Extraction of the speed distribution function from a time-of-flight signal

The molecular-beam speed distribution functions obtained in free-jet expansions using existing time-of-flight (TOF) techniques are subject to distortions caused by the gate function of the beam chopper, A (t), and the dynamic function of the detector and its electronics, g/subd/(t). Mathematically, the TOF signal is represented by a doubly convoluted Volterra integral equation involving the three functions cited above. In this paper, the Volterra integral equation is inverted twice, using the Laplace-transform method, for known functions of g/subd/(t) and A (t). The time-domain distribution function F (t) is decoupled from the functions g/subd/(t) and A (t). Hence, the distortion-corrected speed distribution function is obtained. An example using the CO2 TOF signal demonstrates the numerical inverting technique