A method for operating a light microscope with structured illumination includes: providing illumination patterns by means of a structuring device which splits impinging light into at least three coherent beam parts which correspond to a −1., 0., and +1. diffraction orders of light; generating different phases of the illumination patterns by setting different phase values for the beam parts with phase shifters; and recording at least one microscope image for each of the illumination patterns and calculating a high resolution image from the microscope images. Phase shifters are provided not only for the beam parts of the −1. and +1. diffraction orders but also at least one phase shifter for the beam part of the 0. diffraction order. At least two different phase values Φ0 are set with the at least one phase shifter for the 0. diffraction order to provide a plurality of illumination patterns with different phases.