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High Resolution Phase Contrast X-Ray Radiography

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High Resolution Phase Contrast X-Ray Radiography HIGH RESOLUTION PHASE CONTRAST X-RAY RADIOGRAPHY by Benedicta Dewi Arhatari A thesis submitted in total fulfilment of the requirements of the degree of Doctor of Philosophy School of Physics University of Melbourne Australia January 2006 ii Abstract High Resolution Phase Contrast X-ray Radiography Benedicta Dewi Arhatari University of Melbourne Supervisors: Keith A. Nugent and Andrew G. Peele 2006 The conventional approach for x-ray radiography is absorption contrast. In recent years a new approach that eliminates the usual requirement for absorption and allows the visualization of phase based on refractive index features in a material has been demonstrated. This so-called ”phase contrast imaging” has now been applied using a wide range of radiation and samples. In this work we are motivated by the need to find optimal conditions for achieving high quality phase contrast images. We consider image formation using the free space propagation of x-rays from a point source passing through a sample. This imaging model is a lens-less configuration and, as such, is very useful for x-ray wavelengths where lenses are difficult to fabricate. Although no lenses are used, image magnification is still achieved due to the expansion of the wavefront as it propagates from the point source illumination. The short wavelength and penetrating power of x-rays make them ideal for non-destructive studies of microscopic samples. However, these techniques are also important for investigating larger, non-microscopic samples. An analysis, based on the sensitivity of the method to different feature sizes in the object, was used to successfully develop an image contrast model. It is developed for pure phase samples and samples with a small amount of absorption. The effects of partial coherence are explicitly incorporated. The result of the model is a prediction of the visibility of features of a certain size, which is compared with experimental results. The model gives rise to an objective filtering criterion for optimization of image quality and which allows for the combination of retrieved phase images in the presence of noise obtained at different distances to produce a single high quality image. The technique was applied experimentally using a laboratory micro-focus x-ray source illuminating a series of periodic spaced grid lines on a polyimide film and a series of copper grid meshes and excellent agreement with the model is found. We apply the technique to metal failure detection by imaging micro cracks and corrosion in an aluminium sheet. The model has also been extended to an analysis of 3D phase contrast tomography. We define a reconstruction quality factor which allows us to optimize the tomographic reconstruction for given feature sizes in an object. iii This is to certify that the thesis comprises only my original work towards the PhD, • due acknowledgement has been made in the text to all other material used, • the thesis is less than 100,000 words in length, exclusive of tables, maps, bibli- • ographies and appendices. I authorize the Head of the School of Physics to make or have made a copy of this thesis to any person judged to have an acceptable reason for access to the information, i.e., for research, study or instruction. Signature Date iv Acknowledgements I have been fortunate to have Prof. Keith A. Nugent as my main supervisor who has a visceral enthusiasm for physics and its applications. His bright insight into my research has been the opening of a door to a closed room where I existed trapped in research problems. His invaluable guidance encouraged me to work independently, so that I was stimulated to explore freely my own ideas throughout this research project. I am very grateful to him for all his efforts, guidance, support and kindness over the last four years. My co-supervisor Dr. Andrew G. Peele has always brought a fresh perspective and new ideas to discussions. His excellent ability in numerical computation and his deeply incisive approach in theory and experimental physics was very important to my research. He has followed my project with interest even after he moved to his new position at La Trobe University. He was enthusiastic and very patient when correcting my papers; especially because English is not my first language. He also acquired the tomography experimental data set for this thesis. I am very grateful to him for all his efforts and kindness over the last four years. I would like to thank to Dr. Andrew Melatos as another member of my supervisory panel. He has followed my research progress with enthusiasm and showed readiness to help. I would like to acknowledge Dr. John Thornton (DSTO) for his contribution on published papers and for supplying aluminium sheets, one sample containing mi- cro cracks and another sample containing corrosion. I would like to acknowledge Dr. Philip McMahon, Dr. Brendan Allman, Dr. D. L. Jacobson, and Dr. M. Arif for use of their neutron image data. I also thank Adrian P. Mancuso for producing phase re- trieval images from the neutron data and for all his enthusiasm and help. I would like to acknowledge Dr. Andrew Stevenson (CSIRO) for supplying the gold lithographic mask. I also thank J.P. Hayes (Industrial Research Institute Swinburne) for providing the Kapton sample. I would like to acknowledge the other members of the Optics Group, A/Prof. Robert Scholten, A/Prof. Ann Roberts and A/Prof. Christopher Chantler for their support of my project. My thanks also to the members of the Electronic and Mechanical Work- v shops of the School of Physics who provided some experimental components of this work. My office has been a happy place to work thanks to the cheerful nature and humour of my friends Clare, Sean, Catherine, and Fotios. I have particularly enjoyed innumer- able lunch times with Celine. I appreciate fruitful discussions with Garth and his help in expressing my research outline for this thesis in good sentences. More widely from the optics group, I also thank Nicoleta, Chanh, Justin, Bipin, Harry, Mark, Sam and Luke. My deepest thanks to my parents and my family for their constant love and support. Thanks to my husband and my beloved twin daughters, through mostly happy but also some extremely difficult times. vi Glory be to the Father, and to the Son, and to the Holy Spirit. As it was in the beginning, is now, and ever shall be, world without end. Amen. vii viii Contents 1 Introduction 1 1.1 Statementofproblem ........................... 1 1.1.1 Difference between prior and our research . .. 2 1.2 Researchoutline.............................. 3 2 X-ray imaging 7 2.1 X-rayradiography............................. 7 2.1.1 Phasecontrastasanewapproach . 8 2.2 Basictheory................................ 15 2.2.1 Fresneldiffractionintegrals . 15 2.2.2 Farfielddiffraction. 21 2.2.3 Fresnelnumberinphaseimaging . 22 2.2.4 Twobeamdiffraction. 24 2.2.5 Partialcoherencetheoryinphaseimaging . .. 25 2.3 Phasevisualizationforx-rays. .. 30 2.3.1 Diffractionenhancedimaging . 30 2.3.2 Freespacepropagationphasecontrast . 32 2.4 Phasemeasurement ............................ 33 2.4.1 X-rayinterferometry . 33 2.4.2 Phaseretrieval .......................... 35 3 Experimental facilities 49 3.1 X-raysource................................ 49 3.1.1 X-rayspectrum.......................... 50 ix 3.1.2 Focusingthex-raysource . 52 3.1.3 Finitesourcesize .. .. .. .. .. .. .. 54 3.2 X-raydetectors .............................. 59 3.2.1 Linearityanduniformity . 59 3.2.2 Darkcurrent ........................... 61 3.2.3 Signaltonoiseratio . 61 3.2.4 Quantumefficiency. 62 3.2.5 Spreadfunction.......................... 63 3.2.6 Dynamicrange .......................... 64 3.3 Resolutionandcontrast . 65 3.4 Synchrotronfacility............................ 66 4 Image modelling for transparent samples 71 4.1 Imageformationmodelforaperiodicobject . .... 71 4.2 Numericalmodel ............................. 76 4.3 Experimentaltestofthemodel . 79 4.4 Objectiveimagefiltering . 82 4.4.1 Implicationsfor quantitativephase retrieval . ...... 87 4.4.2 Objective filtering for experimental phase retrieval data. 92 5 Image modelling for complex objects 97 5.1 Imagemodellingfor shortpropagationdistances . ....... 98 5.1.1 Imageformationmodel. 98 5.1.2 Visibilityforpolychromaticphasecontrast . 102 5.1.3 Experimentaltestofthemodel . 104 5.1.4 Applications ...........................107 5.2 Imagemodellingforlongpropagationdistances . ......114 5.2.1 Talboteffect ...........................117 5.3 Simulationresults.............................120 5.4 Conclusions................................124 x 6 Tomography 125 6.1 Principle..................................126 6.1.1 Radontransformtheory . 127 6.1.2 Fourierslicetheorem . 128 6.1.3 Filteredbackprojection . 130 6.2 Extendedmodelfortomography . 131 6.2.1 Samplingrequirements . 139 6.3 Numericalsimulation . 140 6.3.1 Effectofnoise ..........................145 6.4 Experimentresults ............................147 7 Conclusion 155 7.1 Overview .................................155 7.2 Summaryofresults . .. .. .. .. .. .. .. .156 7.3 Suggestionsforfurtherresearch . 158 Appendices 158 A Publications 159 Bibliography 159 xi xii Chapter 1 Introduction 1.1 Statement of problem Phase methods may be categorized in two broad ways: the forward problem and the in- verse problem. The forward problem describes systems for which the phase is rendered visible but does not yield quantitative information about the phase. Usually it is done by measuring intensity which contains phase information. In the forward problem,
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