A localization microscope including an imaging device emitting sample light from a focal plane into an image plane, including an optical-manipulation device for depth-dependent influencing of a point-spread function of the imaging and influencing the point-spread function of the imaging such that a point emitter is imaged in the image plane into an image that is rotationally asymmetrically distorted. A form of the distortion depends on the location of the point emitter with respect to the focal plane and a wavelength of the sample light. The optical manipulation device includes first and second anisotropy elements that anisotropically influence the point spread function to produce rotational asymmetry of the point emitter image. The elements are arranged one behind the other in the imaging direction, with anisotropy axes at an angle to one another. Both elements have differing neutral wavelength at which they do not anisotropically influence the point spread.