Response Function Calibration

Regardless of the method used to calibrate response function, it is useful to have standard corrected spectra of readily available materials to verify that the... 

Procedures for determining the spectral responslvlty or correction factors In equation 2 are based on radiance or Irradlance standards, calibrated source-monochromator combinations, and an accepted standard. The easiest measurement procedure for determining corrected emission spectra Is to use a well-characterized standard and obtain an Instrumental response function, as described by equation 3 (17). In this case, quinine sulfate dlhydrate has been extensively studied and Issued as a National Bureau of Standards (NBS) Standard Reference Material (SRM). 

The approach to standardization used by Haaijman (53) and others (66,67), in which the fluorophor is incorporated within or bound to the surface of a plastic sphere, is more versatile than the use of inorganic ion>doped spheres, since the standard can be tailored exactly to the specifications required by the analyte species. However, this approach increases the uncertainty of the measurement because the photobleaching characteristics of both the standard and the sample must be considered. The ideal approach is to employ both types of standards. The glass microspheres can be used to calibrate instruments and set instrument operating parameters on a day-to-day basis, and the fluorophor-doped polymer materials can be used to determine the concentration-instrument response function. 

Stochastic or probabilistic techniques can be applied to either the moisture module, or the solution of equation (3) — or for example the models of Schwartz Crowe (13) and Tang et al. (16), or can lead to new conceptual model developments as for example the work of Jury (17). Stochastic or probabilistic modeling is mainly aimed at describing breakthrough times of overall concentration threshold levels, rather than individual processes or concentrations in individual soil compartments. Coefficients or response functions and these models have to be calibrated to field data since major processes are studied via a black-box or response function approach and not individually. Other modeling concepts may be related to soil models for solid waste sites and specialized pollutant leachate issues (18). 

The calibration function represents that segment of the response function that is chosen for estimating the analytical value of an unknown sample. 

References. Because the detected fluorescence signal is a direct response of the dye-analyte complex formed, no reference measurement is required. Also no calibration of the probe is required, although the response function of the probe may be needed. 

Standardization The instrument response function can vary from analyzer to analyzer. If calibration transfer is to be achieved across all instrument platforms it is important that the instrument function is characterized, and preferably standardized [31]. Also, at times it is necessary to perform a local calibration while the analyzer is still on-line. In order to handle this, it is beneficial to consider an on-board calibration/standardization, integrated into the sample conditioning system. Most commercial NIR analyzers require some form of standardization and calibration transfer. Similarly, modem FTIR systems include some form of instrument standardization, usually based on an internal calibrant. This attribute is becoming an important feature for regulatory controlled analyses, where a proper audit trail has to be established, including instrument calibration. 

Calibration curves were fitted, and EC50 values were derived using the nonlinear regression package pro Fit 5.5 (QuantumSoft, Zurich, Switzerland). The results of the calibration curve measurements were fitted to a sigmoidal dose-response function of the following form with a slope faetor of 1 ... 

The most common calibration model or function in use in analytical laboratories assumes that the analytical response is a linear function of the analyte concentration. Most chromatographic and spectrophotometric methods use this approach. Indeed, many instruments and software packages have linear calibration (regression) functions built into them. The main type of calculation adopted is the method of least squares whereby the sums of the squares of the deviations from the predicted line are minimised. It is assumed that all the errors are contained in the response variable, T, and the concentration variable, X, is error free. Commonly the models available are Y = bX and Y = bX + a, where b is the slope of the calibration line and a is the intercept. These values are the least squares estimates of the true values. The following discussions are only... 

For calibration of measuring equipment by measurement standards or CRMs, a straight-line response function is usually postulated... 

ICP-MS can provide semiquantitative analysis for about 70 elements by using element response functions built into the instrument software and calibration of only a few elements [205,206]. Most elements are more than 90% ionized in the ICP (with the exception of elements with ionization potentials greater than about 8 eV). Ion transmission efficiency is a smooth function of mass. The natural isotopic abundances of the elements are well known. Therefore, it is possible to predict the relative sensitivities of the elements and any isobaric overlaps. 

Booksh, K.S. and Kowalski, B.R., Calibration method choice by comparison of model basis functions to the theoretical instrument response function, Anal. Chim. Acta, 348, 1-9, 1997. 

The energy calibration was obtained with Si and S Ka fluorescence X-rays excited by means of an X-ray tube. Because the natural widths of the fluorescence X-rays exceed the experimental resolution at least by a factor of two, the response function of the spectrometer was determined from the narrow antipro-tonic transitions pHe(5g — 4/) and pNe(13p — 12o), lines which are not affected by the strong interaction. For the 1.7 keV Balmer a transition from pH, quartz crystals are the only possible choice for the Bragg crystal. The theoretical limit for the resolution of 180 meV was missed by a factor of 1.7 (Table 1). In the case of pD, a silicon crystal was used because of its higher reflectivity. Here, the theoretical limit for the resolution of 360 meV was reached [21]. 

A successful X-ray spectroscopy of the quality required for the pionic hydrogen experiment is based on a narrow and well understood response function of the crystals. An energy calibration or an optimization can not be achieved with ffuorescence X-rays produced with X-ray tubes. Their width is an order of magnitude broader than the resolution of the crystals. The line shape is moreover influenced by poorly determined satellite lines. 

Calibration is used here to describe whatever process is used to relate observed spectral frequencies and intensities to their true values, and validation is a procedure to verify the calibration and determine the magnitude of experimental error. Raman spectroscopy is a demanding technique in terms of reproducibility and accuracy and involves a variety of instrumental configurations. Calibration is often the source of irreproducibility and inconsistency in reported Raman spectra. This chapter is divided into four general sections frequency calibration (10.2), response function calibration (10.3), absolute response calibration (10.4), and a summary of procedures (10.5). For each section, standards and procedures for instrument validation are considered. 

The majority of Raman spectra reported in the literature are uncorrected for instrument response, so one could argue that the most common response correction is none at all. Uncorrected spectra are still valuable for qualitative applications involving comparison of peak frequencies and for quantitative comparisons where the response function is unknown but constant. For example, a quantitative analysis of two components based on the relative heights (or areas) of two Raman bands can be calibrated with known solutions and applied to unknowns without determination of the response function. However, there are many situations in which response function calibration is important, including variations in relative intensity with different instruments, variations caused by instrumental drift or repair, and subtraction of library spectra (see Fig. 5.6). If a quantitative analysis is based on a calibration curve without response correction, a new curve must be collected if a change in response... 

---