British Journal of Radiology (2004) 77, 395-404
© 2004 British Institute of Radiology
doi: 10.1259/bjr/32514512
Comprehensive analysis of the spectrometric determination of voltage applied to X-ray tubes in the radiography and mammography energy ranges using a silicon PIN photodiode
R A Terini, PhD
1,2
M A G Pereira, BSc
1
R Künzel, MSc
1,3
P R Costa, PhD
1 and
S B Herdade, PhD
1
1 Serviço Técnico de Aplicações Médico-Hospitalares, Instituto de Eletrotécnica e Energia, Universidade de São Paulo, Av. Prof. Luciano Gualberto, 1289, Cidade Universitária, CEP. 05508-010, São Paulo, SP, 2 Departamento de Física, Pontifícia Universidade Católica de São Paulo, R. Marquês de Paranaguá, 111, Consolação, CEP. 01303-050, São Paulo, SP and 3 Instituto de Física, Universidade de São Paulo, R. do Matão, Travessa R, 187, Cidade Universitária, CEP. 05508-900, São Paulo, SP, Brazil
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Abstract
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This work describes the analysis of factors which affect the results of estimation of the electron accelerating potential (kVp) applied to an X-ray tube, through determination of the end point of the energy spectrum of the emitted radiation beam. Measurements have been performed utilizing two spectrometers each with a silicon PIN photodiode: one operating at room temperature, and the other, a high resolution spectrometer, with a Peltier cooler. Both were directly irradiated by different X-ray beams. Both systems work at low voltage and without liquid nitrogen cooling, thus avoiding the drawbacks presented by germanium detectors. Each kVp value was determined by linear regression of the end of the spectrum, so as to give, simultaneously, the best fit to the experimental data and low standard deviation for the kVp value. Detector energy resolution and calibration, counting statistics and high voltage waveform ripple have been investigated in order to establish better experimental conditions and to optimize measurement time. Results of measurements carried out with X-ray tubes connected to single-phase, three-phase or constant potential units, using additional filtration of Cu, Al or Mo (for mammographic beams), are presented. The variations resulted in kVp uncertainties up to 0.1 kV.
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Introduction
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Precise determination of the peak potential (kVp) applied to conventional and mammographic X-ray tubes is necessary if one wishes to reduce the radiation dose received by patients and clinical staff, while obtaining high quality images. As is well known, small changes in the kVp value can produce significant increases in patient dose, due to the approximately quadratic dependence between air kerma and kVp [1]. The relationship between dose and kVp will vary with the part of the body being imaged and the kVp range utilized. Martin et al [2] studied abdominal anteroposterior (AP) radiographs and reported a mean variation in equivalent dose to the liver of 3.5% per kVp unit in the 60–120 kV range, with 1% per kVp unit from 90 kV to 100 kV, and 13% per kVp unit in the 60–70 kV range.
In addition to an intense direct beam dose, the scattered beam also contributes significantly to patient dose. For instance, Fung and Gilboy [3] found that during posteroanterior (PA) chest radiography the dose to the ovary and testes increased at a rate of 2% per kVp unit in the range 60–100 kV using a non-grid technique. Thus a small change or inaccuracy in the kVp settings will produce significant changes in the patient dose.
Frequently, kVp calibration of X-ray emitters is made based on invasive or non-invasive meters, which typically have a minimum calibration accuracy of 1%. Thus, when these devices are recalibrated, the inaccuracy of the calibration method must be low enough to avoid an undesirable increase in patient dose.
In previous work [4], a statistical method has been described for calculation of the peak kilovoltage (kVp) through the experimental determination of the end point in the energy spectrum of the radiation emitted by an X-ray tube. These measurements were carried out with good accuracy utilizing detectors that work at room temperature, such as Si PIN photodiodes, which do not need cumbersome liquid nitrogen dewars and high voltage bias supply as would be the case with Ge detectors, with significant increase in portability and reduction of the equipment cost. For a tube connected to a three-phase waveform voltage generator, errors in the values of kVp were between 0.06 kV and 0.16 kV, in the potential range 50–100 kV. In the same range, uncertainties of mean values obtained with an invasive high voltage (HV) divider varied from 0.3 kV to 0.6 kV, so spectrally determined kVp values could serve as standards for the calibration of the HV divider. Subsequently, non-invasive kVp meters could be tertiary-calibrated in simultaneous kVp measurements with the voltage divider.
The present work intends: (1) to evaluate the influence of detector energy resolution and calibration, counting statistics and high voltage waveform ripple on the determined kVp values, in order to analyse the practicality of the method; and (2) to extend the method to the kVp calibration of mammography systems.
Nowadays, there are some compact, cooled semiconductor detectors commercially available [5, 6], with energy resolution similar to that of HPGe and Si(Li) detectors but with lower efficiency, appropriate for the high fluence rate of photons from diagnostic X-ray tubes. Thus, it is interesting to investigate the advantages of using these devices compared with those that work at room temperature.
On the other hand, in practice, single-phase, three-phase, multipulsed and constant potential waveform generators can be used in X-ray equipment. When a kVp value is set on each piece of equipment, the reading is commonly made from a digital display connected to some built-in circuit or to an external voltage divider. To calibrate these devices, using the measured beam spectrum, it is necessary to know more about the definition of the quantity displayed by each, what its relationship is with the spectrally determined value and how they are affected by high voltage waveforms with different ripples [7].
The display of voltage dividers provides the highest voltage value (absolute kVp) during the exposure and non-invasive kVp meters, depending on the manufacturer, may provide measurements either of the absolute kVp or of the average peak potentials (kVpav), i.e. the average of the maxima of the voltage waveform occurring throughout the exposure time. Additionally, when the kVp is determined by linear regression of the end part of the beam energy spectrum, the quantity determined is kVpav [8], which agrees with kVp in constant potential waveforms, allowing results to be compared.
For non-cooled clinical equipment (three-phase and single-phase), spectra have to be obtained during several short exposures; thus, we expect that each spectrum end point, determined by linear regression, represents an average of the maxima of the voltage waveform corresponding to each single exposure. Therefore, this average may be also compared with the average of the individual kVp values read in the display of the voltage divider, for calibration of the divider in kVpav.
Many tests carried out at the Department of Hospital Applications, Instituto de Eletrotécnica e Energia, Universidade de São Paulo (IEE-USP) include measurements of kVp, as a main physical quantity or as a control parameter, for the comparison of X-ray equipment performance with national and international standards [9, 10]. In addition, the Department performs calibration of non-invasive devices utilized in quality control routines and needs to guarantee the reliability of the instruments utilized as standards in this task. The present investigation contributes to examinations of the compliance of the experimental procedures of these laboratories with the IEC/ISO guide 17025 [11], in terms of the evaluation of the uncertainties related to the measured quantities.
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Materials and methods
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Instrumentation
For the measurements of energy spectra, the following equipment has been used:- a spectrometer consisting of: a Hamamatsu S3071 silicon PIN photodiode (Hamamatsu Photonics K.K, Shizuoka, Japan), with 19.6 mm2 active area, inside a copper cylinder with a 6.4 mg cm–2 Al window; an eV 550 (eV Products, Saxonburg, PA) or an Ortec 142 IH (EG&G Ortec, Oakridge, TN) charge sensitive pre-amplifier, and an Ortec 572 linear shaping amplifier;
- a high resolution Amptek XR-100CR spectrometer (Amptek, Inc., Bedford, MA), with a 7 mm2 Si PIN photodiode detector cooled by Peltier cells, and an Amptek PX2T shaping amplifier.
In both configurations, after amplification, the pulses were sent to an Amptek MCA 8000 multichannel analyser and a computer with PMCA acquisition and analysis software.
The spectrometers' calibration data have been determined through Gaussian curves fitted by least squares method to peaks of the measured spectra of X-rays and gamma-rays emitted by calibrated radioactive sources of 241Am, 133Ba, 109Cd and 57Co (AEA Technology QSA GmbH, Oxford, UK). Energy data from Firestone [12] were used as standards. The calibration straight lines were obtained by least squares fit of the determined peak channels. Figure 1
shows, for comparison, three 241Am energy spectra measured with the following detector configurations: (i) Hamamatsu S3071 photodiode + Ortec 142 IH pre-amplifier, (ii) Hamamatsu S3071 photodiode + eV 550 pre-amplifier and (iii) Amptek XR -100CR. These spectra were all corrected for the dependence of detector full energy absorption efficiency on photon energy, as described in reference [13].
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Figure 1. Three 241Am X-ray and gamma-ray spectra obtained with the detector configurations used in this work (Hamamatsu S3071 photodiode + Ortec 142 IH pre-amplifier, Hamamatsu S3071 photodiode + eV 550 pre-amplifier and Amptek XR 100CR), after corrections for the variations of detector full energy absorption efficiency with photon energy [13]. All spectra were normalized to the 59.54 keV peak maximum.
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X-ray beams were produced (1) by a clinical Siemens Heliophos 4B system with a Siemens W/Re rotating anode tube (Siemens, Brazil), 12° anode angle, with about 2.0 mm Al inherent filtration, connected to a three-phase or a single-phase generator, and (2) by an oil cooled constant potential Philips MGC 40 system (Philips Industrial X-Ray GmbH, Hamburg, Germany) with a 22° angle W anode, 4 mm Be inherent filtration tube.
For part of the measurements, the Philips MGC 40 system was used with additional molybdenum filtration 0.04 mm thick and fine focus, to simulate mammography beam characteristics [14, 15]. This is an unusual procedure used only for research purposes. Additional copper (for radiology beams) or aluminium (for some of the mammography beams) filtration was used to decrease the intensity of low energy photons, so reducing the probability of pulse pile-up in the detection system [16]; in this way, it was possible to decrease dead time and thus, to accumulate a larger number of counts in the final region of the spectrum in a shorter period. This reduced the probability of spurious counts beyond the end-point. Table 1 shows the selected filtration for each kVp and beam type. The criteria for the choice of these filtrations will be described in the next section.
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Table 1. Values of extra added filtration determined by the simulation method described (see text) for each nominal kVp utilized, for radiography and mammography kVp ranges. In the fourth column, values represent the Cu filtration actually used to avoid pulse pile-up in the spectrometer
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Additionally, the Amptek pre-amplifier was covered at the sides with lead and copper sheets and placed in a thick aluminium box, provided with a window in which were set two 2.0 mm thick tungsten collimators, with hole diameters ranging from 50 µm to 2000 µm, for intense beams. These collimators were placed 40 mm apart using a lead and copper cylindrical spacer, the smaller one near the detector window to reduce the incident beam fluence rate (Figure 2). Lead collimators were also fitted to the X-ray tube housing window in order to reduce the X-ray field size and scattered radiation. Care was taken to control tube current when beam fluence rate became excessive. In the present work, counting losses due to the dead time of the detection system have been kept below 5% for the three-phase and single-phase voltage generators (that were operated in pulsed radiographic mode) and below 1% for the constant potential equipment.
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Figure 2. Schematic cross-sectional view of Amptek detector housing. A: aluminium box; C: tungsten collimators spaced by a lead/copper cylinder; D: Si PIN detector; P: lead and copper sheets; W: detector beryllium window. Full box dimensions are 92 mm x 140 mm.
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Potentials were applied to the tubes in 10 kV steps for radiographic beams ranging from 40 kV to 110 kV for the single-phase and the three-phase generators, and from 50 kV to 120 kV for the constant potential apparatus. Focal spot to detector distances were, respectively, 1 m and 4.2 m. Mammographic beams were produced by the Philips tube, with tube potentials ranging from 20 kV to 40 kV, and the focal spot to detector distance was 5.3 m.
Selection of additional filtrations for the kVp determination
In a previous paper, Silva et al [4] presented a method for determining the suitable filtration for obtaining kVp values through X-ray spectra. In the present work, this method was improved in order to quantify more accurately this filtration. For this purpose, theoretical spectra were generated using the semi-empirical model of Tucker, Barnes and Chakraborty [17, 18], based on the quantum theory of Bremsstrahlung. This model produces spectra which agreed well with those obtained experimentally. Spectra were calculated using a MathCAD routine (Mathsoft, Inc., Cambridge, MA) for each tube potential, taking into account the tube target angle and composition and the inherent filtration, and using different copper or aluminium filter thicknesses. Figure 3 shows examples of generated spectra in the mammography energy range with different added aluminium filtration.
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Figure 3. Theoretical spectra N(E) generated using the model of Tucker et al [17], taking into account the characteristics of the Philips X-ray tube, for 28 kV and some values of added aluminium filtration, without molybdenum.
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Figure 4 illustrates the change of the ratio (Nend)2/Nmax with x (mm Al), where Nend is the number of counts at a channel 2 keV from the end of the spectrum, and Nmax is the number of counts at the channel corresponding to the maximum of each spectrum. In this example the ratio reaches a maximum value for an added filtration of 0.6 mm Al. The thickness determined in this way for each kVp, for both radiography and mammography beams, was adopted as the ideal filtration to be utilized to maximize the number of high energy photons in the measurement process for kVp determinations (see Table 1
). A mathematical relationship was determined for adjusting each set of calculated filtration values, as follows:
for the mammography range, and
for the radiology range.
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Figure 4. Ratio between squared counts at the end and at the maximum of the Bremsstrahlung spectrum (Nend)2/Nmax, for several aluminium filtration thicknesses x (mmAl), with 28 kV tube potential. In this case, the maximum corresponds to 0.6 mm Al additional filtration.
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In practice, the nearest available thickness to these extra filtration values or a higher value when it was necessary to reduce pulse pile-up was used.
To adapt the constant potential system for producing mammography beams, a Mo thickness was chosen in order to produce the same half value layers required in quality control standards [19]. For the Philips tube, the best value was 0.04 mm Mo.
Method for the determination of kVp values
The method adopted for determining peak potential (kVp) values from the measured spectra [4] was implemented by using another MathCAD routine, which consists of fitting two straight lines, one for the background beyond the endpoint and the other for the final region of the measured spectrum (counts per channel vs channel (or channel–1)). The abscissa (in keV) of the point corresponding to the intersection of these two lines provides the numerical value of the spectrally determined kVp applied to the X-ray tube.
A frequent problem with this method is the choice of the ideal energy range to perform the linear regression. If the number of experimental points is large, the statistical error will be smaller, but the quality of the straight line fitting will be poor. In the study presented here, an optimum energy range has been determined in order to minimize both statistical error, 
c, in the kVp value, and the parameter 
2red (reduced chi-squared), used to quantify the goodness of the fit. In order to obtain this optimum energy range, for each kVp the minimum value of the product
was determined within the 98% confidence interval for 2red [20, 21]. Thus, the corresponding value of kVp was adopted as the better kVp value for that case.
Factors affecting the spectral kVp values
Depending on the procedure adopted for spectrometric determination of the peak potential, the experimental time spent and the cost of the detection equipment could be reduced or increased. In order to optimize this procedure, the following factors that could influence the determination of kVp values have been analysed:
Ripple of the high voltage waveform applied to the X-ray tube
For this purpose, different sets of measurements were carried out with single-phase, three-phase and constant potential X-ray systems, in order to determine the energy spectra for several tube potentials and currents.
Spectrum counting statistics
Spectra of X-ray beams from the same X-ray machine, taken during different measurement times, were used to check the influence of counting statistics on the kVp values and errors.
Energy resolution of the detectors utilized for the spectrometric measurements
In this case, different configurations of Si PIN detectors (see previous sections) were used, both cooled and at room temperature, to determine the way in which this factor can affect X-ray spectra and corresponding kVp values and uncertainties.
Accuracy of the calibration procedure
Analysis of the influence of the spectrometer calibration process was made by varying the number of X- and gamma-lines (energies) considered in the calibration and verifying how the final kVp error was affected in each case. For this purpose, spectra from the previously mentioned radioactive sources were combined in sets of 1, 2, 3 or 4 sources, in order to obtain between 4 and 12 lines for the calibration of the spectrometer.
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Results and discussion
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Figure 5a shows the measured raw spectra corresponding to 90 kVp, with single-phase and constant potential generators, both measured with the Amptek system, for two different amplifier gains. Figure 5b in the high energy region of the raw spectra, shows the straight lines which best fit the experimental data in the linear regression process. The higher the voltage ripple, the higher the curvature of the end part of the measured spectrum, and thus the smaller the angle between channel axis and regression line.
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Figure 5. (a) Raw spectra at 90 kVp, with single-phase and constant potential generators, measured with the Amptek PIN photodiode system, with two different amplifier gains. (b) Details of the high energy region of the same raw spectra showing the straight lines that best fit the experimental data in the linear regression process, according to the method described in the text.
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Figure 6a shows a measured mammography X-ray spectrum and its corresponding corrected spectrum, which was obtained by applying corrections for the variation of the spectrometer efficiency with photon energy, beam attenuation in air and detector cover, as well as for Compton scattering, to the raw data [13]. The corrected spectrum confirms the end-point value found with the raw spectrum. Figure 6b is a detailed plot of the regression line fitted to the end portion of this raw spectrum.
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Figure 6. (a) Raw and corrected spectra obtained with a cooled PIN photodiode in an Amptek XR100 CR system for a nominal applied voltage of 35 kV and additional filtration 0.04 mm Mo, to simulate a mammographic beam. The 22 keV peak of the measured spectrum corresponds to fluorescence X-rays from the photodiode Ag back contact; this peak was suppressed in the spectrum stripping process. (b) Details of the end region of the measured spectrum with the straight lines corresponding to the linear regression and to the background. The value adopted, in this case, as the spectrum end point was 417.76 (equivalent to 35.012 keV) for determination of the kVp value.
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Table 2 shows the propagation of the partial errors in the determination of kVp, for measurements obtained with the S3071 Hamamatsu photodiode, operating with eV and Ortec pre-amplifiers, as compared with the Amptek system [22]. As would be expected, the poorer the detector energy resolution, the worse the final error (k) of the kVp values, because its calibration and the determined end-points are less accurate. However, apart from this general trend, results show that even with a system with better energy resolution, the accuracy of the final kVp values will be better only if the statistics of measured spectra are also better. Table 2 shows that the significant difference between the calibration accuracies of Hamamatsu photodiode + eV 550 pre-amplifier and of XR 100CR system remains masked by the higher errors due to the low counting statistics. The difficulty of reaching good counting statistics using non-fluoroscopic equipment is that there is no tube cooling and thus counts in the spectrum must be accumulated using many short time X-ray exposures, taking care to avoid damage to the X-ray tube.
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Table 2. Examples of error propagation in the determination of tube voltages applied to an X-ray tube by a three-phase generator, from measured spectra. The 6th and 8th columns show, respectively, the percent error c due only to the regression at the end of spectrum and the error k due to the detector calibration plus the regression
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Table 3 shows the trend in the influence of high voltage waveform ripple on the spectrally determined kVp values. The data show that, in general, as the ripple increases, the uncertainties of the determined end-point channel also increase.
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Table 3. Examples of error propagation in the determination of tube voltages applied to an X-ray tube by the single-phase and three-phase generators and by the constant potential system, from the spectra obtained with the XR 100CR system. Columns show the percent error c due only to the regression at the end of the spectrum and the error k due to the detector calibration plus the regression
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Table 4 shows the results of the kVp determined for the measurements made in the mammography range, with variable thickness Al added filter or only with fixed 0.04 mm Mo filter. In the latter measurements, an Al filter additional to the Mo filter can allow an increased tube current and thus reduce the measurement time.
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Table 4. Results for the kVp determined through X-ray spectra with the cooled PIN photodiode, utilizing the W anode constant potential tube in the mammographic range. Values obtained by adding a variable thickness of Al or a fixed 0.04 mm Mo filter are shown
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Table 5 shows the trend of the accuracy of the determined kVp values when the total accumulated counts increases, improving the counting statistics. Results show that, for the tube with the three-phase generator, there are no meaningful changes in the kVp values and accuracies, in the measured range of accumulated counts at the Bremsstrahlung maximum. On the other hand, for the tube with smaller voltage ripple, kVp error will vary from 0.04% to 0.02%, in the radiographic energy range, when the counts at the maximum of the Bremsstrahlung spectra vary from 130 to 640. For the mammography beams, this variation ranges from 0.11% to 0.08% when the counts at the maximum of the spectra after the Mo K-edge vary from 100 to 660. For more than 400 counts at the maxima, errors seem to be stabilized in these ranges. The larger exposure times used with mammographic beams are justified because molybdenum filters absorb most of radiation above the 20 keV K-edge. As mentioned above, an Al filter added to the Mo filters could allow a reduction of the necessary exposure time; this would be very useful if a clinical mammographic tube were used.
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Table 5. Analysis of the influence of counting statistics in spectrometric determination of kVp. Values were determined from spectra of X-ray beams from, for radiographic beams, the three-phase and the constant potential biased tubes, and for mammographic beams, the constant potential W anode tube with 0.04 mm Mo additional filter. These spectra have been measured during several exposure times with the Amptek detector. The 5th column shows the percent error c due only to the regression at the end of the spectrum and the last column, the error k due to the detector calibration plus the regression, in each case
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Figure 7 shows some examples of the effect of the number of energy lines utilized in the process of spectrometer calibration on the determined kVp values. It is clear that when more lines are used the kVp final error is less. Results show that the obtained kVp values stay constant, between the error limits, for 6 or more lines and the error represents a small variation (up to 0.05%). Statistics of counts in the spectra of the radiation emitted by the calibration sources also can play a meaningful role in the total uncertainty of kVp values. The data presented in Table 5 for constant potential radiology beams have been obtained using a calibration time much higher than the previous data set (three phase), showing very little contribution to the total kVp error. Thus the observed variation was only due to the regression process.
The reproducibility of the Amptek detection system was tested in an independent set of measurements. Several measurements were performed using an 241Am source, at different hours of the day, but during the same time and in the same room. Gaussian curves were fitted to all the main X-ray and gamma-ray spectral peaks, up to 60 keV, and the centroids were determined. Results showed that the mean values varied by less than 0.1% and their errors were smaller than 0.02%. Previous measurements performed with the Hamamatsu photodiode + eV 550 pre-amplifier, working at room temperature, had shown that centroids changed by less than 0.2%.
Direct measurements of the kVp were performed, for comparison, using a Dynalyzer III voltage divider and display (Radcal, Co., Monrovia, CA) and two non-invasive instruments, namely an RMI model 240 A (Gammex RMI, Inc., Middleton, WI) and an RTI model PMX III (RTI, Inc., Mölndal, Sweden). Measurements with the spectrometer were always made keeping the incident radiation flux low, through collimators and/or setting large distances between focal spot and detector, and if necessary, reducing tube current. On the other hand, with the non-invasive meters, measurements must be made in the manufacturer's prescribed configurations of peak voltage, tube current and positioning. The voltage divider can be utilized in both situations. Due to these differences in measuring conditions, averaged kVp values from the voltage divider were compared with spectrometric values and separately, with averaged values obtained from the kVp meters in another set of measurements. Table 6 presents examples of the results obtained for the three-phase generator, with the Amptek XR 100CR system, as compared with the voltage divider and the two kVp meters.
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Table 6. kVp values obtained through simultaneous measurements made electrically with Dynalyzer III high voltage divider, as well as in the primary beam with an Amptek XR 100CR spectrometer, for calibration of the divider. Results were obtained from an X-ray tube connected to a three-phase generator. kVp values from the voltage divider are the average of several individual values obtained from various X-ray exposures and the respective uncertainties are mean standard deviations. kVp values at non-invasive meters were obtained from their calibration curves relative to the divider, obtained from another set of measurements; for both of the meters, nominal accuracy for the readings was 2%
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Conclusions
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This work is a sequel to a previous paper by Silva et al [4], and has analysed the influence of factors such as detector energy resolution and calibration, counting statistics and high voltage waveform ripple, in determining peak kilovoltage (kVp) applied to X-ray tubes through the measurement of the spectrum of the emitted radiation, using silicon PIN photodiodes cooled or at room temperature.
Results show that the spectroscopic method is sensitive to variations due to some factors which can also affect the readings of invasive and non-invasive kVp meters.
Table 7 summarizes the results showing the contributions of each factor mentioned to the accuracy of spectrally determined kVp values. In mapping the behaviour of these results and their uncertainties, one can better plan how to apply this procedure and how to analyse results from different X-ray emitters and detector systems, both in conventional radiography and in mammography.
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Table 7. Analysis of the effect of the individual contributions to the uncertainties of the spectrally determined kVp values, with the Amptek detector. k represents the percent kVp error due to the detector calibration plus the spectrum regression and  kVp is the maximum variation of the kVp uncertainty with each parameter, in each kVp range
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Results illustrate the possibility of optimizing the calibration procedure of X-ray voltage dividers with digital displays based on their comparison with the data obtained through beam spectral measurements. Results also show that:- If there are no mixed radioactive sources available in a laboratory, depending on the desired accuracy, it is possible to use as few as two sources for a good calibration of the spectrometer, provided that six or more energies are utilized. Counting statistics will play a significant role in the uncertainties of the calibration data obtained.
- On the other hand, it is clear that the better the detector energy resolution, the smaller the calibration uncertainties and the final kVp error. Nevertheless, this reduction will only be noted with enough counting statistics, as with the last two configurations shown in Table 2.
- It is also possible to verify that the uncertainty of the determined kVp values decreases for small voltage ripples, mainly because the corresponding spectrum high-energy region is less curved. These results are in agreement with the data of Costa and Caldas [23], who compared X-ray spectra from machines of different high voltage waveform ripples to spectra calculated by Tucker, Barnes and Chakraborty, the TBC model [17], generalized for any voltage ripples.
- Counting statistics, in the attainable range up to about 500 counts at the Bremsstrahlung maximum, seems to play little or no role in the spectrometric kVp accuracy, depending on the tube voltage ripple. Probably a much higher number of counts will produce better results but with excessively large measurement time and tube load.
Although all these effects are small and somewhat interdependent, results show that, with enough counting statistics, the largest influences to be considered in the process of kVp determination are the uncertainties introduced by the detector calibration and resolution, and the high voltage ripple.
Care must be taken to maintain low counting losses due to the dead time of the counting system, in order to minimize pulse pile up. This effect deforms the end part of the spectra impairing the determination of kVp.
It is also convenient to avoid spectral kVp determination around 70 kVp because the tungsten K-edge (
69.5 keV) sharply decreases the counts in the end part of the spectrum, impairing kVp determination.
High voltage dividers are calibrated, in general, by means of electrical measurements that need to be performed periodically, generally by the manufacturer or by standard calibration laboratories. It is a time-consuming and high cost procedure, often beyond the resources of the users. The spectrometry method can be better utilized in the laboratory environment, for instance, in the secondary calibration of voltage dividers in kVpav. These devices can be used, in turn, for the tertiary calibration of portable non-invasive kVp meters, which are largely used in radiodiagnostic quality control routines, most of them indicating at least kVpav readings.
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Acknowledgments
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We thank the technical staff of the Technical Section of Tests in Electromedical Equipment, IEE-USP, especially Mr L Pidone, for help with the measurements made with the single-phase and the three-phase apparatus and for the provision of data referring to the calibration of non-invasive kVp meters. We also thank Mr F Y Kanashiro, for help with the constant potential measurements and data analysis.
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Footnotes
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This work was partially supported by the Brazilian agency FAPESP. 
Received for publication January 17, 2003.
Revision received October 14, 2003.
Accepted for publication October 22, 2003.
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Abstract
Introduction
) as a function of the number of energy lines utilized for spectrometer calibration, for the same set of measurements with 50 kV nominal three-phase potential applied to the tube. In the same graph, the percentage total kVp error for each number of lines used is shown (
). This is affected only by the change of calibration conditions.