The invention relates to a diffractive optical element which comprises a first substrate and a second substrate, between which a liquid crystal layer is provided. The diffractive optical element also has strip-shaped electrodes on the first substrate and strip-shaped electrodes on the second substrate. The electrodes on the first substrate are arranged at an angle of greater than 50° relative to the electrodes on the second substrate. Furthermore, the electrodes on the first substrate and the electrodes on the second substrate are controllable in such a way that a defined out-of-plane field can be produced in a respective overlapping area of the electrodes on the first substrate with the electrodes on the second substrate. The diffractive optical element can be used in a display device for displaying preferably three-dimensional scenes.