On the performance of the ICP algorithm

We present upper and lower bounds for the number of iterations performed by the Iterative Closest Point (ICP) algorithm. This algorithm has been proposed by Besl and McKay as a successful heuristic for matching of point sets in d-space under translation, but so far it seems not to have been rigorously analyzed. We consider two standard measures of resemblance that the algorithm attempts to optimize: The RMS (root mean squared distance) and the (one-sided) Hausdorff distance. We show that in both cases the number of iterations performed by the algorithm is polynomial in the number of input points. In particular, this bound is quadratic in the one-dimensional problem, under the RMS measure, for which we present a lower bound construction of Ω(nlogn) iterations, where n is the overall size of the input. Under the Hausdorff measure, this bound is only O(n) for input point sets whose spread is polynomial in n, and this is tight in the worst case.We also present several structural geometric properties of the algorithm under both measures. For the RMS measure, we show that at each iteration of the algorithm the cost function monotonically and strictly decreases along the vector Δt of the relative translation. As a result, we conclude that the polygonal path π, obtained by concatenating all the relative translations that are computed during the execution of the algorithm, does not intersect itself. In particular, in the one-dimensional problem all the relative translations of the ICP algorithm are in the same (left or right) direction. For the Hausdorff measure, some of these properties continue to hold (such as monotonicity in one dimension), whereas others do not.     

ICP-AES测定陶瓷器皿中微量溶出铅、镉的研究

用4%乙酸溶液萃取分离日用瓷表面微量溶出元素Pb和Cd后,采用电感耦合等离子体原子发射光谱(ICP-AES)法进行了分析,对影响其测量的各种因素进行了较详细的研究,确定了实验的最佳测定条件。结果表明,方法的检出限为0.023(Pb)和0.006μg/L(Cd),回收率为98.0%~104.0%,RSD小于3.5%。该法准确、快速、简便,应用于日用瓷中的微量溶出铅、镉的测定,结果满意。     

微波消解-ICP-AES法测定塑料中Pb和Cd

采用微波消解法进行溶样,以ICP-AES法测定塑料中Pb和Cd的含量。Pb、Cd的回收率分别为96.0%~102.0、93.3%~105.0%。Pb、Cd测定结果的相对标准偏差分别为0.567%、1.19%(n=10)。Pb和Cd的检出限分别为0.02、0.005 mg/L。该方法适用于多种塑料中Pb和Cd含量的快速分析。     

Characterization of particles made by desolvation of monodisperse microdroplets of analyte solutions and particle suspensions for nanoparticle calibration in inductively coupled plasma spectrometry

Particles produced by low-temperature desolvation of monodisperse microdroplets of analyte standard solution and nanoparticle suspensions in argon were collected on Si-wafers and studied applying scanning electron microscopy and X-ray microprobe techniques. At desolvation temperatures of about 150 °C, the particles from standard solutions are most often spherical and solid with good reproducibility and the analyte elements together with the unavoidable accompanying elements from trace contamination seem to be homogeneously distributed in the particles. However, there are surprising exceptions, particularly at higher temperatures, where analyte elements are separated in the particle by reduction or crystallization, as shown with Au and Ca standard solutions, respectively. Drying droplets of a diluted suspension of 250 nm gold particles at 200 °C revealed another interesting result, the production of relatively stable concave balloons of ∼ 3 µm in diameter including the Au particles. The balloon sheath was formed of compounds made of the contaminant elements in the suspension. The morphology of the particles is discussed in consideration of the Peclet number, the ratio of evaporation rate to analyte diffusion coefficient. The consequences of particle size and morphology for calibration purposes in nanoparticle characterization by ICP spectrometry are discussed.     

Flow injection system for the on-line preconcentration of Pb by cloud point extraction coupled to USN–ICP OES

A novel method for the determination of Pb by on-line cloud point extraction coupled to inductively coupled plasma optical emission spectrometry with ultrasonic nebulization (USN–ICP OES) is presented. The cloud point system was formed in the presence of non-ionic micelles of polyethyleneglycolmono-p-nonylphenylether (PONPE 7.5) and was retained in a minicolumn filled with particles of PTFE. Since the micelles of PONPE were able to extract Pb from the solutions, the use of a complexing reagent was not necessary. Afterwards, the surfactant-rich phase containing the analyte was removed from the minicolumn with nitric acid and introduced into the ultrasonic nebulizer. A total enhancement factor of 150 was obtained for a preconcentration time of 3.3 min, with respect to the direct determination of Pb by conventional ICP OES. The values of the detection (3σ) and quantification (10σ) limits for the preconcentration of 10 mL of sample solution were 0.09 µg L^{− 1} and 0.2 µg L^{− 1} respectively. The precision, expressed as the relative standard deviation (RSD), for 10 replicate determinations at 5.0 µg L^{− 1} Pb level was 6.0%. Verification of the accuracy was carried out by analysis of two certified reference materials (NIST SRM 1640e and VKI QC Metal LL1). The method was successfully applied to the determination of Pb in drinking water samples.     

Determination of Hg and Pb in compact fluorescent lamp by slurry sampling inductively coupled plasma optical emission spectrometry

Mercury and lead were determined in an extraction solution applied to compact fluorescent lamps by axial view inductively coupled plasma optical emission spectrometry (ICP OES). The solution contained 50% v/v HNO₃ and 10% v/v H₂O₂. The compact fluorescent lamps were treated by removing the socket and breaking the rest of the lamp inside the solution, followed by placing the mixture in an ultrasonic bath for 1 h. The mixture was filtrated in a coarse paper filter and the resulting extraction slurry was analyzed. The determination of Pb in the slurry required calibration by the analyte addition technique, while for Hg, external calibration was adequate. The quantification limits (10 s, n = 7), for Hg (194.164 nm) and Pb (220.353 nm) were, respectively, 10 and 30 µg per lamp. Analysis of spiked samples demonstrated reasonable accuracy of the method, with recoveries in the range from 99 to 120% for Hg and from 91 to 107% for Pb. Fifteen analyzed samples showed Hg masses per lamp in the range from 1.6 to 27 mg, and six samples were above the limit allowed by the European Community that is 5 mg per compact lamp. The values for Pb were between 0.07 and 0.75 mg per lamp. By filtrating the slurry in a membrane filter, and analyzing the resulting solution, it was found that all Hg was extracted to the liquid phase of the slurry, while a fraction of about 40% m/v of Pb is retained in the solid particles. The lamp cover glass, after extraction of the phosphor layer, was also analyzed for Hg and Pb. The concentration of Hg in the glass is quite low; however, the Pb content is high.     

Arsenic speciation by gradient anion exchange narrow bore ion chromatography and high resolution inductively coupled plasma mass spectrometry detection

Based on gradient anion exchange chromatography (AEC), a new strategy in As-speciation was evaluated. A narrow bore chromatographic system with lower flow rates (≤300 μL) well suitable for the low flow requirements of higher efficiency nebulizers was splitless coupled to a high resolution sector field ICP MS. The AEC system takes full advantage of the detector sensitivity allowing more diluted samples (50–100 times) to be injected, delivering substantially less sample matrix to the column and a lower eluent load to the plasma. The unique plasma compatibility of the NH₄NO₃-eluent salt used in this study enabled high linear salt ramps in gradient applications, highly reproducible retention times (±1%) and detection limits in the low ng/L range. The separation conditions were applied on two different polymeric anion-exchangers: a low capacity, weakly hydrophobic material (AS11, Dionex) and a more frequently used higher capacity, higher hydrophobic material (AS7, Dionex). On both columns, As-species (As(III/V), MMA, DMA, AsB) and Cl⁻ were separated in less than nine minutes and co-elution was circumvented by adapting the separation pH to the optimal column selectivity. The key-advantage of the NH₄NO₃-eluent is that it can adopt any separation pH without compromising the eluent strength which is not possible with all other eluents used so far. The influences of chloride and methanol were investigated and found not to affect the chromatographic performance. Column deposits caused strong reversible As(v) adsorption which reduced As(v) to As(III). A corresponding phosphate excess in the injected sample eliminated the adsorption and prevented artefacts in As(v)/As(III) ratios. The method applied to ground water samples provided robust separations and is compatible with any sample preservation procedure.     

流动注射-阳离子交换预富集-ICP-AES 法在线分析磷矿中钙、镁、铝、铁的研究

用 732型强酸性阳离子交换树脂分离富集 ,并与改进的流动注射 (双流路 )相结合 ,建立了新型、高效的流动注射 -阳离子交换预富集 - ICP- AES在线分析体系。研究了酸度、流速、淋洗剂浓度等的选择、共存离子的干扰情况并应用于矿样的分析。 Ca,Mg,Al,Fe各元素的检出限分别为 0 .9μg/ L,0 .6 μg/ L,5.5μg/ L,1 .4μg/ L;1 0次测量的相对标准偏差分别为 3.4 4% ,1 .53% ,1 .6 0 % ,2 .58%。回收率在 93.0 %～ 1 0 1 .4 %之间。分析速度可达每小时 4 0个样品。     

Determination of Platinum,Palladium, Ruthenium,Rhodium, and Iridium in Ultrabasic Rock from the Great Dyke of Zimbabwe by Inductively Coupled Plasma–Optical Emission Spectrometry

Platinum, palladium, ruthenium, rhodium, and iridum were determined in ultrabasic rock from the Great Dyke of Zimbabwe by inductively coupled plasma optical emission spectrometry. The limits of detection for these elements were less than 7 ng/g. The samples were fused at 1100°C to separate the noble metals which were enriched into a nickel sulfide button and dissolved in hydrochloric acid. The insoluble noble metals were filtered, dissolved in aqua regia in a boiling water bath, and determined by inductively coupled plasma optical emission spectrometry. This method was employed for the characterization of large quantities of ultrabasic rock from the Great Dyke of Zimbabwe.     

Determination of the mineral composition of fresh bovine milk from the milk-producing areas located in the State of Sergipe in Brazil and evaluation employing exploratory analysis

In this work, the mineral composition of fresh bovine milk obtained from the milk-producing areas of the Brazilian State of Sergipe was examined. A dry-ashed digestion method and the ICP OES technique were used for the quantification of mineral elements (e.g., Ca, Mg, K, Na, P, Sr and Zn) in 27 samples of milk collected from properties located in milk-producing areas around Nossa Senhora da Glória. The following ranges of values (% m/v) were obtained: 0.063 to 0.117 for Ca; 0.060 to 0.114 for P; 0.024 to 0.064 for Na; and 0.087 to 0.164 for K. The ranges of values (mg L^− 1) for the other mineral elements were also found: 0.68 to 1.89 for Sr; 2.46 to 5.73 for Zn; and 54.2 to 109.9 for Mg. Additionally, the exploratory evaluation of the 27 milk samples was performed using principal component analysis (PCA) involving seven variables dealing with the effect of different management systems (conventional and organic) on milk composition. The results show that there are indeed differences between the mineral composition of milk from properties that use organic practices and those that use conventional management practices.