Optimizing Measurement Precision

To enhance the precision of the surface acoustic wave velocity measurement by the V (z) curve technique, the two sides of (31) are differentiated and after taking logarithms of both sides, we obtain the following equation  

Equation (32) shows that the errors in the measmement of the surface acoustic wave velocity are the sum of the errors in the values of the velocity of the coupling medium, the frequency of the acoustic wave, and the distance of the period. Therefore, to minimize the measurement error, it is necessary to maintain constant temperature for the coupling medium to stabilize the frequency of the acoustic wave, and measure accurately the movement of the acoustic lens along the Z-axis. 

Many of refinements in the techniques for precision measurement have been reported. Liang et al developed a SAM which can obtain complex V (z) curves based on a nonparaxial formulation of the V (z) integral, and a refiectance function of a liquid-solid interface by inverting the V(z) curves formed at frequencies of 10 MHz or less. Endo et al. improved the above-mentioned SAM in terms of a mechanical movement and an increased frequency range (up to 3.00 GHz) to obtain higherprecision measurement.  

Quantitative data (i.e., velocities of surface acoustic waves) obtained by a spherical lens, which is commonly used for acoustic imaging, may not be expected to provide information on the elastic anisotropy of materials. A cylindrical lens (i.e., line-focus lens) and a measuring method were developed to overcome this issue. This technique is especially useful when the substrate is anisotropic in the nanoscaled thin film system. 

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Ratzlaff, K. L., and bin Darus, H., Optimization of Precision in Dual Wavelength Spectrophotometric Measurement, Anal. Chem. 51, 1979, 256-261. 

Optimal setting as found for each of these parameters. Measurement precision of a few parts in ten thousand was achieved. Experiments were conducted using both the reflection mode as well as the thru-transmission mode. 

Matrix ENDOR of spin probes that reside in an internal interface has the potential to provide detailed information on the microscopic structure of this interface, but measurement techniques and data analysis are still in their infancy, so that only semiquantitative information can be obtained to date. Development of more precise and sensitivity-optimized measurement techniques and better quantification of the spectra are now in progress. 

The fact that only 2000 channels are available is irrelevant as the spectra can be regarded as a 2000 channel slice of a 4096-channel spectrum - or 8192 or 16384 channel spectra, for that matter. What matters is the number of channels within a peak. These spectra were recorded at about 0.5 keV/channel and I deduced in Chapter 5, Section 5.5.2 that this is, in many respects, optimal for best peak area measurement precision. 

The ion optical and detector systems of MC-ICP-MS instruments are optimized for precise isotopic analysis via static multiple collection and, as in TIMS, they are suitable for the resolution of small isotopic anomalies at the 10-100 ppm level [31, 32]. In addition, the ICP ion source of MC-ICP-MS provides excellent ionization efficiencies for most elements of the periodic table. For example, MC-ICP-MS can achieve ion yields of up to about 0.5,1, and 2%, when sample solutions of Zn, Cd, and Pb, respectively, are analyzed using a desolvating nebulizer. As such, the technique of MC-ICP-MS is extremely versatile, allowing precise isotopic measurements for a wide range of elements (Figure 10.3). 

The steady-state operation of the ICP source is beneficial for the correction of instrumental mass bias by standard-sample bracketing, where the raw (measured and uncorrected) isotope ratio data of a sample are referenced to the results obtained for an isotopic standard, which is preferentially analyzed before and after each sample [27, 35]. This technique is similar to the standardization method commonly used in gas source isotope ratio mass spectrometry. To account best for drifts in instrumental mass bias, which can be particularly severe for light elements such as Li and B, data collection often utilizes multiple but short analytical measurements for samples that are each bracketed by standard analyses. Switching between samples and standards can be very rapid, if long washout protocols are not required, and mass spectrometric measurements of about 5 min or less have been used to optimize the precision of Li and Mg isotope ratio measurements by MC-ICP-MS [111, 112]. 

If the sensor bore does not correspond to the required tolerances, the sensor front touches the sensor bore in many cases, and the sensor loses its sensitivity. In technical language, this effect is called force shunt and can cause measurement errors of up to 30%. For this reason, cavity pressure sensors have recently developed that are initially built precisely into a sleeve and then calibrated in a second step [1]. The actual sensor is thus protected during installation, and measurement errors through the installation are excluded (PRIASAFE principle). The determined sensitivity is eventually stored in the sensor body itself as a code, so that no adjustments in the subsequent electronics in the industrial use have to be made [2]. The optimal measuring ranges are determined automatically as soon as the sensor is connected to the electronics (PRIASED principle). 

So, when evaluating isotopic ratio precision, it is important that the measurement protocol and peak quantitation procedure are optimized. Isotope precision specifications are a good indication regarding what the instrument is capable of, but once again, these will be defined in aqueous-type standards, using relatively short total measurement times (typically 5 min). For that reason, if the test is to be meaningful, it should be optimized to reflect your real-world analytical situation. 

Therefore, the measurement precision of the sensor hardware has to be very good. But, even with an idealized sensor hardware, the extinction cross sections of particles are determined with uncertainties of at least 2 % with data block sizes of 10,000 values [4]. This is caused by the statistical uncertainty, due to the finite number of values, which are used to calculate the mean value and the root mean square deviation of the transmission signal. Therefore, a determination of particle size distributions with an advanced SE-Method is fairly difficult. However, a reliable process monitoring with the SE-Method is possible, which enables the detection of relative changes of the mean particle sizes (see also measurement results in the next section). Therefore, the pinhole diameters, as well as the length of the measurement volume, have to be adjusted to realize a mean value of the transmission and a theoretical relative extinction cross section within the optimal range. 

The development of on-line sensors is a very costly and time-consuming process. Therefore, if one has available a dynamic model of the reactor which predicts the various polymer (or latex) properties of interest, then this can be used to guide one in the selection and development of sensors. Ideas from the optimal statistical design of experiments together with the present model expressed in the form of a Kalman filter have been successfully used (58) to select those combinations of existing or hypothetical sensors which would maximize the information that could be obtained on the states of the polymerization system. Both the type of sensors and the precisions necessary for them are easily investigated in this way. By changing the choice of the measurement matrix and... 

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