The invention relates to time-of-flight mass spectrometers with pulsed ionization of samples, for example by matrix-assisted laser desorption (MALDI), where the samples are located on a sample support and are irradiated and ionized one after the other in a grid by a position-controlled desorption beam. An ion-optical puller lens arrangement is positioned in front of the sample support, with at least one of the lens diaphragms in the arrangement being subdivided into segments, and a voltage supply being able to supply the segments, or some of them, with different voltages, depending on the impact position of the desorption beam on the support plate. It is then possible to virtually shift the effective ion-optical focusing center of the lens away from the axis, and to focus an ion beam, which is generated off the real lens axis, into a beam which runs essentially parallel to the real lens axis, with no time phase shift for ions of the same mass. This beam can be brought back onto the axis by an x/y deflection unit, for example for operating the time-of-flight mass spectrometer with a reflector.