Diagnostic Radiology Physics
A Handbook for Teachers and Students
D.R. Dance S. Christofides A.D.A. Maidment I.D. McLean K.H. Ng
Technical Editors
Diagnostic Radiology Physics eachers and Students
1
This publication provides a comprehensive review of topics relevant to diagnostic radiology physics. It is intended to provide the basis for the education of medical physicists in the field of diagnostic radiology. Bringing together the work of 41 authors and reviewers from 12 countries, the handbook covers a broad range of topics including radiation physics, dosimetry and instrumentation, image quality and image perception, imaging modality specific topics, recent advances in digital techniques, and radiation biology and protection. It is not designed to replace the large number of textbooks available on many aspects of diagnostic radiology physics, but is expected to fill a gap in the teaching material for medical radiation physics in imaging, providing in a single manageable volume the broadest coverage of topics currently available. The handbook has been endorsed by several international professional bodies and will be of value to those preparing for their certification as medical physicists, radiologists and diagnostic radiographers.
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the agency’s statute was approved on 23 october 1956 by the conference on the statute of the iaea held at united nations headquarters, new york; it entered into force on 29 july 1957. the headquarters of the agency are situated in Vienna. its principal objective is “to accelerate and enlarge the
Diagnostic RaDiology Physics:
a hanDbook foR teacheRs anD stuDents
enDoRseD by:
aMeRican association of Physicists in MeDicine, asia–oceania feDeRation of oRganiZations
foR MeDical Physics,
euRoPean feDeRation of oRganisations foR MeDical Physics
inteRnational atoMic eneRgy agency Vienna, 2014
albania algeRia angola aRgentina aRMenia austRalia austRia aZeRbaijan bahaMas bahRain banglaDesh belaRus belgiuM beliZe benin boliVia
bosnia anD heRZegoVina botsWana
bRaZil
bRunei DaRussalaM bulgaRia
buRkina faso buRunDi caMboDia caMeRoon canaDa
centRal afRican RePublic chaDchile china coloMbia congo costa Rica cÔte D’iVoiRe cRoatia cubacyPRus cZech RePublic DeMocRatic RePublic
of the congo DenMaRk DoMinica
DoMinican RePublic ecuaDoR
egyPt el salVaDoR eRitRea estonia ethioPia fijifinlanD fRance gabon geoRgia geRMany
gReece guateMala haiti holy see honDuRas hungaRy icelanD inDia inDonesia
iRan, islaMic RePublic of iRaQiRelanD
isRael italy jaMaica jaPan joRDan kaZakhstan kenya
koRea, RePublic of kuWait
kyRgyZstan
lao PeoPle’s DeMocRatic RePublic
latVia lebanon lesotho libeRia libya liechtenstein lithuania luXeMbouRg MaDagascaR MalaWi Malaysia MaliMalta
MaRshall islanDs MauRitania, islaMic
RePublic of MauRitius MeXico Monaco Mongolia MontenegRo MoRocco MoZaMbiQue MyanMaR naMibia nePal netheRlanDs neW ZealanD nicaRagua nigeR nigeRia noRWay
Pakistan Palau PanaMa
PaPua neW guinea PaRaguay PeRuPhiliPPines PolanD PoRtugal QataR
RePublic of MolDoVa RoMania
Russian feDeRation RWanDa
san MaRino sauDi aRabia senegal seRbia seychelles sieRRa leone singaPoRe sloVakia sloVenia south afRica sPain sRi lanka suDan sWaZilanD sWeDen sWitZeRlanD syRian aRab RePublic tajikistan
thailanD
the foRMeR yugoslaV RePublic of MaceDonia togotRiniDaD anD tobago tunisia
tuRkey uganDa ukRaine
uniteD aRab eMiRates uniteD kingDoM of
gReat bRitain anD noRtheRn iRelanD uniteD RePublic
of tanZania
uniteD states of aMeRica uRuguay
uZbekistan
VeneZuela, boliVaRian RePublic of
Viet naM yeMen ZaMbia ZiMbabWe
the agency’s statute was approved on 23 october 1956 by the conference on the statute of the iaea held at united nations headquarters, new york; it entered into force on 29 july 1957. the headquarters of the agency are situated in Vienna. its principal objective is “to accelerate and enlarge the contribution of atomic energy to peace, health and prosperity throughout the world’’.
IAEA Library Cataloguing in Publication Data
Diagnostic radiology physics : a handbook for teachers and students. — Vienna : international atomic energy agency, 2014.
p. ; 24 cm.
sti/Pub/1564 isbn 978–92–131010–1
includes bibliographical references.
1. Radiology, Medical — handbooks, manuals, etc. 2. Medical physics — handbooks, manuals, etc. 3. Radiation dosimetry. 4. Diagnostic imaging.
i. international atomic energy agency.
all iaea scientific and technical publications are protected by the terms of the universal copyright convention as adopted in 1952 (berne) and as revised in 1972 (Paris). the copyright has since been extended by the World intellectual Property organization (geneva) to include electronic and virtual intellectual property. Permission to use whole or parts of texts contained in iaea publications in printed or electronic form must be obtained and is usually subject to royalty agreements. Proposals for non-commercial reproductions and translations are welcomed and considered on a case-by-case basis. enquiries should be addressed to the iaea Publishing section at:
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© iaea, 2014 Printed by the iaea in austria
september 2014 sti/Pub/1564
all iaea scientific and technical publications are protected by the terms of the universal copyright convention as adopted in 1952 (berne) and as revised in 1972 (Paris). the copyright has since been extended by the World intellectual Property organization (geneva) to include electronic and virtual intellectual property. Permission to use whole or parts of texts contained in iaea publications in printed or electronic form must be obtained and is usually subject to royalty agreements. Proposals for non-commercial reproductions and translations are welcomed and considered on a case-by-case basis. enquiries should be addressed to the iaea Publishing section at:
Marketing and sales unit, Publishing section international atomic energy agency
Vienna international centre Po box 100
1400 Vienna, austria fax: +43 1 2600 29302 tel.: +43 1 2600 22417
email: [email protected] http://www.iaea.org/books
one of the important activities of the iaea is the education of professionals responsible for the application of radiation. this is no less true in radiation medicine than in other fields, where the physics professional not only needs to understand the physical principles involved, but must also have a sound knowledge of their application to medical practice. consequently, the iaea has a long history of supporting education in these areas through the use of guidance documents and, importantly, more directly through cooperation programmes, including the support of Member states in developing their own university infrastructure for postgraduate education programmes in medical physics, the development of clinical training guides and, more recently, web based educational resources.
in 2005, the iaea published Radiation oncology Physics: a handbook for teachers and students, as a result of a process of determining a harmonized syllabus for university education of medical physicists in radiation oncology.
following the success of this publication, it was apparent that a similar need existed in the other two specialities of medical physics, namely diagnostic radiology and nuclear medicine. this need has been recognized as a result of the growing importance of medical imaging in all areas of radiation medicine, including radiation oncology, and also because of the growing awareness of the increasing use of complex diagnostic equipment and techniques, such as computed tomography, mammography and interventional radiology. in parallel with this, the past decade has seen the digitization of image based medical technology, with its inherent need for quality processes.
this handbook is intended to provide the basis for the education of medical physicists initiating their university studies in the field of diagnostic radiology.
this has been achieved with the contributions of 41 authors and reviewers from 12 different countries. the 24 chapters include a broad coverage of topics relevant to diagnostic radiology physics, including radiation physics, dosimetry and instrumentation, image quality and image perception, imaging modality specific topics, recent advances in digital techniques, and radiation biology and protection. the handbook is not designed to replace the large number of textbooks available on many aspects of diagnostic radiology physics, which will still be necessary to deepen knowledge in the specific topics reviewed here.
it is expected that this handbook will successfully fill a gap in the teaching material for medical radiation physics in imaging, providing, in a single volume, the largest possible coverage available today. its wide dissemination by the iaea will contribute to the harmonization of education in diagnostic radiology physics and will be the source reference for much of the iaea clinical
endorsement of this handbook has been granted by following international professional bodies: the american association of Physicists in Medicine (aaPM), the asia–oceania federation of organizations for Medical Physics (afoMP) and the european federation of organisations for Medical Physics (efoMP).
the following international experts are gratefully acknowledged for making major contributions to the development of an earlier version of the syllabus: R. nowotny (austria) and M. sandborg (sweden). the following individuals made major contributions to this handbook as technical editors:
s. christofides (cyprus), D.R. Dance (united kingdom), a.D.a. Maidment (united states of america) and k.-h. ng (Malaysia). the iaea scientific officers responsible for the project were (in chronological order) F. Pernička, i.D. Mclean and h. Delis.
EDITORIAL NOTE
Although great care has been taken to maintain the accuracy of information contained in this publication, neither the IAEA nor its Member States assume any responsibility for consequences which may arise from its use.
The use of particular designations of countries or territories does not imply any judgement by the publisher, the IAEA, as to the legal status of such countries or territories, of their authorities and institutions or of the delimitation of their boundaries.
The mention of names of specific companies or products (whether or not indicated as registered) does not imply any intention to infringe proprietary rights, nor should it be construed as an endorsement or recommendation on the part of the IAEA.
The IAEA has no responsibility for the persistence or accuracy of URLs for external or third party Internet web sites referred to in this book and does not guarantee that any content
the application of physical principles to reveal internal structures of the body sparked the imagination of the medical profession in the late 19th century and rapidly became the foundation of the practice of diagnostic radiology.
the efforts of physical scientists have continued to fuel innovation in medical imaging through a progression of technologies, including the specialization of X ray imaging devices for examination of the breast, blood vessels, moving vessels, teeth and bone density. the use of high frequency sound waves has allowed the instantaneous imaging of soft tissues without the dangers associated with ionizing radiation. the use of mathematical image reconstruction has allowed the visualization of sections of the body, free from the confusion caused by overlying tissue as seen in the computed tomography scanner and the magnetic resonance imager, while the developments in computers have allowed the electronic capture, processing and transfer of medical images.
as was quickly discovered with the application of X rays for medical imaging, the use of radiation on living tissue is not without risk of biological injury. the measurement of radiation, its interaction with matter and its biological effects have led to the studies of radiation dosimetry, radiation biology and epidemiology. these studies are becoming more important in modern radiological imaging as the number, length and complexity of X ray procedures received by the population continues to increase rapidly.
it is in this complex environment that the medical physicist, along with radiologists and radiographers, plays a significant role in the multidisciplinary team needed for medical diagnosis. Medical physicists need to be able to advise on the principles and practice of imaging equipment and assist in purchase processes and quality assurance. they are required to measure the radiation dose received by staff and, most importantly, by the patients undergoing diagnostic examinations. they should be able to advise on the optimal image quality needed for the diagnostic process and to be able to contribute to scientific research. they are also well equipped to assume responsibility for the safe use of radiation at a medical facility.
this book is dedicated to students and teachers involved in programmes that train professionals for work in diagnostic radiology. it teaches the essential physics of diagnostic radiology and its application in modern medicine. as such, it is useful to graduate students in medical physics programmes, residents in diagnostic radiology and advanced students in radiographic technology programmes. the level of understanding of the material covered will, of course, be different for the various student groups; however, the basic language and knowledge for all student groups is the same. the text is also a key reference for
the text is written to support a set of courses whose content provides the necessary diagnostic and interventional radiological physics knowledge for all of modern diagnostic radiology. While the text is mainly aimed at diagnostic radiology professionals, certain parts may also be of interest to professionals in other branches of medicine that use ionizing radiation for the treatment of disease (radiation therapy and nuclear medicine). the contents are also useful for physicists who are involved in studies of radiation hazards and radiation protection (health physics).
this book represents a collaborative effort by professionals from many different countries, who share a common goal of disseminating their diagnostic radiology physics knowledge and experience to a broad international audience of teachers and students.
s. chRistofiDes D.R. Dance
a.D.a. MaiDMent i.D. Mclean k.-h. ng
chaPteR 1. funDaMentals of atoMic anD nucleaR
Physics . . . 1
1.1. intRoDuction . . . 1
1.2. classification of RaDiation . . . 1
1.2.1. electromagnetic radiation . . . 1
1.2.2. Particulate radiation . . . 2
1.2.3. ionizing and non-ionizing radiations . . . 3
1.3. atoMic anD nucleaR stRuctuRe . . . 3
1.3.1. basic definitions . . . 3
1.3.2. atomic structure . . . 5
1.4. X Rays . . . 7
1.4.1. the production of characteristic X rays and auger electrons 7 1.4.2. Radiation from an accelerated charge, bremsstrahlung . . . . 9
chaPteR 2. inteRactions of RaDiation With MatteR . . . . 11
2.1. intRoDuction . . . 11
2.2. inteRactions of Photons With MatteR . . . 12
2.2.1. Photoelectric effect . . . 13
2.2.2. thomson scattering . . . 15
2.2.3. coherent (Rayleigh) scattering . . . 17
2.2.4. compton scattering by free electrons . . . 19
2.2.5. scattering and energy transfer coefficients . . . 22
2.2.6. incoherent scattering . . . 22
2.2.7. Pair and triplet production . . . 23
2.3. Photon attenuation coefficients . . . 24
2.3.1. linear attenuation coefficient . . . 24
2.3.2. exponential attenuation . . . 25
2.3.3. Mass attenuation coefficient . . . 25
2.3.4. Mass energy transfer coefficients and mass energy absorption coefficients . . . 25
2.3.5. contribution of individual interactions to the total mass attenuation coefficient . . . 26
2.3.6. coefficients for compounds and mixtures . . . 28
2.4. inteRactions of electRons With MatteR . . . 29
2.4.1. ionizational (collisional) interactions and ionizational stopping power . . . 29
2.4.2. Radiative interactions and radiative stopping power . . . 30
2.4.5. linear energy transfer . . . 32
2.5. Data souRces . . . 32
chaPteR 3. funDaMentals of DosiMetRy . . . 35
3.1. intRoDuction . . . 35
3.2. Quantities anD units useD foR DescRibing the inteRaction of ioniZing RaDiation With MatteR . . . 35
3.2.1. Radiation fields: fluence and energy fluence . . . 36
3.2.2. energy transferred, net energy transferred, energy imparted 37 3.2.3. kerma and collision kerma . . . 38
3.2.4. kerma for photons . . . 39
3.2.5. absorbed dose . . . 41
3.2.6. kerma and absorbed dose . . . 42
3.2.7. Diagnostic dosimeters . . . 44
3.3. chaRgeD PaRticle eQuilibRiuM in DosiMetRy . . . 44
3.3.1. cPe . . . 44
3.3.2. Relationships between absorbed dose, collision kerma and exposure under cPe . . . 46
3.3.3. conditions that enable cPe or cause its failure . . . 48
3.4. caVity theoRy. . . 48
3.4.1. bragg–gray cavity theory . . . 49
3.4.2. the fano theorem . . . 50
3.4.3. other cavity sizes . . . 50
3.5. PRactical DosiMetRy With ion chaMbeRs . . . 52
chaPteR 4. MeasuRes of iMage Quality . . . 55
4.1. intRoDuction . . . 55
4.2. iMage theoRy funDaMentals. . . 56
4.2.1. linear systems theory . . . 56
4.2.2. stochastic properties . . . 59
4.2.3. sampling theory . . . 61
4.3. contRast . . . 63
4.3.1. Definition . . . 63
4.3.2. contrast types . . . 64
4.3.3. greyscale characteristics . . . 65
4.4. unshaRPness . . . 66
4.5. noise . . . 73
4.5.1. Poisson nature of photons . . . 74
4.5.2. Measures of variance and correlation/covariance . . . 75
4.5.3. noise power spectra . . . 77
4.5.4. noise power spectra of a cascaded imaging system . . . 80
4.6. analysis of signal anD noise. . . 82
4.6.1. Quantum signal to noise ratio . . . 82
4.6.2. Detective quantum efficiency . . . 83
4.6.3. signal to noise ratio . . . 85
4.6.4. snR2/dose . . . 88
chaPteR 5. X Ray PRoDuction . . . 89
5.1. intRoDuction . . . 89
5.2. funDaMentals of X Ray PRoDuction . . . 89
5.2.1. bremsstrahlung . . . 89
5.2.2. characteristic radiation . . . 90
5.2.3. X ray spectrum . . . 91
5.3. X Ray tubes . . . 93
5.3.1. components of the X ray tube . . . 93
5.3.2. cathode . . . 93
5.3.3. anode . . . 96
5.4. eneRgiZing anD contRolling the X Ray tube . . . 102
5.4.1. filament circuit . . . 103
5.4.2. generating the tube voltage . . . 103
5.4.3. exposure timing . . . 106
5.4.4. falling load . . . 107
5.5. X Ray tube anD geneRatoR Ratings. . . 107
5.5.1. X ray tube . . . 107
5.5.2. tube housing . . . 109
5.6. colliMation anD filtRation . . . 109
5.6.1. collimator and light field . . . 109
5.6.2. inherent filtration . . . 110
5.6.3. added filtration . . . 111
5.6.4. compensation filters . . . 111
5.7. factoRs influencing X Ray sPectRa anD outPut . . . 112
5.7.1. Quantities describing X ray output . . . 112
5.7.2. tube voltage and current . . . 112
5.7.3. tube voltage ripple. . . 113
chaPteR 6. PRojection RaDiogRaPhy . . . 117
6.1. intRoDuction . . . 117
6.2. X Ray iMage foRMation . . . 117
6.2.1. components of an imaging system . . . 117
6.2.2. geometry of projection radiography . . . 119
6.2.3. effects of projection geometry . . . 120
6.2.4. Magnification imaging . . . 125
6.2.5. contrast agents . . . 126
6.2.6. Dual energy imaging . . . 126
6.2.7. technique selection . . . 126
6.3. scatteReD RaDiation in PRojection RaDiogRaPhy . 130 6.3.1. origins of scattered radiation . . . 131
6.3.2. Magnitude of scatter . . . 131
6.3.3. effect of scatter . . . 134
6.3.4. Methods of scatter reduction — antiscatter grids . . . 135
6.3.5. other methods of scatter reduction . . . 139
chaPteR 7. RecePtoRs foR PRojection RaDiogRaPhy . . . . 145
7.1. intRoDuction . . . 145
7.2. geneRal PRoPeRties of RecePtoRs . . . 146
7.2.1. Receptor sensitivity . . . 146
7.2.2. Receptor X ray noise . . . 149
7.2.3. greyscale response and dynamic range . . . 151
7.2.4. Receptor blur . . . 153
7.2.5. fixed pattern noise . . . 155
7.3. filM anD scReen filM systeMs . . . 155
7.3.1. systems . . . 155
7.3.2. the screen . . . 156
7.3.3. Photographic film and the photographic process . . . 159
7.3.4. greyscale characteristics of film images . . . 161
7.3.5. Reciprocity . . . 163
7.3.6. screen film imaging characteristics . . . 163
7.4. Digital RecePtoRs . . . 167
7.4.1. Digital imaging systems . . . 167
7.4.2. computed radiography . . . 168
7.4.6. comparisons of digital and analogue systems . . . 181
chaPteR 8. fluoRoscoPic iMaging systeMs . . . 183
8.1. intRoDuction . . . 183
8.2. fluoRoscoPic eQuiPMent . . . 183
8.2.1. the fluoroscopic imaging chain . . . 183
8.2.2. automatic exposure control . . . 189
8.2.3. electronic magnification . . . 190
8.3. iMaging PeRfoRMance anD eQuiPMent configuRation . . . 190
8.3.1. contrast . . . 190
8.3.2. noise . . . 192
8.3.3. sharpness . . . 192
8.3.4. artefacts . . . 192
8.4. aDjunct iMaging MoDes . . . 194
8.4.1. Digital acquisition imaging . . . 194
8.4.2. Digital subtraction angiography . . . 194
8.5. aPPlication sPecific Design . . . 197
8.5.1. Remote fluoroscopy systems . . . 197
8.5.2. Vascular and interventional radiology . . . 198
8.5.3. cardiology . . . 199
8.5.4. neuroradiology . . . 199
8.5.5. Mobile fluoroscopes . . . 199
8.6. auXiliaRy toPics . . . 199
8.6.1. spot film device . . . 200
8.6.2. operating modes . . . 200
8.6.3. Recursive filtering . . . 201
8.7. DosiMetRic consiDeRations in fluoRoscoPy . . . 202
8.7.1. skin dose indicators . . . 202
8.7.2. Radiation safety considerations for patient protection . . . 204
8.7.3. Radiation safety considerations for operator protection . . . 205
chaPteR 9. MaMMogRaPhy . . . 209
9.1. intRoDuction . . . 209
9.2. RaDiological ReQuiReMents foR MaMMogRaPhy . . 209
9.3. X Ray eQuiPMent . . . 212
9.3.1. tubes, filters and spectra . . . 213
9.3.4. aec . . . 220
9.3.5. Magnification mammography . . . 221
9.4. iMage RecePtoRs . . . 223
9.4.1. screen film mammography . . . 223
9.4.2. Digital mammography . . . 226
9.5. DisPlay of MaMMogRaMs . . . 229
9.5.1. Display of film mammograms . . . 229
9.5.2. Display of digital mammograms . . . 229
9.6. bReast toMosynthesis . . . 231
9.7. bReast ct . . . 232
9.8. coMPuteR aiDeD Diagnosis . . . 232
9.9. steReotactic bioPsy systeMs . . . 234
9.10. RaDiation Dose. . . 235
chaPteR 10. sPecial toPics in RaDiogRaPhy . . . 241
10.1. intRoDuction . . . 241
10.2. Dental RaDiogRaPhy . . . 242
10.2.1. introduction . . . 242
10.2.2. technology . . . 242
10.2.3. Dental dosimetry . . . 245
10.3. Mobile RaDiogRaPhy anD fluoRoscoPy . . . 246
10.3.1. introduction . . . 246
10.3.2. technology . . . 246
10.3.3. image quality . . . 247
10.3.4. Radiation protection . . . 247
10.4. DXa . . . 247
10.5. conVentional toMogRaPhy anD toMosynthesis . . 251
10.5.1. Principles . . . 251
10.5.2. tomographic applications . . . 254
chaPteR 11. coMPuteD toMogRaPhy . . . 257
11.1. intRoDuction . . . 257
11.2. PRinciPles of ct . . . 257
11.2.1. X ray projection, attenuation and acquisition of transmission profiles . . . 257
11.2.2. hounsfield units . . . 259
11.3.3. the X ray tube and generator . . . 264
11.3.4. collimation and filtration . . . 264
11.3.5. Detectors . . . 264
11.4. iMage ReconstRuction anD PRocessing . . . 267
11.4.1. general concepts . . . 267
11.4.2. object space, image space and Radon space . . . 267
11.4.3. filtered backprojection and other reconstructions . . . 268
11.5. acQuisition . . . 273
11.5.1. scan projection radiograph . . . 273
11.5.2. axial ct scan . . . 274
11.5.3. helical ct scan . . . 275
11.5.4. MDct scan . . . 276
11.5.5. cardiac ct . . . 276
11.5.6. ct fluoroscopy and interventional procedures . . . 278
11.5.7. special applications . . . 279
11.6. ct iMage Quality . . . 280
11.6.1. image quality . . . 281
11.6.2. clinical observer studies . . . 284
11.6.3. effect of acquisition and reconstruction parameters on image quality . . . 285
11.6.4. artefacts . . . 287
chaPteR 12. Physics of ultRasounD . . . 291
12.1. intRoDuction . . . 291
12.2. ultRasonic Plane WaVes . . . 292
12.2.1. one dimensional ultrasonic waves . . . 292
12.2.2. acoustic pressure and intensity . . . 293
12.2.3. Reflection and transmission . . . 293
12.2.4. attenuation . . . 295
12.3. ultRasonic PRoPeRties of biological tissue . . . 296
12.3.1. sound speed, acoustic impedance and attenuation coefficient . . . 296
12.3.2. scattering . . . 296
12.3.3. non-linear propagation . . . 297
12.4. ultRasonic tRansDuction . . . 298
12.4.1. Piezoelectric devices . . . 298
12.4.2. transmitted pulse . . . 298
12.4.3. Radiation and diffraction . . . 299
12.5.2. continuous wave Doppler . . . 302
12.5.3. Pulsed wave Doppler . . . 304
12.6. biological effects of ultRasounD . . . 306
12.6.1. bioeffects mechanisms . . . 306
12.6.2. acoustic output metrics . . . 307
12.6.3. Patient safety considerations . . . 308
chaPteR 13. ultRasounD iMaging . . . 311
13.1. intRoDuction . . . 311
13.2. aRRay systeM PRinciPles . . . 311
13.2.1. electronic focusing and beam steering . . . 311
13.2.2. array beam characteristics . . . 313
13.2.3. Multifocal imaging methods . . . 317
13.3. b-MoDe instRuMentation anD signal PRocessing . . 317
13.4. MoDeRn iMaging MethoDs . . . 320
13.4.1. contrast enhanced imaging . . . 320
13.4.2. tissue harmonic imaging . . . 322
13.4.3. coded excitation imaging . . . 322
13.4.4. three and four dimensional imaging . . . 323
13.5. colouR floW iMaging . . . 324
13.5.1. flow imaging modes . . . 324
13.5.2. tissue Doppler imaging . . . 325
13.6. iMage aRtefacts anD Quality assuRance . . . 326
13.6.1. b-mode image artefacts . . . 326
13.6.2. speckle . . . 328
13.6.3. Quality assurance phantoms and methods . . . 330
chaPteR 14. Physics of Magnetic Resonance . . . 333
14.1. intRoDuction . . . 333
14.2. nMR . . . 334
14.2.1. the nucleus: spin, angular and magnetic momentum . . . 334
14.2.2. external magnetic field and magnetization . . . 335
14.2.3. excitation and detection . . . 338
14.3. RelaXation anD tissue contRast . . . 339
14.3.1. T1 and T2 relaxation . . . 339
14.3.2. bloch equations with relaxation terms . . . 341
14.4. MR sPectRoscoPy . . . 345
14.5. sPatial encoDing anD basic Pulse seQuences . . . 346
14.5.1. slice selection . . . 346
14.5.2. frequency and phase encoding . . . 347
14.5.3. field of view and spatial resolution . . . 349
14.5.4. gradient echo imaging . . . 350
14.5.5. spin echo imaging . . . 353
14.5.6. Multislice imaging . . . 355
14.5.7. 3-D imaging . . . 356
14.5.8. Measurement of relaxation time constants . . . 357
chaPteR 15. Magnetic Resonance iMaging . . . 361
15.1. intRoDuction . . . 361
15.2. haRDWaRe . . . 361
15.2.1. the static magnetic field subsystem . . . 361
15.2.2. the radiofrequency subsystem . . . 365
15.2.3. gradient coil design and specifications . . . 367
15.2.4. computer and control systems . . . 368
15.2.5. common imaging options . . . 368
15.3. basic iMage Quality issues . . . 369
15.3.1. B0 field strength, homogeneity and shimming . . . 369
15.3.2. B1 homogeneity and flip angle adjustment . . . 369
15.3.3. Phantoms, equipment assessment and coil loading . . . 370
15.3.4. snR and contrast to noise ratio . . . 371
15.3.5. spatial resolution . . . 371
15.3.6. image acquisition time . . . 372
15.4. MR iMage acQuisition anD ReconstRuction . . . 373
15.4.1. gradient echo sequences . . . 373
15.4.2. spin echo sequence . . . 373
15.4.3. fast spin echo sequence . . . 374
15.4.4. inversion recovery sequences and applications: short time inversion recovery and fluid attenuated inversion recovery . . . 374
15.4.5. common sequence options: spatial and chemical saturation techniques . . . 375
15.4.6. ultrafast imaging sequences: echo planar imaging and spiral techniques . . . 376
15.4.7. MR angiography sequences . . . 376
15.4.10. Diffusion measurements . . . 378
15.4.11. brain activation measurements . . . 380
15.4.12. Dynamic contrast enhanced MRi . . . 380
15.4.13. MR spectoscopy sequences . . . 380
15.5. aRtefacts . . . 384
15.5.1. Motion . . . 384
15.5.2. aliasing or ‘wrap around’ . . . 384
15.5.3. Metal objects . . . 384
15.5.4. chemical shift . . . 385
15.5.5. truncation . . . 385
15.5.6. system related artefacts . . . 385
15.6. safety anD bioeffects . . . 386
15.6.1. static field considerations: Projectile, effects on implants, physiological effects . . . 387
15.6.2. Rf field considerations: tissue heating, specific absorption rate, burn injuries . . . 388
15.6.3. gradient field considerations: Peripheral nerve stimulation, sound pressure levels . . . 390
15.6.4. common MR contrast agents . . . 391
chaPteR 16. Digital iMaging . . . 393
16.1. intRoDuction . . . 393
16.2. iMage encoDing anD DisPlay . . . 393
16.2.1. characteristics of digital data . . . 393
16.2.2. Display of digital images . . . 395
16.3. Digital iMage ManageMent . . . 397
16.3.1. Picture archiving and communications systems . . . 397
16.3.2. DicoM . . . 404
16.3.3. Radiology information system–hospital information system interfacing, health level 7 . . . 411
16.3.4. ihe . . . 412
16.4. netWoRking . . . 415
16.5. iMage coMPRession . . . 416
16.5.1. Purpose . . . 416
16.5.2. transformation and coding . . . 416
16.5.3. ‘lossless’ compression . . . 417
16.5.4. ‘lossy’ compression . . . 418
chaPteR 17. iMage Post-PRocessing anD analysis . . . 423
17.1. intRoDuction . . . 423
17.2. DeteRMinistic iMage PRocessing anD featuRe enhanceMent . . . 425
17.2.1. spatial filtering and noise removal . . . 425
17.2.2. edge, ridge and simple shape detection . . . 429
17.3. iMage segMentation . . . 437
17.3.1. object representation . . . 438
17.3.2. thresholding . . . 440
17.3.3. automatic tissue classification . . . 441
17.3.4. active contour segmentation methods . . . 445
17.3.5. atlas based segmentation . . . 448
17.4. iMage RegistRation . . . 449
17.4.1. transformation models . . . 450
17.4.2. Registration similarity metrics . . . 451
17.4.3. the general framework for image registration. . . 453
17.4.4. applications of image registration . . . 454
17.5. oPen souRce tools foR iMage analysis . . . 456
chaPteR 18. iMage PeRcePtion anD assessMent . . . 459
18.1. intRoDuction . . . 459
18.2. the huMan Visual systeM . . . 459
18.2.1. the human eye . . . 459
18.2.2. the barten model . . . 460
18.2.3. Perceptual linearization . . . 463
18.2.4. Viewing conditions. . . 463
18.3. sPecifications of obseRVeR PeRfoRMance . . . 464
18.3.1. Decision outcomes . . . 464
18.3.2. statistical decision theory and receiver operating characteristic methodology . . . 465
18.3.3. signal to noise ratio . . . 468
18.4. eXPeRiMental MethoDologies . . . 469
18.4.1. contrast–detail methodology . . . 469
18.4.2. forced choice experiments . . . 470
18.4.3. Roc experiments . . . 471
18.5.2. observer performance in uncorrelated gaussian noise . . . . 474
18.5.3. observer performance in correlated gaussian noise . . . 474
chaPteR 19. Quality ManageMent . . . 477
19.1. intRoDuction . . . 477
19.2. Definitions . . . 477
19.2.1. QMs . . . 478
19.2.2. Qa . . . 478
19.2.3. Qc . . . 479
19.2.4. Quality standards and good practice . . . 479
19.3. QMs ReQuiReMents . . . 479
19.3.1. general requirements . . . 480
19.3.2. the role of the medical physicist . . . 480
19.4. Qa PRogRaMMe foR eQuiPMent . . . 481
19.4.1. Multidisciplinary team . . . 482
19.4.2. structure of an equipment Qa programme . . . 482
19.4.3. outline of Qc tests . . . 487
19.4.4. specification for test equipment . . . 488
19.5. eXaMPle of a Qc PRogRaMMe . . . 488
19.5.1. Qc programme for X ray tubes and generators . . . 489
19.5.2. Qc programme for screen film radiography . . . 489
19.5.3. Qc programme for digital radiography . . . 493
19.6. Data ManageMent . . . 495
chaPteR 20. RaDiation biology . . . 499
20.1. intRoDuction . . . 499
20.1.1. Deterministic and stochastic responses . . . 499
20.1.2. Diagnostic radiology . . . 500
20.1.3. international organizations on radiation effects . . . 500
20.2. RaDiation injuRy to DeoXyRibonucleic aciD . . . 501
20.2.1. structure of deoxyribonucleic acid . . . 501
20.2.2. Radiation chemistry: Direct and indirect effects . . . 501
20.2.3. Dna damage . . . 502
20.3. Dna RePaiR . . . 503
20.4. RaDiation inDuceD chRoMosoMe DaMage anD biological DosiMetRy . . . 504
20.6.2. linear quadratic model . . . 506 20.6.3. target theory . . . 506 20.7. concePts of cell Death . . . 507 20.8. cellulaR RecoVeRy PRocesses . . . 507 20.8.1. sublethal and potentially lethal damage repair . . . 507 20.8.2. fractionation effect . . . 508 20.8.3. Dose rate effects . . . 508 20.9. RelatiVe biological effectiVeness . . . 508 20.10. caRcinogenesis (stochastic) . . . 509 20.10.1. Mechanism of multistage carcinogenesis . . . 509 20.10.2. Mechanism of mutation induction . . . 509 20.10.3. Risk models . . . 510 20.10.4. time course and latency period . . . 511 20.10.5. Dose–response relationship for cancer. . . 511 20.10.6. Dose and dose rate effectiveness factor . . . 511 20.10.7. cancer risk . . . 512 20.11. RaDiation injuRy to tissues (DeteRMinistic) . . . 514 20.11.1. tissue and organ anatomy . . . 514 20.11.2. expression and measurement of damage . . . 515 20.12. RaDiation Pathology: acute anD late effects . . . 516 20.12.1. acute and late responding normal tissues . . . 516 20.12.2. Pathogenesis of acute and late effects . . . 516 20.12.3. Radiation induced skin reaction . . . 517 20.12.4. Radiation induced cataract formation . . . 519 20.13. RaDiation genetics: RaDiation effects on
feRtility . . . 519 20.13.1. target cells for infertility . . . 519 20.13.2. Doses necessary for temporary and permanent sterility . . . 520 20.13.3. genetic effects . . . 520 20.14. fetal iRRaDiation . . . 521 20.14.1. fetal irradiation: effects versus gestational date . . . 521 20.14.2. What to do when the fetus has been exposed to radiation . . 522 chaPteR 21. instRuMentation foR DosiMetRy . . . 525 21.1. intRoDuction . . . 525 21.2. RaDiation DetectoRs anD DosiMeteRs . . . 526 21.2.1. general characteristics of radiation detectors . . . 526 21.2.2. Properties of diagnostic radiology dosimeters . . . 526
21.3.2. application hints for ionization chambers . . . 533 21.4. seMiconDuctoR DosiMeteRs . . . 535 21.4.1. theory of operation . . . 536 21.4.2. application hints for semiconductors . . . 536 21.5. otheR DosiMeteRs . . . 537 21.5.1. film dosimetry: Radiographic film and radiochromic film . 537 21.5.2. thermoluminescent dosimetry . . . 538 21.5.3. osl . . . 541 21.5.4. Dosimetric applications of tlD and osl . . . 542 21.6. DosiMeteR calibRation . . . 542 21.6.1. standard free air ionization chamber . . . 543 21.6.2. ssDl calibration . . . 543 21.6.3. field calibration . . . 545 21.7. instRuMents foR MeasuRing tube Voltage
anD tiMe . . . 546 21.8. instRuMents foR occuPational anD Public
eXPosuRe MeasuReMents . . . 548 chaPteR 22. Patient DosiMetRy . . . 551 22.1. intRoDuction . . . 551 22.2. aPPlication sPecific Quantities . . . 552 22.2.1. iak . . . 552 22.2.2. entrance surface air kerma . . . 553 22.2.3. X ray tube output . . . 554 22.2.4. kaP . . . 554 22.2.5. air kerma–length product . . . 555 22.2.6. Quantities for ct dosimetry . . . 555 22.3. Risk RelateD Quantities . . . 558 22.3.1. organ and tissue dose . . . 559 22.3.2. MgD . . . 559 22.3.3. equivalent dose . . . 560 22.3.4. effective dose . . . 560 22.4. MeasuRing aPPlication sPecific Quantities. . . 561 22.4.1. general considerations . . . 561 22.4.2. Measurements using phantoms and patients . . . 563 22.4.3. free-in-air measurements . . . 564 22.4.4. Radiography . . . 566
22.4.8. Dental radiography . . . 572 22.5. estiMating Risk RelateD Quantities . . . 572 22.5.1. Determination of organ dose conversion coefficients . . . 573 22.5.2. backscatter factors . . . 576 22.5.3. use of data . . . 576 22.6. Dose ManageMent . . . 582 22.6.1. Population based dose surveys . . . 582 22.6.2. DRls . . . 583 22.6.3. local dose audit . . . 586 chaPteR 23. justification anD oPtiMiZation in
clinical PRactice . . . 589 23.1. intRoDuction . . . 589 23.2. justification . . . 590 23.2.1. Referral guidelines for imaging . . . 591 23.2.2. sensitive populations . . . 592 23.2.3. high skin dose examinations . . . 593 23.2.4. Population screening . . . 593 23.2.5. informed consent . . . 593 23.3. oPtiMiZation . . . 594 23.3.1. equipment, guidelines and image criteria . . . 596 23.3.2. good practice . . . 597 23.3.3. optimization — two practical examples . . . 604 23.4. clinical auDit . . . 607 23.4.1. objectives . . . 607 23.4.2. coverage of radiological practices . . . 609 23.4.3. standards of good practice . . . 610 23.4.4. Relationship with other quality assessment and
regulatory control . . . 611 23.4.5. Methods and practical organization . . . 611 23.4.6. Role of the medical physicist . . . 612 chaPteR 24. RaDiation PRotection . . . 615 24.1. intRoDuction . . . 615 24.2. the icRP systeM of RaDiological PRotection . . . 615 24.2.1. situations, types and categories of exposure . . . 616 24.2.2. basic framework for radiation protection . . . 617
24.3.1. introduction . . . 619 24.3.2. Responsibilities . . . 619 24.3.3. Responsibilities of the licensee and employer . . . 620 24.3.4. Responsibilities of other parties . . . 621 24.3.5. Radiation protection programme . . . 622 24.3.6. education and training . . . 623 24.4. MeDical eXPosuRes . . . 623 24.4.1. introduction . . . 623 24.4.2. DRls . . . 624 24.4.3. Quality assurance for medical exposures . . . 625 24.4.4. examination of pregnant women . . . 625 24.4.5. examination of children . . . 626 24.4.6. helping in the care, support or comfort of patients . . . 626 24.4.7. biomedical research . . . 627 24.4.8. unintended and accidental medical exposures . . . 627 24.5. occuPational eXPosuRe . . . 627 24.5.1. control of occupational exposure . . . 628 24.5.2. operational quantities used in area and personal dose
monitoring . . . 628 24.5.3. Monitoring occupational dose . . . 629 24.5.4. occupational dose limits . . . 631 24.5.5. Pregnant workers . . . 632 24.5.6. accidental and unintended exposure . . . 632 24.5.7. Records . . . 632 24.5.8. Methods of reducing occupational exposure . . . 633 24.6. Public eXPosuRe in RaDiology PRactices . . . 636 24.6.1. access control . . . 636 24.6.2. Monitoring of public exposure . . . 636 24.6.3. Dose limits . . . 637 24.7. shielDing . . . 637 24.7.1. Dose and shielding . . . 637 24.7.2. Primary and secondary radiations . . . 638 24.7.3. Distance to barriers . . . 638 24.7.4. shielding terminology . . . 638 24.7.5. basic shielding equation . . . 639 24.7.6. Workload . . . 639 24.7.7. Design criteria and dose constraints . . . 640 24.7.8. occupancy . . . 641
24.7.12. construction principles . . . 659 24.7.13. Room surveys . . . 661 aPPenDiX: anatoMical noMenclatuRe . . . 667 abbReViations . . . 669 syMbols . . . 675 contRibutoRs to DRafting anD ReVieW . . . 681
FUNDAMENTALS OF ATOMIC AND NUCLEAR PHYSICS
k.-h. ng
university of Malaya, kuala lumpur, Malaysia D.R. Dance
Royal surrey county hospital, guildford, united kingdom
1.1. intRoDuction
knowledge of the structure of the atom, elementary nuclear physics, the nature of electromagnetic radiation and the production of X rays is fundamental to the understanding of the physics of medical imaging and radiation protection.
this, the first chapter of the handbook, summarizes those aspects of these areas which, being part of the foundation of modern physics, underpin the remainder of the book.
1.2. classification of RaDiation
Radiation may be classified as electromagnetic or particulate, with electromagnetic radiation including visible light, infrared and ultraviolet, X rays and gamma rays (fig. 1.1), and particulate radiation including electrons, positrons, protons and neutrons.
1.2.1. Electromagnetic radiation
electromagnetic waves can, like all waves, be characterized by their amplitude, wavelength (λ), frequency (ν) and speed. the amplitude is the intensity of the wave. the wavelength is the distance between identical points on adjacent cycles. the frequency is the number of complete wave oscillations per unit time. the speed of the wave is equal to the product of the frequency and the wavelength, and its magnitude depends upon the nature of the material through which the wave travels and the frequency of the radiation. in a vacuum, however,
the speed for all electromagnetic waves is a constant, usually denoted by c, and in which case:
c = λν (1.1) for X rays, wavelength is usually expressed in nanometres (nm) (1 nm = 10–9 m) and frequency is expressed in hertz (hz) (1 hz = 1 cycle/s = 1 s–1).
When interactions with matter are considered, electromagnetic radiation is generally treated as series of individual particles, known as photons. the energy of each photon is given by:
E = hν (1.2) where the constant h is known as Planck’s constant. in diagnostic radiology, the photon energy is usually expressed in units of keV, where 1 electronvolt (eV) is the energy received by an electron when it is accelerated across of a potential difference of 1 V.
1.2.2. Particulate radiation
in diagnostic radiology, the only particulate radiation that needs to be considered is the electron. this has a rest mass of 9.109 × 10–31 kg and a rest
FIG. 1.1. The electromagnetic spectrum. MRI: magnetic resonance imaging.
1.2.3. Ionizing and non-ionizing radiations
Radiation is classified as ionizing or non-ionizing, depending on its ability to ionize matter:
● non-ionizing radiation cannot ionize matter.
● ionizing radiation can ionize matter, either directly or indirectly:
—Directly ionizing radiation: fast charged particles that deposit their energy in matter directly, through many small coulomb (electrostatic) interactions with orbital electrons along the particle track.
—Indirectly ionizing radiation: X or gamma ray photons or neutrons that first transfer their energy to fast charged particles released in one or a few interactions in the matter through which they pass. the resulting fast charged particles then deposit their energy directly in the matter.
the minimum energy required to ionize an atom, i.e. to remove an electron, is known as the ionization potential. for elements, its magnitude ranges from a few electronvolts for alkali metals to 24.5 eV for helium. for water, it is 12.6 eV.
electromagnetic radiation of frequency higher than the near-ultraviolet region of the electromagnetic spectrum is ionizing, whereas electromagnetic radiation with energy below the far-ultraviolet region (e.g. visible light, infrared and radiofrequency) is non-ionizing.
1.3. atoMic anD nucleaR stRuctuRe 1.3.1. Basic definitions
the atom is composed of a central nucleus surrounded by a cloud of negatively charged electrons. Most of the mass of the atom is concentrated in the atomic nucleus, which consists of Z protons and (A minus Z) neutrons, where Z is known as the atomic number and A the atomic mass number of the nucleus. the proton and neutron have nearly identical rest masses; the proton has a positive charge identical in magnitude to the negative electron charge, and the neutron has no charge. in a non-ionized atom, the number of electrons and number of protons are equal. the radius of an atom is about 0.1 nm, whereas the radius of the nucleus is much smaller, about 10–5 nm.
Protons and neutrons are commonly referred to as nucleons; they have identical strong attractive interactions, and are bound in the nucleus with the strong force. in contrast to electrostatic and gravitational forces that are inversely proportional to the square of the distance between two particles, the strong force
between two nucleons is a very short range force, active only at distances of the order of a few femtometres. At these short distances, the strong force is the predominant force, exceeding other forces by several orders of magnitude.
Some basic definitions and descriptions are as follows:
● Atomic number Z: number of protons and number of electrons in an atom.
● Atomic mass number A: number of protons Z plus number of neutrons N in an atom (A = Z + N).
There is no basic relation between A and Z, but the empirical relationship 1.98 0.0155 2/3
Z A
= A
+ (1.3)
furnishes a good approximation for stable nuclei.
● A nucleus X with atomic mass number A and atomic number Z is denoted
AX
Z ; for example, an isotope of cobalt with 60 nucleons is abbreviated 6027Co, the 226Ra nucleus as 22688Ra.
● An element may be composed of atoms that all have the same number of protons, but have different numbers of neutrons, i.e. have different atomic mass numbers A. Atoms of identical atomic number Z but differing atomic mass numbers A are called isotopes of a given element.
● Unified atomic mass unit μ: A unit used for specifying the masses of atoms.
It is equal to 1/12 of the mass of the 12C atom or 931.5 MeV/c2.
● Atomic weight Ar: A dimensionless physical quantity, the ratio of the average mass of the atoms of an element to the unified atomic mass unit.
The average is a weighted mean over all the isotopes of the particular element, taking account of their relative abundance.
● Atomic mass M: Expressed in unified atomic mass units. The atomic mass M is for a particular isotope and is smaller than the sum of the individual masses of constituent particles because of the intrinsic energy associated with binding the particles (nucleons) within the nucleus.
● Atomic g-atom (gram-atom): Number of grams that correspond to NA atoms of an element, where NA is Avogadro’s constant (6.022 × 1023 atoms/g-atom). The above definition of atomic weight means that Ar g of each element contains exactly NA atoms. It follows that:
— Number of atoms, Nam, per unit mass of an element:
NA
N = (1.4)
— number of electrons, ZNam, per unit mass of an element:
am A
r
ZN Z N
=A (1.5)
— number of electrons, ZNaV, per unit volume of an element:
aV am A
r
ZN ZN ZN
ρ ρ A
= = (1.6)
where ρ is the density of the element.
● note that Z/Ar ≈ 0.5 for all elements, with the exception of hydrogen, for which Z/Ar = 1. actually, (Z/Ar) slowly decreases from 0.5 for low Z elements to 0.4 for high Z elements.
● if we assume that the mass of a molecule is equal to the sum of the masses of the atoms that make up the molecule, then for any molecular compound there are Na molecules per g-mole of the compound, where the g-mole (gram-mole or mole) in grams is defined as the sum of the atomic weights of the atoms making up the molecule.
1.3.2. Atomic structure
the modern quantum mechanical model of the atom is built on the work of many physicists. the idea of a dense central nucleus surrounded by orbiting electrons was first proposed by Rutherford in 1911. his model, however, being based on classical physics, had a number of unsatisfactory features. for example, it could not explain the observed emission spectra of the elements. bohr elaborated Rutherford’s atomic model in 1913, based on classical, non-relativistic mechanics, by adding the concept of angular momentum quantization. his model is based on four postulates:
(i) electrons revolve about the Rutherford nucleus in well defined, allowed orbits (shells), the central attractive coulomb force of attraction between the electrons and the positively charged nucleus being balanced by the centripetal force arising from the orbital motion.
(ii) While in orbit, the electron does not lose any energy in spite of being constantly accelerated (this postulate is in contravention of classical physics, which predicts that an accelerated charged particle will lose energy in the form of radiation).
(iii) the angular momentum of the electron in an allowed orbit is quantized and only takes values of nћ, where n is an integer and ћ = h/(2π), where h is Planck’s constant.
(iv) an atom or ion emits radiation when an electron makes a transition from an initial orbit with quantum number ni to a final orbit with quantum number nf for ni > nf.
While the work of bohr was a major breakthrough, successfully explaining aspects of the behaviour of the hydrogen atom, the singly ionized helium atom and the doubly ionized lithium atom, etc., the story did not stop there. through the work of heisenberg, schrödinger, Dirac, Pauli and others, the theory of quantum mechanics was developed. in this theory, the electrons occupy individual energy states defined by four quantum numbers, as follows:
● the principal quantum number, n, which can take integer values and specifies the main energy shell;
● the azimuthal quantum number, l, which can take integer values between 0 and n–1, and which specifies the total rotational angular momentum for the electron;
● the magnetic quantum number, m, which can take integer values between –l and +l and which specifies a component of the angular momentum;
● the spin quantum number, s, which takes values –½ or +½ and specifies a component of the spin angular momentum of the electron.
according to the Pauli exclusion principle, no two electrons can occupy the same state and it follows that the number of electron states that can share the same principal quantum number, n, is equal to 2n2.
the energy levels associated with these four quantum numbers can be understood using energy level diagrams such as those shown in fig. 1.2 for hydrogen and tungsten. in these diagrams, each value of the principal quantum number above n = 1 gives rise to a band (or shell) of states of similar energies (shown as a single energy for simplicity). the energy levels associated with the various electron orbits (not drawn to scale) increase with Z and decrease with quantum number n and the average distance from the nucleus. the outer electronic shell (valence shell) determines the chemical properties of the element.
the energy bands associated with n = 1, 2, 3, etc., are known as the k, l, M, etc., bands. the structure of each band arises from small differences in energy associated with both the l and s quantum numbers.
1.4. X Rays
1.4.1. The production of characteristic X rays and Auger electrons
When charged particles pass through matter, they interact with the atomic electrons and lose energy through the processes of excitation and ionization.
ionization can also be produced as photons pass through matter by interactions such as the photoelectric effect (see section 2.2.1) and incoherent scattering (see section 2.2.6). excitation occurs when there is a transfer of some of the incident particle’s energy to electrons in the absorbing material, displacing them to shells further from the nucleus (i.e. to higher energy levels) and leaving a vacancy in the original shell. if the transferred energy exceeds the binding energy of the electron, ionization occurs, resulting in the electron being ejected from the atom.
an ion pair, consisting of the ejected electron and the ionized, positively charged atom, is then formed.
While the smallest binding energies (ionization potentials, see section 1.2.3) for electrons in carbon, nitrogen and oxygen are 11.3, 14.5 and 13.6 eV, respectively, the average energy required to produce an ion pair in dry air (mostly nitrogen and oxygen) is 33.97 eV. the energy difference (approximately 24 eV) is the result of the excitation process.
Whenever a vacancy is created in an inner electronic shell, whether by excitation or ionization, it is filled by an electron from a more distant (outer) shell. this results in a vacancy in this second outer shell, which is then filled by an electron (if available) from an even more distant outer shell, and the whole FIG. 1.2. Energy levels for hydrogen and tungsten. Possible transitions between the various energy levels are shown with arrows.
process repeats, producing a cascade of transitions. the energy released in each transition is carried away by the emission of electromagnetic radiation or by an electron ejected from another outer shell, known as an auger electron. Depending on the atomic number of the material, and the electronic shells involved, the electromagnetic radiation may be in the visible, ultraviolet or X ray portions of the spectrum. the energy of this radiation is characteristic of the particular atom, since it is equal to the difference in the electron binding energies of the initial and final states for the particular transition, which depends on atomic number. X rays thus emitted are known as characteristic or fluorescent X rays. a naming convention is used in accord with the shell in which the vacancy occurred. X rays emitted in association with an electron transition to the k shell are known as k characteristic X rays, and X rays resulting from an electron transition to the l shell are known as l characteristic X rays, and so forth. subscripts are used to denote the shell from which the vacancy is filled. the subscript a is used to denote radiation emitted for a transition between neighbouring shells and subscript b to denote radiation emitted for a transition between non-neighbouring shells. hence, a kα X ray is emitted for a transition between l and k shells and a kβ X ray for a transition between M or n and k shells (fig. 1.3). further subscripts are used as necessary to indicate which subshells are involved in the transition. the lines kα1, kα2,kβ1 and kβ2 are visible in the X ray spectrum shown in fig. 5.2 from a tungsten target X ray tube. for X ray spectra from a molybdenum target, however, the energies of the subshells are closer together and the splitting of the kα and kβ lines is often not resolved (see the molybdenum spectrum shown in fig. 9.7).
as noted above, the energy carried away is the difference in binding energies between the initial and final states. for example, for tungsten, the energies of the kα and kβ X rays are given by:
E(kα1) = Eliii – Ek = –10.2 – (–69.5) = 59.3 keV (1.7) E(kα2) = Eli – Ek = –11.5 – (–69.5) = 58.0 keV (1.8) E(kβ1) = EMiii – Ek = –2.3 – (–69.5) = 67.2 keV (1.9) E(kβ2) = Eniii – Ek = –0.4 – (–69.5) = 69.1 keV (1.10) When an auger electron carries away the energy difference between the initial and final states, a further vacancy is created in an outer shell. for example, if the initial transition is from an M to a k shell, and the auger electron is also emitted from the M shell, there will be two resultant vacancies in the M shell. the kinetic energy of the auger electron is thus determined by the difference between
energies associated with the two vacancies that are created. for example, for the transition just described for a tungsten target, the energy of the auger electron is given by:
E(auger) = Ek – EM – EM = – [(–69.5) – (–2.3) – (–2.3)] = 64.9 keV (1.11) for a molybdenum target, the equivalent energy balance for the emission of an auger electron is shown in fig. 1.3.
FIG. 1.3. Transition of an electron in the M shell of molybdenum to fill a vacancy in the K shell followed by the emission of (a) a Kβ characteristic X ray and (b) an Auger electron.
When considering energy deposition in matter following the creation and subsequent filling of a vacancy, it is important to know whether a fluorescent X ray or an auger electron is emitted. the probability of emission of a fluorescent X ray is known as the fluorescent yield, ω. since either a fluorescent X ray or an auger electron must be emitted, the probability of emitting an auger electron is 1 – ω. auger electron emission is more important for materials of low atomic number and for transitions amongst outer shells. the k fluorescence yield is close to zero for materials of low atomic number, but increases with increasing atomic number and, for example, is 0.007, 0.17, 0.60 and 0.93 for oxygen, calcium, selenium and gadolinium, respectively.
1.4.2. Radiation from an accelerated charge, bremsstrahlung
Most of the interactions that fast electrons have as they pass through matter are with the atomic electrons. they can, however, also have inelastic interactions with atomic nuclei. in such interactions, the electron path will be deflected and
energy transferred to a photon, which is emitted. because the photon is emitted in association with a slowing down of the electron, it is known as bremsstrahlung, which means ‘brake radiation’ in german (see sections 2.4 and 5.2). the energy of the emitted photon can take any value from zero up to the energy of the initial electron, so that the passage of a beam of electrons though matter is accompanied by the emission of a spectrum of photons covering this energy range. bremsstrahlung photons are the major component of the X ray spectrum emitted by X ray tubes (see chapter 5).
the probability of bremsstrahlung emission is proportional to the value of Z2 and is thus higher for higher atomic number materials such as tungsten (Z = 74). however, even for this material, the efficiency of bremsstrahlung production is less than 1% for 100 keV electrons. the angle of emission of the bremsstrahlung photons depends upon the electron energy. for electron energies much greater than the rest mass of the electron, the angular distribution is peaked in the forward direction, but as the electron energy decreases, the position of the peak moves so that it is at an angle to the forward direction. When the electron energy is low, the radiation is mainly emitted between 60° and 90° to the forward direction.
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