Calibration instrument response function

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. 

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. 

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. 

Luminescent standards have been established for use in calibrating fluorescence spectrometers and have been suggested for Raman spectroscopy in the past (18). The standard is a luminescent material, usually a solid or liquid, that emits a broad reproducible luminescence spectrum when excited by a laser. Once the standard is calibrated for a particular laser wavelength, its emission spectrum is known, and it can provide the real standard output , d)i(AF) depicted in Figure 10.8. In practice, a spectrum of the standard is acquired with the same conditions as an unknown then the unknown spectrum is corrected for instrument response function using the known standard... 

Recalibration of the instrument response function reduces or eliminates most of the instrumental factors that lead to relative intensity variations over time. For example, a luminescent standard could be used at the beginning of each session as described in Section 10.3.3. Use of the same standard and correction procedure during qualification could establish the true value of one or more peak ratios for future reference. Table 10.9 shows results for this approach applied to the example of calcium ascorbate. The ratio of the 767- and 1587 cm" peak intensities was monitored after calibration of the response function with a luminescent standard. The standard deviations listed in Table 10.9 for the 767/1582 peak height ratio provide indications of the reproducibility of the response correction and sample spectra. 

KG Ray, RL McCreery. Simplified calibration of instrument response function for Raman spectrometers based on luminescent intensity standards. Appl Spectrosc 51 108-116, 1997. 

KJ Frost, RL McCreery. Calibration of Raman spectrometer instrument response function with luminescence standards An update. Appl Spectrosc 52 1614-1618, 1998. 

Unless the Raman instrument response function is corrected for after the measurement of the Raman spectrum of DLC, the fluorescence background slope from the same DLC sample will vary when measured on different Raman instruments. This variation in slope will be most pronounced if a sample is measured on two totally different instruments, either from two different manufacturers or two different models from the same manufacturer. However, there can sometimes also be seen small differences in slopes when DLC is measured on two instruments of the same make and model. Calibration of the x axis (cm ) in Raman spectroscopy is straightforward and easy and is offered as standard hardware and software from all Raman manufacturers. Therefore, frequency measurements, like the measurement of the G-band position, are usually very transferable from one instrument to another. However, calibrating the y-axis response is not straightforward and there is still no widely accepted correct method to do so. As a consequence, the... 

Sizing of such particles demands fine and accurate resolution from the PDPA. Some recent works have attempted to point out limitations in the instrument response function (PDPA calibration) for the small particle size range. However, it can be shown both theoretically and experimentally that with the correct PDPA configuration, even very small particles, down to 0.5 um can be sized with adequate resolution. 

Functions of Standards. Fluorescent standards can be used for three basic functions calibration, standardization, and measurement method assessment. In calibration, the standard is used to check or calibrate Instrument characteristics and perturbations on true spectra. For standardization, standards are used to determine the function that relates chemical concentration to Instrument response. This latter use has been expanded from pure materials to quite complex standards that are carried through the total chemical measurement process (10). These more complex standards are now used to assess the precision and accuracy of measurement procedures. 

The linearity of a method is defined as its ability to provide measurement results that are directly proportional to the concentration of the analyte, or are directly proportional after some type of mathematical transformation. Linearity is usually documented as the ordinary least squares (OLS) curve, or simply as the linear regression curve, of the measured instrumental responses (either peak area or height) as a function of increasing analyte concentration [22, 23], The use of peak areas is preferred as compared to the use of peak heights for making the calibration curve [24],... 

Calibration is also used to describe the process where several measurements are necessary to establish the relationship between response and concentration. From a set of results of the measurement response at a series of different concentrations, a calibration graph can be constructed (response versus concentration) and a calibration function established, i.e. the equation of the line or curve. The instrument response to an unknown quantity can then be measured and the prepared calibration graph used to determine the value of the unknown quantity. See Figure 5.2 for an example of a calibration graph and the linear equation that describes the relationship between response and concentration. For the line shown, y = 53.22x + 0.286 and the square of the correlation coefficient (r2) is 0.9998. 

A procedure which enables the response of an instrument to be related to the mass, volume or concentration of an analyte in a sample by first measuring the response from a sample of known composition or from a known amount of the analyte, i.e. standard. Often, a series of standards is used to prepare a calibration curve in which instrument response is plotted as a function of mass, volume or concentration of the analyte over a given range. If the plot is linear, a calibration factor... 

A compound or element added to all calibration standards and samples in a constant known amount. Sometimes a major constituent of the samples to be analysed can be used for this purpose. Instead of preparing a conventional calibration curve of instrument response as a function of analyte mass, volume or concentration, a response ratio is computed for each calibration standard and sample, i.e. the instrument response for the analyte is divided by the corresponding response for the fixed amount of added internal standard. Ideally, the latter will be the same for each pair of measurements but variations in experimental conditions may alter the responses of both analyte and internal standard. However, their ratio should be unaffected and should therefore be a more reliable function of... 

Erom Equations 12.46 and 12.47, one sees that ThEEE retention is related to (l/5j), but not specifically to a conventional analyte property, such as molar mass M or particle diameter d. However, since HSj depends on M or d, it also mediates the dependence between R and M or d. At constant Tq conditions, the relationship between X, M, and AT can be experimentally exploited by using standards. Eor instance, in polymers mass characterization, monodisperse or polydisperse standards can be employed for a specific polymer-solvent system. Once the relationship X vs. M, that is, the so-called calibration curve, is obtained, it is universal, that is, valid for any ThFFF instrument [3]. A typical calibration function, which relates the instrumental response to analyte property (in this case M), is... 

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... 

The multivariate quantitative spectroscopic analysis of samples with complex matrices can be performed using inverse calibration methods, such as ILS, PCR and PLS. The term "inverse" means that the concentration of the analyte of interest is modelled as a function of the instrumental measurements, using an empirical relationship with no theoretical foundation (as the Lambert Bouguer-Beer s law was for the methods explained in the paragraphs above). Therefore, we can formulate our calibration like eqn (3.3) and, in contrast to the CLS model, it can be calculated without knowing the concentrations of all the constituents in the calibration set. The calibration step requires only the instrumental response and the reference value of the property of interest e.g. concentration) in the calibration samples. An important advantage of this approach is that unknown interferents may be present in the calibration samples. For this reason, inverse models are more suited than CLS for complex samples. 

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