Abstract: The invention relates to the positional adjustment of a cutting tool in a machine tool for the purpose of ensuring that the cutting tool is exactly in its correct position prior to starting machining operations. The machine tool is of the kind having a cutting tool support displaceable relative to the bed along two axes which are perpendicular to each other. The apparatus provided for the above purpose in accordance with the invention includes an optical projector producing in a stationary plane a picture of the tip of the cutting tool, including its cutting edge. When the tool support is displaced along either axis, the position of the picture on the plane changes accordingly. A stationary linear array of photosensitive diodes is arranged parallel to one of the axes of displacement of the tool support so that individual diodes will be covered or uncovered by the picture when it travels across the plane upon displacement of the tool support.