The invention relates to the use of a time-of-flight mass spectrometer to analyze substance molecules which are ionized by laser desorption, particularly by matrix-assisted laser desorption (MALDI). In detail it relates to the process for improving mass resolution by the known method of delayed acceleration (sometimes called delayed extraction) of the ions, and devices for the performance of this method. The invention consists of using an optical device with gridless apertures for the acceleration of the ions and refocusing the ion beam divergence due to the lens effect of the apertures, by means of a lens arrangement in the drift region of the time-of-flight spectrometer. For laser light pulses, illumination, and observation, there are further lateral holes in the electrodes of the optical device.