1. Method for correcting distortions of a particle-optical apparatus, the particle-optical apparatus comprising: a particle source for producing a beam of particles, an object plane on which an object to be imaged is placed, and when illuminated, having an intermediate image plane where a pattern is generated, a condenser system for illuminating the object plane with the beam of particles, a projection system for forming an enlarged image of the object plane by imaging particles transmitted through the object on an image plane, the projection system introducing pincushion or barrel distortions, a detector for detecting the enlarged image, in which the detector comprises multipoles, the method comprising: producing a beam of particles; illuminating the object plane with the beam of particles; generating a known pattern in the intermediate image plane; forming an enlarged image on the image plane of the object plane by imaging particles transmitted through the object, measuring the pincushion or barrel distortions introduced by the projection system into the image of the known pattern, and exciting the multipoles in such a way that the pincushion or barrel distortions in the enlarged image caused by the projection system are at least partially corrected.