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Design of a solid tank prototype optical computed tomography scanner Ogilvy, Andrew 2018

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Design of a Solid Tank PrototypeOptical Computed TomographyScannerbyAndrew OgilvyB.Sc. Hons., The University of British Columbia, 2016A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF SCIENCEinThe College of Graduate Studies(Medical Physics)THE UNIVERSITY OF BRITISH COLUMBIA(Okanagan)August 2018© Andrew Ogilvy, 2018The following individuals certify that they have read, and recommend to the Collegeof Graduate Studies for acceptance, a thesis/dissertation entitled:Design of a Solid Tank Prototype Optical Computed Tomography Scannersubmitted by Andrew Ogilvy in partial fulfillment of the requirements of the degree ofMaster of ScienceAndrew Jirasek, I. K. Barber School of Arts & SciencesSupervisorMichelle Hilts, I. K. Barber School of Arts & SciencesSupervisory Committee MemberJesse Tanguay, I. K. Barber School of Arts & SciencesSupervisory Committee MemberJohnathan F. Holzman, School of EngineeringUniversity ExamineriiAbstractPurpose: The objective of this work is to design a new prototype fan-beam opticalcomputed tomography (OCT) scanner for three-dimensional radiation dosimetry. Primarydistinctions are a solid acrylic tank and the inclusion of iterative reconstruction techniques(IR) into the scanning methods. This scanner attempts to address artifacts related to colorand index matching baths that are often found with OCT for gel dosimeters. As a result ofthe solid tank design there is lensing that the fan-beam experiences while passing througha gel dosimeter, this lensing makes filtered back projection (FBP) less suitable than IR forimage reconstruction.Methods: The two distinct features of this scanner are the use of a solid tank as analternative to refractive index (RI) matching baths, and the inclusion of IR rather thanFBP for image reconstruction. A polished acrylic block functions as a solid tank that isused to reduce the effects of material RI mismatch. Five arrays of 64 photodiode detectors(0.8mm x 0.7mm) were run in series to collect optical projection data. The detectorssat flush against the acrylic. A gel rotates inside a hole in the acrylic block and eachprojection is taken at 0.5 degree steps for 360 degrees before and after irradiation. Thescanner properties were evaluated by imaging radiochromic silicon gel dosimeters.Results: Spatial frequency was measured using the modulation transfer function foundfrom the edge spread function of a cylindrical attenuating object. The average spatial fre-quency measured was 3.111 cycles/mm. Image geometry was measured by placing opaqueobjects of known geometry inside of a gel and comparing the ratio of their pixel distancesto their ratio geometric distances. The pixel ratio found with this system was 2.63px/mm.Conclusion: This work provides an alternative to traditional matching bath methods ofaddressing color and index matching for OCT of gel dosimeters. The inclusion of iterativereconstruction provides an alternative to filtered back projection. The system is capableof scanning 0.8mm slices of cylindrical volumes in under 3 minutesiiiLay SummaryGel dosimeters have great prospects at being a tool used to advance radiation treatmentcapabilities through three dimensional dose registration. As it stands right now there is noparallel to gel dosimeters in this regard, however they are a cumbersome and specific toolthat requires specialized readout. This paper proposes a new design for an optical computedtomography scanner which could be used to readout gel dosimeters. In traditional scanningsystems there is an index matching bath which acts to correct for changes to the path of alight caused by a transition from one media to another. Index matching baths can also bea source for many errors and are general not an ideal component of most scanning systems.The design in this paper attempts to remove as much need for an index matching bath aspossible.ivPrefaceI was the lead investigator for the projects located in Chapters 3, 4, and 5, where Iwas responsible for all major areas of concept formation, data collection, and analysis,with guidance from Andrew Jirasek, Michelle Hilts, and Jesse Tanguay of this research’ssupervisory committee. This is with the exception of the content relating to the inclusionof algebraic reconstruction technique where it was a collaborative effort between NickMantella, Steve Collins, and myself.vTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiiDedications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xivChapter 1: Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Radiotherapy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1.1 Modern Radiation Therapy . . . . . . . . . . . . . . . . . . . . . . . 21.2 Radiation Dosimetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.2.1 Point Dosimeters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.2.2 Planar Dosimeters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.2.3 Indirect 3D Dosimetry . . . . . . . . . . . . . . . . . . . . . . . . . . 81.2.4 3D Dosimetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81.3 Gel Dosimeters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.3.1 Fricke Gel Dosimeters . . . . . . . . . . . . . . . . . . . . . . . . . . 101.3.2 Polymer Gel Dosimeters . . . . . . . . . . . . . . . . . . . . . . . . . 111.3.3 Solid Plastic Dosimeters . . . . . . . . . . . . . . . . . . . . . . . . . 121.3.4 Scattering and Absorbing Dosimeters . . . . . . . . . . . . . . . . . 121.4 Readout Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131.4.1 Magnetic Resonance Imaging . . . . . . . . . . . . . . . . . . . . . . 131.4.2 X-Ray Computed Tomography . . . . . . . . . . . . . . . . . . . . . 16viTABLE OF CONTENTS1.4.3 Optical Computed Tomography . . . . . . . . . . . . . . . . . . . . . 181.5 Thesis Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18Chapter 2: Computed Tomography Background . . . . . . . . . . . . . . . . 202.1 Generations of Computed Tomography . . . . . . . . . . . . . . . . . . . . . 202.2 Image Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222.2.1 Radon Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222.2.2 Filtered Back Projection . . . . . . . . . . . . . . . . . . . . . . . . . 242.2.3 Iterative Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252.3 Optical CT Scanner Types . . . . . . . . . . . . . . . . . . . . . . . . . . . 262.3.1 Cone Beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272.3.2 Broad Parallel Beam . . . . . . . . . . . . . . . . . . . . . . . . . . . 272.4 Considerations for Optical CT . . . . . . . . . . . . . . . . . . . . . . . . . 282.4.1 Streak Artifacts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282.4.2 Ring Artifacts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282.4.3 Refraction and Matching Baths . . . . . . . . . . . . . . . . . . . . . 282.4.4 Path Length Attenuation . . . . . . . . . . . . . . . . . . . . . . . . 30Chapter 3: Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . 323.1 Previous Scanner Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323.1.1 Unresolved Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333.2 New Scanner Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353.3 Materials and Arrangements . . . . . . . . . . . . . . . . . . . . . . . . . . . 373.3.1 Fan Creation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373.3.2 Solid Matching Tank . . . . . . . . . . . . . . . . . . . . . . . . . . . 373.3.3 Photodiode Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . 383.3.4 Electronics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383.3.5 Universal Motion Controller . . . . . . . . . . . . . . . . . . . . . . . 383.3.6 Gel Containers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393.3.7 Gel Creation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393.4 Data Acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403.5 Data Processing and Image Reconstruction . . . . . . . . . . . . . . . . . . 40Chapter 4: Results and Discussion 1: Scanner Design and Image Recon-struction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434.1 Scanner Design Changes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434.1.1 New Laser System . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434.1.2 Solid Tank . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454.1.3 Gel Containers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474.1.4 Gel Creation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484.2 Image Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48viiTABLE OF CONTENTS4.2.1 Ring Artifacts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484.2.2 Limited Field-Of-View . . . . . . . . . . . . . . . . . . . . . . . . . . 504.3 Algebraic Reconstruction Technique . . . . . . . . . . . . . . . . . . . . . . 514.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52Chapter 5: Results and Discussion 2: Pre-commissioning . . . . . . . . . . . 555.1 Image Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 555.2 Spatial Frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56Chapter 6: Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 636.1 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65viiiList of TablesTable 4.1 Iterative Method Results . . . . . . . . . . . . . . . . . . . . . . . . . 52Table 5.1 Spatial Frequency Proof-of-Concept . . . . . . . . . . . . . . . . . . . 61ixList of FiguresFigure 1.1 An image showing a Varian Medical Systems Millennium 120 leafMLC creating an irregular shape. Image courtesy of Paul Ionele. . . 3Figure 1.2 A diagram of the tip of a farmer type ion chamber. . . . . . . . . . 5Figure 1.3 A photo of a set of TLDs with a quarter for size comparison. Imagecredit to CNMC Company. . . . . . . . . . . . . . . . . . . . . . . . 6Figure 1.4 A photo an nPAG polymer gel dosimeter that has been irradiatedin a cross-beam pattern. . . . . . . . . . . . . . . . . . . . . . . . . 9Figure 1.5 An image displaying a) absorption attenuation and b) scatteringattenuation. Image credit to Warren Campbell. . . . . . . . . . . . 13Figure 1.6 a) Paramagnetic orientation of hydrogen nuclei with out an externalmagnetic field. b) Hydrogen nuclei with an external magnetic field,showing both parallel, and anti-parallel orientations. c) A close upof a hydrogen nuclei precessing longitudinally. d) A view of thetransverse axis, showing the incoherent phase of precessions and theresulting signal. e) Transverse component of dipole moments afterbeing phased, and the resulting signal which dampens with time asthe moments de-phase. f) An example of a T1 relaxation and T2decay graph with time, created using multiple RF pulses. Imagecredit to Warren Campbell [1]. . . . . . . . . . . . . . . . . . . . . . 15Figure 1.7 An image showing the creation of a 1D projection from x-ray beamspassing through an object. Image credit to Warren Campbell. . . . 17Figure 1.8 A diagram showing how Snell’s law affects a ray as it passes throughthe interface between two media. . . . . . . . . . . . . . . . . . . . . 19Figure 2.1 First and second-generation CT systems used a translate-rotate methodof scanning a given object. . . . . . . . . . . . . . . . . . . . . . . . 21Figure 2.2 A) The Third-generation of CT is characterized by an x-ray tubeand an arc of detectors attached a gantry. The gantry rotates aroundthe object collecting throughout. B) The Fourth-generation of CTis characterized my a stationary ring of 360 degrees of detectors.The x-ray tube rotates on a gantry. . . . . . . . . . . . . . . . . . . 22xLIST OF FIGURESFigure 2.3 A simple image (left) and the corresponding sinogram (right) aftera 180-degree radon transform in half degree steps. . . . . . . . . . 24Figure 2.4 The unfiltered filtered backprojection reconstruction of the imagefrom Fig.2.3 (left) compared to the same image reconstructed usinga ramp filter (right). . . . . . . . . . . . . . . . . . . . . . . . . . 25Figure 2.5 This example depicts a ray bj passing through multiple pixels xijwith varied optical densities. The length of the ray path througheach pixel is calculated in the A matrix. . . . . . . . . . . . . . . . . 26Figure 2.6 An optical CT slice that clearly shows streaking artifacts caused byseams (left) and ring artifacts caused by faulty detectors (right). . 29Figure 3.1 An schematic diagram of the old scanner from a top down view.Image credit to Warren Campbell. . . . . . . . . . . . . . . . . . . . 33Figure 3.2 An image of a slice collected using the previous version of the scan-ner, highlighted in red is a pair of ring artifacts, and outlined inyellow are a speckled, blotchy pattern. . . . . . . . . . . . . . . . . . 35Figure 3.3 An image of a slice collected using the previous version of the scan-ner. The object imaged is the same index matching fluid as thatwhich surrounds the container. The previous speckle and ring arti-facts are removed or lessened. . . . . . . . . . . . . . . . . . . . . . 36Figure 3.4 A flow diagram depicting the steps taken during data processing. . 41Figure 4.1 An image showing the drift of the in profile intensity over the courseof approximately 8 hours. . . . . . . . . . . . . . . . . . . . . . . . . 44Figure 4.2 A photo which clearly shows an example of total internal reflectionhappening along the outer walls of the solid tank. . . . . . . . . . . 46Figure 4.3 A transmission sinogram (Top) made from I and I0 scans collectedin identical locations with no modifications to either. The sinogramhas been zoomed in (Bottom) to showcase a region affected by thebad detectors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49Figure 4.4 A filtered backprojection reconstructed slice of a dyed water (refer-ence scan without dye). The left reconstruction uses interpolationto replace the data collected by faulty detectors. The right recon-struction shows the resulting image if the data is set to zero ratherinterpolated, showcasing which regions are affected by these detectors. 50Figure 4.5 A optical density sinogram from a slice of dyed water with an opaqueobject within it (reference scan without dye or object). The leftsinogram shows the cropped faulty detectors passing over an edgein the sinogram. The right sinogram shows the resulting sinogramafter the faulty data has been interpolated and highlights the affect1D interpolation has on an edge. . . . . . . . . . . . . . . . . . . . . 50xiLIST OF FIGURESFigure 4.6 A filtered backprojection slice reconstruction with a piece of opaquetape on the outside surface of the container. It can be seen that thetape fails to reconstruct properly due to a limited-FOV. . . . . . . . 51Figure 4.7 A simulation of the path that a set of rays in a fan beam wouldtravel. The left shows a top down view of the system. The rightshows a zoomed in portion focusing on the totally internally reflectedrays and the corresponding un-imaged region inside the container. . 52Figure 4.8 A comparison of many iterative reconstruction methods using a ra-diochromic gel phantom. (a) Component Averaging, (b) Cimmino,(c) Diagonally Relaxed Orthogonal Projections, (d) Landweber,(e) Simultaneous Algebraic Reconstruction Technique, (f) FilteredBackprojection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53Figure 5.1 Two reconstructed images with pixel distances of geometric objectshighlighted. The first experiment (left) shows an inconsistent ratiobetween objects. The second experiment (right) shows a consistentratio between objects. . . . . . . . . . . . . . . . . . . . . . . . . . . 56Figure 5.2 A gel phantom that was made in three stages to measure spatialfrequency. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57Figure 5.3 An example batch of reconstruction permutations where 12 I scanswere reconstructed with the same I0. The way that the artifacts(red) appear in all reconstructions shows the artifacts are associatedwith the I0 scan. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58Figure 5.4 An example of one of the best reconstruction permutations, show-casing the poor quality of the edge in the slice. . . . . . . . . . . . . 59Figure 5.5 A zoomed in region of a slice showing the cylindrical insert in imagespace. The irregular pattern inside the insert is due to schlierenartifacts from poorly mixed glycerol. . . . . . . . . . . . . . . . . . . 60Figure 5.6 A radial plot and corresponding cropped ESF depicting the edge ofeach quadrant of the cylindrical insert. . . . . . . . . . . . . . . . . 61Figure 5.7 The calculated MTF of each of the quadrants of the cylindrical in-sert. The MTF50 is highlighted in the image and their values arelisted in Table 5.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62xiiAcknowledgmentsI would like to thank my supervisor Dr. Andrew Jirasek of the I. K. Barber School of Arts& Sciences at the University of British Columbia. His door was always open so that I couldstop by to confirm that something was actually wrong, and wasn’t not crazy. His guidance hasprepared me well for continuing my research in a PhD. I would also like to thank my supervisorycommittee members, Dr. Michelle Hilts, and Dr. Jesse Tanguay. Their input and specializedperspective helped to grow my own understanding of this project.I must also acknowledge Nick Mantella, Steve Collins, and Mark Robinson (BCCA Machin-ist). Nick performed the preliminary work required to enable ART to be integrated into thisproject and wrote the first versions of much of the code. Steve continued on from Nick’s workand fleshed it out into the system that we have today. And Mark for his continued help inthe design, engineering, and manufacturing required during the course of this research. Addi-tionally, I’d like to thank the previous researchers on this project, David Rudko and WarrenCampbell. Without their work at the University of Victoria the idea for this research wouldn’texist.I would like to thank the students, scientists, and staff of the UBCO I. K. Barber School ofArts & Sciences, specifically Paul Ionele. He was the only other UBCO Medical Physics student,and working with him made the courses, research, and presentations much less daunting. Myinitial inspiration to pursue physics came from a UBC alumnus, my high-school physics teacherDarryl Barber.Finally I would like to thank my Mom and Dad. Even though they didn’t understand mostof what they were reading, they went over every report and every page of this thesis lookingfor improvements wherever they could find them. I’m still going to make you call me MasterAndy from now on though. That’s how this works, right?xiiiDedications“What exactly do you do every day?”“Science stuff”“Yeah, but what kind of science stuff?”-My wonderful girlfriend Jessie,about 2 years into my research.We’ve been together for 6 fantastic years, you’re super cool and I love you. You ignoredme when I needed to be ignored and you gave me attention when I needed attention. I’mbasically still a moody teenager. My supervisor also called me a dolt for not having youin my dedications in a previous draft.xivChapter 1IntroductionThe objective of this work is to design a new prototype fan-beam optical computed tomog-raphy scanner for three-dimensional radiation dosimetry. The intent is to design a scanner thatincreases the easy of usability, without loss of quality or speed. Improvements in the field ofoptical computed tomography and gel dosimetry could increase the quality of advance radiationtreatment verification for use in cancer treatment.This chapter describes the fields of study relevant to the scope of research. Section 1.1provides a brief background on the clinical use of radiotherapy. Section 1.2 describes the needfor dosimetry and the various types of dosimeters available. Section 1.3 is an overview of geldosimeters and their physical properties. Section 1.4 discusses the available methods for readingthe property changes of gel dosimeters. Section 1.5 is a description of the scope of this thesis.1.1 RadiotherapyRadiation therapy is a non-surgical approach to treating cancerous tumors. It is used inover 50% of all cases, either as the sole treatment modality or in tandem with other modalitiessuch as surgery or chemotherapy [2]. The purpose of cancer treatment is to remove or destroycancer cells that are capable of spawning a colony (clonogenic). Where applicable, the simplestapproach is to cut out the cancerous tissues through surgery. Surgery removes the bulk ofthe cancer cells, and radiation or chemotherapy is used to remove microscopic cells that mayremain in the affected area. Patient health, anatomical location of the tumor, or patient choicecan affect whether or not surgery is a treatment option. When surgery is not an option it ispossible to achieve tumor control using radiation, chemotherapy, or a combination of radiationand chemotherapy [3].11.1. RadiotherapyTypical radiation therapy treatments involve high energy photons or electrons that havebeen generated using a linear accelerator. The high energy particles are capable of penetratingand damaging tissues within the patient. Cellular damage is achieved by particles collidingwith cell DNA, located within the nucleus. Breaks in the DNA strand may initiate cell death[2]. The damage caused by radiation therapy does not discriminate between cancer cells andnormal tissue. As a result, effective cancer treatment requires locational knowledge of cancercells and targeted delivery of radiation.To properly determine the location and geometry of the tumor, patients are CT scanned,and from the scan the tumor is contoured in 3D. The planning target volume (PTV) is a contourthat encompasses the entire volume of the tumor, as well as margins for microscopic tumor cells,patient setup errors, and tumor motion [4]. During treatment planning, sensitive organs andother critical structures are also contoured so that when the treatment planning system (TPS)calculates the dose to a region it can easily be determined if too much dose is being given to aspecific tissue. It is during treatment planning that optimal beam configuration is determinedincluding requirements for beam modification devices, such as wedges or boluses.1.1.1 Modern Radiation TherapyThe two primary treatment priorities are to first, provide a lethal dose of radiation to theentirety of the tumor volume and second, to limit the damage to the surrounding normal tissue.Due to the penetrating nature of radiation, damage is done to normal tissue on the way to thedepth of the tumor, and any additional dose will continue to damage normal tissue past thedepth of the tumor. This can be mitigated by using multiple treatment fields from multipletreatment angles, allowing for the entry and exit dose to be spread across more normal tissues.The normal tissue is then exposed to more tolerable levels of radiation than if all treatmentwere delivered at a single treatment angle. Forward treatment planning calculates the impactof the planned treatment on both the target tissue and critical structures where damage mustbe limited.The introduction of multi-leaf collimators (MLC) allows for beam intensity to be moreaccurately conformed around the tumor, and to exclude critical structures [5]. MLCs are a set of21.1. Radiotherapytunsten blades (leaves) that that can translate to create custom shapes (Fig.1.1). Additionally,MLC leaves can move in real-time during a treatment allowing the TPS to create a plan thatincludes MLC movement and dose delivery, resulting in the desired dose distribution [6]. Thisis the basis for inverse-planning, where the TPS is given a list of constraints and goals. Anoptimizer then calculates a treatment that will deliver a lethal dose to the cancer volume whilelimiting damage to critical structures according to the constraints.Figure 1.1: An image showing a Varian Medical Systems Millennium 120 leaf MLC creating anirregular shape. Image courtesy of Paul Ionele.Using multiple beams to help spare normal tissue is extrapolated into volumetric modulatedarc therapy (VMAT), which is one of the dominant modern radiation therapy delivery methods.In a VMAT treatment dose is delivered while the linear accelerator gantry rotates around thetarget in an arc. While rotating, the MLCs are continuously moving to conform the beam tothe desired beams eye view for a given treatment angle. Steeper dose gradients around thetumor volume can be achieved using VMAT than fixed beam treatments [7]. This is ideal for31.2. Radiation Dosimetrytreatment of tumors located near or inside critical structures; however this increase in precisionis dependent on the spatial accuracy of the treatment. Factors such as patient positioning andtumor movement are immensely important when considering precise treatments. Methods suchas image guided radiation therapy (IGRT) and 4D (3D + time) radiation therapy are used, butresearch is ongoing to improve patient position, and treatment accuracy where tumors positionand volume change during treatment.1.2 Radiation DosimetryGiven the increasing complexity of radiation treatments, it is imperative that the reliabilityand accuracy of a treatment is quantifiably tested before patient use. A dosimeter providesa way to measure the absorbed dose to a location or region. It detects dose by a measurablephysical property that responds proportionally with dose. This property could be an electricalsignal, a change in color or density, or absorption or release of electrons. Any of these couldbe used to measure dose provided physical property response is reliable and consistent enoughfor the intended purpose. Dose in radiation is given in units of Gray (Gy), where 1 Gy = 1Joule/kilogram.Other important characteristics to consider for dosimeters are measurement precision, lin-earity of dose response, dose and dose rate dependence, energy response, directional dependence,and spatial resolution [8]. Most dosimeters do not have ideal performance across all character-istics, meaning the choice of dosimeter must be made judiciously considering the requirementsof the application being measured. Dosimeters can measure dose at a single point, or in twoand three dimensions.1.2.1 Point DosimetersPoint dosimeters measure the dose collected in a single position in space. There are manytypes of point dosimeter that can be found in a modern cancer clinic: Ionization chambers,thermoluminescent dosimeters (TLD), optically stimulated luminescent dosimeters (OSLD),semiconductor dosimeters, and diamond detectors. The two most prevalent of those are ioniza-41.2. Radiation Dosimetrytion chambers and TLDs [9].Ionization chambers are typically a sealed cavity in which a gas fills the space between twoelectrodes (Fig.1.2). Incident ionizing radiation collides with the gas particles, ionizing it andfreeing charges. A voltage is applied across the electrodes causing the freed charges to movetowards the electrodes where they are collected and measured as an electric current. The energyrequired to ionize the gas contained in the chamber is known, meaning the absolute dose canbe calculated from the current reading [9]. Through systems such as the American Associationof Physicists in Medicine (AAPM) TG-51 protocol the equivalent absolute dose in water can becalculated from the ion chamber reading [10]. Ion chambers are often used for commissioningand monitoring the beam output of treatment units.Figure 1.2: A diagram of the tip of a farmer type ion chamber.TLDs are a crystalline dielectric material that has been doped with materials that createimpurities capable of trapping electrons at higher energies (Fig. 1.3) [11]. Ionizing radiation isabsorbed by electrons in the material, and the electrons are promoted from the valence bandinto the conduction band. Rather than releasing the energy and falling back to the valenceband the electron may be trapped at a higher energy for an extended period of time. To releasethe trapped electrons the TLD is heated such that the electron can escape the trap and re-enterthe conduction band [9]. The storage of these electrons is the measurable property, because if51.2. Radiation Dosimetrythe electrons can be released they will emit light at an energy equal to the band gap betweenthe valence and conduction bands. The intensity of the emitted light is proportional to theradiation dose that the TLD received [9]. TLDs must be rigorously calibrated to convert thelight intensity to an accurate measure of the absorbed dose of the dosimeter. Clinically, TLDsare used as point-measurements during treatment by taping them to the patient in regions ofinterest. They also serve as personal radiation dosimeters for workers interacting with or nearradiation [12].Figure 1.3: A photo of a set of TLDs with a quarter for size comparison. Image credit to CNMCCompany.1.2.2 Planar DosimetersPlanar dosimeters are capable of mapping dose distributions in a 2D space. Planar dosime-ters fall into two main categories: film and flat panel detector arrays. Film dosimeters measuredose through a chemical reaction that has a readable response, whereas flat panel detector ar-61.2. Radiation Dosimetryrays use a series of point detectors to pixelate a 2D area. The primary clinical planar dosimetersare photographic film, radiochromic film, and electronic portal imaging device [9].Photographic films feature an emulsion layer of microscopic silver bromide (AgBr) fixed ingelatin on either one of both sides of a supporting film. When exposed to ionizing radiationthe silver ions take on an electron and become solid silver atoms. The developed image is anopaque dose map of silver atoms with increased optical density corresponding to higher doses.Photographic dosimeters have unrivaled spatial resolution such that the limiting factor is thatthe tools cannot readout dose at the level of spatial resolution recorded. In clinically applicabledose ranges photographic films show linearity in response with dose, and reasonable dose rateindependence [9]. In more recent years, photographic film has fallen out of favor due to the costand time requirements of wet chemical processing. Photographic films also tend to be quitesensitive to environmental effects such as high temperature, or high humidity. An alternativeto photographic films are newer dye-based films.Gafchromic film is a type of radiographic, or dye based film dosimeter that changes colorwhen exposed to ionizing radiation. In medical dosimetry gafchromic film is one of the widestspread commercial products. There are a number of gafchromic products that specialize indifferent applications, such as effective dose range, frequency of response, dose rate dependence,and susceptibility to environmental parameters [13]. The benefits of radiochromic film are thatit has high spatial resolution, and is an absolute dose detector. The physical dimensions ofgafchromic films limit their use for large-field dosimetry [13]. Depending on the scanningtechnique, radiochromic films can reach sub millimeter resolution.Most linear accelerators come equipped with an electronic portal imaging device (EPID),which is a flat panel detector array that can be used for planar dosimetry. It is generallycomprised of a number of amorphous silicon photodiodes which build an electrical charge pro-portional to dose [14]. It should be noted that above the photodiode there is a scintillatingscreen that converts x-rays to a visible light signal. This means that EPIDs are an indirectdosimeter, as the photodiode itself is not measuring the incident dose, but rather a conversionfrom scintillating screen. As an example of scale the Varian aS500 amorphous silicon device(Varian Medical Systems; Palo Alto, CA, USA) has 512x383 pixels and a resolution of 0.784mm71.2. Radiation Dosimetry[15]. The active area of which is 40 x 30cm2. An EPID is positioned opposite to the treatmenthead, and rotates with the gantry. Portal imaging is used quite frequently in a clinical settingfor patient position verification.1.2.3 Indirect 3D DosimetryThree-dimensional dosimetry can be inferred from arrangements of two-dimensional (2D)detectors. One clinically used example is the ArcCHECK— quality assurance device by SunNuclear. The ArcCHECK— features a helical cylinder of diodes, point dosimeters in a 2Darray. Each detector has an active area of 0.64mm2 and the detectors are spaced 1cm apart[16]. The cylinder is filled with a tissue equivalent material, and dose is recorded on entry andexit of the device. The result of measurement with an ArcCHECK— is a 2D dose map thatholds 3D information. The expected 2D dose map can be calculated using the machine TPS,and compared against the ArcCHECK— measurement. It should be noted that the detectorsare sparsely distributed so the 2D dose map is inferred from the detectors sampling the dose.Further, the 3D volume dose map is inferred from the 2D dose map, based on the plan calculatedby the TPS.Point dosimeters can be arranged on a plane to measure dose in two dimensions, which is aflat panel detector array. However arranging point dosimeters in three dimensions means thatthe detectors become part of the medium that the photons need to traverse. The application ofarranging point dosimeters as a three-dimensional volume is limited by tissues equivalence. De-tectors inside of the volume are collecting photons that have traversed other detectors, alteringthe dose that would be detected. This issue can be corrected by a rigorously calibrated system,but the ideal solution would be to use a 3D dosimeter rather than an indirect 3D dosimeter.1.2.4 3D DosimetryA three-dimensional dosimeter measures dose throughout a volume. The dose from a treat-ment can be measured in three-dimensions rather than inferred. Ideal characteristic of a 3Ddosimeter is tissue equivalence, which can be achieved or easily calculated by using dosimetersmade from one continuous material. The leading 3D dosimeter is the gel dosimeter, although81.3. Gel Dosimetersthere aren’t many 3D dosimeters used clinically. An example of a gel dosimeter would be apolymer gel dosimeter (PAG) which turns opaque when irradiated by the formation of polymerchains. Gel dosimeters are discussed in-depth in Section 1.3.1.3 Gel DosimetersGel dosimeters are radiation sensitive materials that result in a dose proportional, physicalchange when irradiated (Fig.1.4). When fixed in a near tissue equivalent material (gelatin,plastic, silicone, agarose, etc) that can form a continuous 3D volume. Gel dosimeters themselvesare direct dosimeters as the incident radiation has a direct impact on the measured response.Figure 1.4: A photo an nPAG polymer gel dosimeter that has been irradiated in a cross-beampattern.The series of events that led to modern 3D gel dosimetry was a set of disconnected discoveriesdating as far back as 1927. In 1927, Fricke and Morse published a paper in The AmericanJournal of Roentgenology, Radium Therapy, and Nuclear Medicine showing that a chemicalreaction of ferrous sulphate solutions can be caused by roentgen rays (x-rays) as a measure of91.3. Gel Dosimetersradiation dose [17]. In 1950, Day and Stein explored the chemical effects of ionizing radiationin dyed gels that changed color when irradiated [18]. In 1957, Alexander, Charlesby, and Rossshowed that polymers can be cross-linked when exposed to radiation [19]. In 1957, Andrews,Murphy, and LeBrun formulated a gel that when mixed with a dye would visibly display dosemeasurements due to a change in electrical conductivity and pH after irradiation [20]. In 1958,Hoecker and Watkins developed a dosimeter that polymerized when irradiated. All of these arediscoveries of materials that respond physically to dose in a measurable way [21]. Gel dosimetersgenerally fall into one of three classifications: polymer gel dosimeter, Fricke gel dosimeter, orsolid plastic dosimeter.1.3.1 Fricke Gel DosimetersThe discoveries above as well as many others led to modern 3D gel dosimetry foundedprimarily by Gore, Kang, and Schulz in 1984, where they manufactured a method of readingdose distributions using MRI [22]. Their work was done on Fricke gel dosimeters, which appliesthe reaction discovered by Fricke and Morse. Fricke gel dosimeters are based on the principlethat ionizing radiation can convert ferrous ions (Fe2+) into ferric ions (Fe3+). It was foundthat ferric ions could be temporarily held in place using gelatin matrix, and MRI could be usedto measure the amount of ferric ions created. In 1998, Kelly, Jordan, and Battista formulateda Fricke gel that is viable for measurement with optical CT [23]. Rather than using MRI, axylenol orange color indicator was added to the gel and the ferric ion-radiation reaction couldbe seen as a change in opacity of the gel, which can then be measured using light on the visiblespectrum.In 1992, it was shown that the ferric ions in Fricke gel material diffuse gradually, meaningthere is generally a small window of less than two hours to make measurements of clinicalaccuracy [24]. Many gelling mediums such as gelatin, agarose, sephadex, and polyvinyl alcoholhave been used to reduce diffusion, but in the 1990s most researchers shifted towards researchwith polymer gel dosimeters which did not suffer from diffusion effects [1, 25]. An advantage thatFricke gels have over polymer gel dosimeters is that the basis for attenuation is absorption ratherthan scatter, which is described in more detail in Section 1.3.4. Additionally, an advantageFricke gels have over polymer gels is a much faster response time (around one hour) after101.3. Gel Dosimetersirradiation than polymer gels which must be allowed time to fully polymerize (over 12 hours,usually overnight) [25].1.3.2 Polymer Gel DosimetersThe use of polymer systems for radiation dosimetry was proposed as early as 1954 withAlexander et al., and experimental investigation with polymer dosimetry was performed byHoecker et al. (1958), and Boni (1961) [19, 21, 25, 26]. In 1992, Kennan et al. discovered therelation that the nuclear magnetic resonance longitudinal relation rate of Bis increased withabsorbed dose [27]. Then in 1993, Maryanski et al. proposed a gel dosimeter based on thepolymerization of acrylamide (AAm) and N,N-methylene-bis-acrylamide (Bis) monomers con-tained within an agarose matrix [28]. This dosimeter was dubbed BANANA, because of thenot so obvious acronym formed from Bis, AAm, nitrous oxide, and agarose. When irradiated,the monomers form polymer chains, and those chains arrange in webs or beads. Using MRI theamount of polymer chains formed in BANANA gels could be measured. Later in 1994, Maryan-ski et al. revised the recipe to use aqueous gelatin rather than agarose which was patented andmarketed under the more logical acronym BANG (Bis, AAm, nitrogen, and aqueous gelatin)[29]. To differentiate between the commercial product and avoid trademark infringement, au-thors preparing and studying gels of the same design refer to them as polyacrylamide gels (PAG)[25].In addition to dosimetry readings that are detectable by MRI, it was found that the radiatedarea of the gel increased in optical density (opacity), while still remaining translucent. Thisfinding led to a pair of papers by Gore and Maryanski et al. that were published in 1996 [30, 31].The first papers outlined the development of a three dimensional optical CT scanner, and thesecond paper discussed some of the optical properties of BANG polymer gels. In these papers itwas reported that there is a measurable change in refractive index (0.5%) over a dose of 1 to 14Gy, meaning that distortion of projections is unlikely to be significant. They found that thereis no significant dispersion of visible light within the gel, and finally from their findings theypostulated that the light extinction observed in the irradiated BANG gel was caused entirely byscattering and not absorption. The effect this has on signal will be discussed in Section 1.3.4.111.3. Gel Dosimeters1.3.3 Solid Plastic DosimetersThe primary plastic dosimeter is PRESAGE®, a dosimeter that was developed in 2003 byHeuris Pharma LLC, and introduced by Adamovics and Maryanski in 2004 [32, 33]. It is ahard-plastic, optically transparent, low-scatter, absorbing dosimeter. PRESAGE® dosimeterscontain radiochromic leuco-dyes, contained within a polyurethane matrix, that darken to ablue-green color when irradiated. The leuco-dyes attenuate light by absorbing photons, butthere is a component of scatter as well. PRESAGE® dosimeters suffer from the same scatterrelated issues as polymer gel dosimeters where scatter can be reduced at the cost of contrast[34]. This relation is to a lesser extent than polymer gels, because absorption is the primarymode of attenuation [25]. A large benefit of PRESAGE® dosimeters is that they can be castin a mold, shaped (drilled, cut, sanded, etc), and they do not require a container to maintaintheir shape, which can be a major cause of artifacts in both polymer and Fricke gel systems.Additional advantages are insensitivity to oxygen, and strongly reduced diffusion of irradiatedmaterial [25].1.3.4 Scattering and Absorbing DosimetersAttenuation of visible light is caused by absorption and scattering interactions betweenincident photons and the material being scanned (Fig. 1.5). The likelihood of interactionby absorption is dependent on whether the molecular energy levels of the material match theincident photons, and the likelihood of interaction by scattering is dependent on the size ofthe scattering molecules relative to the incident photon wavelength. Consideration of a geldosimeters attenuation type must be taken when designing an optical CT system.The polymer chains in polymer dosimeters predominantly scatter light as their methodof attenuation. This is not ideal because the source of radiation induced optical contrast iscaused by scattering photons, meaning attenuated photons are then redirected with a newtrajectory that can potentially be detected which then provides false information thus loweringthe contrast. For some systems, the scatter due to attenuation has been shown to influence themagnitude of reconstructed attenuation coefficients by over 10% [35]. The impact of scatterrelated errors can be reduced by reducing the number density of the scattering source, in this121.4. Readout TypesFigure 1.5: An image displaying a) absorption attenuation and b) scattering attenuation.Image credit to Warren Campbell.case polymer chains. This is at direct conflict with the fact that scattering is the primary sourceof contrast; however some researchers have shown promising results with low-scatter systems[25].Attenuation by absorption has a clear advantage over scattering because attenuated photonsare removed, thereby not impacting readings other than the specific location that the photonswere removed. The primary available absorption dosimeters are Fricke gel dosimeters, and someplastic dosimeters, such as PRESAGE, which both use radiochromic dyes to absorb photons.1.4 Readout TypesThe readout method for a particular gel dosimeter must be appropriate for the physicalquality that changes in that dosimeter as it is exposed to radiation. Some dosimeters can beread using a variety of readout types, while others are only readable by one specific readouttype. The primary readout methods for gel dosimeters are magnetic resonance imaging (MRI),x-ray computed tomography (CT), and optical CT.1.4.1 Magnetic Resonance ImagingGel dosimeters contain a significant portion of water (as high as 90%) which is the primarysource of hydrogen ions (H+) that are measured using MRI. Hydrogen ions (protons) have areasonably large magnetic moment and a very large relative abundance in humans. Protons131.4. Readout Typesare paramagnetic, which means that a sample of protons in the absence of a magnetic fieldhas no net magnetic moment (Fig.1.6a). Each proton is facing a random direction cancelingeach other. However, in the presence of an external magnetic field (B0), the hydrogen nucleiwill orient themselves either parallel or anti-parallel (requires higher energy) to the externalmagnetic field (Fig.1.6b). This alignment means that there will be some average net magneticmoment (Mz = M0) parallel to B0 for the sample of hydrogen nuclei, and the size of the momentis dependent on how many nuclei are parallel or anti-parallel (equal parts would mean Mz = 0).If the external magnetic field were to be removed the nuclei would lose alignment and returnto a random arrangement [36].The magnetic moments (µ) in a magnetic field experience a torque which causes a precessionof the nuclei in a circular path around the longitudinal axis of B0 (Fig.1.6c). The precessionalfrequency ω0 is given by the Larmor Equation:ω0 = γB0, (1.1)where γ is the gyromagnetic ratio which is a value that relates the precessional frequency fora specific element to the external magnetic field depending on the field strength. As described,all of the nuclei precessions are out of phase and incoherent (Fig.1.6d). If the nuclei have energytransferred to them by a radio frequency (RF) pulse at the same frequency as the precession,then the phases will synchronize and become coherent (Fig.1.6e). This phase coherence canbe imagined as all hydrogen nuclei rotating in unison such that it appears as a single rotatingnet magnetic moment (Mxy) in the transverse plane. This rotating net moment then caninduced a voltage on a distant coil using Faraday’s Law. Phase coherence decreases with timeexponentially, meaning the voltage reading on the coil will appear as a dampened sinusoid.This dampening of the sinusoid is referred to as T2* decay, which is a measure of the decreasein peak amplitude with time after a single RF pulse that causes phase coherence.Additionally, some of the nuclei will absorb the energy from the RF pulse causing themto flip from being parallel with B0 to the higher energy anti-parallel arrangement. If enoughenergy was absorbed such that there were an equal number of parallel and anti-parallel then141.4. Readout TypesFigure 1.6: a) Paramagnetic orientation of hydrogen nuclei with out an external magneticfield. b) Hydrogen nuclei with an external magnetic field, showing both parallel, and anti-parallel orientations. c) A close up of a hydrogen nuclei precessing longitudinally. d) A viewof the transverse axis, showing the incoherent phase of precessions and the resulting signal. e)Transverse component of dipole moments after being phased, and the resulting signal whichdampens with time as the moments de-phase. f) An example of a T1 relaxation and T2 decaygraph with time, created using multiple RF pulses. Image credit to Warren Campbell [1].Mz would become zero. Over time the hydrogen nuclei will release the absorbed energy and Mzwill return to M0 at an exponential rate. This is referred to as T1 relaxation and characterizesthe time it takes to return back to the initial value M0 after Mz is affected by an input RF151.4. Readout Typespulse.These two quantities, T1 and T2, are influenced by their surroundings, which is what allowsMRI to be used to readout gel dosimeters (Fig.1.6f). In Fricke gels, ferrous ions and ferricions are both paramagnetic substances that drastically reduce the T1 and T2 rates of hydrogennuclei even in small concentrations. Ferric ions alter the T1 decay rate by more than 19 timesas much as the same concentration of ferrous ions. There is also linear relationship betweenthe T2 decay of a region with respect to the absorbed dose. These qualities allow for MRIto readout Fricke gels [22]. In polymer gels, as polymerization increases, hydrogen nuclei arebound closer together. This allows for energy to transfer between hydrogen nuclei faster, thusincreasing how quickly the nuclei de-phase [25]. Because polymerization increases with respectto dose, polymer gels can be readout using MRI.The benefits of MRI for gel dosimetry are primarily linear dose response in Fricke gels [37].Additionally, MRI scanning protocols are accessible, and MRIs have well understood accuracyand precision [38]. Depending on the facility and country, MRI scanner access for gel dosimetryrange from highly available to inaccessible. MRI scanners are out matched by other scannersin signal-to-noise ratio (SNR), image artifacts, spatial resolution, and scan time.1.4.2 X-Ray Computed TomographyComputed tomography is an imaging method that is used to create cross-sectional imagesof objects, by taking many projections in a 180 degree arc around the object, and from thesepictures a virtual slice is reconstructed [36]. In a clinical environment x-ray radiation is themost common radiation used to image patients with CT. Each projection profile is functionallysimilar to a common 2D x-ray image, such as a traditional bone x-ray. As the x-rays passthrough the object the rays can be absorbed according to the photoelectric effect (likelihood ofan interaction proportional to the atomic number cubed) or scattered according to the Comptoneffect (likelihood of an interaction proportional to the materials electron density). This meansthe x-rays that are absorbed or scattered will not reach the detector behind the object.In x-ray imaging all of the 3D material between the x-ray source and the detector is projected161.4. Readout Typesonto the detector as a single 2D image. This collected signal is called the radio-density (RD).This individual profile projection does not give a reasonable 3D perspective of the object. Anexample would be a region that absorbs a majority of the x-rays may show up brighter in theimage, but the image does not provide depth information in the incident direction (Fig1.7).For CT scanning at least 180 degrees of projections are taken and then the arc of projections isused to reconstruct a cross-sectional slice [36]. The radio-density can be calculated accordingto the Beer-Lambert Law:I = I010−µxI = I010−RDRD = log10I0I(1.2)Figure 1.7: An image showing the creation of a 1D projection from x-ray beams passing throughan object. Image credit to Warren Campbell.The RD is the product of its linear attenuation coefficient of the material (µ) and thepath length through the material (x). The final signal after passing through the material isrepresented by I, and the initial input signal is I0.For readout of gel dosimeters, most x-ray CT imaging is performed using commerciallyavailable kilovoltage CT scanners. Due to the widespread accessibility of conventional x-rayCT scanners in hospitals and radiation therapy centers, x-ray CT is an attractive readout171.5. Thesis Scopemethod for gel dosimetry. Additional benefits of these high quality commercial scanners arethat they have a high signal-to-noise ratio, and a very fast scan time. The primary drawback isthat the change in density with respect to dose is very small for gel dosimeters, meaning x-rayCT readout provides sub-optimal image contrast [25].1.4.3 Optical Computed TomographyThe active mechanism for image creation in optical CT is the same as for x-ray CT describedin Section 1.4.2. A change in beam intensity due to passing through objects, viewed frommultiple angles, can be used to create an image. In x-ray CT, x-ray light is attenuated primarilythrough density changes and is associated with the radio-density. In optical CT, visible light isattenuated primarily through changes in opacity which relates to the optical-density (OD).Optical CT uses radiation with frequencies in the visible light spectrum, which means specialconsideration must be given to refractive interactions at interfaces through Snells Law:n1 sin θ1 = n2 sin θ2 (1.3)Where n is the refractive index of a medium, and θ is the angle from the normal to theboundary of the medium. The use of visible light for optical CT introduces the flexibilityinherent in optical systems. Quick and relatively low cost adjustments can be made to theapparatus by adding optical devices such as mirrors, polarizing lenses, beam spreaders, or evenvaried light sources. A more detailed discussion of the optical CT is given in Chapter 2.1.5 Thesis ScopeThe purpose of this work is to examine the design, development, and commissioning of aprototype optical CT scanner for three-dimensional radiation dosimetry. This research attemptsto address artifacts related to color and index matching baths that are often found with opticalCT for gel dosimeters. As a result of the solid tank design there is lensing that the fan-beam181.5. Thesis ScopeFigure 1.8: A diagram showing how Snell’s law affects a ray as it passes through the interfacebetween two media.experiences while passing through a gel dosimeter, this lensing makes filtered back projectionless suitable than algebraic reconstruction technique. Previous iterations of scanner design andresearch on this project was performed by former University of Victoria (UVic) graduate studentDavid Rudko and former UVic doctoral student Warren Campbell. During undergraduateresearch with previous iterations of this scanner the author of this thesis identified areas forimprovement and redesign.19Chapter 2Computed Tomography BackgroundThis chapter describes a background of information and history relevant to computed to-mography. Section 2.1 provides a brief summary of four generations of CT. Section 2.2 outlinesthe process and methodology of image reconstruction. Section 2.3 showcases a number of opticalCT scanner designs other researchers have used. Section 2.4 describes factors to be consideredthat are unique to optical CT.2.1 Generations of Computed TomographyThe development of CT scanners can be grouped into seven generations. In this sectiononly the first four are discussed as they are the most common types used for the scanning of geldosimeters. The first generation of CT scanner featured a pencil beam x-ray tube and a twodetector array. The x-ray tube and the detectors would translate across the field of view (FOV)to collect one profile (Fig.2.1). The detector array and the tube would then rotate 1 degree andthe x-ray tube would translate across the FOV to collect another profile. This process wouldbe repeated until 180 degrees of information were collected, which took over 4 minutes to scan[36].The second generation of CT scanner used the same rotate-translate method of collection.However it introduced the use of a narrow fan-beam, and increased the number of detectorsfrom 2 to 30. The increase in number of detectors improves spatial resolution. The result ofthe generational improvements was a larger reconstructed image matrix in less time. Lateriterations of second generation CT scanners were capable of scans in tens of seconds, allowingfor acquisition to be achieved in a single breath hold [36].Translational movements were not ideal due to the large inertial forces required to stop and202.1. Generations of Computed TomographyFigure 2.1: First and second-generation CT systems used a translate-rotate method of scanninga given object.reverse direction of the detectors and x-ray tube. In the third generation of CT scanner a widefan-beam with a matching arc of detectors (400-1000) is fixed to a rotating gantry (Fig.2.2a).The wide fan and the detectors allow for angular sampling over the whole FOV, which eliminatesthe need for translational movements and significantly reduces scan time. The gantry rotates ona circular track continuously collecting projections. The removal of translational movements,and the introduction of continuous collection significantly reduced scan times down to a fewseconds as compared to 4 minutes in first generation scanners. Fixing the detectors and x-raytube to the gantry introduced ring artifacts as a result of the detectors not being calibratedwith respect to each other [36].The fourth generation of CT scanner was designed specifically with the reduction of ringartifacts in mind. Ring artifacts are caused because in a third generation scanner, the referenceinformation used to calculate the projection data is not collected from the same detector thatcollects the measurement information. This means the miscalibration of a detector propagatesthrough the backprojection making a ring artifact. To combat this, a stationary 360 degreering of detectors is used, and the x-ray tube still rotates on a gantry (Fig.2.2b). The result of a212.2. Image Reconstructionstationary detector array is that while the gantry rotates the reference signal can be collecteddiscretely for each detector, which means any miscalibration in the detectors can be accountedfor with the I over I0 calculation [36].Figure 2.2: A) The Third-generation of CT is characterized by an x-ray tube and an arc ofdetectors attached a gantry. The gantry rotates around the object collecting throughout. B)The Fourth-generation of CT is characterized my a stationary ring of 360 degrees of detectors.The x-ray tube rotates on a gantry.2.2 Image Reconstruction2.2.1 Radon TransformThe radon transform and its inverse are two defining calculations for computed tomography.Mathematically, a radon transform is the integral transform that can be used to generateprojection data for an unknown two or three dimensional function representing an unknowndensity. In this case the output of a radon transform will be the same as that collected in a222.2. Image Reconstructiontomographical CT scan. Johann Radon introduced the radon transform in 1917 along withits inverse form. These mathematical expressions were critical to the evolution of tomographicimaging, especially CT.In the continuous case, the radon transform of a two-dimensional function f(x, y) withprojections along angles θ where θ is 0 ≤ θ ≤ pi is given byRf ≡ p(ρ, θ) =∫ ∞−∞∫ ∞−∞f(x, y)δ(x cos θ + y sin θ − ρ)dxdyRf ≡ p(ρ, θ) =∫ ∞−∞f(ρ cos θ − l sin θ, ρ sin θ + l cos θ)dl (2.1)Where the δ-function converts the 2D integral into a line integral dl along x cos θ+y sin θ = ρ.After a discrete radon transform is performed, that information is arranged in a sinogram p(ρ, θ)(Fig.2.3) [3]. This is an image of parallel projections that have been collected from differentprojection angles. In CT scanning, beams and detector arrangements must be taken intoconsideration. In the case of parallel-beam geometry, projections in a full rotation around anobject would contain redundant information. If 360 degrees of projections were collected usingparallel-beam geometry, only 180 degrees of information would be unique, because the following180 degrees are simply a mirrored representation of the first half.In the case of a fan-beam geometry, the projections must be taken at additional angles beforereceiving redundant information. It should be noted that with fan-beam geometry, redundancyfor all discrete elements in a specific projection will not occur at the same projection angle.An example would be that the center-most element is redundant at angles 0 and 180, butthat is untrue for elements near the edge of the fan. This effect makes fan-beam sinogramsappear slanted compared to their corresponding parallel-beam sinogram. Fan beam data canbe rearranged to its equivalent parallel-beam representation using scripts that rearrange theelements accordingly.232.2. Image ReconstructionFigure 2.3: A simple image (left) and the corresponding sinogram (right) after a 180-degreeradon transform in half degree steps.2.2.2 Filtered Back ProjectionIn the case of optical CT the sinogram is collected using lasers and detectors that measure theprojection information at given projection angles. Tomographic images can be reconstructedusing a method called backprojection. This is one method of calculating the inverse radontransform that takes the intensities of each projection and smears them in image space alongthe angle on which the projection was acquired. The entry and exit of each projection introducesunwanted blurring of the image with respect to 1/r (Fig.2.4).The removal of this 1/r blurring can be achieved by convolving the projection with a de-convolution kernel in a process aptly named filtered back projection (FBP). This convolution isperformed by converting the sinogram data at each projection angle to the frequency domainwith a 1-D discrete Fourier transform (DFT), multiplying it by the kernel, and then performingan inverse DFT to reconstruct the sinogram. The deconvolution kernel acts as a high-pass orsharpening filter. A number of different filters are used in filtered back projectection, the mostnotable filters are the ramp, Shepp-Logan, Cosine, Hamming, and Hann.242.2. Image ReconstructionFigure 2.4: The unfiltered filtered backprojection reconstruction of the image from Fig.2.3(left) compared to the same image reconstructed using a ramp filter (right).2.2.3 Iterative MethodsIterative reconstruction is a technique that takes an input image, usually a FBP image, anduses that to reconstruct a more accurate image through iteration. In iterative reconstruction,forward projections of the input image are compared to the actual measurement projectionswith variations recorded in an error matrix. The error matrix is used to inform the followingiteration, with the goal of eventually minimizing the error matrix by making small changes to theestimate of the image. Iterative construction can be performed with a variety of approaches.The most notable examples are algebraic reconstruction technique (ART) and simultaneousiterative reconstruction technique (SIRT).Both ART and SIRT serve to solve large linear equations of the form Ax = b where the imagepixel values are contained in vector x, the measured angular projections are stored in vector b,and the matrix A represents the image creation process or system matrix. For conventional CTapplications the b vector is the measured sinogram, and the A matrix is calculated beforehandfrom models of the system parameters such as geometry, medium interactions, etc. In Figure2.5, the optical density in pixel xij can be calculated provided that the exact path each rayfollowed through each pixel (from A) that resulted in projection b.252.3. Optical CT Scanner TypesFigure 2.5: This example depicts a ray bj passing through multiple pixels xij with variedoptical densities. The length of the ray path through each pixel is calculated in the A matrix.2.3 Optical CT Scanner TypesIn 1996, Gore et al. introduced the first optical CT scanner which resembled the firstgeneration of conventional CT [30]. Their design featured a pencil-beam laser that passedthrough a beam-splitter. The beam-splitter acted to collect a reference signal with one beam,and the second beam would pass through the remainder of the system. After transmittingthe splitter the beam was reflected off one of two opposing mirrors outside of a square indexmatching bath. The mirrors would translate in unison such that the beam would sweep acrossthe scanned object. After a sweep is complete, the object would be rotated within the bathto the next projection angle. Signal collection was achieved by measuring the beam intensityafter passing through the tank and comparing it to the reference signal collected by the beamsplitter.MGS Research, Inc. has released a commercial pencil-beam scanner called the OCTOPUS—laser CT scanner. Due to the small width of a pencil-beam at any given moment during a scanonly a small volume is illuminated. This helps to minimize the conflicting relationship between262.3. Optical CT Scanner Typescontrast and scatter for scatter-based attenuating dosimeters [39]. As with first generation CTscanners the translating nature of the scan creates relatively long scan times compared to otherscanner geometries.2.3.1 Cone BeamIn 1999, Wolodzko et al. introduced a new design for an optical CT scanner. It featured adiffuse light panel that would image the entirety of a dosimeter contained in an index matchingbath at one moment and collected the image through a CCD camera [40]. The CCD cameraresides on the other side of a lens and aperture that only accepts a conical beam large enoughto cover the sample volume. The CCD measures an entire 2D projection at each projectionangle. Because the entire volume is illuminated at once scatter errors are quite significant withthis type of scanner, making polymer gels a poor choice of dosimeter for this system [41]. Thisdesign runs opposite to conventional cone-beam CT where a source generates a conic beaminto a 2D detector array. Modus Medical Devices Inc created a commercialized version of thisdesign called the Vista— optical CT scanner.2.3.2 Broad Parallel BeamKristajic´ and Doran devised a method of quickly scanning the entire gel volume in the sameway that Wolodzko et al. did, but they did so with parallel beam geometry [42]. In their designa conical laser-emitting diode (LED) beam passes through a lens which shapes the beam toparallel geometry. The LED illuminates the dosimeter and then passes through an identicallens to focus the light to a CCD. A lens and aperture are in front of the CCD to reduce straylight contamination. This scanner design has the same scatter constraints as the cone beamcounterpart, and is not suitable for scatter based dosimeters.272.4. Considerations for Optical CT2.4 Considerations for Optical CT2.4.1 Streak ArtifactsStreaking artifacts are present in optical CT particularly when the scanner must scanthrough mediums with regions prone to excessive scatter [36]. If at some point during a scan,an error causes a single projection element to be read higher or lower than the actual value,the error will propagate into image space as a streak. In gel dosimetry these regions can befound at the seams of the gel vessel where two halves of the vessel were fused together. It is arough plastic weld that scatters excessively. A method of removal for this is to crop the affectedprojections and interpolate over them before using filtered backprojection.Streaks can also be found at the edges of the vessel where micro-scratches or inconsisten-cies occur (Fig.2.6). The scatter that happens on the vessel walls can be removed through aprocess known as flask registration. This process is a method of collection for both referenceand measurement signal that ensures that both scans begin at nearly the exact same locationensuring that each scattering artifact found in either scan will be collected by the same detectorat the same angle. When the ratio of reference and measurement data is taken it will reducethe scatter caused by inconsistencies on the vessel surface.2.4.2 Ring ArtifactsRing artifacts occur when an error with a single element persists through all projectionangles [36]. Depending on the nature of the error it will show in image space as a bright ordark ring around the center of the image. Most ring artifacts are the result of response errorswith individual detector elements. Again, the affected data can be cropped and interpolatedover, but this can lead to large segments of data being approximate.2.4.3 Refraction and Matching BathsOptical light refracts or appears to bend when it crosses a boundary of two different refrac-tive indices. In x-ray CT, the short wavelength of x-ray makes refraction nearly non-existent.However, for optical CT it is a significant issue. Optical CT designs must minimize the refrac-282.4. Considerations for Optical CTFigure 2.6: An optical CT slice that clearly shows streaking artifacts caused by seams (left)and ring artifacts caused by faulty detectors (right).tion opportunities for a beam. Refractive index (RI) is a dimensionless property that depends onwavelength. When a photon confronts an interface of two different RIs at a non-perpendicularangle it will refract. To combat this effect, nearly all optical CT designs contain some sort ofindex matching fluid contained in a bath to reduce refractive deviations.The challenges of managing bath and vessel refraction can be due to a number of issues.Baths typically have a significant volume of index matched fluid in them (1-15L). The fluidcan evaporate or separate over long scanning periods, changing the index. Oil based baths maygenerate Schlieren patterns in the viewing area of the scan due to the rotations of the gel duringscanning. A variety of approaches have been used to minimize refraction.High-viscosity oil based baths have been experimented with and proved slow to mix anddifficult to clean. Some experimenters opted to reduce the bath to as small as 10ml. Theyachieved this by creating a solid tank of polyurethane that is formulated to have the sameindex of refraction as the scanned gel dosimeter. The index of refraction within the solid tankis constant, and index matching fluid is only used in the small 2.5mm air gap between the solidtank and the gel vessel.292.4. Considerations for Optical CTOther experimenters have created their own algebraic reconstruction technique that includesrefraction correction (ART-rc) and allows them to scan in a dry setting. In this case a raytracing algorithm was modified such that it calculates the path lengths of the rays and correctsfor refractive effects during the iterative reconstructing process.For optical CT apparatus that use fan-beam geometry, a matching bath, and photodiodedetectors it can also be difficult to ensure that the refractive effects caused by the bath wall areminimized. Several approaches to minimize this have been researched.The bath walls could be shaped in the arc of the fan, such that the bath would look like anarced segment of a compact disk with the light source located at the focal point of the curvedbath. With this arrangement each individual ray in the beam is expected to interact with thebath wall at a perpendicular angle meaning that there are approximately no refractive effectson the beam.Another option to minimize the bath wall refractive considerations could be to construct asystem where the light source, detecting device, or both are also submerged in the bath. Thiswould eliminate any angle of incidence with a bath wall.2.4.4 Path Length AttenuationIn both optical and x-ray CT, the object being scanned generally has an approximatelycircular cross-section. This circular cross-section introduces an affect where photons passingthrough the periphery of an attenuating object will pass through less material than more centralrays. This creates an affect where changes to the OD or RD at the periphery appear lesssignificant than those in the center. In x-ray CT adjustments are made to the incident beamwith a bow-tie filter to correct this effect, however it is generally inexact. A benefit to indexmatching baths is that they can double as a color matching bath. The index matching fluid canbe dyed to make it such that the background opacity of the fluid is the same as the backgroundopacity of the object to be scanned. Assuming each ray passes through an equal amount offluid, the color matching component of the bath will allow for uniform attenuation from thetarget at the cost of a reduction in signal strength due to passing through more color matched302.4. Considerations for Optical CTmedium.31Chapter 3Materials and MethodsThe scanner was designed to overcome many of the issues identified during previous workwith a different scanner [1]. Section 3.1 describes the previous scanner and both the physicaland optical issues associated with it. Section 3.2 describes the scanner design process withregard to the intended improvements. Section 3.3 outlines the final scanner as it was used inthe research. Section 3.4 covers the data acquisition process, and Section 3.5 summarizes theimage reconstruction process.3.1 Previous Scanner DesignThe previous scanner (Fig. 3.1) featured a 3mW, 632.8nm, laser diode module that hadan adjustable line-creating head to form a 60 degree fan shape. The laser intensity could beadjusted using a programmable DC voltage power supply (B & K Precision; Yorba Linda, CA,USA). The laser was mounted such that it could be moved along three axes (x,y,z). The tilt ofthe laser could not be adjusted easily. The fan-beam entered a large index matching bath thatalso has a fan shaped construction such that each ray of the laser will transit the walls of thetank at a perpendicular angle which removes refractive effects.The gel dosimeter was contained in a container suspended in the index matching bath by aband clamp holder attached to a pair of motion controlling stages (Newport; Irvine, CA). Themotion controlling stages allowed the gel to be moved vertically and rotationally. Inputs for thecontrol of these stages were produced in MATLAB (MathWorks Natick, MA), and operated bya Universal Motion Controller (Newport; Irvine, CA). The Universal Motion Controller had aresolution of 0.0005 degrees rotationally, and 1mm vertically.The fan-beam would pass through the gel dosimeters and into a 320 element multihole323.1. Previous Scanner DesignFigure 3.1: An schematic diagram of the old scanner from a top down view. Image credit toWarren Campbell.collimator with 0.7mm x 0.8mm holes cut for each detector element that extended back 15mmto the photodiode detector. The depth of the collimators was significant because it limited theangles that light could enter the collimator from, reducing the collection of scattered light. The320 detector elements were made of five 64 detector array, and they were positioned along thearc of the fan such that the middle of each array was equidistant from the laser.3.1.1 Unresolved IssuesIndex Matching TankThe design of the matching tank introduces a number of issues. The large volume of theindex matching bath (over 15L) applied enough strain on the tank to regularly compromise itsshape and integrity. This led to leaks, cracks, and warping that had to be addressed throughouttesting. The bath was a solution primarily made up of propylene glycol and water which couldbe configured to match the color and refractive index of a Fricke gel. During long scan timesthe mixture could be seen separating which also compromised results because as the materialsseparate the refractive index of the bath changes.333.1. Previous Scanner DesignPrecessionThe mounting apparatus used to suspend and rotate the gel in a bath was prone to precessionabout the rotational axis. In sinogram space this precession was a large as 8 pixels. The gelswere removed from the scanner when irradiated meaning the I and I0 collections could haveprecessions that are out of phase. This precessional mismatch was a source for many artifactsin the information collected, the most prominent of which is a geometrical mismatch betweenobjects in the I and I0 collections. Geometrical mismatches are especially prominent aroundedges where the I over I0 ratio can be heavily skewed by taking the ratio of objects on eitherside of the edge.StreakingThe gel containers used during experimentation with this scanner consisted of two halvesthat were fused together. The rough plastic weld was the source of two opposing large scattersources.Unattributed ArtifactsImage data collected by the previous scanner suffered from two primary artifacts, an exampleis shown in Figure. 3.2. The first artifact was a speckled, blotchy pattern highlighted in yellow.The artifact was primarily located in the central region of the image, and the central detectorson the sinogram. The artifact persisted when two back-to-back readings are used for I and I0,which in theory would give an image that is uniform inside the container. The second artifactwas a pair of rings. It was later determined that the cause of these ring artifacts was fromfaulty detectors that would read inconsistent values.To rule out the optics of the apparatus and the gel containers, a container was filled with thecurrent index matching fluid and scanned twice (I and I0). The reconstructed image containedneither of the artifacts (Fig. 3.3). This narrowed the focus on the cause of the artifacts toa few things: improper index or color matching, faulty detectors, or a unique quality of theabsorbance based gels being tested in this CT system.343.2. New Scanner DesignFigure 3.2: An image of a slice collected using the previous version of the scanner, highlightedin red is a pair of ring artifacts, and outlined in yellow are a speckled, blotchy pattern.Two independent tests were conducted to establish if the artifacts could be recreated inspecific test conditions. The first test involved changing the color index of the fluid in thecontainer, and the second test involved changing the index of refraction of the fluid in thecontainer. The result of the first test was that when dye was added to the container thespeckled pattern was not visible, however the ring artifacts appeared. The result of the secondtest found that when the refractive index in the container was increased the speckle artifactsappeared, and the rings were not visible.3.2 New Scanner DesignThe new scanner was designed to address many of the issues identified during testing withthe previous scanner. Specific design objectives were to:− create a mechanically stabile tank, to prevent warping and cracking;− decrease the volume of the matching bath required;− decrease the precession of the gels;353.2. New Scanner DesignFigure 3.3: An image of a slice collected using the previous version of the scanner. The objectimaged is the same index matching fluid as that which surrounds the container. The previousspeckle and ring artifacts are removed or lessened.− minimize refractive index mismatches; and− create a new gel container without seamsThe goals of the project were to prototype and design a solid tank. The tank would be a solidPoly(methyl methacrylate) (PMMA) plastic block with a bore hole cut through it that the gelwould rotate in. The rational for this approach is a minimization matching bath requirements.The solid tank would address structural integrity and decrease the color and refractive indexmatching requirements of the bath. In turn it would introduce the requirement for very precisemachining, gel container, and gel rotation apparatus. Additionally, refractive index changesbetween solid materials would be known, and with the introduction of algebraic reconstructiontechnique (ART) the path changes of the light due to refraction could be accounted for in thereconstruction.363.3. Materials and Arrangements3.3 Materials and Arrangements3.3.1 Fan CreationThe fan-beam is created using an Edmund Optics laser diode. The laser has a wavelengthof 635nm, and a 70 mW maximum output. The laser diode is fixed to an Edmund OpticsTECHSPEC® Optical Cage System along with a 60 degree line-generating lens. The cagesystem insures accurate alignment between the laser and the lens. At the end of the cagesystem is a series of beam constrainers that serve to reduce the amount of light that enters thetank. The thickness of the line fan is reduced by passing through a 2mm slit, and the width isreduced by two adjustable blades that translate horizontally. This apparatus is referred to asthe fan constrainer.3.3.2 Solid Matching TankThe tank was designed to be solid so that the material surrounding the object to be scannedwould homogenous, eliminating issues with matching bath inconsistencies. The only refractivefluid required would be that which fills the gap between the tank and the container. This is aconsiderable reduction in the active volume the liquid required from over 15L to under 50mL.A 344mm long, rectangular, PMMA tank featured a 104mm diameter borehole drilled with itscenter 235.5mm from the laser side of the tank. The entry, exit and bore edges of the blockwere polished for optical clarity using NOVUS Plastic Polish—. The gel containers that wouldbe used had an outer diameter of 101.6mm (4in) making the gap between the tank and the gelcontainer wall averaged approximately 1.2mm. It should be noted that some material is lostduring the sanding and polishing process which could affect the gap size by up to 1mm. Therear wall of the tank was specially milled using a CNC machine such that the detectors couldbe pressed flush against the block with no collimator. The lack of collimator was to remove anadditional refractive interface. The lack collimator increases the possibility for ambient lightpollution. The tank was then fixed to an optical table with 4 through holes and screws.373.3. Materials and Arrangements3.3.3 Photodiode DetectorsThe detector array forms a continuous 256mm line, consisting of five linear 64-elementphotodiode detector arrays (S8865 Series, Hamamatsu; Hamamatsu City Japan). Each of the320 photodiode elements has an active area of 0.8mm by 0.7mm with a 0.1mm spacer betweeneach active area. The pitch of each detector is 0.8mm. This model of detectors is a reversebiased silicon photodiode detector that produces charge linearly with respect to light intensity.Each detector stored their measurement as a 14-bit value ranging from 1 to 16384. Previousresearch had established that dark noise makes any reading less than 50 counts unreliable.Values greater than 14500 are also unreliable due to saturation.The five arrays are mounted to the PMMA block such that the photosensitive area is flushagainst the block, and the edges of each array are flush with the other arrays. During imageprocessing the inactive area of the detectors is ignored, and it is assumed that the active areais 0.8mm wide with no space between detector elements. This effectively makes a 256mm wideby 0.8mm photosensitive area.3.3.4 ElectronicsThe electronics for the detector readout were developed by Warren Campbell during researchconducted in 2015. Details can be found in Section 4.1.5 of that PhD thesis. A short summarywould be that a motherboard switches between reading out each of the five detector arrays andstores their readings on the on-board memory. After a scan is complete is transfers the data toa windows computer through a USB connection.3.3.5 Universal Motion ControllerThe gel container is suspended in the bore hole by a mount attached to a pair of motioncontrolling stages (Newport), allowing for movement vertically and rotationally. The gel mountis attached to the rotational stage. The rotational stage is then connected to the verticalstage, which is clamped to a pillar fixed to the optical table. The inputs for these controlstages were produced in MATLAB, and operated by a Universal Motion Controller (Newport).383.3. Materials and ArrangementsThe rotational stage has a resolution of 0.0005◦, maximum velocity of 80◦/s, and maximumacceleration of ± 320 ◦/s2. The vertical translating stage has a resolution of 1µm, maximumvelocity of 2.5 mm/s, and a maximum acceleration of ± 10mm/s2.3.3.6 Gel ContainersThe gel containers were constructed from a transparent, 4.000” outer diameter, by 0.125”wall thickness cast acrylic tubing (ePlastics, San Diego, CA). The tube was cut to 10cm inheight and fitted with a press-fit base and lid. A tapped hole was added to the lid so that thecontainer could be connected to the motion controlling stages by a custom made mount designedto reduce precession. The cast acrylic tube was manufactured with a mismatch between theinner and outer diameter causing variance in the wall thicknesses (manufacturing tolerance of±20%). Because the gel containers were cut from a long continuous tube, there are no seamspresent on the scanning faces of the container.3.3.7 Gel CreationThe gels used were FlexyDos3D gels developed by De Deene et al. in 2015 [43]. Thebenefits of Flexydos3D are that it is an absorption based, transparent silicone elastomer, non-toxic gel that is relatively easy to fabricate, and has easily tunable mechanical properties. Itis a dosimeter that is capable of deformable study, and it has high tissue equivalent between100kV and 20MV.Flexydos3D gels have only four ingredients 1) Sylgard®184 Silicone Elastomer, 2) Syl-gard®184 Curing Agent, 3) chloroform, 4) leucomalachite green (LMG). Sylgard®184 acts asthe structure for the gel, chloroform is the source of radiation induced free radicals, and LMGis the leucodye. For irradiation scanning, the composition used to create the gels was (w/w)0.025% LMG, 5% chloroform, and the remainder was elastomer and curing agent mixed at a10 to 1 ratio respectively. The components were thoroughly mixed in a beaker and the air wasevacuated from the mixture in a vacuum chamber. Once the majority of the air bubbles wereremoved from the mixture it was poured into the gel container and evacuated once more toremove bubbles added during the transfer. Finally, the dosimeter is cured for 2-4 hours in an393.4. Data Acquisitionoven set to 60◦C.3.4 Data AcquisitionThe CT scans were performed using moving acquisition. This means that a signal is sent tothe rotational motion controlling stage to initiate rotation at a constant velocity. During themotion the detectors rapidly collect and store the information in the on-board memory, whichhas the capacity to store up to 6500 projections. Projections are collected alternating betweena high detector integration time (23.81ms) and a low detector integration time (10.89ms).The low and high integration times are used for detector off-set correction during the imagereconstruction.With the dosimeter rotating at a set speed (2.96◦/sec), it is assumed that the rotationalspeed multiplied by the time stamp that the projection was taken at is equal to the projectionangle at which it was taken. During a scan 1600 projections at each integration time werecollected over 360 degrees meaning a total of 3200 projections are taken per slice. Projectionsare stored on the memory in a matrix nxm matrix where n is the number of projections and mis the number of detector elements. This means that when the data is read out it is arranged inthe form of a sinogram containing information of both integration times. The low integrationtime and high integration time sinograms are isolated from the raw data. Separately, there are1600 projections for each sinogram, which are then binned angularly into half degree steps andaveraged to create a 360 degree, 720 projection sinogram.3.5 Data Processing and Image ReconstructionData processing serves several purposes: correcting detector offsets, converting fan-beamcollections to equivalent parallel beam collections, replacing corrupt or faulty data with inter-polated values, and creating the final cross-sectional image. The data processing work flowdiagram (Fig. 3.4) gives a visual representation of the steps which are described below in moredetail.403.5. Data Processing and Image ReconstructionFigure 3.4: A flow diagram depicting the steps taken during data processing.The first step in the data processing is to clean both of the varied integration time sinogramsby setting all over-saturated (>14500) detector readings and under-saturated (<50) detectorreadings to a not-a-number NaN value. At this point the detectors offset correction is applied.This is achieved by comparing the low and high integration times of each sinogram element.The slope (signal vs integration time) between each reading is calculated, and the y-interceptis taken as the detector offset and is subtracted from the high integration time data. Thesecorrections are applied to both the reference scan (I0) and the signal scan (I).From the corrected data the optical density (OD) sinogram can be calculated according toEq.1.2. At this point the OD sinogram represents a 360 degree fan-beam collection. Using theMATLAB function fan2para the sinogram is converted to an equivalent 360 degree parallel-beam sinogram. In this system there is a known issue with certain detectors being faulty. Thefirst 5-9 detectors of each array read inconsistent values. It is believed that this is caused by amotherboard issue when switching between arrays during the scan. All of the data collected bythese detectors is set to a NaN value. All NaN values are then 2D interpolated over using thesurrounding data. The interpolation method used was a MATLAB Central script inpaint nanssubmitted by John DErrico [44].413.5. Data Processing and Image ReconstructionThe processed 360 degree sinogram is then cut into two 180 degree sinograms, a front halfand a back half. These two halves are collected from opposite sides, so in effect one of themis redundant. The back half is flipped about the axes of rotation such that both sinogramsare in the same orientation. The two halves are then averaged together ray-by-ray to assistwith noise reduction. This leaves a single 180 degree parallel-beam sinogram that can be usedto reconstruct the CT image. The image was then reconstructed using two different methods,1) in MATLAB (iradon function) using filtered backprojection with a Ramp-Hamming filter,or 2) using the Landweber method of algebraic reconstructing with a custom A matrix thatincludes refraction into the ray paths.42Chapter 4Results and Discussion 1: ScannerDesign and Image ReconstructionThis chapter will discuss the results of the newly designed scanner and image reconstructionmethods. Section 4.1 covers the results of changes to the physical design of the scanner. Sec-tion 4.2 outlines the artifacts relating to data collection and filtered backprojection with thisscanner. Section 4.3 showcases the progress made in the introduction of algebraic reconstruc-tion technique to this scanner’s image reconstruction. Section 4.4 discusses the results of thischapter and offers potential avenues for improvement during future experimentation.4.1 Scanner Design Changes4.1.1 New Laser SystemThe previous scanners laser diode module (LDM) was found to have an intensity drift withtime (Fig.4.1) and was replaced. The new LDM wavelength (635nm) is more photosensitivewith the detectors used than the previous LDM. The new laser’s intensity can be adjustedby varying the voltage from a power supply over a range of 0V to a maximum of 5V with aresolution of 0.01V. Given the optics and detectors of our system the effective range of voltagewas actually 2.08V to 2.15V, and in some cases regions of over-saturation would exist at onevoltage and a reduction of 0.01V would result in other regions undersaturating.The mounting system was redesigned to overcome issues with the previous laser mount. Inthe old system, a curved ring was secured to the body of the laser. The ring was then fit intoa corresponding clamp that allowed for alignment adjustments to be made. The friction clampholding two matching curved surfaces together worked well for enabling smooth adjustments434.1. Scanner Design ChangesFigure 4.1: An image showing the drift of the in profile intensity over the course of approxi-mately 8 hours.to any angle, but was easily disturbed by bumps or movement of the laser cable. This systemwas replaced by a cage system (Edmund Optics). The new cage system is significantly lesssusceptible to physical perturbation. However the mounting of the fan constrainer is stillsusceptible to physical perturbation. The fan constrainer requires longer mounting rails on thecage system to be properly secured.The purpose of the fan constrainer system was twofold. The first purpose is to reduce theamount of unnecessary light that enters the tank by constraining the thickness of the laser. Theactive height of the detectors is only 0.8mm. Without the fan constrainer, the laser thicknessis over 1cm at the detector surface. This serves to reduce the thickness of the fan to 2mm, andremove excess light. Due to total internal reflection between the solid tank and the surroundingair “extra” laser light entering the tank could stay in the block for a number of bounces whichcould be an issue considering the lack of collimator.444.1. Scanner Design ChangesThe second purpose was to remove laser rays that had a direct path from the laser to thedetectors without passing through the contents of the bore hole. Before implementation of thefan constrainer, the light readings of the detectors collecting direct-path rays tended to be veryhigh compared to detectors without direct-path rays. This forced the use of lower intensitylight to reduce the risk oversaturating the detectors collecting direct-path rays. Additionally,the impact of the gel attenuation on the optical density (OD) was dampened by the increasein signal from direct-path rays. From Eq.1.2, if the I (eg 1500) signal was half the value of I0(eg 3000) after passing through the bore the ratio would read 0.5, if however a constant 10000from the direct-path rays were added to those numbers before taking the ratio the calculatedOD response would be much closer to 1.4.1.2 Solid TankOverall the solid tank is significantly less cumbersome than the previous tank design. Thesolid tank design has constraints with total internal reflection, mounting, precession, and bathdisplacement.The effects of total internal reflection (TIR) were underestimated in the design of this tank.From Eq. 1.3, it can be found that the critical angle between PMMA and air is 42.21◦, whichmeans any rays incident at a PMMA to air interface with an incident angle greater than 42.21◦will reflect off the boundary without losses. Prior to the construction of the fan constrainerssome rays at the periphery of the fan would reflect off the sides of the block back into thedetectors rather than exiting the block (Fig.4.2). Imperfections in the block, such as pilot holescause additional light scattering even when outside of the laser’s field-of-view.The tight tolerance between the bore wall and the gel container introduces additional needfor precession minimization. Previously, the precession constraint was only associated with theimage processing stage of the system, with this new system there is also a physical constraint.In cases where the gel container scrapes against the bore wall it can ruin the optically clearfinish on the gel container, or abrade the polish of the tank. This effect forces the manufacturingof a new container and disassembly of the tank to re-polish the bore surface. In this system amount extender 10 cm long is required to fix the gel container to the motion controllers because454.1. Scanner Design ChangesFigure 4.2: A photo which clearly shows an example of total internal reflection happeningalong the outer walls of the solid tank.of bath displacement. Over a distance of 15cm (extender + gel container) a precession of only0.45 degrees would be enough to cause container to scrape against the bore.The water in the reservoir that sits beneath the bore gap is displaced when a container islowered into the bore. For single slice scanning this is not an issue as the volume of the reservoircan be set to the value that perfectly displaces water to fill the bore gap. In volumetric scansthis is more problematic because if a gel container that is 10cm long and 10cm diameter wereto be scanned over 750mL of water would need to be displaced between the bottom slice andthe top slice. Initial plans to allow for this were to place walls on top of the solid tank thatwould contain the displaced water, and a minor slope would let the water run back into thereservoir. This proved problematic for two reasons. The first is that placing walls on topof the container made it so that removing gel container from the scanner could not happenwithout first disconnecting the mount extender, which is something that would introduce moreprecessional variance. The second reason is that the water level of the displaced water would464.1. Scanner Design Changesrise above that of the gel container lid which is not water tight. The introduction of water tothe gel can disconnect the gel from the container wall which creates pockets of water or air. Insome cases water allowed for the gel to become fully disconnected from the gel container androtate freely inside the container. During experimentation, the gel container was lowered toa level when the water would not overflow from the bore hole. Small amounts of water wereadded or removed to vary how deep the container could be submerged.4.1.3 Gel ContainersThe new design of the gel containers was successful at eliminating the seam artifacts. Vari-ation in the container wall thickness further increased the need for precession reduction. Dueto the cost of the container, reusability was considered important, leading to additional focuson the design of the base and lid.The cost of the tubing is over $50 USD/ft and 3-5 containers can be made from a foot oftubing. Initially, when creating gel containers a goal was to be able to reuse them in an effortto minimize costs. The first designs of the container had a base that was cemented in placewith an epoxy, and the lid was fixed by screws that fit into tiny tapped holes in the 0.125”thickness of the tube. The tapped holes were quick to crack the faces of the container understress. It was nearly impossible to remove the gels from the container without damaging theoptical clarity of the container walls. The goal of easy gel removal is why both the base andthe lid became a press-fit design. Because the gel is a silicone base, when pressed on it expandsacting similar to a gasket. One of the only ways to remove the gel without risking damage tothe container was to drill holes through the gel to give the silicone room to expand to whenpressed upon.The press-fit base became a source of many issues during gel creation. In the event that thefit wasn’t tight enough uncured gel would leak out of the bottom. During the vacuuming phaseof creation, air bubbles are removed by expanding the bubbles in a vacuum and then rapidlybringing the chamber back to normal pressure, collapsing the bubble in the process. This isrepeated multiples to remove all bubbles. The re-introduction of air to the chamber allows airto fill the gaps in the press-fit base and once the chamber was vacuumed the air in the base474.2. Image Reconstructionwould expand and leak into the gel. This effect was also found during the curing phase whereair in the fit would expand from heat and leak into the gel. During the curing phase of the gelcreation, the stress on the tube from the press-fit base would cause the container tube to warpwhile under heat for multiple hours. The warping of the tube wall created issues in the walloptics, increased the risk of bore-hole scuffing, and compromised quality of the press-fit.4.1.4 Gel CreationDuring the experimentation the gel recipe chosen based on the recommendation of De Deeneet al. [43]. Working with these gels was a challenge, especially regarding reusability of the gelcontainers, and cleaning of equipment. Both components of the Sylgard 184 are water repellant,and can only be removed by extremely potent chemicals such as MEK (methyl ethyl ketone).Sylgard has designed products to remove the cured and uncured forms of Sylgard 184, howeverthey are not distributed in non-industrial quantities. In an effort to make the gels easier toremove from the gel containers the ratio of elastomer to curing agent was varied, but thetest yielded inconclusive results regarding removability. Cured gels often leave a thin film ofsilicone residue on surfaces they have cured in. This film can be challenging to remove withoutsmudging or damaging the gel container. When not completely eliminated through cleaning,the remaining film became a source of artifacts in subsequent scans using the same container.4.2 Image Reconstruction4.2.1 Ring ArtifactsIn this research it was found that the source of the ring artifacts is the result of the faultydetectors. A test was performed where two identical scans were taken back-to-back, each scanrepresenting I and I0 respectively. If each of the scans were truly identical, then the calculatedtransmission sinogram would read 1 everywhere. From Figure.4.3 we can see that there aredetectors that are not reading consistently which is causing lower transmission regions to appear.From this image, detector 1-22, 59-64, 124-128, 188-192, 250-256, and 308-320 are readingunreliably, meaning a total of 58 detectors are failing. This equates to 18.1% of all data beinginterpolated over 1-dimensional instead of measured. Figure 4.4 shows a visual representation484.2. Image Reconstructionof where these faulty detectors manifest in image space using filtered backprojection. Thefaulty detectors were set to zero rather than interpolated over and compared against the sameimage that has interpolation. The effect of the faulty detectors is clearly highlighted when theinterpolated region occurs at an area with steep signal change such as an edge (Fig. 4.5).Figure 4.3: A transmission sinogram (Top) made from I and I0 scans collected in identicallocations with no modifications to either. The sinogram has been zoomed in (Bottom) toshowcase a region affected by the bad detectors.494.2. Image ReconstructionFigure 4.4: A filtered backprojection reconstructed slice of a dyed water (reference scanwithout dye). The left reconstruction uses interpolation to replace the data collected by faultydetectors. The right reconstruction shows the resulting image if the data is set to zero ratherinterpolated, showcasing which regions are affected by these detectors.Figure 4.5: A optical density sinogram from a slice of dyed water with an opaque object withinit (reference scan without dye or object). The left sinogram shows the cropped faulty detectorspassing over an edge in the sinogram. The right sinogram shows the resulting sinogram afterthe faulty data has been interpolated and highlights the affect 1D interpolation has on an edge.4.2.2 Limited Field-Of-ViewThis system has artifacts that are introduced because of a limited field-of-view (FOV).Figure 4.6 shows a simulated model to illustrate the optics. There are a set of rays that aretotally internally reflected at the periphery of the container. This corresponds to an area of thegel that will not be measured in a projection at a specific projection angel because the regionis outside of the FOV. An experiment was performed where an opaque mark was made on theoutside of the gel container 4.7. Opaque objects in optical CT generally have a blurring effect504.3. Algebraic Reconstruction Techniqueassociated with them, however it was found that in the image the region containing the markdid not reconstruct completely.Figure 4.6: A filtered backprojection slice reconstruction with a piece of opaque tape on theoutside surface of the container. It can be seen that the tape fails to reconstruct properly dueto a limited-FOV.4.3 Algebraic Reconstruction TechniqueThis section of the research was performed solely by Steve Collins at the University of BritishColumbia Okanagan. The results of his work investigating algebraic reconstruction technique(ART) influenced design decisions while researching this project.A number of different algorithms were compared against filtered back projection (Fig. 4.8).It was found that the Landweber method produced the best image quality regarding signal-to-noise ratio and the steepness of dose gradients, while preforming worse in contrast-to-noise514.4. DiscussionFigure 4.7: A simulation of the path that a set of rays in a fan beam would travel. The leftshows a top down view of the system. The right shows a zoomed in portion focusing on thetotally internally reflected rays and the corresponding un-imaged region inside the container.than the others (Table 4.1). The other methods depicted a significant amount of blurring intheir reconstructions.Table 4.1: Iterative Method ResultsCAV Cimmino DROP Landweber SARTSNR 0.4911 0.5059 0.4897 0.8563 0.7287CNR 2.7953 3.6110 2.8472 1.3942 2.83284.4 DiscussionThis chapter outlined the results of changes made to the physical design of the scanner,characterization of persistent image artifacts, and the introduction of iterative reconstruction.The improvements made to the laser mounting system greatly increased the system’s resis-tance to perturbation and simplified the steps required to align optical components (mirrors,lenses, filters, etc). The introduction of the fan constrainer reduced the amount of unnecessaryor detrimental laser light entering the tank. Future considerations for the laser apparatus wouldbe to calculate and simulate the benefit of placing the laser much further from the tank witha narrower fan angle. This would make it so the rays entering the tank would have less of a524.4. DiscussionFigure 4.8: A comparison of many iterative reconstruction methods using a radiochromic gelphantom. (a) Component Averaging, (b) Cimmino, (c) Diagonally Relaxed Orthogonal Pro-jections, (d) Landweber, (e) Simultaneous Algebraic Reconstruction Technique, (f) FilteredBackprojection.variation in incident angles than a closer, wide-angle fan would. The introduction of a voltagedivider to the powering system would be beneficial to increasing the resolution of the voltagesupplied to the laser. Additionally, longer cage rails should be added to accommodate the fanconstrainers.The solid tank proved less cumbersome than the previous tank design. The primary con-straints introduced by the solid tank design are total internal reflection, mounting, precession,and bath displacement. Future iterations of the solid tank design should more strongly considertotal internal reflection and focus on only allowing the minimal light necessary to complete ascan. Additionally, designs could feature a coating of a light-absorbing material, such as blackacrylic paint, as a means of filtering out reflected light. Future designs may want to find asolution that places the motion controllers closer to the scanning region so that precession isminimized and find a more elegant solution to the displacement of water. A design mightachieve these objectives by rotating the gel from beneath and translating the laser/detection534.4. Discussionsystem vertically along the volume. This would remove the displacement constraint because thecontainer would only rotate, and the removal of gel translation would remove the requirementfor a mount extender.The new gel containers became a source of many issues during the manufacturing. They werecapable of containing gels without introducing seam artifacts present in commercial alternatives.However, currently they are cost and time inefficient, and the end result is still fairly unstablewith regards to air removal, and bubble formation along the inside container surface. Duringexperimentation, it was concluded that containers could only be used a single time. Futureresearch may want to further explore the possibility of reusability as cost consideration iscurrently a disadvantage gel dosimetry has over dosimetry alternatives (eg. ArcCHECK). Theframework for a reusable design exists but in spite of many attempts, it was not solved duringthis research.Currently, one of the largest artifact sources in this scanner is the faulty detectors. They arethe cause of 18.1% of the data being fabricated through 1D interpolation. The obvious solutionfor this problem is to replace the faulty detector arrays, or replace the electronics relating tothe array switching. This problem does however expose a flaw in traditional matrix processingmethods used on sinograms. For an accurate interpolation to be performed over these regionsit would need to interpolate sinusoidally, following the path of the rotating object. There areexperimental interpolation MATLAB scripts that incorporate edge detection, but this does nothelp for scans of objects with OD gradients.Near the end of this research it was determined that the scanner has a limited FOV. Becausethis limited FOV problem was only discovered near the end of the research, a solution has notbeen found at the time of this writing and the impact it has on the image reconstruction is notwell known. Future researchers can address this problem by considering this in future design,or looking into existing solutions that can be applied during image processing.54Chapter 5Results and Discussion 2:Pre-commissioningThis chapter discusses the commissioning that was performed on the scanner. Section 5.1details experiments to determine the geometry of physical objects in image space. Section 5.2discusses experiments that contributed to the understanding of this system’s spatial frequency.5.1 Image GeometryDuring initial experiments the location of the gel container wall was misunderstood in imagespace. An experiment was performed to try to characterize the physical size of a pixel in imagespace by placing an object of known size inside of a container filled with water. It was foundthat the object had a diameter of 24 pixels in image space, compared to a physical diameterof 6mm. This gave a ratio of 4px/mm. Using this ratio to find the container wall in the imagewas not possible, as what was thought to be the wall was only 240px in diameter, which is adiameter of 60mm from the assumed ratio.This test was revisited after the construction of the fan-constraining blades. This timethe experiment was performed by placing an object of known size inside of a gel to mold acavity in the gel. The cavity was then filled with an index matched material, and some patentblue dye was added between the reference and signal scans. It was found that the objectdiameter in image space was 67px and 25.5mm diameter physically (Fig.5.1). This gave a ratioof 2.63px/mm. From this ratio the assumed container wall was measured, and it read 266pxwith a physical diameter of 101.6mm (ratio of 2.63 as well). This same ratio could be found inthe opaque mark test that was performed to displace the limited FOV (Fig. 4.6).555.2. Spatial FrequencyFigure 5.1: Two reconstructed images with pixel distances of geometric objects highlighted.The first experiment (left) shows an inconsistent ratio between objects. The second experiment(right) shows a consistent ratio between objects.5.2 Spatial FrequencyA number of experiments were performed attempting to measure the spatial frequency ofthe optical CT scanner. The approach was to create a circular region of attenuation withwell-defined geometry and measure the edge spread function (ESF). The derivative of the ESFgives the line spread function (LSF), and applying a fast-Fourier transform to the LSF givesthe modulation transfer function (MTF). The MTF provides a measure of how well the systemtransfers contrast across spatial frequencies [45]. A system’s MTF is plotted against spatialfrequency in (cycles/mm), and the 50% cutoff frequency (MTF50) is the corresponding systemspatial frequency.Experiment # 1The first experiment was performed by creating a Flexydos3D gel phantom (Fig 5.2). Thephantom was created in the three stages. The first stage used a Flexydos3D recipe modified tohave one quarter of the active ingredients (chloroform and LMG). Weight by weight the recipewas 89.54% elastomer base, 8.954% curing agent, 1.250% chloroform, and 0.00625% LMG. Themixture was poured into the container and then a 25.5mm diameter, polished brass rod withaccurate cylindrical geometry was placed into the gel. After the gel cured, the rod was removed565.2. Spatial Frequencyand a standard mixture of Flexydos3D (Section.3.3.7 was poured into the cylindrical mold leftby the rod, and cured. The final stage was pouring a top layer of gel with no chloroformor LMG, leaving a transparent silicone region. Flexydos3D background opacity is dependenton the fraction of active ingredient in the mixture meaning the insert should have a higheropacity than the surrounding material. The top layer was placed for a reference signal (I0).The phantom was not scanned for 4 days after the final stage was cured because it takes sometime for the background opacity of the gel to build up [43].Figure 5.2: A gel phantom that was made in three stages to measure spatial frequency.The resulting images contained many artifacts related to air bubbles along the containerwall likely caused from heating and cooling multiple times. The images from this experimentwere not used for system commissioning, but it does display a proof of concept for this typeof phantom for commissioning in the future. An additional thing learned from this experimentwas that the active ingredients diffuse into surrounding material. That is thought to be thecause of the bright halo surrounding the circular edge as the scanning of this phantom tookplace roughly 6 days after the first stage was cured. Additionally, 2 months later it could beseen by visual inspection that the background opacity had begun to diffuse into the transparenttop layer.Experiment # 2This experiment was performed a second time with additional emphasis on ideal phantommanufacturing. Qualitatively the gel was also affected by many bubbles and particulate con-tamination. In this experiment the entire volume of the gel was scanned and the result was575.2. Spatial Frequencythat 12 reference scans (I0), and 12 signal scans (I) were collected. All possible permutationsof I and I0 were reconstructed in an attempt to find a combination with as few manufacturingdefects as possible. It was found that most of the visual artifacts were caused by the I0 scans(Fig. 5.3). The best results showed the higher-attenuation edge, but the quality was too poorto attempt ESF measurement (Fig 5.4).Figure 5.3: An example batch of reconstruction permutations where 12 I scans were recon-structed with the same I0. The way that the artifacts (red) appear in all reconstructions showsthe artifacts are associated with the I0 scan.585.2. Spatial FrequencyFigure 5.4: An example of one of the best reconstruction permutations, showcasing the poorquality of the edge in the slice.The results of this experiment showcased the pixel-ratio problem outlined in Section 5.1.During manufacturing the insert was placed approximately equidistant from the container centerand the container wall. In the image it appears significantly close to the edge. This experimentwas the trigger for the creation of the fan constraining blades, and additional investigation intothe pixel-ration. The experiment was repeated after creation of the fan constraining blades.Future attempts to measure spatial frequency using this method will require more delicate andclean phantom manufacturing specifically regarding the introduction of air bubbles.Experiment # 3The third experiment was performed using the Sylgard 184 without any active ingredient. Acylindrical mold was made in the gel the same way as in experiment one stage one. Rather thanfilling the mold with a gel with a different attenuation it was filled with a dyed index matchingfluid made from a mixture of water, glycerol, and patent blue. The quality of the data foundin this third iteration was still poor overall due to manufacturing challenges, but the clarity ofthe edge was much higher. A proof-of-concept MTF analysis was performed on this data set,observing each of the 4 quadrants of the circular mold.The image was cropped to the region of interest (ROI) (Fig. 5.5). The centroid of the shapewas located, and pixels were binned according to their distance away from the centroid in 1pixel steps. The average of those binned pixels was plotted as a radial plot from the centerof the ROI. The ESF was cropped from the radial plot as the region from maximum signal595.2. Spatial Frequencystrength to minimum signal strength (Fig. 5.6]). The antiderivative of the ESF gives a PSF,and an FFT of the PSF displays the MTF (Fig. 5.7). The 50% cutoff frequencies for eachquadrant can be seen in Table 5.1. Assuming that the measured pixel ratio of 2.63px/mm fromSection 5.1 is correct the average MTF50 found was 3.111cycles/mm.Figure 5.5: A zoomed in region of a slice showing the cylindrical insert in image space. Theirregular pattern inside the insert is due to schlieren artifacts from poorly mixed glycerol.605.2. Spatial FrequencyTable 5.1: Spatial Frequency Proof-of-ConceptBottom Right Bottom Left Top Left Top Right MeanQuadrant Quadrant Quadrant QuadrantMTF50 1.339 1.040 1.118 1.234 1.183(cycles/px)MTF50 3.522 2.735 2.940 3.245 3.111(cycles/mm)In the data analysis of this experiment the centroid of the ROI was determined but the valuewas rounded to the nearest integer value for easier data manipulation. This analysis couldbe improved in the future by interpolating the ROI to more accurately position the center.Additional improvements would be to oversample the edge, analyze the edge data withoutaveraging the pixels, and to combine the data from all four quadrants into one set. Previousiterations of this scanner were also capable of greater than 1cycle/mm spatial frequency.Figure 5.6: A radial plot and corresponding cropped ESF depicting the edge of each quadrantof the cylindrical insert.615.2. Spatial FrequencyFigure 5.7: The calculated MTF of each of the quadrants of the cylindrical insert. The MTF50is highlighted in the image and their values are listed in Table 5.1.62Chapter 6ConclusionThe objective of this work was to design a new prototype fan-beam optical computed to-mography scanner for three-dimensional radiation dosimetry. In this research a solid acrylictank was proposed and manufactured as an alternative to conventional optical CT refractiveindex matching baths. The tank was constructed from a solid block of acrylic with a hole boredthrough it. Excessive total internal reflection was present when the bore-gap between the tankand the gel container was air so a low volume bath was constructed that would act as a waterreservoir to fill the gap with water.A new design for gel containers was created to eliminate the seam artifacts that are presentwhen scanning with commercially available gel containers. The new containers were opticallyideal for scanning, but they were a large source of challenges when using them to manufactureFlexyDos3D gels. During gel manufacturing, the containers were a source of air bubbles whilein a vacuum chamber, and the container began to warp during the curing phase. Other concernswith using the new gel containers were cost and time efficiency.Images were constructed using the Landweber algebraic reconstruction technique, and it wasfound that they are capable of images of similar quality to those from filtered backprojection.The added benefit of ART was that it considers the ray path changes due to refraction andallows for a more accurate reconstruction than filtered backprojection.During the commissioning a number of challenges arose that had to be addressed such aseffect of the rays that had a direct path from laser to detector without transiting the bore, andthe effect of the limited FOV of the scanner. The direct path rays were successfully removedfrom the system by the creation of a fan constrainer. This change allowed for the full imagespace to be observed, while prior to creation the image space was thought to be much smaller.636.1. Future WorkThis new understanding of the image space showed that the scanner was not viewing the entireregion of interest and thus was susceptible to limited FOV artifacts. A solution to the limitedFOV problem was not found in this research.In light of those challenges some pre-commissioning was performed. The image geometrywas found by analyzing the pixel-to-mm ratio between physical objects and their correspondinggeometry in image space. Additionally a set of proof-of-concept experiments were performed toget a sense of the scanners spatial resolution. These experiments should be revisited in a morerobust manner, in addition to other commissioning experiments such as low contrast resolution,high contrast resolution, and signal-to-noise ratio.6.1 Future WorkWhile rigorous commissioning still needs to be applied to this design, the proof-of-conceptexperiments and qualitative results show that with the inclusion of ART and a solid tank,a small amount of index matching fluid can be used in lieu of a full index matching tank.The purpose of reducing the volume is to increase ease-of-use for the system. The nature ofwater displacement in small volumes makes it challenging to have a system where the objectof interest is becoming gradually more submerged to form a 3D scan. New systems shouldexplore the idea of a vertically stationary object where the solid tank and the small volumebath translate vertically across the object to scan it. The most challenging components to thinkabout are water-proofing the translating bath while still maintaining the optical clarity of theacrylic polish. The polish is easily compromised by rubbing or scraping, so a water tight systemshould be conscious of polish integrity during extended use.One of the largest causes for concern in this research was the limited FOV artifacts intro-duced by TIR. These were the result of the desire to use a homogenous material (water) to fillthe bore-gap. There are a variety of common oils that are significantly closer to the RI of acrylicthan water is. Future work may want to look at the possibility of incorporating these oils intothe design, specifically regarding optical clarity, optical density of the oil, and consequences ofthe low surface tension of oil.64Bibliography[1] Warren Campbell, PhD thesis, University of Victoria, 2015. → pages x, 10, 15, 32[2] Michael Joiner and Albert van der Kogel. 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