This paper discusses the optimization of the display function of an image display with respect to properties of the human eye/brain system. The optimization minimizes the contrast information loss through the display/human observer system and is based on the threshold contrast curve or the curve of just noticeable differences, JND, which one can acquire by psychophysical experiments or physical measurements. It was found that, given the luminance dynamic range of an image display system, the optimum display function is the inverse of the scaled visual response function which is approximately independent of the absolute values of the threshold contrast. In particular, in good approximation, the optimum display function is independent of the spatial frequencies of the displayed image. With an analytical model of the threshold contrast curve, it is shown how the perceived dynamic range depends on factors such as the display device noise, internal scatter and the maximum luminance. The optimum display function based on the threshold contrast curve was employed with a CRT monitor. Preliminary results indicate that an improvement in the overall contrast resolution of clinical images can be achieved compared to operating the CRT with its original display function. The optimum display function guarantees maximum utilization of the contrast information transfer capabilities of a display device uniformly over the available display range. Its suitability as standard for image displays is reiterated. Often, however, for given display tasks, the best display function considering intrinsic image noise, perception requirements, and the desired certainty of perceiving a given contrast detail may be different from the optimum display function. A look-up table should then adapt the display function from the standard optimum state to a task-specific function.