Introduction
History
Present State
Future Direction
Physics of Radiography
Nature of Radiation
X-Radiation
Gamma Radiation
Activity
Decay Rate
-Carbon 14 Dating
Ionization
Inverse Square Law
Interaction of Radiation and Matter
Linear Attenuation Coefficient
Half-Value Layer
Sources of Attenuation
-Compton Scattering
Geometry Unsharpness
Filters in Radiography
Scatter/Radiation Control
Radiation Safety
Equipment & Materials
X-ray Sources
Radio Isotope Sources
Radiographic Film
Exposure Vaults
Techniques & Calibrations
Imaging Consideration
Contrast
Definition
Radiographic Density
Film Characteristic Curves
Exposure Calculations
Controlling Quality
Film Processing
Viewing Radiographs
Radiograph Interp - Welds
Radiograph Interp - Castings
Advanced Techniques
Real-time Radiography
Computed Tomography
XRSIM
History of Radiography
X-rays were discovered in 1895 by Wilhelm Conrad Roentgen (1845-1923) who was a Professor at Wuerzburg University in Germany. Working with a cathode-ray tube in his laboratory, Roentgen observed a fluorescent glow of crystals on a table near his tube. The tube that Roentgen was working with consisted of a glass envelope (bulb) with positive and negative electrodes encapsulated in it. The air in the tube was evacuated, and when a high voltage was applied, the tube produced a fluorescent glow. Roentgen shielded the tube with heavy black paper, and discovered a green colored fluorescent light generated by a material located a few feet away from the tube.
He concluded that a new type of ray was being emitted from the tube. This ray was capable of passing through the heavy paper covering and exciting the phosphorescent materials in the room. He found that the new ray could pass through most substances casting shadows of solid objects. Roentgen also discovered that the ray could pass through the tissue of humans, but not bones and metal objects. One of Roentgen's first experiments late in 1895 was a film of the hand of his wife, Bertha. It is interesting that the first use of X-rays were for an industrial (not medical) application, as Roentgen produced a radiograph of a set of weights in a box to show his colleagues.
Roentgen's discovery was a scientific bombshell, and was received with extraordinary interest by both scientist and laymen. Scientists everywhere could duplicate his experiment because the cathode tube was very well known during this period. Many scientists dropped other lines of research to pursue the mysterious rays. Newspapers and magazines of the day provided the public with numerous stories, some true, others fanciful, about the properties of the newly discovered rays.
Public fancy was caught by this invisible ray with the ability to pass through solid matter, and, in conjunction with a photographic plate, provide a picture of bones and interior body parts. Scientific fancy was captured by the demonstration of a wavelength shorter than light. This generated new possibilities in physics, and for investigating the structure of matter. Much enthusiasm was generated about potential applications of rays as an aid in medicine and surgery. Within a month after the announcement of the discovery, several medical radiographs had been made in Europe and the United States, which were used by surgeons to guide them in their work. In June 1896, only 6 months after Roentgen announced his discovery, X-rays were being used by battlefield physicians to locate bullets in wounded soldiers.
Prior to 1912, X-rays were used little outside the realms of medicine and dentistry, though some X-ray pictures of metals were produced. The reason that X-rays were not used in industrial application before this date was because the X-ray tubes (the source of the X-rays) broke down under the voltages required to produce rays of satisfactory penetrating power for industrial purposes. However, that changed in 1913 when the high vacuum X-ray tubes designed by Coolidge became available. The high vacuum tubes were an intense and reliable X-ray source, operating at energies up to 100,000 volts.
In 1922, industrial radiography took another step forward with the advent of the 200,000-volt X-ray tube that allowed radiographs of thick steel parts to be produced in a reasonable amount of time. In 1931, General Electric Company developed 1,000,000 volt X-ray generators, providing an effective tool for industrial radiography. That same year, the American Society of Mechanical Engineers (ASME) permitted X-ray approval of fusion welded pressure vessels that further opened the door to industrial acceptance and use.
A Second Source of Radiation
Shortly after the discovery of X-rays, another form of penetrating rays was discovered. In 1896, French scientist Henri Becquerel discovered natural radioactivity. Many scientists of the period were working with cathode rays, and other scientists were gathering evidence on the theory that the atom could be subdivided. Some of the new research showed that certain types of atoms disintegrate by themselves. It was Henri Becquerel who discovered this phenomenon while investigating the properties of fluorescent minerals. Becquerel was researching the principles of fluorescence, wherein certain minerals glow (fluoresce) when exposed to sunlight. He utilized photographic plates to record this fluorescence.
One of the minerals Becquerel worked with was a uranium compound. On a day when it was too cloudy to expose his samples to direct sunlight, Becquerel stored some of the compound in a drawer with his photographic plates. Later when he developed these plates, he discovered that they were fogged (exhibited exposure to light). Becquerel questioned what would have caused this fogging. He knew he had wrapped the plates tightly before using them, so the fogging was not due to stray light. In addition, he noticed that only the plates that were in the drawer with the uranium compound were fogged. Becquerel concluded that the uranium compound gave off a type of radiation that could penetrate heavy paper and expose photographic film. Becquerel continued to test samples of uranium compounds and determined that the source of radiation was the element uranium. Bacquerel's discovery was, unlike that of the X-rays, virtually unnoticed by laymen and scientists alike. Relatively few scientists were interested in Becquerel's findings. It was not until the discovery of radium by the Curies two years later that interest in radioactivity became widespread.
While working in France at the time of Becquerel's discovery, Polish scientist Marie Curie became very interested in his work. She suspected that a uranium ore known as pitchblende contained other radioactive elements. Marie and her husband, French scientist Pierre Curie, started looking for these other elements. In 1898, the Curies discovered another radioactive element in pitchblende, and named it 'polonium' in honor of Marie Curie's native homeland. Later that year, the Curies discovered another radioactive element which they named radium, or shining element. Both polonium and radium were more radioactive than uranium. Since these discoveries, many other radioactive elements have been discovered or produced.
Radium became the initial industrial gamma ray source. The material allowed castings up to 10 to 12 inches thick to be radiographed. During World War II, industrial radiography grew tremendously as part of the Navy's shipbuilding program. In 1946, man-made gamma ray sources such as cobalt and iridium became available. These new sources were far stronger than radium and were much less expensive. The manmade sources rapidly replaced radium, and use of gamma rays grew quickly in industrial radiography.
Health Concerns
The science of radiation protection, or "health physics" as it is more properly called, grew out of the parallel discoveries of X-rays and radioactivity in the closing years of the 19th century. Experimenters, physicians, laymen, and physicists alike set up X-ray generating apparatuses and proceeded about their labors with a lack of concern regarding potential dangers. Such a lack of concern is quite understandable, for there was nothing in previous experience to suggest that X-rays would in any way be hazardous. Indeed, the opposite was the case, for who would suspect that a ray similar to light but unseen, unfelt, or otherwise undetectable by the senses would be damaging to a person? More likely, or so it seemed to some, X-rays could be beneficial for the body.
Inevitably, the widespread and unrestrained use of X-rays led to serious injuries. Often injuries were not attributed to X-ray exposure, in part because of the slow onset of symptoms, and because there was simply no reason to suspect X-rays as the cause. Some early experimenters did tie X-ray exposure and skin burns together. The first warning of possible adverse effects of X-rays came from Thomas Edison, William J. Morton, and Nikola Tesla who each reported eye irritations from experimentation with X-rays and fluorescent substances.
Today, it can be said that radiation ranks among the most thoroughly investigated causes of disease. Although much still remains to be learned, more is known about the mechanisms of radiation damage on the molecular, cellular, and organ system than is known for most other health stressing agents. Indeed, it is precisely this vast accumulation of quantitative dose-response data that enables health physicists to specify radiation levels so that medical, scientific, and industrial uses of radiation may continue at levels of risk no greater than, and frequently less than, the levels of risk associated with any other technology.
X-rays and Gamma rays are electromagnetic radiation of exactly the same nature as light, but of much shorter wavelength. Wavelength of visible light is on the order of 6000 angstroms while the wavelength of x-rays is in the range of one angstrom and that of gamma rays is 0.0001 angstrom. This very short wavelength is what gives x-rays and gamma rays their power to penetrate materials that light cannot. These electromagnetic waves are of a high energy level and can break chemical bonds in materials they penetrate. If the irradiated matter is living tissue, the breaking of chemical bonds may result in altered structure or a change in the function of cells. Early exposures to radiation resulted in the loss of limbs and even lives. Men and women researchers collected and documented information on the interaction of radiation and the human body. This early information helped science understand how electromagnetic radiation interacts with living tissue. Unfortunately, much of this information was collected at great personal expense.
Present State of Radiography
In many ways, radiography has changed little from the early days of its use. We still capture a shadow image on film using similar procedures and processes technicians were using in the late 1800's. Today, however, we are able to generate images of higher quality and greater sensitivity through the use of higher quality films with a larger variety of film grain sizes. Film processing has evolved to an automated state, producing more consistent film quality by removing manual processing variables. Electronics and computers allow technicians to now capture images digitally. The use of "filmless radiography" provides a means of capturing an image, digitally enhancing, sending the image anywhere in the world, and archiving an image that will not deteriorate with time. Technological advances have provided industry with smaller, lighter, and very portable equipment that produce high quality X-rays. The use of linear accelerators provide a means of generating extremely short wavelength, highly penetrating radiation, a concept dreamed of only a few short years ago.
While the process has changed little, technology has evolved allowing radiography to be widely used in numerous areas of inspection. Radiography has seen expanded usage in industry to inspect not only welds and castings, but to radiographically inspect items such as airbags and canned food products. Radiography has found use in metallurgical material identification and security systems at airports and other facilities.
Gamma ray inspection has also changed considerably since the Curies' discovery of radium. Man-made isotopes of today are far stronger and offer the technician a wide range of energy levels and half-lives. The technician can select Co-60 which will effectively penetrate very thick materials, or select a lower energy isotope, such as Tm-170, which can be used to inspect plastics and very thin or low density materials. Today gamma rays find wide application in industries such as petrochemical, casting, welding, and aerospace.
Addressing Health Concerns
It was in the Manhattan District of US Army Corps of Engineers that the name "health physics" was born, and great advances were made in radiation safety. From the onset, the leaders of the Manhattan District recognized that a new and intense source of radiation and radioactivity would be created. In the summer of 1942, the leaders asked Ernest O. Wollan, a cosmic ray physicist at the University of Chicago, to form a group to study and control radiation hazards. Thus, Wollan was the first to bear the title of health physicist. He was soon joined by Carl G. Gamertsfelder, recently graduated physics baccalaureate, and Herbert M. Parker, the noted British-American medical physicist. By mid 1943, six others had been added. These six include Karl Z. Morgan, James C. Hart, Robert R. Coveyou, O.G. Landsverk, L.A. Pardue, and John E. Rose.
Within the Manhattan District, the name "health physicist" seems to have been derived in part from the need for secrecy (and hence a code name for radiation protection activities) and the fact that it was a group of mostly physicists working on health related problems. Activities included developing appropriate monitoring instruments, physical controls, administrative procedures, monitoring radiation areas, personnel monitoring, and radioactive waste disposal. It was in the Manhattan District that many of the modern concepts of protection were born, including the rem unit, which took into account the biological effectiveness of the radiation. It was in the Manhattan District that radiation protection concepts realized maturity and enforceability.
Future Direction of Radiographic Education
Although many of the methods and techniques developed over a century ago remain in use, computers are slowly becoming a part of radiographic inspection. The future of radiography will likely see many changes. As noted earlier, companies are performing many inspections without the aid of film.
Radiographers of the future will capture images in digitized form and e-mail them to the customer when the inspection has been completed. Film evaluation will likely be left to computers. Inspectors may capture a digitized image, feed them into a computer and wait for a printout of the image with an accept/reject report. Systems will be able to scan a part and present a three-dimensional image to the radiographer, helping him or her to locate the defect within the part.
Inspectors in the future will be able to peal away layer after layer of a part to evaluate the material in much greater detail. Color images, much like computer generated ultrasonic C-scans of today, will make interpretation of indications much more reliable and less time consuming.
Educational techniques and materials will need to be revised and updated to keep pace with technology and meet the requirements of industry. These needs may well be met with computers. Computer programs can simulate radiographic inspections using a computer aided design (CAD) model of a part to produce physically accurate simulated x-ray radiographic images. Programs allow the operator to select different parts to inspect, adjust the placement and orientation of the part to obtain the proper equipment/part relationships, and adjust all the usual x-ray generator settings to arrive at the desired radiographic film exposure.
Computer simulation will likely have its greatest impact in the classroom, allowing the student to see results in almost real-time. Simulators and computers may well become the primary tool for instructors as well as students in the technical classroom.
Nature of Penetrating Radiation
The Electromagnetic Spectrum
X-rays and gamma rays differ only in their source of origin. X-rays are produced by an x-ray generator and gamma radiation is the product of radioactive atoms. They are both part of the electromagnetic spectrum. They are waveforms, as are light rays, microwaves, and radio waves. X-rays and gamma rays cannot been seen, felt, or heard. They possess no charge and no mass and, therefore, are not influenced by electrical and magnetic fields and will generally travel in straight lines. However, they can be diffracted (bent) in a manner similar to light.
Both X-rays and gamma rays can be characterized by frequency, wavelength, and velocity. However, they act somewhat like a particle at times in that they occur as small "packets" of energy and are referred to as "photons." Due to their short wavelength they have more energy to pass through matter than do the other forms of energy in the electromagnetic spectrum. As they pass through matter, they are scattered and absorbed and the degree of penetration depends on the kind of matter and the energy of the rays.
Properties of X-Rays and Gamma Rays
- They are not detected by human senses (cannot be seen, heard, felt, etc.).
- They travel in straight lines at the speed of light.
- Their paths cannot be changed by electrical or magnetic fields.
- They can be diffracted to a small degree at interfaces between two different materials.
- They pass through matter until they have a chance encounter with an atomic particle.
- Their degree of penetration depends on their energy and the matter they are traveling through.
- They have enough energy to ionize matter and can damage or destroy living cells.
X-Radiation
X-rays are just like any other kind of electromagnetic radiation. They can be produced in parcels of energy called photons, just like light. There are two different atomic processes that can produce X-ray photons. One is called Bremsstrahlung and is a German term meaning "braking radiation." The other is called K-shell emission. They can both occur in the heavy atoms of tungsten. Tungsten is often the material chosen for the target or anode of the x-ray tube.
Both ways of making X-rays involve a change in the state of electrons. However, Bremsstrahlung is easier to understand using the classical idea that radiation is emitted when the velocity of the electron shot at the tungsten changes. The negatively charged electron slows down after swinging around the nucleus of a positively charged tungsten atom. This energy loss produces X-radiation. Electrons are scattered elastically and inelastically by the positively charged nucleus. The inelastically scattered electron loses energy, which appears as Bremsstrahlung. Elastically scattered electrons (which include backscattered electrons) are generally scattered through larger angles. In the interaction, many photons of different wavelengths are produced, but none of the photons have more energy than the electron had to begin with. After emitting the spectrum of X-ray radiation, the original electron is slowed down or stopped.
Bremsstrahlung Radiation
X-ray tubes produce x-ray photons by accelerating a stream of electrons to energies of several hundred kilovolts with velocities of several hundred kilometers per hour and colliding them into a heavy target material. The abrupt acceleration of the charged particles (electrons) produces Bremsstrahlung photons. X-ray radiation with a continuous spectrum of energies is produced with a range from a few keV to a maximum of the energy of the electron beam. Target materials for industrial tubes are typically tungsten, which means that the wave functions of the bound tungsten electrons are required. The inherent filtration of an X-ray tube must be computed, which is controlled by the amount that the electron penetrates into the surface of the target and by the type of vacuum window present.
The bremsstrahlung photons generated within the target material are attenuated as they pass through typically 50 microns of target material. The beam is further attenuated by the aluminum or beryllium vacuum window. The results are an elimination of the low energy photons, 1 keV through l5 keV, and a significant reduction in the portion of the spectrum from 15 keV through 50 keV. The spectrum from an x-ray tube is further modified by the filtration caused by the selection of filters used in the setup.
The applet below allows the user to visualize an electron accelerating and interacting with a heavy target material. The graph keeps a record of the bremsstrahlung photons numbers as a function of energy. After a few events, the "building up" of the graph may be accomplished by pressing the "automate" button.
K-shell Emission Radiation
Remember that atoms have their electrons arranged in closed "shells" of different energies. The K-shell is the lowest energy state of an atom. An incoming electron can give a K-shell electron enough energy to knock it out of its energy state. About 0.1% of the electrons produce K-shell vacancies; most produce heat. Then, a tungsten electron of higher energy (from an outer shell) can fall into the K-shell. The energy lost by the falling electron shows up in an emitted x-ray photon. Meanwhile, higher energy electrons fall into the vacated energy state in the outer shell, and so on. K-shell emission produces higher-intensity x-rays than Bremsstrahlung, and the x-ray photon comes out at a single wavelength.
When outer-shell electrons drop into inner shells, they emit a quantized photon "characteristic" of the element. The energies of the characteristic X-rays produced are only very weakly dependent on the chemical structure in which the atom is bound, indicating that the non-bonding shells of atoms are the X-ray source. The resulting characteristic spectrum is superimposed on the continuum as shown in the graphs below. An atom remains ionized for a very short time (about 1014 second) and thus an atom can be repeatedly ionized by the incident electrons which arrive about every 1012 second.
Gamma Radiation
Gamma radiation is one of the three types of natural radioactivity. Gamma rays are electromagnetic radiation, like X-rays. The other two types of natural radioactivity are alpha and beta radiation, which are in the form of particles. Gamma rays are the most energetic form of electromagnetic radiation, with a very short wavelength of less than one-tenth of a nanometer.
Gamma radiation is the product of radioactive atoms. Depending upon the ratio of neutrons to protons within its nucleus, an isotope of a particular element may be stable or unstable. When the binding energy is not strong enough to hold the nucleus of an atom together, the atom is said to be unstable. Atoms with unstable nuclei are constantly changing as a result of the imbalance of energy within the nucleus. Over time, the nuclei of unstable isotopes spontaneously disintegrate, or transform, in a process known as radioactive decay. Various types of penetrating radiation may be emitted from the nucleus and/or its surrounding electrons. Nuclides which undergo radioactive decay are called radionuclides. Any material which contains measurable amounts of one or more radionuclides is a radioactive material.
Types Radiation Produced by Radioactive Decay
When an atom undergoes radioactive decay, it emits one or more forms of radiation with sufficient energy to ionize the atoms with which it interacts. Ionizing radiation can consist of high speed subatomic particles ejected from the nucleus or electromagnetic radiation (gamma-rays) emitted by either the nucleus or orbital electrons.
Alpha Particles
Certain radionuclides of high atomic mass (Ra226, U238, Pu239) decay by the emission of alpha particles. These alpha particles are tightly bound units of two neutrons and two protons each (He4 nucleus) and have a positive charge. Emission of an alpha particle from the nucleus results in a decrease of two units of atomic number (Z) and four units of mass number (A). Alpha particles are emitted with discrete energies characteristic of the particular transformation from which they originate. All alpha particles from a particular radionuclide transformation will have identical energies.
Beta Particles
A nucleus with an unstable ratio of neutrons to protons may decay through the emission of a high speed electron called a beta particle. This results in a net change of one unit of atomic number (Z). Beta particles have a negative charge and the beta particles emitted by a specific radionuclide will range in energy from near zero up to a maximum value, which is characteristic of the particular transformation.
Gamma-rays
A nucleus which is in an excited state may emit one or more photons (packets of electromagnetic radiation) of discrete energies. The emission of gamma rays does not alter the number of protons or neutrons in the nucleus but instead has the effect of moving the nucleus from a higher to a lower energy state (unstable to stable). Gamma ray emission frequently follows beta decay, alpha decay, and other nuclear decay processes.
Activity (of Radionuclides)
The quantity which expresses the degree of radioactivity or the radiation producing potential of a given amount of radioactive material is activity. The curie was originally defined as that amount of any radioactive material that disintegrates at the same rate as one gram of pure radium. The curie has since been defined more precisely as a quantity of radioactive material in which 3.7 x 1010 atoms disintegrate per second. The International System (SI) unit for activity is the Becquerel (Bq), which is that quantity of radioactive material in which one atom is transformed per second. The radioactivity of a given amount of radioactive material does not depend upon the mass of material
present. For example, two one-curie sources of Cs-137 might have very different masses depending upon the relative proportion of non-radioactive atoms present in each source. Radioactivity is expressed as the number of curies or becquerels per unit mass or volume.
The concentration of radioactivity, or the relationship between the mass of radioactive material and the activity, is called "specific activity." Specific activity is expressed as the number of curies or becquerels per unit mass or volume. Each gram of Cobalt-60 will contain approximately 50 curies. Iridium-192 will contain 350 curies for every gram of material. The shorter half-life, the less amount of material that will be required to produce a given activity or curies. The higher specific activity of Iridium results in physically smaller sources. This allows technicians to place the source in closer proximity to the film while maintaining geometric unsharpness requirements on the radiograph. These unsharpness requirements may not be met if a source with a low specific activity were used at similar source to film distances.
Isotope Decay Rate (Half-Life)
Each radionuclide decays at its own unique rate which cannot be altered by any chemical or physical process. A useful measure of this rate is the half-life of the radionuclide. Half-life is defined as the time required for the activity of any particular radionuclide to decrease to one-half of its initial value. In other words one-half of the atoms have reverted to a more stable state material. Half-lives of radionuclides range from microseconds to billions of years. Half-life of two widely used industrial isotopes are 74 days for Iridium-192, and 5.3 years for Cobalt-60. More exacting calculations can be made for the half-life of these materials, however, these times are commonly used.
The applet below offers an interactive representation of radioactive decay series. The four series represented are Th232, Ir192, Co60, Ga75, and C14. Use the radio buttons to select the series that you would like to study. Note that Carbon-14 is not used in radiography, but is one of many useful radioactive isotopes used to determine the age of fossils. If you are interested in learning more about Carbon-14 Dating, follow this link: Carbon-14 Dating.
The Sequence Info button displays a chart that depicts the path of the series with atomic numbers indicated on the vertical axis on the left, and the number of neutrons shown along the bottom. Colored arrows represent alpha and beta decays. To return to the main user interface, click the "Dismiss" button.
Initially, a selected series contains all parent material, and the amount is represented by a colored bar on a vertical logarithmic scale. Each line represents a factor of ten. In order to step forward through the sequence by a specified number of years, you may type the appropriate number into the "Time Step" field and hit "Enter." A negative time step will backtrack through the sequence.
You may choose a step interval in years and progress through each step by pressing the "Enter" key. The "Animate" button will automate the progress through the series. You can either choose a time step before you animate or leave it at zero. If the time step is left at zero, the system will choose time steps to optimize viewing performance.
Ionization
As penetrating radiation moves from point to point in matter, it loses its energy through various interactions with the atoms it encounters. The rate at which this energy loss occurs depends upon the type and energy of the radiation and the density and atomic composition of the matter through which it is passing.
The various types of penetrating radiation impart their energy to matter primarily through excitation and ionization of orbital electrons. The term "excitation" is used to describe an interaction where electrons acquire energy from a passing charged particle but are not removed completely from their atom. Excited electrons may subsequently emit energy in the form of x-rays during the process of returning to a lower energy state. The term "ionization" refers to the complete removal of an electron from an atom following the transfer of energy from a passing charged particle. In describing the intensity of ionization, the term "specific ionization" is often used. This is defined as the number of ion pairs formed per unit path length for a given type of radiation.
Because of their double charge and relatively slow velocity, alpha particles have a high specific ionization and a relatively short range in matter (a few centimeters in air and only fractions of a millimeter in tissue). Beta particles have a much lower specific ionization than alpha particles and, generally, a greater range. For example, the relatively energetic beta particles from P32 have a maximum range of 7 meters in air and 8 millimeters in tissue. The low energy betas from H3, on the other hand, are stopped by only 6 millimeters of air or 6 micrometers of tissue.
Gamma-rays, x-rays, and neutrons are referred to as indirectly ionizing radiation since, having no charge, they do not directly apply impulses to orbital electrons as do alpha and beta particles. Electromagnetic radiation proceeds through matter until there is a chance of interaction with a particle. If the particle is an electron, it may receive enough energy to be ionized, whereupon it causes further ionization by direct interactions with other electrons. As a result, indirectly ionizing radiation (e.g. gamma, x-rays, and neutrons) can cause the liberation of directly ionizing particles (electrons) deep inside a medium. Because these neutral radiations undergo only chance encounters with matter, they do not have finite ranges, but rather are attenuated in an exponential manner. In other words, a given gamma ray has a definite probability of passing through any medium of any depth.
Neutrons lose energy in matter by collisions which transfer kinetic energy. This process is called moderation and is most effective if the matter the neutrons collide with has about the same mass as the neutron. Once slowed down to the same average energy as the matter being interacted with (thermal energies), the neutrons have a much greater chance of interacting with a nucleus. Such interactions can result in material becoming radioactive or can cause radiation to be given off.
Newton's Inverse Square Law
Any point source which spreads its influence equally in all directions without a limit to its range will obey the inverse square law. This comes from strictly geometrical considerations. The intensity of the influence at any given radius (r) is the source strength divided by the area of the sphere. Being strictly geometric in its origin, the inverse square law applies to diverse phenomena. Point sources of gravitational force, electric field, light, sound, and radiation obey the inverse square law.
Interaction Between Penetrating Radiation
and Matter
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When x-rays or gamma rays are directed into an object, some of the photons interact with the particles of the matter and their energy can be absorbed or scattered. This absorption and scattering is called attenuation. Other photons travel completely through the object without interacting with any of the material's particles. The number of photons transmitted through a material depends on the thickness, density and atomic number of the material, and the energy of the individual photons. Even when they have the same energy, photons travel different distances within a material simply based on the probability of their encounter with one or more of the particles of the matter and the type of encounter that occurs. Since the probability of an encounter increases with the distance traveled, the number of photons reaching a specific point within the matter decreases exponentially with distance traveled. As shown in the graphic to the right, if 1000 photons are aimed at ten 1 cm layers of a material and there is a 10% chance of a photon being attenuated in this layer, then there will be 100 photons attenuated. This leave 900 photos to travel into the next layer where 10% of these photos will be attenuated. By continuing this progression, the exponential shape of the curve becomes apparent. |
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The formula that describes this curve is:
The factor that indicates how much attenuation will take place per cm (10% in this example) is known as the linear attenuation coefficient, m. The above equation and the linear attenuation coefficient will be discussed in more detail on the following page.
Transmitted Intensity and
Linear Attenuation Coefficient
For a narrow beam of mono-energetic photons, the change in x-ray beam intensity at some distance in a material can be expressed in the form of an equation as:
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Where: |
dI |
= |
the change in intensity |
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|
I |
= |
the initial intensity |
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|
n |
= |
the number of atoms/cm3 |
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|
s |
= |
a proportionality constant that reflects the total probability of a photon being scattered or absorbed |
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|
dx |
= |
the incremental thickness of material traversed |
When this equation is integrated, it becomes:
The number of atoms/cm3 (n) and the proportionality constant (s) are usually combined to yield the linear attenuation coefficient (m). Therefore the equation becomes:
|
Where: |
I |
= |
the intensity of photons transmitted across some distance x |
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|
I0 |
= |
the initial intensity of photons |
|
|
s |
= |
a proportionality constant that reflects the total probability of a photon being scattered or absorbed |
|
|
m |
= |
the linear attenuation coefficient |
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|
x |
= |
distance traveled |
The Linear Attenuation Coefficient (m)
The linear attenuation coefficient (m) describes the fraction of a beam of x-rays or gamma rays that is absorbed or scattered per unit thickness of the absorber. This value basically accounts for the number of atoms in a cubic cm volume of material and the probability of a photon being scattered or absorbed from the nucleus or an electron of one of these atoms. The linear attenuation coefficients for a variety of materials and x-ray energies are available in various reference books.
Using the transmitted intensity equation above, linear attenuation coefficients can be used to make a number of calculations. These include:
- the intensity of the energy transmitted through a material when the incident x-ray intensity, the material and the material thickness are known.
- the intensity of the incident x-ray energy when the transmitted x-ray intensity, material, and material thickness are known.
- the thickness of the material when the incident and transmitted intensity, and the material are known.
- the material can be determined from the value of m when the incident and transmitted intensity, and the material thickness are known.
