electric sector lens system was designed to stigmate high order coded aperture patterned beam which shows simulated gains in signal intensity of 50x are achievable using these techniques. iv Dedication Dedicated to my friends and family for all of their support, and to my mother and father, the greatest teachers I have ever known. v Contents Abstract ......................................................................................................................................... iv List of Tables ................................................................................................................................. ix List of Figures ................................................................................................................................ x Acknowledgements ................................................................................................................... xix 1. Introduction ............................................................................................................................... 1 1.1 Motivation ......................................................................................................................... 1 1.2 Background ....................................................................................................................... 3 1.2.1 Miniaturizing the Mass Spectrometer ...................................................................... 3 1.2.2 Spatially Coded Apertures in Spectrometry............................................................ 6 2. System Design and Experimental Methods ........................................................................ 15 2.1 Magnetic Sector ............................................................................................................... 15 2.2 Ion Source ........................................................................................................................ 18 2.3 Detector ............................................................................................................................ 26 2.4 Sample Introduction ....................................................................................................... 28 2.5 Coded Aperture Fabrication ......................................................................................... 29 2.6 System Summary ............................................................................................................ 32 3. One-Dimensional Spatially Coded Aperture Mass Spectrometry ................................... 34 3.1 Aperture Coding Model ................................................................................................ 37 3.2 Forward Model Derivation ........................................................................................... 39 3.3 Forward Model Calibration .......................................................................................... 41 vi 3.4 Experimental Results and Discussion ......................................................................... 44 3.5 Conclusion ....................................................................................................................... 54 4. Two-Dimensional Spatially Coded Aperture Mass Spectrometry .................................. 55 4.1 Experimental ................................................................................................................... 56 4.2 Forward Model Calibration .......................................................................................... 58 4.3 Results and Discussion .................................................................................................. 60 4.4 Conclusion ....................................................................................................................... 68 5. A Miniature Mattauch-Herzog Mass Analyzer Utilizing Spatially Coded Apertures . 70 5.1 Simulation of Spatial Aperture Coding in the Mattauch-Herzog Geometry ......... 73 5.1.1 Geometric Optics Transfer Matrix Calculation ..................................................... 74 5.1.2 Particle Tracing Using COMSOL and C# ............................................................... 78 5.2 Experimental Verification of Spatial Aperture Coding in the Mattauch-Herzog Geometry ............................................................................................................................... 84 5.3 Conclusions ..................................................................................................................... 86 6. A Novel Stigmatic Double Focusing Mass Spectrograph Utilizing Spatially Coded Apertures...................................................................................................................................... 87 6.1 Introduction ..................................................................................................................... 87 6.2 Extended Length Ion Source ......................................................................................... 88 6.3 Electric Sector Modifications ......................................................................................... 90 6.4 Capped Electric Sectors ................................................................................................. 98 6.5 Linear Field for Beam Stigmation .............................................................................. 101 6.6 Conclusion ..................................................................................................................... 105 7. Future Work ........................................................................................................................... 107 vii 7.1 Coded Aperture Mass Spectrometry ......................................................................... 107 7.2 Segmented Electrode Electric Sector Applications .................................................. 109 8. Conclusion ............................................................................................................................. 117 Appendix A................................................................................................................................ 119 Idealized Transfer Function for 90 Degree System ........................................................ 119 Appendix B ................................................................................................................................ 121 Generalized Forward Model Derivation. ........................................................................ 121 Explicit Forward Model for the 90-degree MS. .............................................................. 124 Propagation Kernel Derivations. ...................................................................................... 126 Path-length Dependent Magnification. ........................................................................... 128 References .................................................................................................................................