A method for processing an object, with material being removed from the object, includes directing a particle beam on the object so that a location of incidence of the particle beam on the object carries out a movement along a principal scanning path and a movement along a sub-scanning direction oriented transverse to the principal scanning path. The movement of the location of incidence of the particle beam along the sub-scanning direction is controlled on the basis of a reference signal and a detection signal. The method also includes modulating the directing of the particle beam in accordance with the reference signal, and detecting secondary particles and producing the detection signal, which represents an intensity of the detected secondary particles. Controlling the movement of the location of incidence of the particle beam along the sub-scanning direction is implemented using the principle of homodyne detection.