What's the difference between MTF (Modulation Transfer Function) and CTF (Contrast Transfer Function)?

CTF expresses the lens contrast response when a "square pattern" (chessboard style) is imaged; this parameter is the most useful in order to assess edge sharpness for measurement applications. On the other hand, MTF is the contrast response achieved when imaging a sinusoidal pattern in which the grey levels range from 0 and 255; this value is more difficult to convert into any useful parameter for machine vision applications.