Hollow cathode discharge lamps (HCLs) have been successfully used in recent years as calibration sources of optical astronomical spectrographs. The numerous narrow metal lines have stable wavelengths, which makes them well suited for m/s calibration accuracy of high-resolution spectrographs, while the buffer-gas lines are less stable and less useful. Accordingly, an important property is the metal-to-gas line-strength ratio (Rmetal/gas). Processes inside the lamp cause the light to be emitted from different regions between the cathode and the anode leaing to the emission of different beams with different values of Rmetal/gas. We used commercially- available HCLs to measure and characterize these beams with respect to their spatial distribution, their angle of propagation relative to the optical axis, and their values of Rmetal/gas. We conclude that a good imaging of an HCL into a fiber-fed spectrograph would consist of an aperture close to its front window in order to filter out the parts of the beam with low Rmetal/gas, and of a lens to collimate the important central beam. We show that Rmetal/gas can be further improved with only minor adjustments of the imaging parameters, and that the imaging scheme that yields the highest Rmetal/gas does not necessarily provide the highest flux.