Köhler illumination is a method of specimen illumination used for transmitted and reflected light (trans- and epi-illuminated) optical microscopy. Köhler illumination acts to generate an even illumination of the sample and ensures that an image of the illumination source (for example a halogen lamp filament) is not visible in the resulting image. Köhler illumination is the predominant technique for sample illumination in modern scientific light microscopy. It requires additional optical elements which are more expensive and may not be present in more basic light microscopes. History and motivation Prior to Köhler illumination critical illumination was the predominant technique for sample illumination. Critical illumination has the major limitation that the image of the light source (typically a light bulb) falls in the same plane as the image of the specimen, i.e. the bulb filament is visible in the final image. The image of the light source is often referred to as the filament image. Critical illumination therefore gives uneven illumination of the sample; bright regions in the filament image illuminate those regions of the sample more strongly. Uneven illumination is undesirable as it can introduce artifacts such as glare and shadowing in the image. Various methods can be used to diffuse the filament image, including reducing power to the light source or using an opal glass bulb or an opal glass diffuser between the bulb and the sample. These methods are all, to some extent, functional at reducing the unevenness of illumination however they all reduce intensity of illumination and alter the range of wavelengths of light which reach the sample. To address these limitations August Köhler designed a method of illumination which uses a perfectly defocused image of the light source to illuminate the sample. This work was published in 1893 in the Zeitschrift für wissenschaftliche Mikroskopie and was soon followed by publication of an English translation in the Journal of the Royal Microscopical Society. Köhler illumination has also been developed in the context of nonimaging optics. Optical principles The primary limitation of critical illumination is the formation of an image of the light source in the specimen image plane. Köhler illumination addresses this by ensuring the image of the light source is perfectly defocused in the sample plane and its conjugate image planes. In a ray diagram of the illumination light path this can be seen as the image-forming rays passing parallel through the sample. Köhler illumination requires several