1. A method for determining the vessel diameter of optically accessible blood vessels based on digital, monochromatic images showing intensities of reflections of the blood vessels and a vessel-free environment, the vessel-free environment being an environment surrounding the blood vessels, comprising: illuminating the blood vessels and the vessel-free environment with a light source for simultaneous recording of spectrally different monochromatic images simultaneously with different wavelengths of an illumination beam, which correspond to a spectral difference of the image, each wavelength adapted to a color channel of a color camera serving to record the images received by the color channel; detecting blood vessels, a longitudinal direction of the blood vessels, and the vessel-free environment from the images; determining the intensities of reflections of the blood vessels and the vessel-free environment; scaling the intensities of the reflections determined in a first monochromatic image to intensities of reflections obtained from a second monochromatic image of a different wavelength which is recorded simultaneously with the first monochromatic image; and determining the vessel diameter, within a range of 20 to 100 micrometers, from a logarithmized ratio of an intensity of a reflection of the vessel-free environment of the blood vessel and the intensity of a reflection of the blood vessel, the intensities being determined in the first monochromatic image.