Modulation Transfer Function

MTF describes the complex interaction between resolution and contrast.
Resolution is measured in lines/mm.

The lens designer finds contrast and resolution in conflict. Increasing one reduces the other.
Historically, Zeiss was reputed to design their lenses for maximum resolution,
while Leica apparently tended to favour maximum contrast.
Design decisions like these, partly account for the differing image results of different lens brands.

Modulation Transfer Function

An ideal lens would perfectly transmit 100% of the light that passes though it.
Real lenses have losses.

Measured in terms of contrast, these losses produce modulation of contrast.
modulation: simply another word for variance.

Modulation Transfer Function (MTF) is one measurement that evaluates a lens' performance;
Shows contrast reproducibility of the lens using characteristic spatial frequencies (lines per mm).

Modulation of contrast is measured at different spatial frequencies: Numbers of contrasting bars on a test target, ranging from 0 to 100 lines per millimeter.

Also astigmatic affection, shows different modulation transfer functions, along meridional and sagittal planes.

Meridonial and Sagittal planes
Astigmatic Affection (exaggerated) in Meridonial and Sagittal planes

Nikkor MTF chart
Modulation of Contrast as a function of radial distance from centre of lens

The figure above shows the MTF chart for a Nikkor 50mm f/1.4 lens.

The solid lines are meridonial while the dotted lines represent sagittal measurements.

Horizontal axis is in mm. from the image center toward the edges,
Vertical axis shows contrast value, for fixed spatial frequencies of 10 lines/mm and 30 lines/mm.

The MTF chart for each lens is based on the value at the max. aperture of the lens;

In the off-axis field, contrast reproducibility of the lens for sagittal direction and meridional direction varies with astigmatic affection.
The path of 10 lines/mm indicates the contrast reproducibility of the lens (the higher and straighter is better).
The higher and straighter the 30 lines/mm-path is, the higher the resolution of the lens.
Note that the lens performance can not be measured only with MTF chart.
Softening or blurring of color also governs measurement.

Carl-Zeiss K8 MTF tester

This instrument measures the modulation transfer function of photographic lenses at infinity (∞) object distance.
The measurement is performed in real-time at three different spatial frequencies.
Measurement is based on a line image analysis by means of a scanning slit system.
Zeiss K8 MTF tester
Carl-Zeiss K8 MTF tester

Lens Chuck
Lens chuck on Carl-Zeiss K8 MTF tester