Instrument response width

Farrens and Song<40) have replaced the original spark source with a picosecond diode laser in a multiplexed dual wavelength T-formatfluorometer.(41)With an overall instrumental response width of ca. 300 psec full-width half-maximum (FWHM), near-IR fluorescence lifetimes as low as 75 psec in the case of l,l -diethyl-4,4 carbo-cyanine iodide (DCI) (excitation 660 nm) and decay components as low as 48 psec in the case of 124 kDa oat phytochrome (excitation 752 nm) were reported. 

The significance of instrument band width and modulation transfer function was discussed in connection with Equation (3) to characterize the roughness of nominally smooth surfaces. The mechanical (stylus) profilometer has a nonlinear response, and, strictly speaking, has no modulation transfer function because of this. The smallest spatial wavelength which the instrument can resolve, 4nin> given in terms of the stylus radius rand the amplitude aoi the structure as... 

With mode-locked lasers and microchannel plate photomultipliers, the instrument response in terms of pulse width is 30-40 ps so that decay times as short as 10-20 ps can be measured. 

A point which may need emphasis, stated clearly in Hunter ( 2 ), is the precise interpretation of the confidence band about the predicted amount. This is important since without a clearly understood meaning, the interval will not be useful for assessing the precision of the predicted amounts or concentrations nor for comparing the results from various laboratories. Another reason the user of these methods must understand the interpretation is because increased precision can be achieved in at least two ways -by additional replication of the standards, which reduces the width of the confidence band about the regression line, and by performing multiple determinations on the unknowns, which reduces the width of the interval about the mean instrument response of the unknown. The interval for U is then given by... 

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. 

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 ... 

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. 

The time-resolved measurements were made using standard time-correlated single photon counting techniques [9]. The instrument response function had a typical full width at half-maximum of 50 ps. Time-resolved spectra were reconstructed by standard methods and corrected to susceptibilities on a frequency scale. Stokes shifts were calculated as first moments of cubic-spline interpolations of these spectra. 

A time response function of the apparatus can be measured by upconversion of the excitation beam. The width of such measured instrument response function is 280fs (FWHM). Comparing this result with the width of the autocorrelation function of the dye laser 110fs we observe 170fs broadening of the instrument response function due to group velocity... 

Figure 3. Normalized to their integral intensities photoluminescence spectra of C6o single crystal at 5 K under excitation of light with energy of 2.84 eV a) pure fullerite C60 (b) helium-intercalated fullerite C6oi (c) differed spectrum. The (a) and (b) PL spectra were corrected for instrumental response. The recording spectrometer slit width was 2.6 nm.

Representative OHD-RIKES data obtained in benzene at room temperature are shown in Fig. 2. The spike at zero delay time arises from the electronic hyperpolarizability of the liquid, and its width is indicative of the effective instrument response. Although the pulses used are quite short, appreciable... 

Figure 11-5. Pump-probe transient ionization signal of 1,3-DMU in the gas phase with the pump and probe wavelengths at 251 and 220 nm, respectively. Hollow circles represent experimental data, and the solid line is a theoretical fit including a single exponential decay convoluted with the instrumental response (dashed trace). The exponential decay constant is 52 ns, while the full width at half maximum of the Gaussian function is 5.5 ns...

The experimental data was fitted, as shown in Fig. 5.10, to a convolution of this response function with the instrument response function. As the result, the decay time T-2/2 was estimated to be 1.1 0.1 ps. Recently, the population lifetime Ti of G-phonons was measured by incoherent time-resolved anti-Stokes Raman scattering and the lifetime was found to be 1.1-1.2 ps in semiconducting SWNTs [57]. Therefore, one can reasonably assume ipu Ti at room temperature. This result is consistent with the conventional Raman line width of semiconducting SWNTs [58]. The observed short lifetime of the G-phonons implies anharmonic mode coupling between G-phonons and RBM-phonons [59]. In fact, a frequency modulation of the G mode by the RBM has been reported, suggesting the anharmonic coupling between these vibrations [56]. 

Due to the finite width of the lamp pulse (2-5 ns) and the time jitter in the detection system (voltage discriminators, TAC, photomultiplier tube) the experimental decay F(tj) is a convolution of the instrument response function and the tme decay curve... 

Examples of the instrument response function and observed fluorescence are shown in Figure 3. The data set in the top plot of F%ure 3 was obtained by observing light scattered from a glucose solution with both the output monochromator of the dye laser and the emission monochromator set to 366 nm. Thus this represents the instrument s intrinsic response. Note that the full width at half the maximum height of the peak (FWHM) is about 2 ns, greater than the laser s quoted 200-300 ps this implies that the detection electronics do not respond instantaneously on this time scale. The lower plot of Figure 3 shows the observed fluorescence from 10 pM dansylamide, with excitation at 366 nm and emission monitored at 560 nm. The monoexponential lifetime was determined to be about 2.5 ns. 

Fig. 7.10. Fluorescence rise and decay curves of band M (monomer) and band E (excimer) (at 365 and 420 nm, respectively) recorded at two different channel widths. 2exc 297 nm. The instrumental response function for the excitation laser pulse is shown in figure a. (Reprinted with permission from ref. [22]). 

Line sources are capable of producing the best linear relationship between instrument response and concentration. For optimum linear response, the halfwidth of the source line used for excitation should be less than the half-width of the absorption line of the sample. This requirement is met by most line sources, since at temperatures of the flame, absorption lines of the sample undergo substantial Doppler and collisional broadening whereas the corresponding source lines remain narrow. 

The LDH/NADH pyruvate ternary complex concentration is quite low, and it was found that the concentration of LDH/NADH + pyruvate equals approximately that of the LDH/NAD+ lactate. A temperature increase tips the equilibrium from right to left. Figure 15.10 shows the time-resolved fluorescence emission of NADH at 450 nm in response to a T-jump from 10 to 23 °C. There are two instrument response times one near 30 ns, which is the pulse width of the laser irradiation heating the sample, and the second is diffusion of heat out from the laser interaction volume that occurs around 15 ms (the latter response is not shown). Fitting the data (solid line) with a function of multiexponentials yielded four rates, as indicated on Fig. 15.10, in addition to these instrument response functions. 

Pulse-probe transient absorption data on the rise time of prompt species such as the aqueous electron can be used to measure the instrument response of the system and deduce the electron pulse width. Figure 7 shows the rise time of aqueous electron absorbance measured with the LEAF system at 800 nm in a 5 mm pathlength cell. Differentiation of the absorbance rise results in a Gaussian response function of 7.8 ps FWHM. Correcting for pathlength, the electron pulse width is 7.0 ps in this example. 

The signal bandwidth of an analog signal recording technique is limited by the bandwidth of the detector. In other words, the width of the instrument response function, or IRF, cannot be shorter than the width of the single electron response, or SER, of the detector. The SER is the pulse that the detector delivers for a single photoelectron, i.e. for a single deteeted photon. 

The effective resolution of a TCSPC experiment is characterised by its instrument response function (IRF). The IRF contains the pulse shape of the light source used, the temporal dispersion in the optical system, the transit time spread in the detector, and the timing jitter in the recording electronics. With ultrashort laser pulses, the IRF width at half-maximum for TCSPC is typically 25 to 60 ps for microchannel-plate (MCP) PMTs [4, 211, 547], and 150 to 250 ps for conventional short-time PMTs. The IRF width of inexpensive standard PMTs is normally... 

Fig. 4.8 Left. Unmodulated light recorded with a counter data width, Ndac, of 0 bit, 7 bit and 9 bit. Right. Corresponding electronic instrument response functions. The curves are shifted for better display...

A number of typical detectors are described under Sect. 6.4, page 242. The main selection criteria are the transit-time spread and the spectral sensitivity. Together with the laser pulse shape, the transit-time spread determines the instrument response function (IRF). As a rule of thumb, lifetimes down to the FWHM of the IRF can be measured without noticeable loss in accuracy. For shorter lifetimes the accuracy degrades. However, single-exponential lifetimes down to 10% of the IRF width are well detectable. Medium speed detectors, such as the R5600 and R7400 miniature PMTs, yield an IRF width of 150 to 200 ps. The same speed is achieved by the photosensor modules bases on these PMTs (see Fig. 6.40, page 250). 

Fig. 6.30 R38909U, TCSPC instrument response in linear (left) and logarithmic scale (right). Time scale 100 ps/div., operating voltage -3 kV, preamphfier gain 20 dB, discriminator threshold - 80 mV. The IRF width is 28 ps, FWHM...

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