![[equation graphic]](eqns/eq5-1.gif){kind=small}
By definition, ionizing radiation creates ion-pairs in the matter it passes through. We speak of ion-pairs because ionizing an atom or molecule by removing an electron necessarily leaves a positively charged ion, too. There are five detectors that respond to this ionization as such: the ionization chamber, the proportional counter, the Geiger-Muller tube, the spark chamber, and the cloud chamber. The latter two are of use primarily in physics research, the former three are of use in biomedical applications. As an approximation, the first three can be thought of as the same device operated differently. In each, a volume of gas is surrounded by one electrode and contains in its interior a second electrode. A potential difference is maintained between the electrodes, and the current needed to keep that potential constant is examined by electronic circuits. The distinction between the three types of detector hinges on the selection of the potential difference, and consequently on the nature of the circuits examining the current obtained.
In the case of an ionization chamber, the potential is just large enough to attract most of the ions to the electrode before they encounter oppositely charged ions to neutralize themselves against. The potential is specifically too low for the ions ever to achieve a significant kinetic energy. Thus, the ions collected by the electrode will be some large fraction of those created by incident radiation within the volume of the chamber. This requires very sensitive current measuring circuits, but gives a response that is clearly related to the "ionizing power" of the radiation impinging on it.
In the case of a proportional counter, the potential is large enough for the ions to achieve a significant kinetic energy as they move toward the electrode that attracts them. They thus become in their turn ionizing radiation. If the applied potential is cleverly chosen, each ion-pair created by incident radiation will produce a large number of ion-pairs before everything settles down again. Thus the current at either electrode will not be equal to the number of original ion-pairs created, but will be proportional to it. Because of this amplification, the current detecting circuits need not be as sensitive.
In the case of a Geiger-Muller tube, the potential is so large that the accelerated ions create further ionization, which creates still more ionization, etc., until the capacitance of the tube is entirely discharged, even from a single initial ion-pair. If a greater number of ion-pairs were originally created by the incident radiation there is no difference in the output signal. If a very large potential is applied to a Geiger-Muller tube, the electric field at the inner electrode will be so large that it rips electrons off of the molecules of the gas, spontaneously creating ions. This is an expensive light bulb! When operated normally, a Geiger-Muller tube indicates merely that some ionizing radiation passed through the detector volume. It gives no indication of where within that volume, nor does it indicate the amount of ionization produced, nor does it indicate the energy of the incident radiation, nor the energy it deposited in the detector. The electronic circuits that examine the current that must flow in order to maintain a fixed bias potential will therefore simply count current pulses.
An issue with all of these detectors is the range of incident particle energies for which they function properly. Usually there is a portion of the housing surrounding the sensitive volume that is designed as the "input window" through which the measured radiation is expected to enter. Typical thicknesses for Geiger-Muller tube windows are between 1 and 2 mg/cm2, with the result that beta radiation below about 30 keV will not be detectable. Ionization chamber detectors designed for safety surveys are often constructed with windows of aluminized mylar. Beryllium is also used, both for X-ray generator exit windows, and for some detector input windows. The primary disadvantage arises in fabrication: it is expensive to machine because of the precautions that must be taken to control the release of beryllium dust into the air. Airborne beryllium dust is highly toxic (two orders of magnitude worse than strychnine).
Now that the distinctions between ionization chambers, proportional counters, and Geiger-Muller tubes have been established, we discuss elaborations of the proportional counter, known as the wire-counter, multi-wire counter, and (generically) as the position-sensitive proportional counter. For these detectors the interior electrode is a wire or a collection of parallel wires. The charge collected on the wire proceeds towards both ends, but arrives at the closer end before it arrives at the farther end. Electronics are mounted at both ends and the relative time of arrival is used to deduce the location along the wire from which the charge started. The wire counter is a 1-dimensional device, the multi-wire counter is a 2-dimensional device. Multi-wire counters can be made with one plane of parallel wires, using the relative charge collected on adjacent wires to locate the event in the perpendicular direction, or two planes at right angles to each other can serve as the two electrodes. These detectors provide information about the position and about the degree of ionization, compared to the regular proportional counter that provides information only about the degree of ionization.
There are two groups of detectors that produce visible light when struck by ionizing radiation. Scintillators typically can be used to detect all types of ionizing radiation, although they are often more efficient with some types than others. Cerenkov detectors respond only to charged particles moving very nearly at the speed of light: super high energy protons, pions, or muons, or very high energy electrons. Scintillators absorb all or a large fraction of the incident radiation's energy, typically in a single event and produce a light flash whose total energy is a fraction of the energy absorbed. Cerenkov radiation is typically a very small fraction of the incident particle's energy and is produced continually along its path.
Scintillators are available in both solid and liquid forms. The solid ones include materials used as phosphors in cathode ray tubes such as computer terminals or oscilloscopes, many of which are useful to detect other radiations besides beta. Zinc sulfide, for example, is a very efficient X-ray detector and has been used in CRT's as well. NaI crystals with a small "doping" of thallium (Tl) were developed by Robert Hofstadter of the Cosmic Ray group led by George T. Reynolds at Princeton University in 1948. In 1950 Hofstadter and John A. McIntyre showed how NaI(Tl) could be used for gamma ray spectroscopy, measuring photon energies. They are quite sensitive to most types of ionizing radiation, but must be kept sealed from atmospheric moisture. The liquid scintillators are especially useful when very sensitive detectors are needed, as discussed below in section F. When scintillators are used to detect photons, the process may also be described as fluorescence.
The Cerenkov radiation is the electromagnetic equivalent of a sound wave sonic boom or the wake of a speed boat. It is produced whenever any charged particle moves faster than the speed of light in the local material medium (relativity clearly demonstrates that nothing can move anywhere faster than the speed that light travels in a vacuum). In water and most plastics, the speed of light is typically two-thirds to three-quarters of the speed of light in a vacuum, so by the theory of relativity we can predict Cerenkov radiation in such media for any charged particle with total energy greater than 1.5 times its rest energy, or a kinetic energy greater than half the rest energy. Thus, Cerenkov detectors will be sensitive only to electrons with kinetic energy exceeding 250 keV, and to protons with kinetic energy exceeding 500 MeV. We can see therefore why Cerenkov detectors are rarely used for anything but electrons.
We will touch here on three topics concerning the whole detector system, including the primary detection process and the associated electronics. The first two are related to the behavior of a system exposed to high levels of radiation: consider a graph of detector system output vs radiation intensity. Ideally this would be a straight line, assuming that appropriately comparable units were used to make the measurements. If the system will not give linear response indefinitely as the radiation level rises, does it merely flatten out or will it be paralyzed and indicate lower and lower levels as the radiation increases above some point? These ideas are encompassed in two concepts: detector dead time and saturation.
Many detectors, such as the Geiger-Muller tube, cannot respond to a second quantum of radiation unless it follows the first by an interval greater than the so-called "dead time." In the case of the G-M tube the physics is simple: the tube's capacitance must be at least partially recharged, by the flow of current from the bias supply, before it can produce a pulse large enough to be counted by the electronics. This means essentially that the time during which events were being counted was not the "wall-clock time" but was less than that by the product of the number of events actually counted times the dead time value. Hence the true rate exceeds the observed rate, but the correction is simple if the dead time is known:
by inspection, therefore, ![[equation graphic]](eqns/rsubtrue.gif){kind=small}
. Furthermore, experiments measuring the transmission of the same absorber when presented with high and low intensity beams will permit calculation of the dead time. In this way it is possible to make useful measurements with systems that have large dead times, if correction after the fact is possible. Dead time will result in the response flattening out as the radiation level rises, but will not produce a falling indication.
Geiger tubes, on the other hand, will indicate fewer and fewer events as the radiation level goes up, because they will never get a chance to recharge sufficiently to produce a countable pulse. This saturation effect requires that any Geiger tube detector system used for safety survey measurements include also some mechanism beyond the ratemeter or counter circuit that will be able to indicate the existence of the saturated condition. The simplest solution is a light that will light up only when the bias potential across the tube exceeds some minimum value (thereby indicating that the battery is still working and that the radiation level is not excessive, but this has the drawback that the absence of the light is the danger signal - and that is easy to neglect.
Our third topic concerns the design and operation of ratemeters. A typical ratemeter produces a needle deflection proportional to the rate at which events are occurring. For example, the output pulses from a Geiger-Muller tube can be sent to a discriminator circuit that will respond to those large enough to be believed, and ignore those small ones that are taken as noise. (This is the origin of the saturation effect alluded to above, since the pulses will get progressively smaller as the recharging time between pulses is reduced.) If the response to every accepted pulse is a unipolar (e.g., positive or zero only) output pulse of specified duration, size, and shape, and then the resulting signal is sent through a low-pass filter, the resulting "average" level will range from nearly zero at low event rates to nearly the full amplitude of the standard pulse if the time between events is equal to the duration of the standard pulse. The only requirement for good performance is that the "reaction time" of the low-pass filter, 
= RC, be longer than the time between events. This will enable the needle to give a steady indication. The difficulty in using rate meters in low rate situations is that with such a filter they will also necessarily be slow in responding to real changes in the event rate. One should approach with great caution any safety device with a time constant significantly longer than half a second, since it may contribute appreciably to the delay introduced by human reactions. See Cameron and Skofronick (1978) pages 462,4.
Photographic film is a classical primary detector for ionizing radiation; the discovery of natural radioactivity by Becquerel in 1896 was by observing the fogging of film that had been wrapped in paper that was opaque to visible light. Film is also a detector for secondary light, emitted for example by a scintillator. The physical chemistry of color photographic emulsions is in many respects concealed as industrial trade secret, but more has been published for the conventional black and white emulsions using silver halides. The active compound is distributed throughout the emulsion in the form of tiny crystalline grains. Exposure to light or ionizing radiation "renders the grain developable," producing a latent image that can be destroyed by exposure to light or made visible and permanent by treatment with the appropriate developing and fixing chemicals.
For X-ray films, the energy required to render one grain developable is provided by a single photon. For visible light films, the photons have much less energy but the grains are somewhat smaller. The typical result is that a few thousand visible light photons must strike a grain in order to render it developable. By considering the Poisson statistics, then, it is evident that X-ray film images will show more clearly the random nature of the radiation, while visible light images will have graininess only because of the finite size of the individual grains.
Film's major drawback is its non-linear behavior: the transmission of light through the developed emulsion is a very complicated, although smooth and monotonic, function of the (visible or ionizing) radiation dose received. There is a residual level of randomly developed grains, even in the absence of any exposure to radiation. This background "fog" corresponds to the dark current in a photomultiplier tube (see below), and the variations in it are similarly awkward when trying to make precise measurements of weak signals. At the high dose end of the response curve, any type of film will have a minimum transmission fraction when virtually all grains have been rendered developable. This transmission will be approached gradually, but for large doses to the film very little additional blackening will be observed. The effect overall is rather like "clipping" of an amplifier, except that the output vs. input curve for film is virtually nowhere straight. These ideas were explored more precisely by Hurter and Driffield, in 1890.
There is a second non-linearity in the behavior of film, "reciprocity failure." This refers to the fact that an ideal detector would provide an output that depended on the total energy delivered by the incident radiation, without regard to the duration of exposure; in other words, if a second signal is twice as intense as the first, but persists for half as long a time, then an ideal detector's output would be the same for the two cases. Typically, detectors will exhibit reasonable reciprocity within a range of signal intensities, but will respond less than would otherwise be expected if the signal is of very long duration but very weak, or is of very short duration, but very strong. Counting detectors are almost always intrinsically limited in the maximum rate at which they can count, and therefore limited to a maximum intensity of signal to which they can respond accurately.
Recent work by astronomer Alex G. Smith, and biomedical researchers Catherine Phillips and Edward J. Hahn (reported by Kazarian, 1986), has significantly improved the sensitivity of medical X-ray films. They applied techniques invented by astronomers for recording images of dim stars, reducing the dose required for a given image by a factor of more than two. The films are "pre-sensitized" by baking them in a mixture of nitrogen and hydrogen gases known as "forming gas." These films retain their sensitivity even when used for exposures of a week, as is sometimes done with auto-radiographic techniques in which a specimen is placed in contact with the film to reveal those parts of it that have absorbed radioactively labeled chemicals.
The photomultiplier tube converts individual photons of electromagnetic energy into pulses of electric current. As such it is used in a variety of situations calling for sensitivity to light: spectrophotometers, scintillation counters, particle detectors, automatic headlight dimmers, etc. Many designs are used, but we will frame our discussion in terms of the type shown in Fig. 1.
![[illustration]](figs/fig5-1.gif)
Figure 1: Photomultiplier Tube Construction and Operation. For simplicity of illustration, each electron impacting a dynode is shown ejecting two electrons.
The glass tube envelope is formed with pins through one end for electrical connections to the various internal parts, and the other end finished off as a window through which light can enter the tube. The inside surface of this window is coated with a thin layer of a conducting compound. This material is formulated specifically to be efficient at capturing the photons and transferring each one's energy to a single electron. This electron may then escape from the material into the interior of the tube. This is the photoelectric effect, discussed in Chapter IV, Section B, hence the layer of material that emits photons by this method is known as a "photocathode."
In order for electrons to be ejected from the photocathode, the incident light must have a photon energy greater than the binding energy of the cathode's valence electrons (c. 1 eV) and the photon must be able to penetrate the glass window to reach the cathode layer. The first condition establishes a maximum wavelength to which the tube will respond, and the second establishes a minimum wavelength for response. The requirement for the photons to penetrate the glass input window limits the maximum photon energy (minimum wavelength), excluding the "vacuum ultraviolet" and shorter wavelengths. Typically the response will cover essentially the same wavelength range as the human eye: visible light, although with perhaps some extension into the near infrared and ultraviolet.
The thickness of the photocathode layer is a compromise between getting all of the entering photons to interact with the layer and getting all of the electrons that do receive energy to escape from that layer into the interior of the tube. The best compromise is typically 20 to 50 Ångstroms thick, just barely enough to say that a layer of some specific formula exists. About 10% to 15% of the incoming photons actually eject an electron into the interior of the PMT. Because the cathode layer is so thin, it is common to make the input window out of glass that has a high lead (Pb) content. This makes the glass moderately conducting, thereby helping to keep the entire photocathode at a uniform potential, even when thousands of electrons are ejected at once.
The focus ring electrode is maintained at a potential more negative than that of the photocathode, so that the photoelectrons will be repelled from it, to ensure that more of them hit the first dynode than otherwise would be the case.
The interior of the tube contains a series of electrodes known as dynodes. When an electron is ejected from the photocathode it enters the region between the photocathode and the first dynode. This dynode is maintained at a potential that is roughly 100 Volts more positive than the photocathode. Thus the electron is accelerated toward the dynode, striking it with a kinetic energy 100 eV greater than the at most few eV that it had as it left the cathode. The valence electrons within the dynode are bound with energies of roughly 3 eV, so even if most of the 100 eV of kinetic energy is transformed into heat, each incident electron is still likely to eject several electrons from the dynode.
Beyond the first dynode there is the second dynode, which is maintained at a potential roughly 100 V more positive even than the first. The several secondary electrons, ejected from the first dynode by the original photoelectron, are all accelerated toward the second dynode, which they strike with sufficient energy for each of them to eject several electrons, and so on down the tube. The number of electrons ejected from dynode number n will be roughly 
. Careful selection of the shape and position of the dynodes, together with proper control of the applied potentials, can result in all the electrons from a single photoelectron arriving at the last dynode nearly simultaneously. (See Cember, Fig. 9.9, page 240.)
A photoelectron ejected from the cathode is converted into a pulse of perhaps one million electrons leaving the last dynode. The most positively charged electrode is the anode, which is near the last dynode and is maintained at a sufficiently positive potential to collect all of the electrons ejected from that dynode. The charge that reaches the anode during any interval of time will depend on the number of photoelectrons and on the multiplication at each stage of the dynode structure. The multiplication in turn will depend on the accelerating potential difference from one dynode to the next, and the material of the dynode surface: if the accelerating potential is large, or if the dynode material has many electrons with small binding energies, the average number of electrons ejected by an incident electron will of course be larger.
The circuitry that keeps each of the dynodes at the right potential is normally built into a "Photomultiplier Tube Base" to which connections are made for high-voltage power input (1 to 3 kV DC) and signal output. The essentials of the circuit are as shown in Fig. 2: a multiple resistor voltage divider. A difficulty comes from the fact that the input window glass (often not an electrical insulator, as mentioned above) may contact some other apparatus (this argues for the photocathode to be at system safety ground potential), but one wants the signal from the anode to be fed into sensitive electronics, which argues for keeping the anode potential at or very near the system ground. You cannot have it both ways; if an experiment requires the measurement of constant direct anode currents, such as would result from a continuing weak light reaching the photocathode, the photocathode will be at negative high voltage, and the anode at ground so that an ammeter or amplifier may be connected between the anode and ground.
If, on the other hand, the experiment calls for the detection and measurement of flashes of light, quite acceptable results can be obtained by interposing a "high-pass" (DC blocking) filter between the anode and the following electronics. This permits the anode to be maintained at high positive voltage, and the cathode to be kept at ground. It does not, however, permit the measurement of steady light, only of flashes whose duration is short compared to the time constant of the high-pass filter (see Fig. 3). PM tubes are used in this pulse mode for liquid scintillation counters, diffractometer x-ray detection, and in CAT scanners, for example.
![[illlustration]](figs/figs5-2-3.gif)
| Figure 2: DC-coupled PMT Base Circuit . | Figure 3: AC-coupled PMT Base Circuit. |
The photocathode is very sensitive. Exposing the tube to ultra-violet or blue light can cause the excitation of some of the atomic electrons of the input window glass into states from which they will decay slowly by emitting red or yellow photons that have enough energy to cause ejection of photoelectrons. Thus exposure of the PMT to fluorescent lights or to daylight will cause an excessive anode current to flow for days after, even when no new light is reaching the tube. This "dark current," and particularly the random fluctuations in it, can obscure signals that you are trying to observe or to measure.
Vidicons produce electrical signals for television display from an image focussed on their sensitive areas. Their construction is as shown in Fig. 4. The electron gun assembly is quite conventional; deflection of the beam is typically produced by magnetic fields created by coils. The target is a collection of diodes created by doping a slice of silicon crystal and etching the resulting large junction into a collection of smaller isolated pieces. Insteading of cleaving along these etch lines to create separate diodes, they are left together and connected in parallel by the depositing of suitable metallic conductors.
![[illlustration]](figs/fig5-4.gif)
Figure 4: Vidicon Construction.
When the electron beam is scanned across the back face of the target inside the vidicon, it charges up the capacitance of the diode array, since they are reverse biased and cannot conduct the charge away. The light of the image focussed on the target produces electron-hole pairs, which migrate to discharge the diodes. When next the electron beam scans the target, the current used to recharge the capacitance is a measure of the light that has fallen on that part of the target since the previous scan. Since each photon produces only one electron at the output, sensitive low-noise amplifiers must be used. Because the target and grid are suspended in the vacuum of the tube in close proximity to each other, vidicons are sensitive to vibration.
Charge-coupled device (CCD) image detectors are remarkable tools for light measurement, and have been applied in many fields, including astronomy, X-ray diffraction, analytical spectroscopy, and consumer hand-held video and still cameras. CCDs may have millions of picture elements ("pixels," the smallest region whose intensity is reported) that store and deliver photon-induced charge. These pixels, formed into one- or two-dimensional arrays in the CCD chip, are each square or rectangular, and typically range from 6 to 30 microns along an edge. Scientific-grade CCDs are particularly attractive for use as image detectors when properly cooled (typically to between -20 oC and -120 oC) and slowly read out (on the order of 20 microseconds/pixel, hence several seconds per full frame, as compared with 30 frames per second for broadcast television), because they offer small dark current, high quantum efficiency, low readout noise, and wide dynamic range. See Piccard and Vo-Dinh, 1991, and the references cited there.
CCDs are metal-oxide-semiconductor (MOS) integrated circuit imaging light detectors that have the same primary mechanism as a vidicon: photons create electron-hole pairs in a solid semiconductor. CCDs, however, provide those charges to an amplifier by transferring them through the circuit, instead of by scanning with an electron beam; it is the mechanism used for this transfer that provides the name "charge coupled devices." CCDs collect photogenerated charge in their pixels, possibly over an extended period of time. The accumulated charge at each light sensitive pixel is proportional to the product of the light intensity and exposure time.
The main advantages of a scientific-grade CCD over other multichannel detectors are low readout noise (less than 10 electrons per pixel, when cooled and read out slowly); low dark current (from 2 to 40 electrons/hour per pixel, when cooled); high quantum efficiency (for thinned, backside illuminated CCDs, the peak quantum efficiency can exceed 80%, and even for conventional CCDs, values of over 30% are typical); usable quantum efficiency for wavelengths ranging from approximately 120 nm to 1000 nm; and large full-scale signals (typically between 100,000 and 1,000,000 electrons/pixel).
CCD detectors can also take advantage of a readout method called binning, in which the charge on adjacent pixels is noiselessly combined, increasing the signal, prior to amplification and digitization. The charge in the binned pixels is measured with a single read operation, and therefore with only one dose of the associated noise.
The basic charge transfer technique is known by the phrase "bucket brigade." The sensitive area of the detector is physically divided into a collection of "pixels," usually in a rectangular array of rows and columns. Each row of the detector consists of a sequence of regions with the potential in every third region controlled together. Figure 5 shows the potential energy as a function of position at four consecutive instants during the bucket brigade transfer. The electrons will move to stay in the "bottom" of each bucket (potential well), thus being delivered to the amplifier at the end of the row in the same order that they started (which is their location within the picture being formed), without being mixed, if the potentials are manipulated appropriately.
![[illlustration]](figs/fig5-5.gif)
Figure 5: CCD Bucket Brigade Operation. Observe the progressive migration (to the left in this case) of each group of electrons as it spreads out when its well is wide and is compressed when its well narrows. (All electrons are, of course, identical to each other - the colors are presented as a guide to the eye to track the migration of each group of electrons.)
Because the CCD array is an integrated circuit, it is sensible to include the amplifier on the same chip. The required sensitivity is the same as for a vidicon, since both generate one electron-hole pair per photon detected, but the close proximity of signal source and amplifier permits better performance at a given cost, so that CCD arrays are usually usable at lower light levels than vidicons. Being all solid-state, CCDs are also far less fragile than vidicons, and less subject to problems arising from vibration. Modern consumer video cameras (including "camcorder" camera-VCR combinations) and digital still cameras are usually made with CCD detectors.
To understand how binning is achievable, we need to discuss the organization of a CCD chip in more detail. The bucket brigade illustrated in Fig. 5, above, is implemented in two dimensions. First, the entire frame is constructed as a set of parallel rows, isolated from each other, and simultaneously shifted in the same direction. At the output end of each row, the charges are delivered simultaneously by each row into the designated well of a column-oriented one-dimensional bucket brigade structure. In normal operation, the rows are put through one cycle, delivering the next column's worth of charges, and then their potentials are held stable while that whole column is shifted sequentially to the amplifier. Binning may occur by having two or more cycles of the rows before stopping to shift the combined column of charge to the amplifier. It may also occur at the output of the column, where the charges of several adjacent rows may be combined on the input of the amplifier before they are measured and neutralized.
These vacuum tube devices combine a photocathode input with a phosphor output. A large potential difference between the cathode and phosphor accelerates the electrons ejected by the photoelectric effect so that on impact the resulting glow from the phosphor will consist of many photons. The signal amplification is thus achieved in the same spirit as a photomultiplier tube; it is subject to quantum fluctuations but not to conventional noise sources.
There are two techniques used to ensure that the spatial pattern of light emission from the phosphor area will correspond to the pattern of photoelectron ejection from the cathode area: electrostatic and magnetic focussing. The former provides such a high accelerating electric field strength that transverse spreading is limited to acceptably small values by the short flight time. Magnetic focussing, on the other hand, works by arranging that the flight time provides for an integer number of cycles at the cyclotron frequency for that magnetic field. Thus each electron will follow a spiral path along the surface of a cylinder in space, with all such cylinders for the various electrons ejected from a point intersecting in a line parallel to the axis. If the accelerating electric field strength and the focussing magnetic field strength are properly related, each electron will spiral around an integer number of times, landing at the same place on the phosphor, regardless of its initial direction of ejection. Loss of focus will primarily result from non-uniformity of the fields and from variations in the flight-time caused by variations in the axial component of the initial ejection velocity vector.
If the detector can provide information about an event's location within its sensitive area, then it is known as an "area detector"; photographic film and CCDs are good examples of area detectors. A "point detector," on the other hand, reports only that an event has taken place somewhere within its sensitive region; Geiger-Muller tubes and photomultiplier tubes are examples of point detectors. When speaking of point detectors as such, we do not mean to imply any particular smallness of the sensitive region.
Other things being equal (and the cost, for one, rarely is!) an area detector is preferable to a point detector because it will provide more information for an equal dose of radiation to the target. The only exception occurs if the incident radiation is collimated to form a "pencil beam" of diameter comparable to the sensitive area of the detector, and if nothing could be learned from the scattered radiation's direction and intensity. Conventional CAT scanners do usually meet these last criteria. For speed of operation they often include several beam-detector pairs active at the same time.
Some detectors provide information about the energy deposited by the incident radiation or the number of ion pairs created, other detectors provide information only about the time at which the radiation arrived. Some detectors provide signals that can be analyzed for more than one of those. For example, Geiger-Muller tubes provide time information only, while ionization chambers provide ion-pair creation information only. A proportional counter provides both time and ionization information; the time of the output pulse is at a small, fairly consistent, delay after the passage of the radiation through the sensitive volume. The amplitude of the output pulse is of course proportional to the total ionization within the sensitive volume.
When the amplitude of a signal is of interest, from whatever sort of detector, it can be subjected to "pulse height analysis." Dedicated electronic devices are available to measure and record the height of each pulse. Equivalent performance is also achievable with special interface adaptors for general purpose microcomputers. The usual arrangement of such a "multi-channel analyzer," whether dedicated or microcomputer-based, is to provide two modes of operation, as discussed below.
In the pulse height analysis (PHA) mode, the peak value of each pulse is measured, scaled to an integer value in a fixed range (1 to 4096 is common), and then the memory cell designated by that integer is read out, 1 is added to the old value, and the new count is stored back into that memory cell. In the multi-channel scaler (MCS) mode, the pulses are not measured, merely counted for a set interval of time, storing the successive totals into consecutive memory cells. This mode can be used, for example, to determine the decay of a short-lifetime substance, since the values stored into the several channels would show the decreasing activity as the sample decayed away.
As discussed with reference to Fig. IV-4, the fraction of events that have a chance to be detected depends on the size of the sensitive area of the detector and on the separation between the source and the detector. The mathematical description uses the concept of "solid angle,"
, which is calculated as shown:
![[equation graphic]](eqns/eq5-2.gif){kind=small}
where a is the area on the surface of a sphere of radius r that subtends the same directions as the detector in question. Since the surface area of a sphere is
![[equation graphic]](eqns/eq5-3.gif){kind=small}
we can see that ![[equation graphic]](eqns/solidangle.gif){kind=small}
. There are two techniques for obtaining an effective solid angle for the detector that approaches ![[equation graphic]](eqns/fourpi.gif){kind=small}
: liquid scintillation and well detectors. In the former the source is dissolved in a transparent liquid that is compounded to efficiently convert the kinetic energy of the decay particles into visible light photons. These photons are then detected, typically by a photomultiplier tube. In the latter, the source is located in a well drilled into a solid detector. In both cases, almost every possible direction of travel for the decay particle will intersect the sensitive volume of the detector.
Solid angle considerations also routinely play a role in optical arrangements. The traditional description of the "speed" of a lens is the ratio of its diameter to its focal length, typically expressed, for example, as "this is a 50 mm f/1.8 lens." This description translates as a lens of focal length = 50 mm and diameter = (50 mm/1.8) = 27.8 mm. The "faster" a lens is, i.e., the larger its diameter compared to its focal length, the more of the light leaving the object of interest that will be focussed by the lens onto the detector. Attempts to describe optical arrangements tersely often miss the point that when more than one lens (or concave mirror) is involved, care must be taken to specify both focal length and diameter of every optical element, if an accurate analysis of the light collection efficiency is to be possible.
Dick Piccard revised this file (https://people.ohio.edu/piccard/radnotes/detectors.html) on March 29, 2005.
Please E-mail comments or suggestions to piccard@ohio.edu.