The Application describes a method and devices for manufacturing a broadband cholesteric polarizer having a well-defined bandwidth and edge position. To this end, a liquid-crystalline cholesterically ordered layer comprising reactive chiral monomers and reactive nematogenic monomers having a different reactivity is polymerized by exposure to radiation. The invention is characterized in that the intensity of the radiation is increased substantially, preferably by a factor of 10 or more, when a desired edge position of the band is reached. As a result, the bandwidth and edge position of the reflection band reached at that moment are frozen as it were. A monochromatic sensor can be used to determine whether said edge position has been reached, the wavelength used by the sensor corresponding to the wavelength of the desired edge position of the band. Broadband, cholesteric polarizers having a well-defined bandwidth and edge position can very advantageously be used in a display.