Method for particle beam-induced processing of a defect of a microlithographic photomask

An apparatus comprising:

• a computing device comprising at least one storage device storing at least one computer program including instructions that when executed by the computing device cause the computing device to:
• determine a geometric shape of a defect in an image of at least a portion of a microlithographic photomask as a repair shape,
• subdivide the repair shape into a number of n pixels in accordance with a first rasterization,
• subdivide the repair shape into a number of m pixels in accordance with a second rasterization, the second rasterization emerging from a subpixel displacement of the first rasterization,
• control an activating particle beam and a process gas to be provided at each of the n pixels of the repair shape in accordance with the first rasterization, and
• control the activating particle beam and the process gas to be provided at each of the m pixels of the repair shape in accordance with the second rasterization.