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The non-invasive
X-ray Multimeter
Principles, Advantages, Drawbacks and
Uncertainties
Booklet for the Course “Physics of Diagnostic Radiology”
V 4.0 Jan Lindström
Contents
2T2T2T2T2T2 T2T2T2T2 T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2 T2T2T2T2 T2T2T2T2 T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2 T2T2T2T2 T2T2T2T2 T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2 T2T2T2T2 T2T2T2T2 T2T2T2T 2 T2T2T2T2T2T 2T2T2T2T 2T2T2T2T 2T 2T2T2T 2T2T2T2 T2T2T2T2 T2T2T2T2 T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2 T2T2T2T2 T2T2T2T2 T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2 T2T2T2T2 T2T2T2T2 T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T2T2 T2T2T2T2 T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T 2 T2T2T2T2 T2T2T2T2 T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2 T2T2T2T2 T2T2T2T2 T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2 T2T2T2T2 T2T2T2T2 T2T2T2T 2 T2T2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2 T2T2T2T2 T2T2T2T2 T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T 2T2T2T 2T2T2T2 T2T2T2T2 T2T2T2T2 T2T2T2T 2T2T2T2T 2T2T2T2T 2T
2T2T2T2T2T2 T2T2T2T2 T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2 T2T2T2T2 T2T2T2T2 T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2 T2T2T2T2 T2T2T2T2 T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2 T2T2T2T2 T2T2T2T2 T2T2T2T 2 T2T2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2 T2T2T2T2 T2T2T2T2 T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2 T2T2T2T2 T2T2T2T2 T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2 T2T2T2T2 T2T2T2T2 T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T2T2 T2T2T2T2 T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2 T2T2T2T2 T2T2T2T2 T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2 T2T2T2T2 T2T2T2T2 T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2 T2T2T2T2 T2T2T2T2 T2T2T2T 2 T2T2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2 T2T2T2T2 T 2T2T2T2 T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2 T2T2T2T2 T2T2T2T2 T2T2T2T 2T2T2T2T 2T2T2T2T 2T
2T2T2T2T2T2 T2T2T2T2 T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2 T2T2T2T2 T2T2T2T2 T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2 T2T2T2T2 T2T2T2T2 T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2 T2T2T2T2 T2T2T2T2 T2T2T2T 2 T2T2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2 T2T2T2T2 T2T2T2T2 T2T2T2 T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2 T2T2T2T2 T2T2T2T2 T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2 T2T2T2T2 T2T2T2T2 T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T2T2 T2T2T2T2 T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2 T2T2T2T2 T2T2T2T2 T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2 T2T2T2T2 T2T2T2T2 T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2 T2T2T2T2 T2T2T2T2 T2T2T2T 2 T2T2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2 T2T2T2T2 T2T2T2T2 T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2 T2T2T2T2 T2T2T2T2 T2T2T2T 2T2T2T2T 2T2T2T2T 2T
2T2T2T2T2T2 T2T2T2T2 T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2 T2T2T2T2 T2T2T2T2 T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2 T2T2T2T2 T2T2T2T2 T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2 T2T2T2T2 T2T2T2T2 T2T2T2T 2 T2T2T2T2T2T 2T2T2 T2T 2T2T2T2T 2T2T2T2T 2T2T2T2 T2T2T2T2 T2T2T2T2 T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2 T2T2T2T2 T2T2T2T2 T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2 T2T2T2T2 T2T2T2T2 T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T 2T2T2T2T2T2 T2T2T2T
Acknowledgements and Foreword ...................................................................................................... 2
Introduction ......................................................................................................................................... 3
The peak kilovoltage ........................................................................................................................... 3
Historical background – the quest for determining the energy ........................................................... 4
Radiographic methods ......................................................................................................................... 4
Double-detector devices ...................................................................................................................... 5
Terminology and some useful definitions ........................................................................................... 5
Physics of the non-invasive method .................................................................................................. 10
Practical implementation of the non-invasive method on an X-ray Multimeter ............................... 12
The demonstration Instrument (DIGI-X) .......................................................................................... 12
Determining the total filtration .......................................................................................................... 14
Quick/One shot/Direct-HVL vs conventional HVL .......................................................................... 15
Determining the Exposure time with a Multimeter ........................................................................... 16
Correction Function for tube Voltage measurements ........................................................................ 17
Challenges with Fluoroscopy ............................................................................................................ 18
Long-term factor affecting kVp measurements: Anode ageing ....................................................... 18
The elusive Rhenium peaks – another possible uncertainty factor? .................................................. 21
Dose measurements using a P-I-N diode........................................................................................... 22
Calibration requirements and uncertainties ....................................................................................... 28
Instruments available on the world market ....................................................................................... 29
Summary ........................................................................................................................................... 29
References ......................................................................................................................................... 30
Review Questions .............................................................................................................................. 32
1
Acknowledgements and Foreword
This booklet would not have emerged without the excellent, invasive support of two of my work colleagues and
physicists; Robert Bujila and Jörgen Scherp Nilsson. Special thanks also to Lars Herrnsdorf, R&D fellow at RTI
Electronics AB since the very beginning. Most of the techniques of today’s X-ray Multimeters have at least
some DNA from Lars.
A lot of the collected knowledge in this work is not really trade secrets as such but still hard to get in one place.
There are several brick sized books on Medical Physics but surprisingly the physics behind non-invasive
measurements in Diagnostic Radiology is normally totally lacking in these. Being a course coordinator for
students soon to become professional Medical Physicists, I noticed that there was a gap between the detailed
descriptions of ionisation chambers and X-ray equipment: the non-invasive X-ray Multimeter. It is a common
work tool, normally not receiving any special attention. At the same time, very few actually know how it works.
It was decided that future students should not leave the course on Karolinska without carrying this basic
knowledge with them. Interestingly enough, also some of the experienced physicists at work confessed that their
knowledge of the principles behind the non-invasive technique was partly shallow. Hopefully some gaps of
knowledge can be filled from the content of this humble booklet. At this time, the best on the market (it’s the
only one).
The Author
2016-03-22 Stockholm
2
Introduction
In general, most textbooks in the field of Diagnostic Radiology Physics carefully outline the construction and
principles behind X-ray equipment and measuring devices, such as the ionization chamber. There is however, a
lack of content describing one of the most commonly used measuring devices for X-ray equipment, the so-called
“kVp-meter”. There could be several reasons behind this, one being that widespread knowledge of the principles
behind kVp-meters is non-existent due to it being classified as a “trade secrets”. The aim of this work is to
provide a general principle of how kVp-meters work in order to shed some light on some of these white spots in
knowledge. Further, the general principle presented here is mostly the same for all commercially available kVpmeters.
One of the most important physical quantities, to be measured during development, servicing and QC of
diagnostic radiology equipment is beyond argument the X-ray tube voltage. The tube voltage is a crucial factor
affecting the quantity and quality of X-rays produced during an exposure, and therefore the quality of images.
Accurate and consistent waveforms of the high frequency generators are important in diagnostic imaging in
order to control contrast of the X-ray image as well as radiation dose to the patient [1].
Historically, X-ray tube voltage was measured invasively by breaking the high voltage circuit. Since the early
1980´s, several instruments have been introduced that measure X-ray tube voltage non-invasively, from
measurements of the X-ray beam. In this work, the physics and technical principles behind the determination of
various QC parameters using non-invasive X-ray Multimeters is given along with a discussion of the associated
uncertainties. A background of the history and the evolution of these devices are also provided.
The peak kilovoltage
The current standard used to quantify the energy of photons produced by an X-ray tube is the peak kilovoltage
(kVp). The term and its definition are derived from the fact that in some systems, the accelerating potential is not
constant and varies over time (voltage ripple). The voltage applied across an X-ray tube can be generated by
various types of generators.
Figure 1: X-ray spectrum [2]
The temporal run, i.e. the persistence of the voltage during the current flow depends on the rectifier type and
affects the produced dose. The emitted bremsstrahlung covers a spectrum in which the highest energetic
component accords to the maximum voltage of the tube [2].
A great deal of confusion exists surrounding the term kVp. At present, there is no universally accepted definition
of kVp. Differences exist between definitions by service engineers, physicists and manufacturers. The purpose of
this work is therefore also to differentiate between the major definitions currently in use. A non-invasive meter
may measure the “kVp” using any of the definitions given here. Any chosen definition of kVp involves
interpretation. The factors to consider for an appropriate definition of kVp are:
1. Ability to define a reproducible method for the kVp measurement,
2. Functionality, i.e. ease of use of measurement technique,
3. Clinical relevance of the definition, i.e., relation to image quality
4. Relevance to technical aspects of the X-ray machine and its performance.
3
Historical background – the quest for determining the energy
It has been known since the early beginning of the X-ray era that the X-ray tube emitted electromagnetic rays
with various energies, a spectrum. It was therefore natural to strive for methods to determine the X-ray spectrum.
The correlation between the maximum photon energy and minimum wavelength of a continuous spectrum of the
X-ray beam are correlated with the peak X-ray tube voltage according to the Duane-Hunt equation from 1915
[3]:
𝐸𝑚𝑎𝑥 = 𝑒 ∙ 𝑈 =
ℎ𝑐
(1)
𝜆𝑚𝑖𝑛
where e is the electron charge, h is the Planck constant, c is the velocity of light and U is the tube voltage.
Measuring the maximum energy in keV, i.e.
or the minimum wavelength
of the X-ray spectrum,
gives U directly from (1). The values of all constants are known and the uncertainty of the determination of the
tube voltage depends only on the accuracy of this measurement. With spectrometric methods (outside the scope
of this booklet) an accuracy of some tenths of a kilovolt can be achieved.
Measuring X-ray spectra in a clinical environment has not (yet) become routine since it demands expensive and
highly specialised measuring instrumentation, long setup times (patience) and a high level of expertise for the
evaluation. However, there is a pilot project at Karolinska (2016) where field measurements of X-ray spectra
using a spectrometer are being evaluated.
Radiographic methods
All historical radiographic methods for determining the peak kilovoltage use an attenuating stepwedge placed
onto a radiographic film. When assessing the exposed radiogram, one has to find the step, i.e. density, which
equals that of the so-called reference strip. For every step a kV range is given where the observed density exists.
The manufacturer of the equipment calibrates the kV range-step wedge relationship. These devices were called
penetrameters.
Figure 2: Film penetrameter [4,5]
The two halves of the so-called Ardran-Crooks penetrameter [4,5], consisted of intensifying screens of different
speed; the filter stepwedge was placed over the higher speed type, while the other produced the reference strip.
The Ardran-Crooks penetrameter was originally developed in the effort to corroborate extraordinary claims
made for certain X-ray equipment situated abroad. Therefore there was a need to develop a portable tool [6].
The so-called gyroscope test cassette was produced in the 1980s in the former Soviet Union. In it the uniform
density reference strip is produced by spinning a hole, cut in a lead layer [7].
An advantage of the film based method is relative simplicity. Disadvantages include low accuracy (Wisconsin: ±
4 kV, gyroscope: ± 10 %) and the need for film processing. Therefore determining the value of kilovoltage in
several points requires a lot of time and many radiographic films. Nowadays, these devices are obsolete and have
been replaced by the double-detector devices [7]. With the spread of digital technology, film processing is not
available with a notable exception of Asia. Karolinska abandoned their last radiographic film processing unit in
2010.
A collection of historical methods/devices for the estimation of kVp with corresponding references can be seen
in Table 1 [8]. These methods are all obsolete today but concepts from these devices have survived and can be
4
seen in today’s methods. A more extensive description of obsolete (from a clinical routine perspective) methods
is given in reference [8] (Thesis: Measurement of Peak Kilovoltage Across X-Ray Tubes By Ionization Methods
1966)
Double-detector devices
The approach that eventually led to the modern methods of kVp measurements was that of the “double-detector”
described in 1932 by L. Silberstein [9]. He was the first person to realise that X-ray spectra and corresponding
attenuation curves (i.e. intensity of a transmitted beam as a function of filter thickness) of an X-ray source is
mathematically related to each other with a Laplace transformation. With this relationship, beam attenuation can
be measured using a series of attenuating material with different thicknesses. From those results, the X-ray
spectrum can be calculated. Continuing from the calculated X-ray spectrum, and equation (1), the tube voltage,
U, is then determined. However, this method of calculating the tube voltage is complicated. Simplification of
this method is possible by the recognizing that two points of the attenuation curve are enough for the assessment
of tube voltage, with acceptable accuracy.
Consecutive measurements, as it was practiced earlier (e.g. R. H. Morgan 1944) [10] is a significant source of
uncertainty as the tube voltage may vary for the two exposures. Therefore, modern devices use a detector
arrangement consisting of two detectors, covered by different (possibly interchangeable) filter thicknesses.
During a measurement, both detectors are irradiated simultaneously. Instead of measuring the absolute
transmission for the two detectors, the ratio of transmission between the detector pairs can be used, making the
measurements largely independent of the source to detector distance. Such devices were developed first in the
US in 1970s and in Sweden in the 1980s [7].
Terminology and some useful definitions
Effective energy (keV). It can be advantageous to substitute a polyenergetic X-ray spectrum with a
monochromatic energy. What energy would a (hypothetical) monoenergetic source have to be in order to
produce the same energy fluence (sometimes denoted “intensity”) as the (true) polyenergetic source using the
same number of photons? This energy is defined as the effective energy of a polyenergetic spectrum [2].
Exposure time (ms) is defined as the time between the first and the last transitions through the 50 per cent level
of the peak tube voltage during an exposure. Essentially, exposure time is the time during which the radiation Xray beam is produced. Some manufacturers use different values of the triggering level (e.g. 10% to 75%). The
exposure time may be measured using either invasive or non-invasive equipment.
5
Figure 3: Typical X ray tube voltage waveform from a three-phase six pulse generator
operating at 80 kV tube voltage and 165 ms exposure time.
HVL - Half Value Layer (mm Al). X-ray tube output can be expressed in terms of air Kerma measured free-inair (Kair). A measure of the penetration and the quality of the X-ray spectrum is the HVL. The HVL is the
thickness of an absorber needed to reduce the incident Kair by a factor of two. In diagnostic radiology,
Aluminium is normally chosen as the absorber, giving the HVL (unit: mm Al) [2].
The concept of HVL applies to narrow beam geometries as broad-beam geometry will produce a large degree of
scatter, underestimating the degree of attenuation. The HVL is an indirect measure of photon energy or the
hardness of an X-ray beam.
The HVL can be derived from the Lambert-Beer Law:
I = I0 𝑒 −𝜇𝑥
where I0 is the air Kerma of incident photons, µ is the linear attenuation coefficient for the energy and material
studied and x is the thickness of the material. Substituting x with HVL yields
1/2 = 𝑒 −𝜇𝐻𝑉𝐿
and
HVL = 𝑙𝑛2/𝜇
For a given specific material:

For monoenergetic radiation, the HVL does not change with increasing material thickness.

For polyenergetic X-ray beams, the HVL increases as more material is inserted into the beam
6
Figure 4: Comparison monoenergetic and polyenergetic “Intensity” i.e. Energy Fluence (rate) where
“HVL” is the value obtained from the monoenergetic beam i.e. obtained from the transition E1 to E1. In
reality the HVL value would increase for the polyenergetic beam with added filters and energy i.e.
E5>E4>E3>E2>E1
The HVL can be calculated using a two point approach from a semi-log graph (see figure 5). Thus
Figure 5: Graphs showing the concept of HVL (monoenergetic ideal beam left, polyenergetic, real beam
right)
We want to calculate the HVL by obtaining the linear regression function from the semi-log curve. x is the
absorber thickness, 𝜳̇ is the energy fluence rate measured by an ionisation chamber where the index 0 denotes
the incident energy fluence (no absorber).
ln𝛹̇2 − ln 𝛹̇1
𝑙𝑛 𝛹̇𝐻𝑉𝐿 − 𝑙𝑛𝛹̇1 = [
= 𝑙𝑛
𝛹̇0
2
𝑥2 −𝑥1
̇
] (𝐻𝑉𝐿 − 𝑥1 ) =
̇
ln𝛹 − ln 𝛹1
− 𝑙𝑛𝛹̇1 = [ 2
] (𝐻𝑉𝐿 − 𝑥1 )
𝐻𝑉𝐿 = [
𝛹̇
𝑙𝑛 20 −𝑙𝑛𝛹̇1
(
𝑙𝑛𝛹̇2 − 𝑙𝑛 𝛹̇1
)
𝑥2 −𝑥1
] + 𝑥1 = [
2
𝑥2 −𝑥1
𝛹̇
(𝑙𝑛 ̇ 2 )
𝛹1
(
𝑙𝑛𝛹̇2 − 𝑙𝑛 𝛹̇1
)
𝑥2 −𝑥1
𝛹̇
𝑙𝑛𝛹̇ − 𝑙𝑛 𝛹̇
𝑙𝑛 20 −𝑙𝑛𝛹̇1 +𝑥1 ( 𝑥2 −𝑥 1 )
(
2
𝑙𝑛𝛹̇2 − 𝑙𝑛 𝛹̇1
)
𝑥2 −𝑥1
𝛹̇
𝑙𝑛𝛹̇2 − 𝑙𝑛 𝛹̇1
(𝑥2 −𝑥1 )(𝑙𝑛 0 −𝑙𝑛𝛹̇1 +𝑥1 (
))
=[
[
𝑥2 −𝑥1
𝛹̇
𝑙𝑛 20 −𝑙𝑛𝛹̇1
] =[
1
] = 𝐻𝑉𝐿 − 𝑥1
]=
𝛹̇
𝑙𝑛𝛹̇2 − 𝑙𝑛 𝛹̇1
(𝑙𝑛 0 (𝑥2 −𝑥1 )−𝑙𝑛𝛹̇1 (𝑥2 −𝑥1 )+(𝑥2 −𝑥1 )𝑥1 (
))
2
𝑥2 −𝑥1
𝛹̇
(𝑙𝑛 ̇ 2 )
𝛹1
7
]=
=[
Ψ̇
Ψ̇
(x2 ln 0 −x1 ln 0 −x2 lnΨ̇1 +x1 lnΨ̇1 +x1 lnΨ̇2 −x1 ln Ψ̇1 )
2
2
Ψ̇
(ln ̇ 2 )
𝛹̇
𝛹̇
(𝑥2 𝑙𝑛 0 −𝑥1 𝑙𝑛 0 −𝑥2 𝑙𝑛𝛹̇1 +𝑥1 𝑙𝑛𝛹̇1 )
2
] =[
2
𝛹̇
(𝑙𝑛 ̇ 2 )
Ψ1
(𝑥2 𝑙𝑛
= [
𝛹̇0
𝛹̇
−𝑥1 𝑙𝑛 0 +𝑥1 𝑙𝑛𝛹̇2 )
2
2𝛹̇1
𝛹̇
(𝑙𝑛 ̇ 2 )
𝛹1
(𝑥2 𝑙𝑛
]=[
2𝛹̇
𝐻𝑉𝐿 = [
]=
𝛹1
𝛹̇0
𝛹̇
−( 𝑥1 𝑙𝑛 0 −𝑥1 𝑙𝑛𝛹̇2 ))
2
2𝛹̇1
𝛹̇2
(𝑙𝑛 ̇ )
𝛹1
(𝑥2 𝑙𝑛
]= [
𝛹̇0
𝛹̇
− 𝑥1 𝑙𝑛 ̇0 )
2𝛹̇1
2𝛹2
𝛹̇
(𝑙𝑛 ̇ 2 )
𝛹1
]=
2𝛹̇
𝑥1 ln ̇ 2 −𝑥2 ln ̇ 1
𝛹0
𝛹0
𝛹̇
𝑙𝑛 ̇ 2
]
𝛹1
Which is the formula used by EUREF, IAEA and other official organs.
Linear attenuation coefficient, µ (cm-1). A measure of the fractional attenuation per unit length of a material.
The reciprocal of the linear attenuation coefficient, µ-1, is equal to the mean free path of the X-ray photons in a
medium i.e. the average path length travelled before an interaction takes place. In this work the linear attenuation
coefficient is the spectrum weighted effective attenuation coefficient if not stated otherwise [2].
Peak tube voltage, Û0, (kVp). The maximum photon energy of a given spectrum. Together with information
about the filter in the X-ray beam and the tube voltage waveform, Û0 determines the beam quality and describes
the X-ray beam penetration. A small change in the tube voltage causes considerable changes in both the energy
fluence rate 𝜳̇ (sometimes denoted “intensity”) and in the emitted photon spectrum. I.e. changes will be
observed in the Exposure Index as well as in the image contrast. When Û0 increases, the Kerma rate also
increases accordingly [2].
kVpmax
kVpmax characterizes the maximum voltage applied across an X-ray tube in a specified time interval (t0 - t1)
and it affects the maximum energy of radiation produced.
Figure 6: kVpmax, average and effective values [11]
For acceptance tests, kVpmax, can be of special interest. Short spikes with a higher kV can mean that the X-ray
tube is getting close to the end of its life span. Some overshoot in the beginning of an exposure is not uncommon
and therefore normally not seen as an error. In terms of image quality, kVpmax does not normally play an
important role. This is because of the often short duration of the kVpmax relative to the mean value of the kV for
the exposure. It is the integrating characteristics of imaging detectors downplaying the influence of single
outliers [12].
8
kVpmean
kVpmean is the mean or average value of all X-ray tube voltage peaks during a specified time interval. The
kVpmean is the value often presented by non-invasive instruments unless something else is stated or chosen
[12].
kVeffective or practical peak voltage (PPV)
The effective kV or sometimes denoted the practical peak voltage (PPV) is based on the concept that radiation
generated by high voltage of any waveform produces the same contrast as radiation generated by an equivalent
constant potential. This concept is analogous to the concept of effective energy for a photon spectrum.
The PPV is derived by equating the low level contrast in an exposure produced with an X-ray tube connected to
a generator delivering any arbitrary waveform, to the contrast produced by the same X-ray tube connected to a
constant potential generator (DC). One contrast configuration is selected as being suitable for diagnostic
radiology and a direct link is established between the electrical quantity X-ray tube voltage and the PPV. It is
shown that the spread in total X-ray tube filtration as encountered in medical diagnostic radiology influence the
result of a measurement of the PPVonly to a small extent [12,13].
PPV Calculation
For the PPV determination of an arbitrary waveform the distribution for the occurrence of a voltage value during
a time interval must be calculated.
Figure 7: Arbitrary waveform [12]
The result is a histogram:
Figure 8: Corresponding histogram of an arbitrary waveform [12]
The function of the determined histogram is allocated with a specific weighting function. The result is the
practical peak voltage, an algorithm that determines the equivalent voltage applied to a constant potential X-ray
machine that would produce the same contrast on a radiograph as the generator being tested. It can be
conceptualized as a spectrum adjusted kV [13].
In comparison to other quantities such as kVpmean and kVpmax a direct conclusion about imaging properties
can be taken: The PPV describes the constant potential (ripple free) waveform delivering the identical image
contrast as the waveform being tested and consequently enables users to compare the imaging quality delivered
by different generator types. As most modern generators are of the constant potential type, the challenge of a
9
difference between the older types of halfwave, six-pulse, 12-pulse and DC no longer exist. PPV therefore did
not establish itself as the new universal standard even though it often can be seen as an optional quantity on
modern kVp-meters. However, one should be aware that modern DC generators often exhibit a non-negligible,
very high frequency ripple superimposed on the waveform. A ripple that can be very difficult to catch with some
non-invasive instruments due to their limitations in sampling frequency. This ultra-high frequency ripple
warrants further research to determine its impact on image quality.
Tube charge (mAs) is the product of the X-ray tube current (mA) and exposure time. For a certain peak voltage,
Û0, the mAs-value is proportional to the energy fluence Ψ and the Kerma of the X-ray beam [2].
Tube current (mA) is proportional to the number of photons emitted from the X-ray tube per second. For a
certain peak voltage Û0, the energy fluence rate 𝜳̇ and the Kerma rate are directly proportional to the tube
current value [2].
Physics of the non-invasive method
When X-ray radiation penetrates a metal filter, the modified filtered radiation spectrum approaches
monoenergetic radiation, with increasing filter thickness. This is due to the proportionally higher attenuation of
photons with lower energy. The effect is illustrated in the figure below (fig.10). The solid line represents an
initial spectrum and the broken lines represent the spectrum when filtration is gradually increased. The vertical
axis is energy fluence rate per energy interval [keV m-2s-1/keV] and the horizontal axis is energy [keV]. As an
example a photon has the energy E = hf = 80 keV, where h is Planck's constant and f is wave frequency [2].
Increasing filtration
Increasing mean Energy
Max Energy
Figure 9: Mean Energy (the Effective Energy) will approach the max Energy with increasing filtration.
Note that characteristic radiation peaks submerge for higher filtration
One of the physical quantities used when characterising radiation quality is the effective linear attenuation
coefficient. It can be defined from the following expression:
𝐸
𝛹̇ = ∫0 𝑚𝑎𝑥 𝛹̇0 (𝐸) ⋅ 𝑒 −𝜇(𝐸)𝑥 ⋅ 𝑑𝐸 = 𝛹̇0 ⋅ 𝑒 −𝜇𝑒𝑓𝑓𝑥
(2)
where 𝛹̇ is the energy fluence rate (sometimes denoted "intensity") of the X-ray beam having originally a 𝛹̇ 0
energy fluence rate, passed through an absorber with thickness x, E is the photon energy,  is the linear
attenuation coefficient of the absorber. 𝛹̇ 0(E) is the energy fluence distribution (photon spectrum). The effective
linear attenuation coefficient, eff, can then be described with the following equation:
10
1
𝜇𝑒𝑓𝑓 = − 𝑙𝑛
𝑥
𝛹̇
𝛹̇0
(3)
As we shall see, this equation is fundamental for non-invasive kVp measurements. For the sake of simplicity, it
is assumed from this point on that we are always dealing with spectrally distributed energies with corresponding
mean energies and effective linear attenuation coefficients [14,15].
Plotting µeff against E (keV) using logarithmic scales will result in the graph below. (Fig. 10) For well-filtered Xray spectra (~ > 1mm Cu) there is a near linear correlation between the mean energy (or effective energy) and
the maximum energy and hence the peak tube voltage (Û0).
Figure 10: The correlation between µ and the mean energy E (keV) is shown [15].
Figure 10 displays regions of non-linearity above a tube voltage of approximately 90 kVp. This is due to the
emerging influence of the Compton Effect (µtot = µphoto + µCompton). If µeff can be determined, then the tube
voltage, Û0, can be calculated. As we already have stated (cf. eq. 2), the following relationship is valid for
filtered X-rays penetrating a metal filter:
𝛹̇ = 𝛹̇ 0 𝑒 −µ𝑒𝑓𝑓∙𝑥
(4)
Where 𝛹̇ 0 is the energy fluence rate incident on the metal filter, µ eff is the effective attenuation coefficient and x
is the thickness of the metal filter. The following expression is valid for the linear portion of the curve where the
photo-electric effect dominates:
µeff = k(Û0)-K1
Û0 = (k/µeff)1/K1
(5)
Where K1 and k are constants. The relation between the transmission energy fluence rate 𝜳̇𝒏 and corresponding
thickness xn of a metal filter is shown in figure 11.
Figure 11: Plotting x (filter thickness) vs. ln 𝜳̇ (transmission energy fluence rate), yields semi-linear
curves [15].
11
As can be seen in figure 11, for considerably filtered spectra (𝜳̇⁄𝜳̇𝟎 < 0,01) the transmission curves approach
straight lines. The slope of a curve is related to the peak tube voltage and it is equal to µeff.
−µ𝑒𝑓𝑓 =
ln 𝛹̇2 −ln 𝛹̇1
(6)
𝑥2 −𝑥1
Setting Δ𝑋 = 𝑋2 − 𝑋1 and combining equations (5) and (6) yields; [14,15]
1
ln(𝛹̇1 ⁄𝛹̇2 )
𝑘
∆𝑥
Û0 = [ ∙
−1⁄𝐾1
]
(7)
Practical implementation of the non-invasive method on an X-ray
Multimeter
Equation 7 in the previous section implies, among other things, that this method can only be used where the
photoelectric effect dominates and basically monoenergetic X-rays. However, it is not necessary to estimate
Û0 analytically using this approach. Instead, it can be observed that the ratio 𝛹̇1 ⁄𝛹̇2 is directly proportional to
the peak tube voltage. By a careful choice of filter materials and thicknesses this correlation can be made to
extend far beyond the linear Photo-electric energy region and include energy regions where the Compton Effect
is non-negligible.
In reality, the prerequisite demand on adequate filtration of the X-ray spectrum to obtain a near monoenergetic
transmission spectrum cannot be fulfilled if using only one single ratio pair. This is due to a lower detection limit
of the signal for thick filters (among other factors). Hence a number of filter pairs must be defined, each pair
with an optimum choice of metal filters for the Û0 -range of interest. In theory, the Û0 -value is also independent
of the impinging energy fluence rate since the measuring principle is based on a ratio.
To calibrate a non-invasive X-ray Multimeter based on the ratio principle, we need to know the true Û0 -value.
This is measured by using an invasive method, i.e., a calibrated high voltage divider. The 𝛹̇1 ⁄𝛹̇2 ratio is then
determined for a chosen filter pair. The individual ratio values are obtained as a function, f, of a known range of
Û0 set-values.
The unknown Û0 of an X-ray tube will be determined by the inverse of f and a measured transmission ratio.
Û0 = 𝑓 −1 (𝛹̇1 ⁄𝛹̇2 )𝑓𝑖𝑙𝑡𝑒𝑟 𝑝𝑎𝑖𝑟
(8)
By using the calibrating procedure described in this section, the method does not depend on the conditions
required for the analytical solution in Eq. 7. [14-16].
The demonstration Instrument (DIGI-X)
When introduced to the market in the 1980´s, these non-invasive types of instruments were called electronic
penetrameters, referring to the older film-based penetrameters. In this section we will describe the typical
construction of an X-ray Multimeter based on the ratio-principle.
In the detector part of the instrument, the X-ray beam passes two metal filters of different thicknesses (see Fig.
12). The transmitted energy fluence rates 𝜳̇𝟏 and 𝜳̇𝟐 are measured with two semiconductor sensors (photodiode
type BPW 34 (or similar) + scintillators - Intensifying screen) connected to separate preamplifiers. 𝜳̇𝟏 and 𝜳̇𝟐
are then converted to corresponding output voltages, S1 and S2. The sensors are situated in close vicinity to
ensure a minimum influence on the ratio measurements from the Heel effect. The sensors have well collimated
apertures and are also shielded with lead or other high-Z materials to minimize the scattered radiation. The
demonstration instrument (Manufacturer RTI Electronics AB: type Digi-X) is equipped with six filter pairs for
the determination of Û0 . One sensor pair comprises two identical filters and is dedicated to providing a
mechanism to correctly align the instrument in the X-ray beam (Bal.-filter) resulting in the ratio 1.00 when
correctly positioned. The remaining five sensor pairs cover the range of 35 - 160 kV [14, 15].
During a preset time interval on the instrument, the mean Û0 is determined from an X-ray exposure. If no preset
time is given, the instrument will measure as long as the lowest sensor signal is above the signal detection
12
threshold. The unknown tube voltage is calculated from the ratio of the mean values of the local maxima of S1
and S2, respectively. For a given filter/sensor pair the voltage signal ratio S1/S2 is correlated to Û0 = g(S1/S2).
(Where g = f-1 from Eq. 8.) See Fig. 13.
Figure 12. Typical functional diagram of an X-ray Multimeter estimating the Û0 [15].
The maximum value of 𝜳̇ (max “intensity”) always coincides with the maximum value of the tube voltage
waveform which enables the instrument to calculate the peak tube voltage Û0 (kVp) independently of the curve
form. See fig. 13 [14-16].
Figure 13. Signal level for S2 (higher filtration) S1 (lower filtration) and corresponding U 0 [15].
The individual g-functions corresponding to the five filter/sensor pairs are stored in the instrument. See fig. 14
[14,15].
Figure 14. Û0 as a function of S2/S1 and various filter pairs [15].
13
Since the ratio of S1/S2 is utilised rather than the individual signals, the result does not have a dependency on
waveform. The simultaneous "two-point" measurements eliminate any influence from a fluctuating output. The
detector unit itself has a fixed detector geometry for which the S1/S2 ratios have a low dependence on variations
in field size (scatter), varying distance to source distance and scatter - from materials in the detector vicinity
[14,15].
A typical electronic circuit of a non-invasive meter is shown in figure 15. PIN diodes are normally used to
measure most of the main parameters of the X-ray equipment [17]. Conventional electronic circuits like
comparators, linear gates and ADCs are used.
Figure 15. Circuit diagram for a typical X-ray Multimeter. The PIN diode sensors produce a Voltage that
through the circuit can be interpreted into kVp, Kerma/rate and Exposure time [17].
Determining the total filtration
The total filtration (T) is the equivalent aluminium thickness the primary X-rays must penetrate from the focal
spot to the patient. A total filtration that is low increases the skin dose without improving the image quality. A
method included in the X-ray Multimeter, measures the total filtration directly for a certain tube voltage. The
method is based on the fact that the S1 signal decreases proportionally more than the S2 signal when T is
increased. The ratio S1/S2 will then be a function of the total filtration (T). See fig. 16 [16].
Figure 16. The concept of direct measurement of total filtration in mm Al [15,16].
Analytically, the process of obtaining the total filtration (T) can be described as follows:
14
The filtration experienced by each sensor S1 and S2 is x1 and x2, respectively. Let x1 be the total filtration of the
X-ray tube. An Aluminium filter with a known thickness d is applied on the detector S2, giving the filtration x2.
𝜳̇ 𝟎 is the energy fluence rate from the X-ray tube anode but before any inherent and added filtration of the tube
assembly. Since we expect the effective energy to change during transmission through the filters x1 and x2, due
to the large difference in filtration between S1 and S2, the corresponding difference in effective energy is
represented by two attenuation coefficients. Hence; µ1 and µ2, is the corresponding spectrum averaged weighted
attenuation coefficient (in reality a compound but we are looking for the equivalence in Aluminium).
𝑆1~𝛹̇1 = 𝛹0̇ ∙ e−µ1 x1
(9)
𝑆2~𝛹̇2 = 𝛹1̇ ∙ e−µ2 x2
(10)
and correspondingly
which give
𝛹̇
[ ̇ 2 ] = e−x2µ2
(11)
𝛹1
Taking the logarithm of both sides and knowing that x2 = x1+d, where d is a filter with a known thickness added
to sensor S2 and 𝑥1 is the total filtration of the X-ray tube, yields
1
𝛹̇
𝑑 − µ 𝑙𝑛 [ ̇ 2 ] = x1
2
(12)
𝛹1
𝛹̇
From eq. 12, it can be seen that by knowing the sensor ratio 𝑙𝑛 [ ̇ 2 ], the added filter thickness, d, and the
𝛹1
effective attenuation µ2, the total filtration, x1, can be estimated. However, µ2 , is in practice decided by the preset
kVp on the X-ray generator. I.e. this method of estimating total filtration requires a calibration of the instrument
for a known kVp. Modern meters normally measure the kVp simultaneously.
By calculating the total filtration of the tube during an exposure, it is possible to correct the estimated kVp-value
on the fly, if and when the total filtration deviates from the original calibration conditions of the device. There is
a limit to this correction facility and most modern X-ray Multimeters cannot correct for a total filtration above ~
20 mm Al or 1 mm Cu. It also means that the uncertainty of the estimated kVp no longer is within the
specifications and the manufacturer should be consulted on the level of uncertainty outside the calibration
conditions. Unfortunately, these are not normally given!
Quick/One shot/Direct-HVL vs. conventional HVL
There is a correlation between the total filtration and the HVL-value of an X-ray beam. For many practical
purposes, we are interested in the HVL. The detector of the X-ray Multimeter always calculates the ratio
between the sensor signals S1 and S2, which is a function of kVp. For a known kVp we know it is correlated to
𝑙𝑛2
the effective µeff (cf. eq. 3 and 6) and 𝜇 =
. Thus it is possible to estimate the HVL-value using the basic
𝐻𝑉𝐿
approach of the total filtration method (reserving one unfiltered sensor of a sensor pair) but instead calibrate the
detector ratio against a known HVL-value. This method is sometimes called “Quick-HVL”, “One shot HVL or
“Direct-HVL” depending on instrument manufacturer. Since most modern X-ray Multimeters, have several
sensors detecting the X-ray beam simultaneously, the most optimal sensor pair - or several pairs - is chosen
depending on the given task. I.e. the kVp, total filtration and the HVL can be determined in the same exposure
[16]. A typical uncertainty of the direct method is +/- 10%. The traditional method for determination of HVL can
give rise to an uncertainty of +/- 30% [18] making the direct method superior in this respect. Furthermore, the
direct method is faster and less cumbersome regarding the set-up. Research at Karolinska has shown that several
uncertainty factors are at play when using the conventional method. Some of these uncertainty factors can be
difficult to quantify. Furthermore, the direct method is more practical since there is no need of using dosimeters
or ionisation chambers, neither the sequence of Aluminium filters replacements, as needed in the conventional
method.
The direct method is based on diodes and there may be circumstances where the obtained HVL value can be
questioned (see section on Diodes). This may be the case when X-ray spectra and/or the tube filter material are
largely unknown. The relatively low energy dependence of commercial diode sensors is partly due to an
15
assumption that the X-ray tube filter material is known. The Multimeter will then do a correction of the kVp
value as a result from quantifying an unknown filtration but this correction process does have a limit. (Check
with specifications of the manufacturer). The less energy depending Ionisation Chamber will produce a
satisfactory result in a much wider range of energies and filtrations. It is therefore a recommended method to
always do an Ionisation Chamber based HVL measurement the first time this value is to be obtained on the Xray equipment. From that moment on, the direct method can be used as a check for any trends in the HVL value.
This order of methods is also recommended for the occasion of tube change or work on the filtration.
Determining the Exposure time with a Multimeter
As previously stated, the exposure time for the DIGI-X, (see also p5 definition on Exposure time), is defined as
the time between the first and the last transitions through the 75 percent level of the peak tube voltage during an
exposure. See fig. 17. The demonstration instrument provides two different ways to determine the exposure time:
1) analysing the waveform of Û𝟎 (peak tube voltage)
2) analysing the waveform of 𝜳̇ (energy fluence rate)
The measurement according to method 1 uses voltage dividers connected to the probe input of the demonstration
unit. The trig level of the instrument is set according to the 75% definition for the exposure time to be measured
correctly.
The measurement according to method 2 is made on the S2 waveform of the detector unit. For an X-ray tube
with a typical conventional filtration, the emitted energy fluence is approximately proportional to the square of
the tube voltage:
𝛹~(𝑈0 )2
(13)
The exponent in (13) increases from approximately 2 to 7 when using the sensor pairs of the largest filter
thickness. Therefore, the S1 and S2 waveforms don´t have the same appearance as the Uo waveform. Using one
of the five available filter pairs when determining Û0 , the exponent value in Eq. 13 will vary in the range 5 - 7.
This means that a considerably lower trig level setting must be chosen on the S2 waveform in order to
correspond to the 75% definition. An empirical approach for an X-ray exposure is to set the trig level to 25% of
the peak value of S2 [15].
The trig level is particularly important when determining the exposure time at short exposures where the rise and
fall times cannot be neglected compared to the total exposure time.
Figure 17. The relationship between the tube voltage waveform and the S2 waveform. The two waveforms
are normalised to 1.00. Filter pair 60 - 100 kVp. 16% gives the correct trig. Level [15].
In the case shown in figure 17, the 75 % level of a Uo waveform is corresponding to approximately 16% of the
S2 waveform level (0.16 ~ 0.756) [15].
16
Correction Function for tube Voltage measurements
The residual systematic error in the measurement of Û0 is an estimation of the maximum uncertainty, when all
known systematic errors are expressed as correction factors (c.f). The most important of these factors are the
corrections for total filtration, field size and field homogeneity.
(14)
The value on the display of the demonstration instrument should be multiplied by all c.f - values in order to
minimise all known systematic errors (see fig. 18) [15]. Typical specifications on a modern X-ray Multimeter
can be found in Table 2 [19].
Figure 18. A correction function displaying the most important sources of uncertainty besides the inherent
calibration uncertainty in the g-table [15].
Table 2. Typical specifications of a modern X-ray Multimeter [19].
17
Challenges with Fluoroscopy
Measuring kVp for fluoroscopic systems can be challenging due to the low mA causing high voltage cable
capacitance, which may distort the waveform, resulting in erroneous measurements. The most common type,
high frequency/DC generators, may cause problems in obtaining accurate kVp measurements. I.e. the X-ray
pulse rate from the generator changes with different technique factors and may interfere with the sampling rate
of the kVp meter. Therefore, the coincidence of the meter sampling rate versus the X-ray pulse rate, or lack
thereof, may cause measurement errors [7]. An example of this synchronisation problem is shown in fig.(19). In
this case a variation of 33% in the readings is still observed even when the dose rate has settled. This is a wellknown pitfall and most Multimeter manufacturers describe how to avoid this in their manuals.
Figure 19. Example of Fluoro Pulse Dose rate synchronisation problem. Setting: 3 pulses per second
(pps). Meter setting: 0.8 s measure period. The Dose rate readings of the instrument are shown as figures
above horizontal lines [20].
Long-term factor affecting kVp measurements: Anode ageing
A not so well known phenomenon affecting the measuring accuracy of non-invasive kVp-instrument is the
process of anode ageing. This process has been studied by Nowotny and Meghzifene (2002) [21] who showed
that the influence can be substantial. This ageing process is often mixed up with a very persistent myth in
Medical Physics of Radiology; the build-up of Tungsten on the X-ray tube exit window surface. The myth
assumes that every exposure will lead to a small deposition of Tungsten from the anode to the interior surface of
the X-ray tube. It is then believed that some Tungsten will inevitably be deposed on the exit window thus
increasing the inherent filtration causing the HVL value of the tube to increase with use and age. An extensive
survey was done by Stears et Al (1986) [22] who found no such relationship between HVL increase and
age/frequency of use. In fact, before any measurable effect, the short-circuit created by the deposition, will most
probably make the tube break. However, as we shall see, heavy use of an X-ray tube may cause a measurable
effect. The ageing effect is illustrated in figure 20. The increasing surface roughness of the anode can be clearly
seen from the images.
Figure 20. Images of peripheral part of anode showing the roughening effect on the surface [20].
18
The ageing effect will create a surface of higher roughness (i.e. more surface per surface area) and will increase
the probability of attenuation in the anode (see figure 21 and 22). The lower the energy of the impinging
electrons the larger the elevated attenuation effect due to the increase of roughness. According to Nowotny and
Meghizifene (2002) [20,21], the effect may equal up to 20 µm W added inherent filtration.
Figure 21. Illustration of increased attenuation probability due to increased surface roughness of anode
[20].
For the same voltage applied on an X-ray tube, this will mean a lower output and a higher mean energy of the
emitted X-ray spectrum (See figure 22 and 23).
Figure 22. Spectra from different level of attenuation. An increase of the mean energy can be clearly seen
as well as a lower overall output with increasing Tungsten filtration. Note that the maximum kVp does not
vary [20].
How large is the effect on non-invasive measurements? The device manufacturer Radcal has done a review of
the induced error from Anode ageing [20]. In figure 23, an invasive, so called Dynalyzer is used as a reference
for the kVp measurement for a new and old anode where “old” means substantial surface roughness. It can be
seen that for this particular kVp filter range on the measuring instrument, the effect is observed but is not very
large (~1.5 kV in worst case).
19
Figure 23. Anode surface dependence. Change due to increased Anode roughness. Straight lines showing
uncertainty limits of invasive measurement device “Dynalyzer”. X-ray Multimeter calibrated to fit within
uncertainty range for a new Anode. Multimeter readings shown for “new” and “old” Anode using
identical kVp filter settings on the instrument. The error due to the Tungsten filtration is limited to about
maximum 1.5 kV for this kVp filter [20].
From the description of the principle of the non-invasive instrument in this work, we know that in order to
approach a linear response for the sensors of the instrument, several varying filters are used. This will inevitably
result in a corresponding varying sensitivity to total filtration variations in the X-ray tube. In figure 24, the
change, the instrument reading “new minus old” kVp is plotted against the set kVp (From the Radcal review
[20]). It can be noted that for the 70-120 kVp range filter, the introduced error is substantial, reaching -6 kV and
well outside the 3% calibration limit.
Figure 24. Anode surface dependence. Change for various kVp-filters of non-invasive Instrument. 3%
calibration limits are shown [20].
We are now ready to make some conclusions on the influence on non-invasive kVp-measurements from Anode
characteristics. We know that the surface roughness of the Anode will increase the mean energy and lower the
energy fluence of the X-ray tube. The maximum energy will not be affected. A measurable effect is not likely to
be seen from just time and everyday routine use of an X-ray tube. However, large exposures with high generator
settings may have an effect on the Anode surface.
Finally, from the study of Nowotny and Meghzifene (2002) [21] it has been noted that the geometry of the tube
itself is a factor; i.e. a small angle tube is more susceptible to Anode surface roughness and hence the Tungsten
filtration effect. In other words: small angle tubes with a heavy work load should be kept more under observation
than others
20
The elusive Rhenium peaks – another uncertainty factor?
The Anode material is normally doped with Rhenium to increase the lifespan by increasing the temperature
endurance of the Anode. The Rhenium content may vary; normally between 5-15% of the Anode mass (see fig.
25) [23]. It is worth noticing that most Secondary Standard Dose Laboratories (SSDL) is using fixed Anode
tubes for their calibration procedures, i.e. normally without any Rhenium. The added Rhenium has in practice no
influence on the shape of the bremsstrahlung spectrum (Why?), but will introduce characteristic peaks of its
own. They will be found at: 59.719 keV (Kα2), 61.142 keV (Kα1) and 69.105 keV (Kβ2). They are difficult to
resolve from the ever present Tungsten peaks at 59.321 keV, 67.054 keV and 69.067 keV. In a reference work
by Svahn (1977) [24] various X-ray spectra were measured (cf. fig. 26). From this work it can be concluded that
the Rhenium peaks variations have, in practice, no influence on the image quality and can be disregarded in
Ionisation-chamber Dosimetry.
Figure 25. Effect of the Rhenium content (Re) on the resistance to wear and tear of the Tungsten Anode
covering layer [23].
However, a preliminary study made by the author of this booklet [25] suggests a possible dependence on the
Rhenium content for non-invasive kVp meters under certain conditions. I.e. the non-invasive Multimeters are
calibrated using an X-ray tube inhibiting a fixed Rhenium content (usually 10%). The Rhenium present will give
rise to characteristic peaks in the X-ray spectrum. The Energy fluence from these peaks will vary with the
Rhenium content (everything else remain fixed) and they will be completely absent when using pure Tungsten
Anodes. The effect has been preliminary quantified but is thought to be negligible in most practical cases. We
performed a theoretical study in our department using simulated spectra for various Rhenium content (0-15%) at
100 kVp. The calculations showed negligible influence on modelled kVp measurements, i.e. < 0.2% for
switching from zero Rhenium content to 15%. The effect was totally absent when introducing scintillators on top
of the photodiodes in the calculation model. However, for a simulated “quick-HVL” and equivalent totalfiltration measurement, the uncertainty rose to about 3.5% deviation of the S1/S2 ratio going from zero to 15%
Rhenium content. Depending on the look-up table used in the X-ray Multimeter, the introduced uncertainty from
this Rhenium change was calculated to be in the range of 0.1 – 0.2 mm Al. In practice, a negligible contribution
to the overall uncertainty.
Still, another interesting aspect of the possible influence from variation in Rhenium content is the context of dose
calibrations of diodes.This theoretical influence will vary depending on the energy response correction technique
used (see next section). The magnitude of the uncertainty, if any, has yet to be established through more
research.
21
Figure 26. Spectra of the focal radiation obtained with constant potential of 60 kV to 120 kV. The peaks of
the characteristic K-radiation are not fully disclosed, but their relative values including the continuous
distribution are given in the table in the Figure [24].
Dose measurements using a P-I-N diode
Most modern X-ray Multimeters also has the ability to measure Dose and Dose rate. Some also have connections
for conventional ionisation-chambers. Measuring Dose using a diode is a very convenient task but the
performance and characteristics behind the typical diode used in the Diagnostic Radiology energy range, is
sometimes not well known. The diode itself does not measure air Kerma but exhibits a rather complex electronhole pair mechanism depending on the detector material itself, silicon. It is outside the scope of this work to
describe this mechanism in any detail. We note however, that a high signal level, no need for bias voltage, a
sturdy material composition, no temperature and pressure correction needed, makes the diode an attractive
alternative in QA field work. We will study the typical characteristics of a photodiode not unlike those used in
most commercial Multimeter Instruments (see fig. 27). Aoyama et al. (2002) [26] assessed the output linearity
and dose rate dependence of a photodiode. The diode response was measured using the following x-ray generator
settings: tube voltage of 120 kV with an effective energy of 36 keV, mAs between 1 and 60, focus-to-sensor
distances, FSD, of 90, 120, and 200 cm. The effective energy was determined from the half-value layer of
Aluminium measured with the Radcal 1015 ion-chamber. Results are shown in figs. 28 and 29, respectively, for
output linearity and for dose rate dependence. Output linearity was excellent in a dose range from 0.03 to more
than 10 mGy, three orders of magnitude. No bias voltage was applied.
22
Figure 27. Hamamatsu S2506-04 as representative of the photodiodes used in the commercial instruments.
Note the small physical size [26].
Figure 28. Dose linearity of the photodiode. The response is linear over a wide range, making them ideal
as dose detectors in this sense. Dose measured with Ionisation-Chamber [26].
Figure 29. Dose rate dependence check. Results showing negligible dose rate dependence [26].
23
Figure 30. (Mono-)Energy response of a PIN diode [27]. Note the relative sensitivity to lower energies.
We also see that the relative efficiency of a PIN diode is less than ideal when it comes to the energy response
(see figure 30). The increasing response to low energies makes the bare diode susceptible to scattered radiation.
There are several approaches to adjust the response of a photodiode and we will briefly mention three of them in
more detail:
1.
Filtration. By covering the photodiode with a metal filter such as Copper the lower energy part of the
X-ray spectrum will be virtually eliminated (see fig. 31). The energy response of the diode will improve
at the cost of sensitivity but the filter will also introduce an energy threshold below which the diode no
longer will be able to measure. An advantage of the filtration is that the diode will be more or less
immune to scattered radiation and can therefore in practice be placed on any type of surface. (Compare
with ionisation-chambers). The drawback is the risk of engaging automatic exposure control systems
when doing measurements in X-ray fields due to the X-ray opaque property of the heavy-filtered diode.
Figure 31. Energy dependence of a diode with a metal filter. Note the steep response fall for lower
energies. The cut-off energy is about 30 keV [27].
24
2.
Scintillator/Phosphor. By covering the photodiode sensor area with an optimised scintillator the
energy response will improve virtually without a drop in sensitivity. By applying a scintillator largely
having an inverse energy response compared to the diode (fig. 32) [28], the energy response can be
made nearly linear for a wide range (cf. fig. 34) [29]. It should be noted that this is a delicate task and
usually it is not possible to obtain a perfect ‘summary’ response from applying a scintillator alone.
Disadvantages with Scintillators;
a) Some of the suitable scintillators/phosphors have a long afterglow and thus will introduce an
unlinearity in the dose rate response. The classical Gd2O2S:Tb is one example, having an afterglow
of several ms which is a problem when for instance measuring pulsed radiation of short duration.
b) Temperature dependence (cf. figure 33). A not so well-known characteristic is the sometimes large
temperature dependence of many of the commercially available scintillators. This dependence rule
out any use in absolute dosimetry while it is very difficult to do corrections to overcome this
behaviour (varies between batches of manufactured scintillators). Still, for applications in kVpmeasurements, these scintillators may work (why?)[30].
c)
Hygroscopic and brittle material properties. It is well known that for example CsI is hygroscopic,
meaning it will deteriorate with time due to moist in the environment. It is also a very brittle
scintillator that easily breaks if not handled carefully.
d) Costs. Many of the suitable candidates are very expensive compared to the photodiode itself and
the application technique may push up the costs even further. Particularly if the path of nanotechnique will be followed.
Another way of adjusting the total energy response of the photodiode with a scintillator is to partially
cover the sensor area [29]. This is in theory an excellent technique but due to the individual properties
of the diodes and the scintillator, it is hard to get a consistent result which is of course needed for
commercial production.
In practice, scintillators are applied mostly to increase the overall sensitivity of the diode detector (up to
three times response increase compared to the bare diode is reported [29]) and the energy response is
then not the primary goal (even if it will improve in most cases).
Figure 32. Energy dependence for various scintillator combinations. HED/LED denotes “High/Low
Energy Detector” which is a parameter essentially deciding the thickness of the scintillator [28]. Note the
essentially inverted energy dependence curves compared to the one of photodiodes.
25
Figure 33. Temperature dependence of the scintillation yield of NaI(Tl), CsI(Na), CsI(Tl) and BGO [30].
Figure 34. Energy dependence for various scintillator coverage where 1 denotes total coverage of
photodiode surface. The scintillator in this case is ZnCdS:Ag. Best relative response is given for a 0.9
(90% of sensor area) coverage factor [29].
Perforated filters and filter combinations. This is a further development from the previous two methods
and is made in combination with one or two of them. By applying a pattern of holes in a filter covering the
sensor area, the previously absorbed lower energy X-ray photons will now contribute to the diode signal.
The low energy response will improve and the energy detection range will be extended without impairing
the energy response linearity if done correctly (the filter thickness has to be adjusted accordingly). Often
another filter material is used to cover the holes. A drawback will be an increased directional dependence of
the detector. A “grid” effect. (See figs. 35-37)
26
Figure 35. Typical hole configuration on sensor surface of an energy compensated photodiode. Centre of
the active sensor area is marked [27].
Figure 36. Side view of filter/hole application on photodiode [27].
27
Figure 37. Final energy response curve of filter/hole compensated photodiode. Note the angular
dependence of the dose detector [27].
The hole technique is based on openings whose individual areas is in the range of 15% to 25% of the sensor area.
As can be seen from figure 32, one of the openings is centred over the sensor, while the others are located at the
periphery to preserve a good polar response to at least ±45º [27].
Finally, other ways may to manipulate the energy response is to vary the silicon layer thickness (usually increase
it) or mix silicon sensors with a different semi-conductor material with a different energy response.
To conclude; exactly how the photodiodes are made more ionisation-chamber-like in their energy response, is
largely a trade secret. In a stand-alone mode (without kVp correction), the diodes nowadays have an acceptable
energy response (check the specs.!) but it should always be remembered that they do not measure air Kerma,
they just pretend to do just that and only under the conditions they have been calibrated for.
Calibration requirements and uncertainties
As previously stated, the X-ray tube peak kilovoltage (kVp) is one of the most important parameters affecting
both patient dose and image quality; it is therefore essential to be able to accurately measure the kVp in
diagnostic radiology. Consequently, the calibration of the kVp meters used for quality control of clinical X-ray
systems is crucial [31].
The calibration and adjustment of the X-ray tube voltage of an X-ray generator can be performed at the
manufacturers’ facility or at a calibration laboratory using the direct invasive kVp measurement method.
According to IAEA Code of Practice for Dosimetry in Diagnostic Radiology [31], in the Secondary Standard
Dosimetry Laboratory (SSDL), an invasive device is used to assess the accuracy and stability of the X-ray tube
voltage measured as the practical peak voltage. This device should be able to measure the practical peak voltage
within 1.5 % or 1.5 kV (k=2), whichever is the larger.
However, to the authors knowledge there is no national standard or a laboratory that will calibrate an invasive
voltage divider at very high frequencies. Thus one may argue that the traceability of kVp is in question. It has
been demonstrated that voltage dividers can change their calibration at higher frequencies. The highest frequency
normally calibrated is approximately 8 kHz. Many generators, such as mammographic generators, operate at
frequencies of 10 kHz or higher. In addition, national laboratories will normally not calibrate non-invasive
meters.
All in all, the non-invasive alternative is in practice the most versatile one. Requirements regarding the
specifications for non-invasive kVp measuring devices up to 150 kV are given in IEC 61676 [32].
Recommendations are given that the relative intrinsic error of the practical peak voltage measurement should not
be greater than ±2% over the effective voltage ranges, i.e. 60–120 kV for diagnostic and 24–35 kV for
mammography. In addition, it recommends that a 1.5% limit of variation in response is acceptable at tube
28
filtration ranges of 2.5–3.5 mm Al (for diagnostic radiology applications). At SSDL, the relative expanded
uncertainty of calibration for non-invasive kVp measuring devices (k = 2) should be below +5 % [31].
Instruments available on the world market
There are several manufacturers, producing non-invasive X-ray tube voltage measuring devices. At present these
manufacturers are (2016):
Fluke Biomedical (USA): (trademark Victoreen, Keithley Radiation Instruments – without maintaining the
trademark – and Raysafe/Unfors Instruments), Gammex-RMI and Radcal (USA), PTW-Freiburg (Germany),
IBA Dosimetry (Wellhöfer) and PehaMed (Germany), RTI Electronics (Sweden).
These manufacturers provide a wide selection of instruments. The simplest device measures kVp while the most
advanced devices are able to measure many other parameters (invasive and non-invasive tube current and current
time product, irradiation time, waveforms, dose and/or dose rate, relative dose/mAs linearity, number of pulses,
dose/pulse, pulse rate, also in fluoroscopic mode etc.). Some of the instruments are specialised for
mammography, dental equipment or CTs. Manufacturers emphasize in some cases that their devices are capable
of measuring high frequency generators, and the proper waveform type calibration is chosen automatically. The
majority of the most recent equipment also determines the filtration of the X-ray beam and the simultaneously
measured kVp-value is then used as a correction when necessary (and vice versa!). If recommended calibration
conditions are met, most devices have an uncertainty of about 1.5-2 per cent [7].
Summary
In this work, the principles behind commercial non-invasive kVp meters have been described. The direct method
(invasive) of measuring kVp is by using a high voltage divider. This invasive test device is connected between
the generator and the X-ray tube and provides isolated low level analogue voltage signals proportional to the
kilovoltage applied across the tube. The signal waveforms can be displayed and analysed on an external
oscilloscope or measured by a digital meter. The peak kilovoltage can be visually determined from the voltage
waveform displayed on the oscilloscope. These devices are typically intended for calibration and analysis of Xray generators. They are limited in their dependence on frequency.
Electronic, non-invasive kVp devices provide a measurement based on the change in X-ray transmission through
varying thicknesses of filtration. These devices are accurate (if properly used) and widely used for routine
quality control due to their ease of use. However, it is important to understand how the meter works and what
measurement variables may affect the accuracy of the results. These considerations may vary from one type of
meter to the next and from one generator to another. The kVp meter basically consists of a pair of matched,
closely spaced photodiodes that are filtered by different thicknesses of material, e.g., copper. The ratio of the
signals from the filtered diodes will depend on the energies of the X-ray beam (which are determined by the tube
voltage). This ratio is compared against an appropriate calibration “look-up” table within the device to obtain the
kVp.
Some non-invasive instruments do not measure true peak voltage, but rather a value that is integrated over
exposure time and the ratio of the signals. This value is called effective kV (kVeff) and is lower than the actual
kVp. Knowing the amount of ripple in the waveform, the instrument can correct this value to provide a kVp.
Other instruments track the peaks in the kV signal and hence show the correct peak value (for instance
Raysafe/Fluke, RTI Electronics). Some instruments will automatically select the appropriate waveform
calibration (e.g., single vs. hf/dc) while others require the user to choose the appropriate setting in the
accompanying software.
The user manual should be consulted for limitations and proper operation of the meter. Some instruments need a
limited range of Dose or Dose rate for proper operation and may require reducing distance for measurements at a
low kVp or mA. Others are sensitive to positioning and tilting with respect to the central ray. Still others may
require additional correction factors for use with heavy filtered or exotic filtered, X-ray tubes or high frequency
generators showing considerable high-frequency ripple.
It is crucial that the user is aware of the potential problems that may be encountered, and sceptical of
measurements that deviate from expected results. Perhaps the best advice is to note the unusual reading and
realise that further investigations may be warranted. The investigation could include checking other closely
related parameters and communicating with the service desk of the device manufacturer.
And finally, diodes are extremely useful for dose measurements, but they are not ionisation-chambers. Under
certain conditions, ionisation-chambers should not be replaced by diodes.
29
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31
Review Questions
1.
Why is it important to know the actual kVp on Diagnostic X-ray Equipment?
2.
What are the pros and cons for the non-invasive method compared to the invasive version (probes
connected to the generator)?
3.
Why is it important to check the “balance” of the X-ray Multimeter?
4.
Can the X-ray Multimeter be used on any Anode/Filter combination? Why/Why not?
5.
Why doesn´t the X-ray Multimeter normally show distance dependence when measuring kVp, Exposure
time and “Quick”-HVL?
6.
What is “Quick”-HVL and how does it differ from real HVL measurements? (What uncertainty can be
expected?)
7.
What are the different sources of uncertainty for non-invasive kVp measurements? Also, give example
of uncertainties encountered in the clinical settings vs. the calibration environment.
8.
A diode used as a dose detector has normally energy dependence as is. How is the energy dependence
virtually eliminated in modern “dose detectors”? Describe particularly the difference between an
inherent dose diode in a stand-alone Multimeter unit and an external dose detector diode.
9.
Why does a (photo-)diode based dose detector give a higher signal that an Ion-chamber for the same
generator settings?
10. Under what conditions shouldn´t the dose detector (diode) be used for dose measurements?
32