Impedance plethysmography applied to the head by using a pair of electrodes attached to the scalp surface is known as bipolar Rheoencephalography or REG I and was originally proposed to measure changes in cerebral blood volume related to the heartbeat. REG I was soon discarded in favor of other REG configurations, since most of the signal was shown to be heavily contaminated by the extracranial blood flow. The main goal of this study was to identify and compare the part of the REG I signal caused by scalp blood flow with that originating from non-extracranial sources.A clinical study involving thirty-six healthy volunteers was designed for this purpose. REG I was first registered in each subject under normal conditions. A pneumatic cuff was then placed around the head and was inflated to arrest the scalp blood flow and a second REG I was recorded. Finally, a third REG I was taken immediately after cuff deflation.The REG I signal is attenuated, but not extinguished, during cuff inflation in a wide subject-dependent range ratio from 0.12 to 0.68 (0.37 ± 0.15). The residual REG I signal has a waveform that is markedly different from that obtained before cuff inflation, which supports the hypothesis of the intracranial origin of the residual REG I signal. Additionally, an increase of 22% in REG I amplitude was observed when the head cuff was deflated.Waveform differences between extra and non-extracranial components are significant and these differences could be used in a method to distinguish one from the other. However, a significant part of the REG I signal is caused by a non-extracranial source and, therefore, it should not be used as a footprint of the extracranial blood flow. Maintaining an adequate cerebral blood flow (CBF) is one of the most challenging goals in severe head trauma . FollowiApplying impedance plethysmography to the head was first proposed by Polzer and Schuhfried  to fulfiFrom the beginning, REG has been a controversial technique: the REG signal is known to be contaminated although to an unknown extent by the extracranial circulation. This signal is recorded by injecting a low current between a pair of electrodes attached to the scalp surface, the impedance value being the potential measured between electrodes per unit of current injected. However, the skull has an electrical conductivity lower than that of the scalp and brain tissues. This causes the injected current to have a low resistive pathway through the scalp tissue, so that part of the injected current flows through the scalp instead of crossing through the skull to reach the brain (shielding effect). This extracranial contamination is inherent in the REG signal and may be responsible for the lack of agreement among the results of different research groups. For instance, although some earlier clinical studies suggested that REG I could provide information on changes in cerebral circulation related to aging or diffuse cerebrovascular diseases , some otThis controversy led REG II configurations to be preferred to REG I, even though Basano et al.  did not Research on REG declined after the initially high number of studies and at present it is practically ignored in both Europe and the USA, although REG is widely used in some other countries like China and Russia as a method to assess cerebral blood flow. The main reasons are the persistent extracranial contamination of the REG signal, the lack of knowledge on the mechanism that causes the impedance changes and, consequently, its clinical significance . DespiteThe clinical relevance of the impedance changes recorded intracranially has been shown in several studies. For instance, Bodo et al.  found thOther recent studies on bioimpedance techniques applied to the human head have also shown some clinical value. For instance, Traczewski et al.  establisExtracranial contamination is also present in other biomedical signals in which the brain is observed through the scalp. For instance, in a recent work in which three commercial devices for monitoring cerebral oximetry using near-infrared spectroscopy (NIRS) were tested, all of them showed some degree of contamination from the scalp blood flow (SBF) . HoweverTo sum up, a comprehensive review of REG literature suggests that, whatever the arrangement used, REG is a complex signal which is still not well understood, although it also undoubtedly shows a potential capacity to provide information on cerebral hemodynamics. Since the greatest handicap to REG is extracranial contamination, this study focused on REG I to decompose the signal into two components: one from the SBF and the other from a non-extracranial source. For this purpose we used a method similar to that used by Davie and Grocott  in identThe experiment described here is first part of a broader rheoencephalography study to be undertaken in stages.The experimental protocol was approved by the Ethical Board of the Universitat Politècnica de València . Thirty-six healthy volunteers  aged between 24 and 49 years (33 ± 7 years) were enrolled in this study. Prior to the experiment, the subjects were formally informed as to the purpose of the study and declared to have no previous history of cardiac or neurological diseases. For the tests, the subjects were comfortably seated in a sound-attenuated and air-conditioned laboratory. Firstly, four electrode positions on the coronal plane were located, and the skin was rubbed with sand paper and cleaned with alcohol: C5, C6 and the equidistant points between these standard positions and Cz  probes based on the reflective CNY70 optical sensor  were fixed with collodion to the scalp surface: one on the left side of the head equidistant from the disk electrodes P1) and a second on the sagittal plane equidistant from Cz and the cuff (P2), with the remaining two contralateral to these positions (P3 and P4) . The injected sinusoidal current had a root-mean-square (rms) value of 2 mA and a frequency of 32 kHz. This frequency was chosen as a trade-off between reducing signal noise ratio and decreasing the effects caused by capacitive and inductive lead coupling. A synchronous demodulator was used to provide the real part (R) of the measured impedance changes. The equipment offers three analog outputs: REG I channel; REG II channel when a four electrode arrangement is used; and an additional ECG channel for synchronous purposes. All channels are 0.1–35 Hz bandpass filtered. Gains were individually selectable from 0.5 to 100 V/Ω for REG I; from 5 to 1000 V/Ω for REG II; and from 0.5 to 5 V/mV for ECG. Additionally, a four channel amplifier was also designed for conditioning the PPG signals. All the analog outputs were sampled at 500 Hz, stored and off-line processed with Labview .The experiments were carried out in four sequential 2-minute stages and commenced with the head cuff deflated around the subject’s neck. The first stage was used to control and check the experimental setup, and hence the data obtained were not used in the analyses. During the second stage, the REG I signal between the Cc and Cc’ electrodes, ECG and PPG signals were recorded. The head cuff was then placed around the subjects’ head, inflated to 300 mmHg pressure, after which the same signals were again recorded. Finally, in the fourth stage, the cuff was rapidly deflated and the signals were recorded once more. The data recorded from C5 and C6 were not used in this study.To improve the signal-to-noise ratio, the raw data for each subject at each stage were processed to obtain the ensemble average time-locked to the R wave of the ECG, for a time-window extended from 100 ms previous to 700 ms after the R wave. The mean value was subtracted for each ensemble average and standard deviation  was used as signal strength indicator. A paired two-tailed Student test was performed to compare the rms value of the REG I traces in different cuff conditions.Figure Figure BI); during cuff inflation (σDI); ratio between them (σDI/σBI); rms value of the point by point subtraction of REG I during inflation from that before inflation (σ(BI-DI)); rms value of the point by point subtraction of REG I during inflation from that after inflation (σ(AI-DI)); and, finally, the last row gives statistical values of the time delay for each subject from the R wave of the ECG to the beginning of the impedance fall (tR-F).Table Comparison of the rms value of the REG I traces were performed using a paired two-tailed Student. This analysis shows significant differences between the REG I magnitudes before and during cuff inflation (P < 0.0001), as well as between before and after inflation when REG I during inflation is subtracted from both (P = 0.016).Rheoencephalography emerged in the middle of the last century as a promising method of obtaining information on the CBF. Following technological developments, the research in this field produced new medical devices of indisputable clinical value, including ultrasonography, near infrared spectroscopy, computed tomography and magnetic resonance tomography, among others . Once thIn this work we focused our attention in REG I, since our main objective was to identify the extracranial component of the REG signal and to characterize the waveforms of the additional components. Using a multi-shell theoretical model of the head, we previously found that only two percent of the REG I signal could have a non-scalp origin . HoweverIn our experiments we found that when the cuff is inflated the rms value of REG I falls to an average of 37% of its original value in each subject. In addition, this REG I attenuation varied widely among the subjects, ranging from 12% to 68%. Since the amplitude of the extracranial component of the REG I depends on the SBF, this high variability could be caused by the high variability in the SBF. This result is in agreement with the findings of Klemp et al. , who fouIn this paper, we avoided taking for granted that the residual part of REG I during cuff inflation is of intracranial origin, and therefore that it reflects the CBF. However, our results together with evidence found by other research groups do suggest this is possible. From the physical point of view, it has been shown that pulsatile changes in the brain’s electrical conductivity can be observed as pulses in the electrical impedance of the head, measured by electrodes attached to the scalp surface , 29. TheTherefore, REG I seems to be the weighted sum, of two components in a variable and subject-dependent ratio: one of them would be caused by the SBF and has a saw-tooth waveform Figure C, whereaThe extracranial component of REG I Figure C matchesThe specific mechanisms by which physiological events within the skull can be observed as changes in impedance measured on the scalp are still pending elucidation. The most widely accepted theory is that pulsatile changes in cerebral blood volume cause a pulsatile change in the brain’s electrical conductivity. However, other possible reasons should also be considered, such as changes in impedance caused by a global and pulsatile redistribution of electrical conductor fluids inside the skull , 35.Some limitations of the study should be taken into account. The weight of residual REG during cuff inflation on that before it should only be considered for the electrode positions used in this study. For other positions, two antagonistic effects should be taken into account. Let’s consider, for instance, an REG I recorded from electrodes closer to Cz than those we used in this experiment. On the one hand, an increase of the relative extracranial contribution to REG I could be expected when the electrodes are closer . On the In this study, instead of using a complete electrode set we decided to limit the analysis to a pair of electrode positions only, since our goal was not to define REG I topography, but was twofold: to identify two elementary components and their weights on the REG I; and to make a qualitative analysis of their waveforms.The electrodes at C5 and C6, placed but not used here, were not used in our study because these positions are too close to the head cuff and would therefore be sensitive to electrical conductivity changes on the other side of the cuff.Finally, the impedance changes cancelled by cuff inflation have been estimated by point by point subtraction of each subject’s ensemble REG I average during cuff inflation from that before inflation Figure C. AlthouOur findings suggest that, although a great part of the REG I signal is caused by the scalp blood flow, a significant amount is also due to a non-extracranial source. The ratio in which both sources are mixed in the REG I signal varies greatly among subjects, in some of whom even the non-extracranial component could predominate. Additionally, our results show that both components have substantial waveform differences: while the extracranial component has a predominantly saw-tooth appearance, the intracranial component has the shape of a catenary curve. Waveform differences between extra and non-extracranial components are significant and could be used in a method to distinguish one from the other. However, a significant part of the REG I signal is caused by a non-extracranial source and, therefore, it should not be used as a footprint of the extracranial blood flow.These conclusions allow to address the problem of REG from the point of view of blind source separation: REG II can be considered as a mixture of an intracranial component and an extracranial component. The simultaneous recording of two or more REG signals could therefore be used to extract their components by drawing on waveform differences between both components.Written informed consent was obtained from the patient for the publication of this report and any accompanying images.JJP was born in Valencia, Spain, in 1967. He received the M.S. degree in electrical and electronic engineering in 1992 and the Ph.D. degree in biomedical engineering in 2003 from the Universidad Politecnica de Valencia. He is currently an Associate Professor in the Department of Electronic Engineering of the same university and is member of the Bioelectronic Research Group (I3BH). His main research interests is the analysis of the electric field distribution in biological tissues and its effects.


The main objective of the present paper is to introduce a new approach for measuring and calculation of fundamental power components in the case of various distorted waveforms including those containing harmonics. The parameters of active, reactive, apparent power and power factor, are measured and calculated by using Goertzel algorithm instead of fast Fourier transformation which is commonly used. The main advantage of utilizing Goertzel algorithm is to minimize computational load and trigonometric equations. The parameters measured in the new technique are applied to a fixed capacitor–thyristor controlled reactor based static VAr compensation system to achieve accurate power factor correction for the first time. This study is implemented both simulation and experimentally. Reactive power compensation is a very important issue in the expansion planning and operation of electrical power systems. Traditional solution of the compensation is to use fixed-capacitors or reactors for providing and absorbing reactive power respectively Miller . AnotherStatic VAr systems are generally used in the fast changing events such as arc furnaces and steel industry where the current alters rapidly El-Saady . This tyThe main problem is how these power components are properly described in non-sinusoidal conditions. In the case of non-sinusoidal current and voltage, it becomes essential to use signal processing methods for power measurement. For this purposes, Fourier transform-based methods are usually used for analyzing power system harmonics. Fast Fourier transformation (FFT) algorithm is generally used for these purposes , i(t) and f0 respectively, general equations are given as follows  and i(t) are obtained from the continuous-time waveforms v(t) and i(t) as,The analog waveforms of the current and voltage should be sampled at discrete-times γ-th harmonics can be produced by the below equations respectivelyFor non-sinusoidal signals, Active and reactive power of the γ = 1, the coefficients a1, b1, β1 and α1 should be computed in order to find the first component of the active and reactive power from the equations v(k) and i(k), by utilizing the Goertzel algorithm ,,6), for In this section, the design of TCR–FC based SVC compensation system is simulated by using the Matlab/Simulink 7.13. Simulation is realized concerning to a single-phase SVC system with a static load model as a parallel R–L load. AC voltage source contains various distorted waveforms including those containing harmonics order of 3, 5, 7, 11. The power system and simulation parameters are listed in Table Simulation is modeled and performed three different static load groups separately. Load values, SVC settings and results obtained for simulation are given as tables. In order to obtain the effects of the SVC system, simulations are performed separately for the two different states. First it is assumed that there is no SVC in the system. Then, the SVC is put into the system. According to the before and after compensation, fundamental components of voltage and currents are measured and calculated by using both Goertzel and FFT algorithms separately. The structure diagram of simulation study is given Fig. Fundamental components of the power are calculated by using both Goertzel and FFT algorithms respectively. Computation times were calculated for each algorithm within the sampling period.It is explicitly illustrated from Fig. The structures of control and measurement blocks are given in Fig. According to the Table φ) is nearly close to 1.00 and SVC system has led to the improvement of power factor. In order to provide approximate values obtained from both simulation and experimental studies, the selected parameters for the simulations presented in Table It can be safely said that Goertzel algorithm is faster and superior than FFT compared with computation times. It is seen in Table KP: 0.3, KI: 36. Figure This simulation works are performed using discrete-PI controller. The proportional and integrator gain of the controller is selected as follows: In this study, only harmonic is analyzed by using Goertzel and FFT algorithms in order to obtain fundamental components of voltage and current to calculate power components and power factor. Any harmonic filter design is not implemented to eliminate any harmonic order.In this experimental work, the effect of the new measuring algorithm on the FC–TCR based SVC system is examined for reactive power compensation. The experimental load comprises a coil and resistance connected in parallel. According to the descriptions mentioned above of the SVC system, the general block diagram including voltage and the current measuring unit is depicted in Fig. Voltage and current samples are taken at various point of the circuit. Voltage is directly measured, but current is measured via a current transformer. Current transformers and connection points are illustrated in Fig. Picture of the experimental study is given in Fig. Load values, SVC settings and results obtained for each experimental works are given in Table The setting values and results obtained from the experimental study for each working conditions are shown in Table In addition to that, voltage, current, active, reactive and apparent power and power factor values are displayed on the screen by the use both algorithms before and after compensation respectively.The waveforms of thyristor firing pulse and reactor voltage captured by oscilloscope screen are shown in Fig. The waveform of the voltage and current at CT1, CT2 and CT3 points are captured by the oscilloscope and shown in Fig. In this experimental work, a new method is developed for the FC–TCR based SVC system. In this method, Fundamental components of voltage and current are obtained from the harmonic content network by using Goertzel algorithm instead of FFT. These values are utilized for the calculation of active, reactive, apparent power and power factor for the use of SVC system in order to achieve fast and accurate compensation. This study is realized both simulation and experimental. Simulation studies have shown that the computation time measured by using Goertzel algorithm is faster than FFT algorithm. In this way, power components and power factor values are measured and calculated by minimal hardware and reduced computational time through the use of Goertzel algorithm instead of classical FFT. Power measurement and calculation by utilizing Goertzel algorithm is applied to the FC–TCR based SVC system for the first time in this experimental study.


The National Institute of Standards and Technology (NIST) calibration service for voltage transformers and high-voltage capacitors is described. The service for voltage transformers provides measurements of ratio correction factors and phase angles at primary voltages up to 170 kV and secondary voltages as low as 10 V at 60 Hz. Calibrations at frequencies from 50–400 Hz are available over a more limited voltage range. The service for high-voltage capacitors provides measurements of capacitance and dissipation factor at applied voltages ranging from 100 V to 170 kV at 60 Hz depending on the nominal capacitance. Calibrations over a reduced voltage range at other frequencies are also available. As in the case with voltage transformers, these voltage constraints are determined by the facilities at NIST. This paper describes the National Institute of Standards and Technology (NIST) methodology for calibrating high-voltage capacitors and transformers. This should benefit NIST clients in several ways. First, by understanding how NIST makes these measurements, the clients might be able to define weaknesses in their own measurement procedures and correct them. Second, the clients should be able to make better use of the data in the calibration report . Third, the clients should be able to better specify the required test conditions so that information more pertinent to their needs can be obtained at a lower cost.This paper describes two different calibration services: high-voltage capacitors and voltage transformers. At NIST these two services are performed using the same equipment. In fact, in order to calibrate a voltage transformer, one of the steps is to measure the ratio of two capacitors. The two services are therefore discussed in parallel.There are several different ways to measure the ratio and phase angle of a voltage transformer. Harris  categoriIn the “direct deflection method” the primary and secondary voltage vectors are each directly measured. This approach is, in general, of most value for lower voltage transformers . Even then more accurate, less difficult measurements can be made using one of the other techniques.In the past NIST had used a “comparative null method” to calibrate voltage transformers. The unknown transformer was compared to a NIST reference transformer using a voltage comparator consisting of a variable resistive divider and a mutual inductor. Reference transformers were available with ratios ranging from 1/1 up to 2000/1. Measurement uncertainties in the comparison of the unknown transformer with the reference transformer were ±0.01% for ratio and ±0.3 minutes for phase angle. The ratio and phase angle of the reference transformers were known to about the same accuracy. There are several disadvantages to this approach. Since the comparator has a limited range, several reference transformers must be available to cover the anticipated users’ needs. The ratio and phase angles of each one of these transformers must be carefully determined over the secondary voltage range of interest. These transformers then have to be rechecked at regular intervals to determine if the ratios and phase angles have changed.If a direct measurement method were available that was sufficiently accurate and straightforward to make the calibration of these reference transformers a simple task, then that method could be used to measure the client’s transformer directly. At NIST, the “direct null method” in use originally involved balancing the secondary of the reference transformer against the output of a resistive divider used in conjunction with a variable mutual inductor to provide phase angle balance. Such a measurement was difficult because the resistive divider ratio changed with heating. Since the late 1960s a “direct null method” has been available that is straightforward and accurate and is now used at NIST in place of comparative methods using reference transformers.Capacitors are invariably measured by balancing the unknown capacitor against a known standard using some type of bridge arrangement. There are a variety of such bridges described in the literature . The oneThe main limitation of the Schering bridge is that the low side of the unknown and standard capacitors are not at ground potential at bridge balance. Therefore, without carefully guarding the bridge components, stray currents can affect the bridge accuracy. The voltage applied to the shields to eliminate these stray currents must be adjusted for both magnitude and phase. Unfortunately this procedure is not perfect and bridge accuracy is consequently affected. Another limitation of the Schering bridge is the inherent inaccuracy of the resistance ratio of the two low-voltage arms.The current comparator bridge developed by Kusters and Petersons  allows tThe remainder of this paper is divided into the following subject areas: voltage transformers and capacitors covered by the service, measurement methodology, measurement instrumentation, and analysis of uncertainties. The contents of this paper plus the cited references should provide the reader with a fairly complete description of the voltage transformer and high-voltage capacitor calibration services at NIST.The NIST measurement capabilities are summarized in Presently, voltage transformers  with primary voltages up to 170 kV at a frequency of 60 Hz can be calibrated at NIST. This maximum voltage is imposed by the supply transformer and not by limitations in the measurement instrumentation. Therefore, this constraint should not be considered rigid and clients should contact the NIST about present physical limitations.The largest portion of the voltage transformers submitted to NIST are calibrated with total estimated uncertainties of ±300 parts per million (ppm) in ratio, and ±0.3 mrad in phase angle. These transformers are of sufficient quality to be considered transfer standards. Historically these transformers have shown excellent long-term stability, rarely changing by more than 100 ppm in ratio or 0.1 mrad in phase (at or below rated burden) for periods as long as 30 years or more. In general, the voltage and burden dependence of these transformers are the major contributors to the measurement uncertainties. These uncertainties  meet the accuracy requirements of most NIST clients.±0.1 mrad in phase angle. They are generally designed for use with very small burdens (<15 volt-amperes).Voltage transformers of a higher accuracy class often serve as transfer standards for manufacturers of voltage transformers and voltage transformer test sets (voltage comparators). The estimated uncertainties for these transformers are ±100 ppm in ratio, and The above discussion for voltage transformers assumes a voltage at a frequency of 60 Hz. The National Institute of Standards and Technology has some capability to calibrate voltage transformers from about 50 Hz to 400 Hz (at the lower voltage and power ranges). Such calibrations are infrequent and clients interested in these voltage ranges and measurement uncertainties should contact NIST directly.The maximum voltage for capacitor calibrations is presently 170 kV at 60 Hz. The restrictions are imposed by the supply transformer and not by limitations in the measurement instrumentation. Therefore, this constraint should not be considered time invariant and clients should contact NIST about present physical limitations.C<50,000/{27π60V2} where V is the applied voltage and C is the capacitance). In order to energize the capacitors a resonant circuit is often required to couple the necessary energy into the client’s capacitor. Since this requires the availability of an assortment of series and parallel inductors and capacitors, there are undoubtedly some capacitors that, despite having a burden of less than 50 kVA, cannot be calibrated. The client should contact NIST before submitting a capacitor for calibration. As with voltage transformers, NIST restricts its calibration services to those devices of sufficient quality to be used as transfer standards. This in general depends upon the stability of the capacitor . For example, small two-terminal capacitors  may be significantly influenced by stray capacitance in the measurement circuit. There are cases, however, where one component (capacitance or dissipation factor) is stable and the other is not. For example, power factor capacitors often have relatively stable dissipation factors but have capacitances that vary significantly with applied voltage (even demonstrating hysteresis effects) and temperature. In this case a calibration of dissipation factor would be meaningful. It also is important that the capacitors have connectorsThe maximum power available is 50 kVA  necessitate a four-terminal measurement as shown in Capacitors are measured by balancing the current through the capacitor under test against the current through a standard air or compressed gas capacitor as shown in The client usually only needs to specify the voltage and the frequency. For small capacitors , it is essential that the low-voltage electrode and the conductor leading to the measurement instrumentation be shielded by a grounded conductor. Otherwise, the stray capacitance may cause significant measurement error. The National Institute of Standards and Technology requires some sort of standard connector  at the low-voltage terminal in order to connect to the measurement system. Larger capacitors do not need to be shielded but must be measured as a four terminal admittance because of the non-negligible lead impedance. A description of how this measurement is done will be covered in section 4. Capacitors must be stable and reproducible in order to be considered standards and hence warrant a NIST calibration. Power factor capacitors  are often special cases. Their dissipation factors (in-phase component of the current divided by quadrature component) are often quite stable but their capacitance values are often not. Because of the importance of these capacitors to the electrical industry, they are often acceptable for calibration even though they do not meet normal stability requirements.μA. The current through the client’s capacitor can range from 10 μA to 1000 A.Although the instrumentation has been used to calibrate a million-volt standard capacitor at rated voltage, the instrumentation does impose some limitations on the voltage applied to the capacitor. The only limitation on the maximum voltage is that the current through the standard capacitor should be no larger than 10 mA. In order to have reasonable sensitivity, the current should be at least 10 For the calibration of both capacitors and voltage transformers, the voltage coefficient of the standard capacitor is important. The unit of capacitance at NIST is maintained at low voltage. This value must be transferred to the high-voltage standard capacitors at their working voltages. At NIST, considerable work was done to modify a commercial high-voltage standard capacitor to minimize its voltage coefficient and to determine the magnitude of that voltage coefficient . The NatC is directly proportional to the electrode area and inversely proportional to the electrode separation, the thermal coefficient of the standard capacitor is proportional to the linear coefficient of expansion. Although the laboratories at NIST are fairly stable in temperature, the comparison of the high-voltage standard capacitor to the low-voltage standard  is done at the beginning and conclusion of the measurement process. The average value is then used in order to minimize the problem associated with this thermal drift.Another concern is the temperature dependence of the high-voltage standard capacitor. The typical dependence is about +20 ppm/°C. This dependence arises solely from the thermal expansion of the components of the capacitor. Since ∂C/∂P (to first order in pressure) measured at a temperature of 22.8 °C are shown in Compressed gas standard capacitors can have an additional source of error associated with gas leakage. Values of P, is in units of pascals and the capacitance in picofarads. For a 100-pF capacitor with SF6 as the dielectric gas, a 1-psi (6900-Pa) leak would cause the capacitance to decrease by about 140 ppm. It must be stressed that this change is valid only if the pressure change is caused by the loss of gas and not by the lowering of the gas temperature. As can be seen in 6. Clients using compressed gas capacitors for standards might be advised to monitor the gas pressure with a good quality pressure gauge. Leaking SF6-filled capacitors should be checked often against a good low-voltage standard.The gas pressure, In order to calibrate a voltage transformer, several different parameters must be specified: frequency; windings and/or range; secondary voltage; and burden or impedance across the secondary winding. In some cases, for example when there is a tertiary winding, additional parameters may be required.There are some standard conventions as to which of the primary and secondary taps are to be at low or ground potential and which are to be at rated voltage. Some transformers have one tap of the secondary and one tap of the primary winding marked by a “±”. These two taps are connected together and to ground potential. Some transformers use the designators H1, H2 for the primary taps, and X1, X2 (and Y1 and Y2 for the transformers with two secondaries) for the secondary taps. Sometimes the secondary winding has a third tap, X3. By convention the primary and secondary taps with the largest number are connected together and to ground. If the client wants some other arrangement, NIST should be notified prior to the calibration.−6. The capacitor connected to the secondary usually has the nominal value of 1000 pF. Therefore, for 60-Hz measurements, the capacitor imposes a negligible load (2.7 MΩ or 0.005 volt-amperes at 120 V) on the voltage transformer. Negligible in this case means that the effect of this burden on the measured ratio and phase angle can not be observed at the ppm level. The digital voltmeter (DVM) in The basic measurement circuit is shown in Cs is connected to the burden and the DVM instead of directly to the secondary terminal of the transformer. If the secondary burden were an ANSI standard burden ZZ  . A deriv0, as shown in Ei, and the output voltage with zero burden E0, is:N is the nominal (or turns) ratio of the transformer, RCF is the ratio-correction factor  at zero burden, Γ0 is the angle by which the secondary voltage vector leads the primary voltage vector and Ei, and the output voltage Ec, with secondary burden C (having impedance Zc) shown in RCFc is the ratio correction factor with secondary burden C and Γc is the corresponding phase angle. If the transformer is measured at zero burden (RCF0 and Γ0) and at burden T(RCFt and Γt), the ratio correction factor and phase angle at burden C are approximately given by:Bc = 1/Zc is the burden in Ω−1 of the impedance Zc, andThe voltage transformer will be represented as an ideal transformer with some unknown series output impedance ZC is cosθc, RCFc is the ratio correction factor calculated for burden C, and Γc is the angle by which the secondary voltage leads the primary voltage for burden C.The power factor of burden RCF and phase angle for some secondary burden, C, if the ratio correction factors and phase angles are known at some other burden T, and at zero burden. In practice, at NIST, capacitive burdens are used for the “T” or known burdens in μF can be switched in and out allowing any capacitance value from zero to 63 μF. Since a ZZ burden is equivalent to a 74 μF capacitor at 120 V, two such burden boxes are sufficient for nearly all the calibrations at NIST.Z0 to the impedance of the secondary burden Zt, or Zc. The smaller this ratio, the more accurate are RCFt− RCF0 and Γt− Γ0. If the ratio correction factor difference is 0.001 or less, and if the phase angle difference is 1 mrad or less than μrad for the phase angle if it is assumed that the ratio of the burdens is known with no more than ±1 percent uncertainty. Data over the years has indicated that Several approximations were made to derive RCFt− RCF0 and Γt − Γ0 are likely to be small for a burden as small as 10 volt-amperes and extrapolations can cause large errors. The second reason can be seen from Z0 to heat up and increase in value, leading to errors if T to have a volt-ampere rating the same order of magnitude as the burden of interest C. Also, the values in The above discussion might enable clients of the voltage transformer calibration service to better design their calibration requests. Using The measurement of the ratio and phase angle of a voltage transformer can be affected by the presence of harmonics in the voltage waveform. If a tuned null detector is not used, the balance of a bridge circuit can be difficult in the presence of harmonics and often a precise balance is not possible resulting in increased measurement uncertainties. Harmonics can also lead to errors in measuring the magnitude of the secondary voltage. For example, if an average reading, rms scaled voltmeter measured a 100-V rms fundamental with an in-phase 3-V rms third harmonic, the meter would read 101 V. Setting the voltage to read 100 V on the meter would result in a 1-V discrepancy between the intended and actual voltage. Many transformers have large enough voltage coefficients for this 1-V error in the voltage setting to have a non-negligible effect on the measured ratio correction factor and phase angle. If instead, a true rms voltmeter were used to measure this signal, the measured voltage would be 100.045 V and the resulting error would be negligible. At NIST three different steps are taken to lessen the effects of harmonics. The first is to try to minimize the harmonic content of the power supply. The supply used for most of the calibrations has a total harmonic distortion of order 0.2% of the fundamental. Second, a tuned detector is used to assure that the balance conditions are for the fundamental component of the voltage waveform. And third, all voltage measurements are made with true-rms voltmeters.An additional measurement concern is the voltage coefficient of the high-voltage standard capacitor shown in The calibration of voltage transformers and high-voltage capacitors at NIST requires the combined use of standard capacitors and the current comparator bridge. Standard capacitors have been thoroughly discussed in the literature , 6, 9,. Cx, is balanced against the current in the standard capacitor, Cs, by varying the turns ratios, Ns and Nx.The current comparator bridge can be thought of as a voltage comparator transformer arm bridge in which the detector and power source have been interchanged. Traditionally, the disadvantage of the current comparator bridge versus the voltage comparator bridge is the signal-to-noise level. For high-voltage measurement applications, this is no longer a problem. Kusters and Petersons were the first to develop this bridge for the comparison of two capacitors at high voltage . A basicIxNx = IsNs or:f is the frequency. This balance equation can also be expressed as:Balance is achieved when the signal at the detector D is equal to zero. At balance Cx. The current comparator in Rs. It is nearly impossible to design a stable high-voltage variable resistor with negligible phase angle. Another means is necessary to balance the in-phase current, preferably at low voltage using well-characterized components.The bridge shown in Ns winding, goes to the inverting input of the operational amplifier. This point is at virtual ground so the capacitive current balance, Cf causes the output voltage of the operational amplifier to be a small fraction (Cs/Cf where Cf is approximately 10 μF) of the applied voltage and π radians out of phase with it. The inductive voltage divider allows a known fraction, α, of this output signal to be applied across a standard resistor R. As can be seen from The current comparator shown in Ns reaching the operational amplifier has no phase defect. The in-phase current into the standard winding sN is then equal to:It is necessary that the non-inverted signal be applied to an identical standard resistor as shown in Iout = V2πfCs, the dissipation factor is:Since the quadrature current R can be chosen so that α is direct reading in percent or milliradians.The resistor e at the low-voltage terminal of the capacitor. This voltage signal is inverted as shown in Ns winding through a capacitor Cs′. The current through the unknown capacitor is:In some cases, particularly for larger capacitors, it is necessary to make a four-terminal measurement. This is required when the lead and winding impedances become a significant fraction of the impedance to be measured. Ns winding is:The current reaching the Cs′ is adjusted prior to the measurement to be equal to Cs then If Comparing this with Nd/Nx is 1000). The external current transformer shown in The current comparator bridge is quite straightforward to use and has proven to be rugged in practice. In order to monitor the behavior of NIST’s current comparator bridge, a check standard is maintained. In this case, the check standard consists of two high quality standard capacitors. The ratio of the two capacitors is measured quarterly. For the last 8 years, this ratio has been stable to within about 20 ppm as can be seen in The drift can readily be attributed to the two capacitors. The 9 ppm change between 10/84 and 4/85 occurred apparently after one of the capacitors had been used for another purpose. An independent measurement of that capacitor verified the change. While the use of this check standard cannot prove that the bridge is still working to the ppm level, it can alert the user of changes large enough to affect calibration results. Of course, since the two capacitive currents are largely balanced using stable passive components , one expects that the bridge should be stable. It should be noted that if a transformer winding were to become open or short circuited the result would be dramatic and readily observed by the operator.R, becomes important. The in-phase current entering the Nx winding is:α is the ratio of the inductive voltage divider (α≪1). The dissipation factor Iin/Iout is then equal to:The situation with the dissipation factor (or in-phase current) balance is different as active components play an important role. Also, it is difficult to design a stable dissipation factor standard to act as a check standard. This problem has been overcome by using the circuit in ϵ can be significant at the ppm level and needs to be eliminated. The circuit in The effect of V subtracting Since ϵ≪ α are 0.003, 0.0003, −0.0003, −0.003. With a 1 MΩ resistor and a 1000-pF standard capacitor this enables a near full scale test of the dissipation factor on its four ranges. Recent results are shown in At NIST typical values of DFm (the last two columns) are well within ±0.2% of the measured value. This check is performed at approximately 6-month intervals.Agreement between the calculated values in It is further proposed that an additional check standard be obtained and measured quarterly. Specifically, a voltage transformer measured regularly at a ratio of 10:1 would give an additional check on the phase angle circuitry and on the bridge windings at something other than a 1:1 ratio.The records of the National Institute of Standards and Technology show examples of voltage transformers that have been calibrated at 5-year intervals over a period of 30 to 40 years. Invariably the original uncertainty statement covers any variation in ratio correction factor and phase angle observed over this period of time. Voltage transformers are often used by the client in conjunction with other equipment to measure some quantity. For example, used with a current transformer and watthour meter, a voltage transformer can help provide a measure of the energy consumed by a large power transformer. Thus it is important to the clients of this calibration service to obtain a meaningful uncertainty statement that reflects the contribution the voltage transformer would make to their total error budget.As mentioned earlier in this paper, voltage transformers calibrated at NIST generally fall into two accuracy classes: ±0.03% uncertainty for ratio correction factor, ±0.3 mrad for phase angle; and ±0.01% for ratio correction factor, ±0.1 mrad for phase angle. While it would be possible in some cases to report smaller uncertainties to the clients by more thorough determinations of such parameters as voltage coefficients, proximity effects, and burden dependencies, the present service provides an economical way to present meaningful error statements to the clients and meets their needs.The analysis of the uncertainties for the ratio correction factor measurements are summarized in To calculate the uncertainties reported to the client, the systematic uncertainties tabulated above are algebraically summed and added to three times the root sum of squares of the random uncertainties. The results are shown in The values in Since most of the sources of uncertainty presented in −6 ± 1 % of the measured value for the relative dissipation factor. The values of the standard capacitors used for these comparisons are known to ±10 ppm for capacitance (±1 × 10−6 for dissipation factor). The random uncertainty associated with the capacitance measurement is ±1 ppm and ± 1 × 10−6 for dissipation factor. Conservatively then, NIST could calibrate a client’s capacitor to an overall uncertainty of ±15 ppm in capacitance and ±5 × 10−6 ±1% of the value for dissipation factor. In general, the quoted uncertainty is always larger than this except for low-voltage standard capacitors similar to those used at the National Institute of Standards and Technology. The National Institute of Standards and Technology has the capability to measure the ratio of two capacitors to an estimated systematic uncertainty of ± 1 ppm and ± 1 × 10The uncertainty statements for high-voltage standard capacitors and power-factor capacitors depend on the stability of these devices during the course of the NIST measurements. The stability is influenced by both the voltage dependence of the device and self-heating . Self-heating effects are more important for power-factor capacitors. Some power-factor capacitors demonstrate significant hysteresis effects. Assigning an uncertainty statement to these measurements depends on the specific behavior of the capacitor. If self-heating is a problem the calibration report clearly must specify the amount of time the capacitor was energized before the measurement was made. If hysteresis effects are detected they are so noted. Because of the nature of most of these devices, the calibration reports for capacitors usually include a statement of the form: “the estimated uncertainties quoted apply to the above tabulated values and should not be construed as being indicative of the long-term stability of the device under test.” This statement is also important for the compressed gas insulated capacitors whose values might change significantly by handling during shipping.The actual uncertainty quoted to the client is derived by algebraically summing the systematic uncertainties and adding three times the root mean sum of squares of the random uncertainties. For the capacitance measurement of compressed gas insulated capacitors, the measurement uncertainty will include a 20 ppm contribution because of the possible 1 K variation in temperature of the NIST voltage transformer laboratory. For power-factor capacitors the self-heating variations will dominate ambient temperature effects.


Movalyser 2.3 processed the data from which the following measures were obtained: pattern legibility, linear spatial error and speed of execution. Two expert teachers also judged legibility. Children in the GA showed more number of legible patterns, they were slower to complete the task but they were more accurate in its reproduction. The adjustable school desk facilitates the acquisition of legible graphic patterns. Since stable graphic skills are positively correlated to the production of creative texts, studies unraveling the role of school desks to facilitate handwriting and drawing skills will contribute ultimately children’s literacy and overall educational development.The role of two different layouts of school furniture was investigated in the pattern legibility and spatial–temporal parameters of a graphic skill acquisition. Thirty children from the first grade of elementary school (mean age = 6 years) practiced a graphic task according to a criterion figure. They were assigned to two groups, Group of Fixed School Desk (GF) and Group with Adjustable School Desk (GA). Each child practiced the task on a digital tablet for 25 trials. The software  Learning to write has been a key process in Education as it is vital for literacy. Postman  argues tThe motor skill to write and drawn is critical during the school period as it is involved almost in all school activities. Christensen  points oThe study of handwriting and drawing skills has been a field on its own known under the term graphonomics that aims to investigate the planning and organization of theses actions and its relationship with the resulting spatial traces  to investigate different layouts of school desks, as an independent variable; (2) describe the effects on pattern legibility, spatial and temporal aspects of children’ strokes, these being dependent variables. These last three variables are related to the memory representation that is formed during the handwriting and drawing experiences. Pattern legibility is related to the sequence of action and the spatial and temporal parameters of the strokes are related to relative timing and force  with seven boys and eight girls (n = 15), mean age of 6 years and 9 months, and Group Adjustable School Desk (GA) with nine boys and six girls (n = 15), mean age of 6 years and 7 months.The task involved the reproduction of a graphic pattern similar to a king’s crown Fig. . This grMovAlyzer, version 3.2, developed by Neuroscript Group. This software recognized children’s strokes in terms of space and time allowing for the description of the graphic produced in terms of stroke speed, timing and sequence.The reproduction of the graphic pattern was made on a AIPTEC Tablet, model 8000 U, with a cordless sensitive pressure pen. The tablet was connected to a notebook model Hewlett-Packard Pavillion Intel Dual Core. The collected data was treated by a Software The study focused on the effect of two kinds of school furniture, one standard and fixed (GF), and another that could to be adjustable (GA) to the child’s physical dimensions Fig. . ChildreThe study was conducted in a quiet room in the elementary school attended by the children studied, following an authorization given by the School Principal. In accord with the classroom teacher, each child was invited to take part in a graphic task that was going to take place in another room. Once there, the child was asked whether he or she recognized the figure and then whether he or she could drawn it. The child was asked to reproduce the pattern as accurate and fast as possible in 25 trials. The criterion figure was presented at the top of each sheet serving as model to the children. The instructions stated that the king’s crown should present three tips and a rounded base. The experimenter asked the child to perform the task with his or her preferred hand and not the change hands during practice. The child had visual feedback about the spatial features of the patterns produced and also the time taken to perform it.From the record of strokes the quality of the graphic skill was assessed by two evaluators who judged the degree of legibility considered from the correspondence between the model and the actual drawing. Graphic reproductions were considered legible when the three tips and the rounded base of the crown could be identified. The agreement between the evaluators judgments was tested by an inter-rater agreement index proposed by Thomas et al. . The valMovAlyzer made a recognition analysis of all patterns drawn automatically discarding those that did not match the specifications. The quantitative analysis was based on two measures: total movement time and spatial linear error. Total Movement Time comprehended the time interval from the start of the first stroke to the conclusion of the drawing calculated in seconds. Spatial linear error was calculated as the linear size difference in centimetres between criterion figure (the model) and the actual drawing performed by the children.Legibility was further used as a control to eliminate from the quantitative analysis the drawings that did not correspond to the model. The software The main assumption made in the present study was that the lay out of school desk will interfere with the legibility of the drawing, body posture and also with the spatial and temporal aspects of graphic patterns. Hence, we hypothesized that adjustable school desk will provide better conditions for practicing the drawing. This benefit will be manifested in the children’s performance with the GA doing better than GF in every account.F-ratio was obtained, the Tukey post hoc test with Bonferroni correction was used to locate the differences. For all statistical analyses, significance was accepted at p < 0.05. The Contingency Correlation test was also calculated to search for significant associations between body postures components and legibility of patterns. This type of test is recommended to verify the existence of associations between nominal variables. The statistical analysis was performed using Statistical Package for Social Sciences .For the purpose of the descriptive and inferential statistics, the 25 trials of the practice session were grouped in five blocks with five trials each. The Univariate Cochran’s C and Brown-Forsythe tests were used to test for normality of the resulting data. The differences in pattern legibility and spatio-temporal parameters between the two layouts of school furniture during the practice of the task were tested by a Two-Way ANOVA, Group (2) × Blocks (5) with repeated measures in the second factor. Whenever a significant We expected that adjustable school furniture would allow a posture more appropriate to handwriting and drawing. Indeed, we did find that children from the GA had their body posture’s components organized to favour postures more adequate to handwriting and drawing Table . The bod4,147 = 10.12, p < 0.001, n2 = 0.37. The conduction of a post hoc Tukey Test indicated that the two groups improved legibility with practice but GA showed more legible patterns than GF, particularly at the end of practice (last two blocks).The adjustable school furniture facilitates the body orientation and posture for practicing graphic skills, this should lead to a better pattern legibility. This was confirmed even though children in both groups showed changes in pattern legibility Fig. . Accordip < 0.02. For children in the GF there was a significant correlation between total hand support and pattern legibility: 0.68, p < 0.03. It is worth mentioning that hand support is a component that is not dependent on the layout of the school furniture.One should expect that adequate body posture will correlate positively with pattern legibility. The relationship between school furniture with the quality of drawing is illustrated by The Contingency Correlation Test. We found a significant correlation between some of the body posture’s components and the legibility of graphic patterns. There was a significant correlation for the GA, between total and partial feet support and pattern legibility: 0.72, 9,345 = 12.17, p < 0.002, n2 = 0.26. The conduction of a post hoc Tukey test indicated that the decrease was more marked for the GA with statistically significant differences from Block 1 to 3 and 5. For the GF the statistically significant difference was from Block 1 to 2. In spite of fewer changes during practice, the GF was faster than the GA in all blocks.Pattern legibility is associated with the speed-accuracy trade-off. As the speed of execution increases, the number spatial errors might also increase. Nevertheless, it is expected that as learning progresses, the time to complete the task will decrease, hence the speed of execution will increase to a certain point, i.e. when accuracy is hindered by speed. Body posture can affect the speed-accuracy trade-off in which an adequate body posture for drawing or handwriting may allow the child to perform faster without compromising accuracy (letter legibility). The evaluation of this relationship needs to consider together the results from total time to perform the task and the spatial error. The duration to perform the task decreased for both groups during practice Fig. . A Two-W9,726 = 9.17, p < 0.001, n2 = 0.44. The conduction of a post hoc Tukey test indicated that children in the GA showed statistically significant decrease in linear spatial error from Block 1 to Blocks 4 and 5. In another direction, children in the GF showed an increase in linear spatial error that was statistically significant from Block 1 to Blocks 2, 3, 4 and 5. The GF had also greater spatial linear error in comparison to the GA during all practice.The spatial error showed different rates of change for each group with the GF showing an increase of linear spatial error and a decrease for the GA Fig. . A Two WChildren in both groups, with fixed (GF) and adjustable (GA) school furniture, could benefit from practicing a graphic skill. However, we found evidence that the children’s performance with the adjustable school desk was better in different ways.First, the adjustable school furniture facilitated the adoption of body postures in particular the legibility and the accuracy with which the figure was reproduced. Children in the GA showed more legible patterns during practice and The Contingency Correlation Test confirmed this. It is true that pattern legibility improved for the children in the GF, however, as indicated by Two Way ANOVA, they showed a decrease in the number of legible patterns by the end of practice. The increase of less legible patterns may be related to the body posture the children adopted. Children in the GF rarely showed feet in contact with the surface and back support, together these two components might have contributed to a decrease in the quality of drawing. It has been shown that children who support their back in the chair and put their feet on the ground tend to write better Amudson . In factSecond, the results in regard to duration to complete the drawing and accuracy to perform it were interesting because they corroborate the effect well known as speed-accuracy trade-off. When performing motor actions one has to balance speed and accuracy, as being too fast will hinder accuracy and vice versa (cf. Crossman and Goodeve It is likely that the adjustable school furniture provides better conditions for the stabilization of shoulder and trunk. Children could concentrate on the task of drawing the criterion figure. The result was taking more time to complete the task, though with more accuracy. Feder and Majnemer  indicateIt is acknowledged for quite sometime that the ability to produce handwriting with fluency and legibility is important for expressing and communicating ideas (Phelps et al. The appropriate conditions to facilitate children’s acquisition of handwriting and drawing skills are in order. Adjustable school furniture is important to furnish school settings with the appropriate environment for children to acquire and enhance handwriting and drawing skills much for the benefit of their overall educational development.


It is shown that highly conductive surface electron states are present in Pbx1−SnxSe both in the inverse and direct electron energy spectrum.We suggest a method for detection of highly conductive surface electron states including topological ones. The method is based on measurements of the photoelectromagnetic effect using terahertz laser pulses. In contrast to conventional transport measurements, the method is not sensitive to the bulk conductivity. The method is demonstrated on an example of topological crystalline insulators Pb This method uses the photoelectromagnetic effect induced by pulses of laser terahertz radiation.UPEM between sample contacts oriented perpendicular to the incident radiation direction and to the magnetic field (see insert in the The photoelectromagnetic (PEM) effect is appearance of a voltage drop It comes as a consequence of a diffusive flux of photoexcited electrons in magnetic field, in an analogy to the Hall effect, in which the electron flux is determined by the electric field applied. In the PEM effect, the magnitude and the sign of the signal is defined by the magnetic field and by the direction and the value of the diffusive carrier flux. The charge carrier flux may appear either as a consequence of photogeneration of excess carriers in the surface layer of a semiconductor, or due to heating of free charge carriersx1−SnxSe. In this type of materials, crystalline symmetry replaces the role of time-reversal symmetry in ensuring topological protection. Pbx1−SnxSe form a continuous range of solid solutions for all tin content values 0 < x < 1. The energy gap varies with x passing through zero at x = 0.15 at T = 0 K  Pb T = 0 K 14. In thUPEM ∼ exp(−T/T0)  between the Fermi level and the conduction band edge. Therefore generation of electron-hole pairs is impossible, and the diffusive electron flux may be due only to heating of the electron gas by the terahertz laser radiation without changing its concentration. It is reasonable to assume that the degree of this heating is given by the temperature T0 ≈ 10 K.It is important to note that the sign of the effect corresponds to the net diffusion of charge carriers from the surface to the sample bulk. The origin of the “classical” PEM effect comes from spatial separation of optically excited electrons and holes which diffuse from the sample surface in magnetic fieldThe origin of appearance of the diffusive electron flux upon heating by terahertz radiation comes from the difference in charge carrier mobility of excited electrons nearby the sample surface and the electron mobility in the bulk of a sample. The excited electrons diffuse to the sample bulk while losing their energy. This leads, in turn, to counter diffusion of “cold” electrons from the bulk to the surface to provide the electric neutrality. In course of this process, the electron mobility gradient gives rise to a net flux of electronsn or p.In homogeneous samples, the direction of the net electron flux is defined by the energy dependence of the free charge carrier mobility. If the mobility of excited charge carriers at the surface is higher than in the bulk, the net electron flux is directed from the sample surface to its bulk, in the opposite case, instead, it is directed from the bulk to the surface. In contrast to the Hall effect, the sign of the PEM effect depends only on this direction of the free charge carrier flux and does not depend on the charge carrier type – T > 30 K in Pbx1−SnxSe and the congener compound Pbx1−SnxTe is the phonon scattering. It provides a drop in the electron mobility with increasing electron temperature. In relation to the PEM effect, this drop gives rise to a net electron flux directed from the bulk to the surface with the respective UPEM sign. It was observed previously in Pbx1−SnxTe samples with low free electron concentrationThe main scattering mechanism that defines the mobility temperatures dependence at high temperatures T < 20 K, instead, a temperature independent scattering mechanism becomes predominant since the electron concentration does not change and the resistivity saturates. It may be either the neutral impurity scattering or the strongly screened charged impurity scattering. In both cases, the number of scattering particles does not change with temperature. As shown in our experiment, the free electrons are heated by 10 K by the laser radiation. The free electron mobility either does not change or only slightly drops at 4.2 K < T < 15 K in Pbx1−SnxSeAt the low temperatures x1−SnxSe.The reasons for such an unexpected behavior could arise from two factors. First, there is a possibility that the net electron flux to the bulk could be due not to a change in free electron mobility, but to a change in the free electron concentration. This, in turn, may come out as a result of excitation of surface local electron states with very low binding energies. However a very high dielectric permittivity of the material ϵ ∼ 300 preventsx > 0.15, it would be reasonable to ascribe it to topological surface states of the TCI. However the effect is observed in samples with x < 0.15 as well. It means that the origin of the highly conductive surface electron states responsible for the effect is different. Appearance of highly conductive surface electron states both in the direct and inverse energy spectrum was predicted theoretically for TCI Pbx1−SnxSe and Pbx1−SnxTeIf the PEM effect would be observed only in samples with the inverted energy spectrum with The PEM effect amplitude changed by no more than a factor of 3–4 in different samples. This variation could result from slight difference in the experiment geometry for different samples. Another possible origin for such a variation could come from the scatter of the bulk electron mobility in different samples. On the other hand, the free electron concentration varied by more than two orders of magnitude. It means that the suggested method for detection of highly conductive surface electron states is not sensitive to the free electron concentration in the bulk. It is possible that the method may be applied for other TCI and TI systems as well. A criterion for involvement of topological surface states in the effect observed would be presence of the effect in the TCI or TI state of a system with the inverse energy spectrum and its absence in the situation with the direct spectrum.x1−SnxSe both in the direct and inverse energy spectrum. Therefore it is demonstrated that even if existence of the topological states is confirmed by ARPES experiments .


We describe the distinction between the operation of a short focal length x-ray microscope forming a real image with a laboratory source (convergent illumination) and with a highly collimated intense beam from a synchrotron light source (Köhler illumination). We demonstrate the distinction with a Kirkpatrick-Baez microscope consisting of short focal length multilayer mirrors operating at an energy of 8 keV. In addition to realizing improvements in the resolution of the optics, the synchrotron radiation microscope is not limited to the usual single magnification at a fixed image plane. Higher magnification images are produced by projection in the limit of geometrical optics with a collimated beam. However, in distinction to the common method of placing the sample behind the optical source of a diverging beam, we describe the situation in which the sample is located in the collimated beam before the optical element. The ultimate limits of this magnification result from diffraction by the specimen and are determined by the sample position relative to the focal point of the optic. We present criteria by which the diffraction is minimized. In 1948 Kirkpatrick and Baez –4. The eWhile the microprobe is limited to collecting only one pixel at a time, a true imaging microscope collects all of the pixels in parallel and could in principle be much faster. We have constructed a KB microscope of short focal length using multilayer mirrors, and this instrument has already shown promise as a fast imaging system using a laboratory x-ray source . We haveThese are achieved by the transition from a real image into a geometric projective image. Projective x-ray imaging is normally performed by placing the sample in a diverging beam after an optical element  rather tu and v are the object and image distances from a mirror with radius of curvature R and angle of incidence θ = θB, whose tangential focal length is simply f = (R sin θB)/2. When this “lens maker’s law” is applied separately to the two mutually perpendicular mirrors, the combined equations which constrain a fixed object to have the same image plane for both mirrors are known as the Coddington equations [Our basic arrangement for KB microscopy with synchrotron radiation is illustrated in quations :1u1+1v1iu and iv are the respective object and image distances for the two mirrors, whose centers are separated by d, i.e., u2 = u1 + d, and v2 = v1 − d  corresponds to 4000 pixels. If this image were obtained one pixel at a time, as with a microprobe . For v > if the magnification increases linearly with distance from the focal spot:This means that a projection image is collected downstream of the lens independent of the object position. Furthermore, there is no single image plane for a given object position: an image, which is the spatial modification of the intensity due to absorption by the sample, would be observed at v = iv, u = iu, it is still true that iM = iv/iu.The variable magnification has been tested by an extensive set of images obtained with the synchrotron x-ray beam. Of course, for u1.There are several observations concerning the use of this instrument in the geometric optics limit. First, instead of being limited to a fixed magnification, greater magnifications would be found by simply moving the camera further from the microscope . This woDiffraction effects constrain the above considerations of KB optics in the projective mode. Illumination of an object with a plane wave is in fact the starting point of the Abbe theory of image formation , in whicu1 = 41 cm and the camera at a distance v2 = 41 cm. The image was obtained with the microscope at the Advanced Photon Source on the 1-ID beamline, which has a beam divergence even smaller than that of the 1-BM beamline. The aperture of the first mirror (beam intercepted at the angle of the first Bragg condition at θ = 1.4°) is 0.65 mm. At a wavelength of λ = 0.154 nm, the Rayleigh limit of the optics is 7.6 nm, far smaller than our observable resolution limit.If we now consider Fresnel diffraction from the wires in the grid, the deflection of the first interference maximum from the edge of the image is given by Δy=(u1λ)if < iu < 2if, we assume that the diffracted rays are intercepted by the KB optic and refocused to an image at iv. This is no longer the case in the projection mode, where v > iv. In that case, the divergence angle ∆y′ of the diffracted ray at the image, which is 0 at v = iv, will be given generally byUsing the values above gives a deflection of 7.9 µm, which is consistent with the observed diffraction. We can thus set limits to the practical magnification of projection images. For an object at v > iv is thusThe deflection of the diffracted beam for u1 = 3.1 cm, we can tolerate ∆y′ = 8 µm, which is the limit of our camera resolution. This leads to a maximum distance of the camera of v = 79 cm without the perception of diffraction effects, at which point the horizontal magnification of the image is 28. At this point the magnified image of a wire in the grid would be 140 µm wide. Because of the short focal lengths of the mirrors, it is evident that small changes in specimen position u1 result not only in changes in the magnification of images in the projection regime but also in the degree to which the projected images are limited by diffraction. Unlike the assumption of geometrical optics, diffraction effects do depend on the position of the specimen in front of the optic for a perfectly collimated beam. In particular, iv/iu) permits a larger magnification in projection before the effects of diffraction become visible. By way of comparison, images taken at a specimen position u1 = 4.1 cm instead of u1 = 3.1 cm, for example, should show visible diffraction effects at the camera position of We apply the above calculation to our KB optics for the geometry of the image in The projection images discussed so far consider only the transmitted beam, but similar images can be obtained from beams diffracted from a crystalline sample as well. Dynamical diffraction from nearly perfect crystals would essentially preserve the synchrotron divergence allowing for the use of the KB microscope to obtain variable magnification in x-ray topography. It is also possible for diffraction from a given specimen to produce both parallel and diverging rays.Let us consider the example of a silicon wafer with a patterned overlayer of lattice-mismatched Ge on the surface. Diffraction of an incident synchrotron x-ray beam from the substrate will produce a perfectly reflected beam of parallel rays, while diffraction from the distorted regions at the edge of Ge features could show noticeable divergence. The KB optics could be configured as a synchrotron microscope to image the perfectly reflected beam to show an absorption map of the Ge features, or it could be configured as a real image microscope and directly focus the rays from the distorted regions, producing a surface distortion map.In summary, we have demonstrated the considerations that make the operation of a short focal length KB microscope in a highly collimated synchrotron radiation beam different from operation with a conventional divergent source. Tests at a low-divergence synchrotron beamline of a KB x-ray microscope produced test images with resolution of 1 µm or better, fields of view of 50 µm or more, and image acquisition times as low as 30 ms. Because of the unique aspects of a low-divergence beam, images in projection are obtained beyond the focus for a real image and the magnification in the projection mode varies with the distance of the camera beyond the focal point. Unlike simple geometrical optics, the effect of diffraction by the sample on the image depends on the focal length of the optics and the position of the sample. We have provided criteria that show the limits of projection magnification with KB optics and the effect of sample position.