A convolution approach to calculating the m/z-dependent mass analyzer response in orthogonal acceleration time-of-flight mass spectrometers

A novel computational method is developed to calculate the mass bias of orthogonal acceleration time-of-flight mass spectrometers (OA-TOFMS) by evaluating the m/z-dependent transmission efficiency with which ions strike the surface of the detector and the m/z-dependent ion sampling efficiency with which ions are selected for mass analysis. The theory considers the initial ion energy distribution of the primary ion beam and utilizes mathematical convolution to establish the subsequent trajectory of all ions extracted into the OA-TOFMS. By considering the energy-dependent transmission of ions and the ion sampling efficiency together, the resultant mass bias is estimated. The mathematical description is developed for OA-TOFMS using different ionization sources and ion energy distributions, and several examples covering possible time-of-flight conditions and aspects of their application are considered.