# M

### Master

This is the device in which the timing signals are created to control or synchronize external devices.

### Modulated transfer function

The modulation transfer function (MTF) is commonly used to quantify the resolution of an image sensor that reproduces the contrast at a certain spatial frequency of the scene. Since the photosensitive area of an image sensor consists of discrete pixels, it exhibits a limiting resolution determined by the Nyquist limit based on the discrete sampling theorem. For example, when a black-and-white pattern is viewed with an image sensor, the difference between the black and white signal levels decreases as the pattern becomes finer, finally reaching the point at which the pattern cannot be resolved. The ideal MTF is expressed as follows:

$MTF = sinc\left( \frac{\pi f}{2fn} \right)$

where f and fn are the spatial frequency and spatial Nyquist frequency of the scene, respectively.

However, because of the difficulty of creating an optical sine wave, a test pattern that provides a square wave is generally used. In this case, the spatial frequency response is called the contrast transfer function (CTF) to distinguish it from the MTF. (Note that the CTF can be converted into the MTF by means of a Fourier transform.)

Actual image sensor resolution is determined by the extent of diffusion occurring before the signal charge collects inside the silicon. When the incident photons are absorbed within the depletion layer, the generated charge does not diffuse and is collected by the corresponding pixels. Consequently, the resolution does not deteriorate. In other words, the resolution depends on the depth in the silicon where the incident photons are absorbed. The longer the incident photon wavelength, the more the resolution deteriorates.