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Showing papers on "Calibration curve published in 1998"


Journal ArticleDOI
TL;DR: It was found that the agreement between measurement and calibration curve is better than 1% if beam hardening effects in the acquisition of the CT images can be neglected and an estimation for the overall range precision of proton beams is given.
Abstract: The precision in proton radiotherapy treatment planning depends on the accuracy of the information used to calculate the stopping power properties of the tissues in the patient's body. This information is obtained from computed tomography (CT) images using a calibration curve to convert CT Hounsfield units into relative proton stopping power values. The validity of a stoichiometric method to create the calibration curve has been verified by measuring pairs of Hounsfield units and stopping power values for animal tissue samples. It was found that the agreement between measurement and calibration curve is better than 1% if beam hardening effects in the acquisition of the CT images can be neglected. The influence of beam hardening effects on the quantitative reading of the CT measurements is discussed and an estimation for the overall range precision of proton beams is given. It is expected that the range of protons in the human body can be controlled to better than +/-1.1% of the water equivalent range in soft tissue and +/-1.8% in bone, which translates into a range precision of about 1-3 mm in typical treatment situations.

377 citations


Journal ArticleDOI
TL;DR: In this paper, a multi-fiber optical reflection probe was uniquely calibrated in a downer to obtain quantitatively precise solids holdup, and an iteration procedure was utilized to modify the initial calibration curves.

180 citations


Journal ArticleDOI
TL;DR: In this article, multivariate statistical quality control principles, including control charting of calibration parameters and control samples, are applied to multilevel ion chromatography (IC) calibrations to determine instrument response stability and minimum calibration frequency.

170 citations


Patent
15 Jul 1998
TL;DR: In this paper, a test strip matching the measuring apparatus is set, and the type judgement electrode is electrically connected to a terminal of the set test strip, enabling the measuring device to measure a component to be measured in a liquid test sample.
Abstract: The present invention is to provide a concentration measuring apparatus, a test strip for the concentration measuring apparatus, a biosensor system and a method for forming terminals of the test strip, whereby a component to be measured can be measured by the test strip fit to the target component to be measured. A type judgement electrode is provided separately from a positive electrode and a negative electrode in a measuring apparatus so as to judge the type of a set test strip with the measuring apparatus. Thus only when a test strip matching the measuring apparatus is set, the type judgement electrode is electrically connected to a terminal of the set test strip, enabling the measuring apparatus to measure a component to be measured in a liquid test sample. A measuring apparatus detects a calibration curve information selection change for selecting a calibration curve information corresponding to a production lot of the set test strip thereby to compensate for an error in a measured concentration value of the component.

88 citations


Journal ArticleDOI
TL;DR: In this paper, a multilayer Si structure has been grown consisting of a decreasing B-doped staircase containing seven flat 4-5 μm thick calibration layers doped from 1020/cm3 down to 1015/ cm3 separated by slightly (factor 2-3) higher doped 1-2 μm interface layers.
Abstract: Frequently electrical characterization techniques [such as the spreading resistance probe (SRP)], rely on the availability of a set of well-calibrated, homogeneously doped Si samples to establish the calibration curves (and parameters) necessary for the conversion of resistance measurements into carrier profiles. Although ideally such a calibration should be verified daily, in practice, time considerations limit the daily verification to one (or a few) calibration samples. To remedy this situation a special multilayer Si structure has been grown consisting of a decreasing B-doped staircase containing seven flat 4–5 μm thick calibration layers doped from 1020/cm3 down to 1015/cm3 separated by slightly (factor 2–3) higher doped 1–2 μm thick interface layers. The latter are included to facilitate the SRP calibrations as the SRP correction factor within the calibration layers now becomes very close to one. Since presently, a calibration curve can be generated quickly from a single measurement, daily measureme...

70 citations


Journal ArticleDOI
TL;DR: In this article, three samples of micro-encapsulated thermochromic liquid crystals with different active temperature ranges were calibrated using a hue-based color decomposition system and a dimensionless temperature was defined that collapsed data from all three samples to a single calibration curve.

61 citations


Journal ArticleDOI
TL;DR: In this article, a bulk optical fluorescence based immunosensor capable for multianalyte water analysis is presented. But the sensor is reusable due to its regenerability and cost effective due to the use of components customary in the trade.
Abstract: We demonstrated a bulk optical fluorescence based immunosensor capable for multianalyte water analysis. Calibration curves obtained for 2,4-dichlorophenoxyacetic acid (2,4-D) and simazine had detection limits of 0.035 µg/l and 0.026 µg/1 respectively. The sensor is reusable due to its regenerability and cost effective due to the use of components customary in the trade. Ways to further enhance device sensitivity by means of a high index film deposited on the sensor surface or by employing an integrated optical waveguide as transducer are presented. A concept for the detection of a varying range of analytes on the same transducer is discussed.

58 citations


Journal ArticleDOI
TL;DR: In this article, the functional relationship describing the mixing of the suspension in the tank is expressed in a dimensionless form, and the relationship between the actual and the measured concentration is shown to be linear.
Abstract: Many plots for soil loss measurements are equipped with a sequence of tanks for measuring runoff volume and sediment concentration. The stored water volume is easily determined by a water depth measurement while the sediment concentration is often measured by collecting samples of the mixed suspension. In this paper, using the Π-theorem of dimensional analysis, the functional relationship describing the mixing of the suspension in the tank is expressed in a dimensionless form. The recognized dimensionless groups allow the establishment, for given soil and water depth in the tank, of the relationship (calibration curve) between the actual and the measured concentration. The calibration curve, using measured concentration values obtained from sampling taps located at different heights on the vertical of a tank wall, is shown to be linear. For a given soil, the slope of the calibration curve is related to the water depth. We also show that the same dimensionless groups allow the deduction of a scale-up procedure and the possibility of using a small tank, similar to the field one, for investigating additional effects neglected in the theoretical analysis. The effects of the following factors on the calibration curve are examined: (1) sampling direction along the vertical, i.e. starting the sampling from the upper tap to the lower one or vice versa; (2) mathematical shape of the concentration profile; (3) representativeness of the calibration cufve; (4) sampling volume; (5) water depth into the tank (i.e. filling level); (6) suspension mixing time; (7) grain size distribution of the eroded soil particles for given soil type; (8) time between the end of the erosive event and the starting of the sampling procedure (delay time). Finally, an attempt is made to define a simpler sampling procedure based on a single measurement with a dipped sampler. Copyright © 1998 John Wiley & Sons, Ltd.

56 citations


Journal ArticleDOI
TL;DR: In this article, six stacks of nuclear track detectors (CR39 and Makrofol) were exposed to 158.A.GeV 207 Pb ions at the CERN-SPS.
Abstract: Six stacks of nuclear track detectors (CR39 and Makrofol) were exposed to 158 A GeV 207 Pb ions at the CERN-SPS. The main purpose of the experiment was the calibration of the CR39 nuclear track detector used in a large area experimental search for magnetic monopoles at the Gran Sasso Laboratory (the MACRO experiment). Different targets (C, CH2, CR39, Cu and Pb) were used in order to study also the fragmentation properties of ultrarelativistic lead nuclei. The exposures were performed at normal incidence and at a density of about 2000 ions/cm2. The total number of lead ions in a stack was about 5.8×104. For the stack with the lead target, we measured the base area and the length of the etched cones. We obtain a unique calibration curve for the charge region 7≤Z≤83 combining the two types of measurements. Using the cone length method, we obtain a charge resolution σZ≃0.19e for Z=82 ions using a single measurement in one face of CR39.

49 citations


Journal ArticleDOI
TL;DR: In this article, laser ablation sampling (LAS) in conjunction with inductively coupled plasma-mass spectrometry (ICP-MS) was used for the quantitative multielemental analysis of red maple (Acer rubrum L.) tree rings.
Abstract: Laser ablation sampling (LAS) in conjunction with inductively coupled plasma-mass spectrometry (ICP-MS) was used for the quantitative multielemental analysis of red maple (Acer rubrum L.) tree rings. Slight differences in ablation were corrected using 13C as an internal standard. Calibration standards, consisting of individual tree rings from wood sections sampled from trees along a transect away from a metal smelter, were used to convert integrated signal intensities (cps) into concentrations (mg kg-1). The relative standard deviation (RSD) of element distribution within individual tree rings was <15% for 11 elements analyzed. Calibration curves were calculated for 43Ca, 55Mn, 63Cu, 64Zn, 114Cd, 202Hg, and 208Pb, as only these seven elements had different concentrations in the tree rings used as wood standards. Tree cores from red maple trees growing in contaminated soils adjacent to metal smelters and a discolored core from a tree growing in uncontaminated soil were analyzed by LAS ICP-MS. Differences i...

44 citations


Journal ArticleDOI
TL;DR: In this paper, a calibration procedure for vibrating-tube densimeters is developed which properly accounts for the effects of pressure and temperature on the Young's modulus and internal volume of the vibrating tube.

Journal ArticleDOI
01 Jan 1998-Analyst
TL;DR: In this paper, a procedure for the determination of morphine in non-aqueous, water immiscible, process streams by sequential injection analysis is presented, based upon the chemiluminescence reaction of morphine with acidic potassium permanganate in the presence of sodium polyphosphate, which was carried out in a heterogeneous reaction environment.
Abstract: A procedure for the determination of morphine in non-aqueous, water immiscible, process streams by sequential injection analysis is presented. Detection was based upon the chemiluminescence reaction of morphine with acidic potassium permanganate in the presence of sodium polyphosphate, which was carried out in a heterogeneous reaction environment. The calibration graph (range 0.005–0.12% m/v) was non-linear, with a polynomial equation of best fit of y = –384x2 + 139x – 4.84 (R2 = 0.9990), where y represents the singal (mV) and x represents the morphine concentration (% m/v), and was analytically useful over the range 0.01–0.1% m/v. Precision (as measured by relative standard deviation) was 6.0% for 10 replicate analyses of a non-aqueous morphine standard (0.075% m/v).Methyltriphenylphosphonium permanganate was investigated as an alternative chemiluminescent reagent and was found to deliver a similar analytical performance to potassium permanganate. Sequential injection analysis coupled with chemiluminescence detection afforded results for the determination of morphine in non-aqueous process samples which were in good agreement with those obtained using a standard liquid chromatographic method, with an analytical throughput in excess of 120 h–1.

Journal ArticleDOI
TL;DR: A series of different Yb-doped fibers has been investigated to determine their potential for use as the active elements in fluorescence-lifetime based thermometry, over a wide range from room temperature to 700 °C.
Abstract: A series of different Yb-doped fibers has been investigated to determine their potential for use as the active elements in fluorescence–lifetime based thermometry, over a wide range from room temperature to 700 °C. Heat treatment (“annealing”) has been shown to be necessary in practical applications to achieve consistent and reproducible calibration curves, each of which is consistent with the results of a simple two level model. Each sample studied was found to possess unique sensitivity characteristics, enabling an optimized selection for specific applications. The response of the thermometer and the error in the measurement was found to be, at <±5 °C, consistent with the stability of the calibrated oven used.

Journal ArticleDOI
TL;DR: In this paper, the results of the use of a double-focusing, magnetic sector inductively coupled plasma mass spectrometer (ICP-MS) with ultraviolet (UV) laser ablation (LA) are presented for the bulk analysis of rare earth elements (REEs) in rocks fused with Li2B4O7.
Abstract: Results of the use of a double-focusing, magnetic sector inductively coupled plasma mass spectrometer (ICP-MS) with ultraviolet (UV) laser ablation (LA) are presented for the bulk analysis of rare earth elements (REEs) in rocks fused with Li2B4O7. The sample preparation procedure used a sample to flux weight ratio of 1 : 7, and was identical with a procedure routinely used for X-ray fluorescence (XRF) analyses of major and minor elements in geological materials. Calibration was based on a total of 18 international standard reference materials (SRMs), and Ba was used as an internal standard element for all REEs. The calibration curves were constructed using a weighted regression model. The use of internal standard, without exception, improved the correlation coefficients significantly. The 3σ detection limits were established by a blank sample of SiO2 spiked with Ba, and were in the range from 0.003 μg g–1 (159Tb) to 0.051 μg g–1 (140Ce). The use of a large set of SRMs for calibration gave a good basis for the evaluation of analytical quality, and extensive data for calculated analytical uncertainty are presented. Instrumental precision and the repeatability of the method were studied separately, and no significant difference in these two sets of parameters were found, indicating that the spread of results predominantly was connected to the instrumental measurements. Repeated ablations on the surface of a disk did not influence subsequent measurements with XRF, showing that the fused disks can be stored for future use in XRF and/or LA-ICP-MS analysis.

Journal ArticleDOI
TL;DR: In this article, the enthalpy for alloy formation between the analyte element and the titanium matrix plays an important role in the atomization mechanism and the limits of detection for the 15 elements assayed were between 0.02 (Mg) and 30 ng/g (Sn).
Abstract: Solid sampling electrothermal atomic absorption spectrometry using the boat technique and a transversely heated graphite tube was applied to direct analysis of pieces of high-purity titanium for Al, As, Ca, Co, Cr, Cu, Fe, K, Mg, Mn, Na, Ni, Pb, Sn, and Zn. It was found that the enthalpy for alloy formation between the analyte element and the titanium matrix plays an important role in the atomization mechanism. While the elements Ca, Cu, K, Mg, Mn, Na, Pb, and Zn could be determined without any modification, carbon powder was added to facilitate the vaporization of As, Co, Fe, Ni, and Sn and to eliminate the matrix interferences in the determination of Al and Cr. Quantification was performed by using a calibration curve obtained with use of aqueous standard solutions. Accuracy was checked by comparison of the results with those of three other methods. Sample amounts of up to 30 mg per atomization were applicable. The limits of detection for the 15 elements assayed were between 0.02 (Mg) and 30 ng/g (Sn).

Journal ArticleDOI
TL;DR: In this paper, a simple laminar pipe-flow method for hot-wire anemometer calibration in the low-velocity range is described, where stable flow was generated by draining water from an air-tight container at a constant rate.
Abstract: A simple laminar pipe-flow method for hot-wire anemometer calibration in the low-velocity range is described. The stable flow was generated by draining water from an air-tight container at a constant rate. The influence of humidity variations between calibration and application was analysed. Calibration results were compared with results from another available device. One measurement of the laminar pipe-flow velocity profile using the calibration results was also performed. The present method was demonstrated to be a simple, but accurate, means for low-speed hot-wire anemometer calibration.

Journal ArticleDOI
01 Aug 1998-Talanta
TL;DR: The method was applied to sea water and well water, and the sum of As(III) and As(V) was determined with satisfactory results.

Patent
12 Jan 1998
TL;DR: In this article, a test gas sample containing carbon dioxide 13CO2 as a component gas is introduced into a cell, then the absorbance of light transmitted therethrough at a wavelength suitable for the component gas 13 CO2 is determined, and the concentration of the part gas is determined on the basis of a calibration curve prepared through measurement on test gas samples each containing the component gases in a known concentration.
Abstract: In accordance with the present invention, a test gas sample containing carbon dioxide 13CO2 as a component gas is introduced into a cell, then the absorbance of light transmitted therethrough at a wavelength suitable for the component gas 13CO2 is determined, and the concentration of the component gas is determined on the basis of a calibration curve prepared through measurement on test gas samples each containing the component gas in a known concentration. Further, the concentration of water vapor contained in the test gas sample is measured, and the concentration of the component gas in the test gas sample is corrected in accordance with the measured water vapor concentration on the basis of a correction curve prepared through measurement on the test gas samples each containing water vapor in a known concentration. With the spectrometry, the concentration ratio of the component gas can precisely be determined and corrected by measuring the moisture content in the test gas sample.

Journal ArticleDOI
TL;DR: A selective, sensitive, rapid and reproducible high-performance liquid chromatographic method for the determination of terazosin in plasma is described and the structurally related compound prazosin was used as an internal standard.

Journal ArticleDOI
TL;DR: In this paper, a novel thermal biosensor was made based on heat conduction through a BiTe-thermocouple on alumina plates, which was successfully applied to bovine serum samples where urea could be determined from a calibration graph or by standard addition.

Journal ArticleDOI
TL;DR: An analytical expression for the dose uncertainty for the ESR/alanine dosimetry system is presented, and shown to be rather simple to use, and suggested on obtaining calibration curve parameters and their uncertainties.

Journal ArticleDOI
TL;DR: In this paper, the effect of window symmetry on calibration transfer between spectra measured at different temperatures was investigated for near-IR spectroscopic determination of NaCl in aqueous solutions.
Abstract: Calibration transfer between spectra measured at different temperatures was investigated for near-IR spectroscopic determination of NaCl in aqueous solutions. A principal component regression (PCR) calibration model developed at 23.0 C was transferred to 28.5 C by using a piecewise direct standardization (PDS) method. The effect of window symmetry on calibration transfer was investigated. Only two transfer samples were needed in obtaining a good calibration transfer. The standard error of prediction (SEP) was 0.048 M NaCl when the calibration model developed at 23.0 C was used for predictions at 28.5 C without the standardization. The SEP was reduced to 0.008 M through the standardization, which was very close to 0.006 M obtained from a full set recalibration at 28.5 C and 0.007 M obtained from a general calibration model based on the spectra measured at different temperatures between 23.0 and 28.5 C. The calibration transfer from one temperature to another can save a lot of time in remeasuring the calibration samples and redeveloping a new calibration model at a new temperature.

Journal ArticleDOI
TL;DR: A frequency-tripled Q-switched Nd:YAG laser (355 nm, 10 Hz, 5 mJ per shot, Surelite, Continuum) was used for the ablation of glasses as direct solid sampling for inductively coupled plasma atomic emission spectrometric multichannel detection.
Abstract: A frequency-tripled Q-switched Nd:YAG laser (355 nm, 10 Hz, 5 mJ per shot, Surelite, Continuum) was used for the ablation of glasses as direct solid sampling for inductively coupled plasma atomic emission spectrometric multichannel detection. The colored and transparent glasses were glass standards used for calibration in X-ray fluorescence spectrometry and exhibited a 0.15-3.5 absorbance range at 355 nm. Translation of the target (1 mm s 1) with respect to the laser beam was used over a length of 16 mm. The depths and widths of the corresponding patterns were not related to the absorbance of the samples. However, the analytical line intensities were efficiently compensated for by using the Si(I) 251.611 nm line as an internal standard. The repeatability was therefore improved for Na, K, Ca, Mg, Sr, Ba, Zn, Pb, Al, Fe, and Sb, as well as the correlation coefficients of the regression and the centroid uncertainties of the calibration graph. Preliminary investigations were carried out to evaluate the acoustic signal emitted by the microplasma as external standardization. However, a negative correlation was found with the line intensity signals under our operating conditions.

Journal ArticleDOI
TL;DR: PIME as mentioned in this paper is an alternative approach to membrane extraction referred to as pulse introduction membrane extraction (PIME), where a pulse of sample is injected into the membrane, and steady state is not reached.

Journal ArticleDOI
01 Jan 1998-Analyst
TL;DR: In this paper, surface enhanced Raman scattering (SERS) is proposed as a molecular specific technique for direct measurements of organic molecules in aqueous solutions, where an FT-Raman spectrometer is interfaced with a flow injection manifold operated in the stopped flow mode enabling reproducible collection of SERS spectra.
Abstract: Surface enhanced Raman scattering (SERS) is proposed as a molecular specific technique for direct measurements of organic molecules in aqueous solutions. An FT-Raman spectrometer was interfaced with a flow injection manifold operated in the stopped flow mode enabling reproducible collection of SERS spectra due to the automation of the analysis procedure. For SERS a solid state substrate placed in a newly developed flow-cell was used. Multiple measurements on one single SERS substrate were achieved by rinsing the substrate with reagents such as 3 M KCl or 0.1 M NaOH solutions prior to the next measurements in order to remove retained analytes from the surface of the SERS substrate. This procedure allowed for improved precision as compared with a conventional batch approach. Quantitative aspects were investigated by establishing a calibration curve for nicotinic acid which was used as a model analyte. A linear dependance of the recorded SERS intensities from the logarithm of the analyte concentration was obtained throughout the whole investigated concentration range (0.001–0.1 M, correlation coefficient r2 = 0.97). The standard deviation of the method sx0 was found to be 0.122 mM and detection limit 1.7 mM, respectively. The results demonstrate the potential of SERS spectroscopy to be used as a molecular specific detector in aqueous flow systems such as flow injection analysis.

Journal ArticleDOI
01 Sep 1998-Talanta
TL;DR: The focusing of the laser beam on the surface was optimized to improve the signal-to-background ratio, and consequently the limit of detection was lowered, and the method precision expressed as relative standard deviation (RSD) was better than 6% in the concentration range 200-1000 mug g(-1).

Journal ArticleDOI
TL;DR: The proposed method was successfully developed for the determination of DHEA-S in biological samples and results were better than a similar method reported on previously.
Abstract: A method for the determination of dehydroepiandrosterone sulphate (DHEA-S) in biological samples is described. [7,7,16,16-2H4]-Dehydroepiandrosterone sulphate (2H4-DHEA-S) was synthesized and its applicability was examined as an internal standard with liquid chromatography/atmospheric pressure chemical ionization-mass spectrometry (LC/APCI-MS). Deuterium atoms in 2H4-DHEA-S molecules were not exchanged to hydrogen atoms during the extraction procedure from biological specimens in the determination of DHEA-S with LC/MS. The calibration curve of DHEA-S was linear over the range of 2-500 ng on-column. The detection limit of DHEA-S was 0.5 ng on-column with a signal-to-noise ratio of 3. The relative standard deviations of intra- and inter-assay with 200 ng of standard sample were 3.3 and 5.0%, respectively. These results were better than a similar method reported on previously (Nakajima et al., 1996). The proposed method was successfully developed for the determination of DHEA-S in biological samples.

Journal ArticleDOI
TL;DR: In this article, a Nicolet 410 Fourier (FTIR) spectrophotometer, equipped with a DGTS detector and a sample cell with NaCl windows (nominal pathlength=50 μm), was used for the development of an FTIR method for routine analysis of low trans levels in physically refined oils.
Abstract: A Nicolet 410 Fourier (FTIR) spectrophotometer, equipped with a DGTS detector and a sample cell with NaCl windows (nominal pathlength=50 μm), was used for the development of an FTIR method for routine analysis of low trans levels in physically refined oils. The approach of the study differed from those previously described in that a separate calibration curve was established for each type of oil. Quantitation was established by use of Basic Quant Software® and by measuring the peak height at 967 cm−1 relative to a baseline drawn between 1002 and 932 cm−1. The slope of the different calibration curves established in six vegetable oils (soybean, corn, sunflower, high-oleic sunflower, low-erucic rapeseed, and high-erucic rapeseed) was close to 1 (0.9942–1.0041), and correlation coefficients (r 2) were rather good (0.9990–0.9999). FTIR spectra of 20 soybean oil samples were collected and quantitated with the different calibrations. Compared to previous reported literature data, increased accuracy (mean difference=0.05%; standard deviation of difference=0.11%) and reproducibility (r 2=0.09–0.12%) were obtained when the FTIR spectra were quantitated with a calibration curve based on 10 physically refined soybean oil samples.

Journal ArticleDOI
TL;DR: In this article, a non-nulling calibration method using a seven-hole pressure probe in the range of at intervals both in yaw and in pitch planes is developed and reported.
Abstract: In this paper, a non-nulling calibration method using a seven-hole pressure probe in the range of at intervals both in yaw and in pitch planes is developed and reported. Calibration is carried out in two stages, low angles (for the maximum centre hole pressure) and high angles (other cases). On the basis of the maximum probe pressure reading, the calibration region is divided into seven zones; one central zone and six side zones. The calibration coefficients are derived for each zone. For interpolation, a localized two-variable polynomial is used at each point with the calibration data surrounding it. Zone extension is another useful feature developed here, in which each boundary point of every zone is extended to the nearest calibration point of the adjacent zone. By doing so, for a measuring point falling in between the boundaries of two adjacent zones, one employs the extended zone boundary data for fitting a polynomial. In addition to calibration data, additional data are acquired in the calibration tunnel. These data are used as measured data and calibration curves of suitable zones are used to derive flow parameters. In general, the interpolation errors in flow angles are found to be within and the errors in total and static pressures are within 0.5% and 1% of the dynamic pressure respectively.

Journal ArticleDOI
TL;DR: In this article, a calibration method based on the simultaneous introduction of sample and standard into the plasma by two independent devices is described, where two nebulizers are linked to the ICP by a Y-shaped tube.
Abstract: A calibration method based on the simultaneous introduction of sample and standard into the plasma by two independent devices is described. In this specific implementation, two nebulizers are linked to the ICP by a Y-shaped tube. Figures of merit were determined by comparing the results obtained with those produced using the method of external calibration. ‘Difficult samples’ containing matrices of C, Na, Al or K in concentrations ranging from 1000 to 10 000 ppm were used to provide matrices that produced significant errors when used with external calibration. The test solutions used for this study were mixtures of some of the following elements: Al, Cu, Mg, Fe, Ni, Pb and Zn in one of the matrices described previously. The comparison between the proposed tandem calibration method (TCM) and the method of external calibration clearly indicates that the TCM appears to be a valid alternative to traditional calibration methods, such as standard additions, matrix-matching and internal standards, that are commonly used when external calibration fails to give valid results for fficult samples' introduced into the ICP by means of a nebulizer. Improvement factors in accuracy based on the ratio of the relative error were, on average, of the order of 4 and, in some cases, well in excess of a full order of magnitude. For liquid samples, the precision of the results obtained by the proposed method was limited mainly by the noise of the sample introduction device (about 5% RSD on fficult samples'versus roughly 1% on clean standards) while the accuracy was limited by both the short- and long-term stability of the arrangement, typically around 7% relative error. In addition, the method was found to be easy to implement on existing equipment, inexpensive and potentially well suited for automation.