Response function Gaussian

When the optical length of the sample is much shorter than the other factors such as the length of the electron pulse, the response function takes on a Gaussian shape. As the optical length increases, the shape of the response function becomes trapezoidal. Furthermore, a thick sample causes the prolongation of the electron pulse by electron scattering, which leads to the degradation of time resolution. Therefore the experiment to observe ultrafast phenomena requires the use of a thin sample. 

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. 24 Tunable-diode-laser spectrum of RQ0 of v9 of ethane. Trace (a) is the average of 250,000 scans and exhibits linewidths of 0.0022 cm-1 (the Doppler width is 0.0018 cm-1). Trace (b) results from the deconvolution of the data in trace (a) using a gaussian with a FWHM of 0.0022 cm-1 as a response function. Trace (c) is the Q branch calculated using a model that includes torsional splitting effects Av = 1.95 mk. Trace (c) is calculated for Av = 0.00075 cm-1, which is less than one-half the 300 K Doppler width.

Savitzky-Golay smoothing profile. The response function used was a gaussian with a FWHM of seven points. The weighting scheme used was of the form... 

Figures 5-11 illustrate the restoration process in the presence of a drifting base line. These data are methane absorption lines taken with a four-pass Littrow-type diffraction grating spectrometer. For these data 2048 data points were taken. The impulse response function was approximated by a gaussian. The true width of these lines is approximately 0.02 cm-1.

Fig. 7 Result of inverse-filtering the corrected data of Fig. 6 with a Gaussian impulse response function having a FWHM of 39 units. The Fourier spectrum was truncated after the 35th (complex) coefficient.

Figure 9 shows the result of inverse filtering with a Gaussian impulse response function having a FWHM of 46 units. The Fourier spectrum was truncated after the 30th coefficient. Note that the broader impulse response function should result in narrower restored peaks. Restoring 62 (31 complex) coefficients to the Fourier spectrum of the inverse-filtered result of Fig. 9 by minimizing the sum of the squares of the negative deviations produces the result shown in Fig. 10. Note that these peaks are narrower than those...

The most important parameter of the detection system is its response function. We have studied this extensively in Monte Carlo and other calculations. The calculated time-spectrum response to monoenergetic neutrons is composed of a Gaussian timing curve (2.97-ns FWHM), a trapezoidal contribution from detector thickness and non-axial paths, and an exponential tail, calculated by Monte Carlo, from multiple scattering in the neutron scintillator. (Spectrum distortion due to neutrons multiply scattered by structural and other parts of the apparatus and arriving at the neutron... 

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