MTFs

MTFs, or Modulation Transfer Functions, describe how faithfully an imaging system reproduces contrast at different spatial frequencies. They quantify the system’s ability to transfer detail from a scene to an image, combining effects from optics, sensors, and processing. The MTF is the magnitude of the optical transfer function (OTF), which is the Fourier transform of the system’s point spread function (PSF). While the OTF is complex and includes phase information, the MTF focuses on the amplitude of contrast preservation across frequencies.

Spatial frequency, typically expressed in cycles per millimeter or cycles per image height, encodes how fine a pattern is. The MTF curve shows the ratio of image contrast to object contrast as frequency increases, usually starting near 1 at low frequencies and declining toward zero at higher frequencies. The sampling grid, notably pixel size, introduces a Nyquist limit that caps the highest resolvable frequency.

Measurement and interpretation methods include the slanted-edge method, which derives the MTF from the edge spread function, and direct PSF-based methods. In practice, MTFs are used to assess lenses, cameras, scanners, and displays. They help predict perceived sharpness and inform design decisions, quality control, and standardization.

Several factors influence MTFs: diffraction from the aperture sets a fundamental limit, while lens aberrations, misalignment, coatings, sensor microlenses, demosaicing, and compression can further degrade performance. For displays, the display transfer function describes how well the display reproduces spatial detail, contributing to the overall perceived sharpness of a system.