A chromatic confocal measuring device for the measurement of distances and/or thicknesses of several locations has a light source that emits polychromatic measuring light through a light exit surface. The light source is a laser pumped luminophore-based light source and has an oblong exit surface. The measuring device further has at least one first confocal aperture through which the measuring light passes and which comprises a plurality of punctiform orifices or at least one slit-shaped orifice. The measuring device also includes imaging optics configured to cause a chromatic focus shift of the measuring light and to image the first confocal aperture in a measurement volume so that different wavelengths are focused at different heights. A first receiving and evaluating unit measures the intensity of the measuring light reflected by the measurement object as a function of the wavelength and of the transverse position of the reflection location on the measurement object and determines therefrom distances and/or thicknesses of several locations or of a region of the measurement object extending in at least one spatial direction.