fig1 a to c is repeated the line pattern being shifted somewhat further upon each repetition it is possible in this way for the entire sample region p to be recorded to be imaged with a resolution in the subdiffraction region fig2 shows a schematic of the production of an individual line structure of the illuminating light for reading out the states a that is to say a single line with a maximum that u2014 as set forth above u2014 can be superposed with the intensity zero point 5 of the inventive focal line 10 of the optical signal 4 in accordance with fig2 a the illuminating light is firstly imaged linearly through a suitable optics 11 in a plane fe u2032 conjugate with the focal plane fe an imaging lens 12 is used to focus the illumination line coherently in the pupil plane pe of an objective 13 with the aid of which the illuminating light is focused in the sample 1 the illumination line runs in the x direction in the example illustrated consequently u2014 as shown in fig2 b u2014 the pupil pe is illuminated linearly in the y direction in a centrally symmetrical fashion pupil line 14 as shown in fig2 c u2014 there is likewise produced in the focal plane fe of the objective 13 a linear light.