Response function, instrument

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. 

Figure 4.7 Fluorescence anisotropy decay curves for the PMMA brush swollen in benzene (filled circles) and the free PMMA chain in benzene solution at concentrations of 0.33 (triangles) and 2.9 X 10 g (open circles). The graft density of the brush is 0.46 chains nm . The solid curve indicates the instrument response function. Reproduced with permission from the American Chemical Society.

Fig. 3 Transient absorption spectra of hairpin 3G obtained at increasing delay times following 340 nm excitation with a laser system having a 150 fs instrument response function...

There is significant debate about the relative merits of frequency and time domain. In principle, they are related via the Fourier transformation and have been experimentally verified to be equivalent [9], For some applications, frequency domain instrumentation is easier to implement since ultrashort light pulses are not required, nor is deconvolution of the instrument response function, however, signal to noise ratio has recently been shown to be theoretically higher for time domain. The key advantage of time domain is that multiple decay components can, at least in principle, be extracted with ease from the decay profile by fitting with a multiexponential function, using relatively simple mathematical methods. 

Time resolution of the enthalpy changes is often possible and depends on a number of experimental parameters, such as the characteristics of the transducer (oscillation frequency and relaxation time) and the acoustic transit time of the system, za, which can be defined by ra = r0/ua where r0 is the radius of the irradiated sample, and va is the speed of sound in the liquid. The observed voltage response of the transducer, V (t) is given by the convolution of the time-dependent heat source, H (t) and the instrument response function,... 

When rh delta function, an instantaneous heat deposition, and the resultant voltage response of the transducer is simply the instrument response function, T (t). Although heat depositions cannot be time resolved in this regime, their magnitude and consequently the enthalpy... 

Equations (4.15)—(4.17) and subsequent theoretical expressions for r(t) are the true anisotropy, which is defined here as the fluorescence response to an instantaneous light pulse when measured by an instrument with infinitely rapid temporal response. In a real experiment this is convoluted with the instrument response function, as discussed in a later section. 

Our experiments are typically carried out at DNA concentrations of 20-50 /ig/ml with 1 ethidium per 300 bp, so that depolarization by excitation transfer is negligible.(18) The sample is excited with 575-nm light, and the fluorescence is detected at 630, 640, or 645 nm. Less than one fluorescent photon is detected for every 100 laser shots. The instrument response function e(t) is determined using 575-nm incident light scattered from a suspension of polystyrene latex spheres. 

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. 

Instrumentation. The steady-state fluorescence spectra were measured with Perkin-Elmer MPF-44B fluorescence spectrophotometer. The single-photon counting instrument for fluorescence lifetime measurements was assembled in-house from components obtained from EG G ORTEC. A PRA-510B light pulser filled with gas was used as the excitation source. Instrument response function was obtained with DuPont Ludox scatter solution at the excitation wavelength. 

If b and g are peaked functions (such as in a spectral line), the area under their convolution product is the product of their individual areas. Thus, if b represents instrumental spreading, the area under the spectral line is preserved through the convolution operation. In spectroscopy, we know this phenomenon as the invariance of the equivalent width of a spectral line when it is subjected to instrumental distortion. This property is again referred to in Section II.F of Chapter 2 and used in our discussion of a method to determine the instrument response function (Chapter 2, Section II.G). 

Occasionally, useful information may be gleaned from the observed spectrum of an isolated line without deconvolution, even though the instrument response function is wider than the line itself. We see this in the application of the method of equivalent widths to the determination of line strengths (Chapter 2, Sections II.F and II.G). When more complete knowledge is sought, we can often achieve the desired end by employing fewer degrees of freedom than a true deconvolution process utilizes. 

Z OL collision frequency fractional increase in instrument response-function breadth due to convolution with narrow spectral line... 

Axr, half-width and variance of instrument response function, respectively... 

To illustrate this point, let us suppose that the half-width of a line in either the absorbance or absorptance regime is truly much narrower than the halfwidth of the instrument response function r(x). The measured absorptance then cannot be more than a few percent, at the most. 

Let us establish the required relationships more precisely. Consider a narrow idealized rectangular absorption line AT(x) = rect(x/2 AxL) having half-width AxL and centered at x = 0. Its variance is easily found to be <7l = (2 Axl/3)2. Its area is 2 AxL. Now, let us assume that this line is being used to measure an instrument response function exp( —x2/2cr2) that has Gaussian shape and variance ... 

Because the instrument response function must have unit area, the area under the narrow line is preserved by the measurement process. Recalling that this area is 2 AxL, we may write the absorptance amplitude AL of the observation (which is Gaussian) in terms of its half-width and 2 AxL ... 

Jansson discusses the determination of the instrumental response function as well as its analytical characterization in Chapter 2. 

Fig. 19, an unapodized spectrum [response function (sin nx)/nx = sinc(x)] is shown in trace (b). For such a spectrum there will be sidelobes and negative absorption if the natural linewidths are narrower than the full width of the sine-shaped response function. These are seen in Fig. 19, where the linewidth is three points and the response function width eight points. Here the phrase instrument response function may have a slightly different definition, but the meaning is clear. For such a response function, the direct deconvolution methods fall short. 

This scheme was also used to test pressure-broadening removal in a Raman spectrum. Here, no approximations are needed and any pressure-broadening effects can be considered as part of the instrument response function if the... 

Fig. 11.5 Measurement of lifetime of anthracene in solution by single photon time correlation technique. Fluorescence decay curve of 8 X10-4 M anthracene in cyclohexane in the absence (A) and presence (B) of 0.41 M CC14. Points experimental data Line best fitting single exponential decay convoluted with instrumental response function (C) Time scale 0.322 nsec per channel. (Ref. 13).

The fluorescence quenching of Pe and derivatives has been investigated by fluorescence upconversion. Excitation was performed with the frequency-doubled output of a Ti Sapphire amplifier. The instrument response time was around 240 fs with 0.4 mm thick samples. The data were analysed by iterative reconvolution of the instrument response function with trial functions. For most samples, measurements were carried out at three different wavelengths (438, 475, and 490 nm). Global fits were done with all the available data. 

Fig. 3. Transient FWHM (a) and first moment (b) of the fluorescence spectra of all-trans PSBR in methanol and octanol. For the first ps a finer scale was used. After deconvolving with the 140 fs instrument response function, the fit gave the following decay constants and their amplitudes methanol - 30 fs (0.75), 400 fs (0,15) and 11 ps (0.1), octanol- 120 fs (0.9) and 4.0 ps (0.1).

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