Reconstruction of TOF Spectrometer Experimental Data Using the Step-by-Step Shift Method

Abstract

A method for mathematical treatment is considered for experimental data from pulsed time-of-f light spectrometers, whose response to measurement-initiating pulses is represented by their convolution with the pulse response of the system. The proposed method of step-by-step shifting and its modifications are intended to correct the system response when the initiating pulse is distorted and also to reconstruct the response from a shorter pulse. Within certain physical constraints, this method is an alternative for technical methods associated with difficult scientific and technical problems that require considerable material costs. The inaccuracies of the reconstruction are estimated. An example of the reconstruction of experimental data from the neutron time-of-flight spectrometer at the INR is considered. The method is applicable to reconstruction of output data from any systems that are linear with respect to the input signals and are invariant to time shifts.

Experimental Data Processing Using Shift Methods

“…(3) rapidly decreases with iteration steps. After three iterations: a 2 3 = 0.004, so the accuracy of data reconstruction in other intervals is ∼ 0.4 % (see [5,6] for details). By default, the SbS method reconstructs the data with respect to the element s 0 of the blur kernel S , and if s 0 is not a maximal element, the coefficients in Eqs.…”