Modulation transfer function (MTF), Spatial distortion and Spectral transmission
Lens resolving power: Modulation transfer function (MTF)
The modulation transfer function is the quantitative description of the image quality of a lens, considering all aberration. To define the MTF, the lens reproduces lines (grids) with different distances (spatial frequency in line pairs/mm). The loss of contrast due to the optical reproduction is shown in the MTFgraph for each spatial frequency. The more line pairs/mm that can be distinguished, the better the resolution of the lens.
The ideal lens would produce an image which perfectly matches the object, including all details and brightness variations. In practice this is never completely possible as lenses act as low pass filters. The amount of attenuation of any given frequency or detail is classified in terms of MTF and this gives an indication of the transfer efficiency of the lens. As a brief explanation, large structures, such as coarsely spaced lines, are generally transferred with relatively good contrast. Smaller structures, such as finely spaced lines, are transferred with low contrast.
For any lens there is a point at which the modulation is zero. This limit is often called the resolution limit and is usually quoted in line pairs per millimetre (lp/mm), or with some macro lenses in terms of the minimum line size in µm.
The MTF deteriorates as you move away from the centre axis of the lens towards the edges. This deterioration, often by a factor of 2 or 3, is an important consideration if the resolution is required across the entire image. MTF can also vary dependent on the direction of the lines at a point on the lens due to astigmatism, sometimes very significantly. This is often referred to as the T and S on some MTF charts relating to tangential (the MTF line pairs radiating from the centre of the lens) and sagittal (the MTF at 90 degrees to the T).
There are different ways to illustrate the contrast transformation in mathematical ways. However, two options are the most popular:

The yaxis shows the contrast in percent. The xaxis indicates the location at the sensor (image height), while the zero value indicates the center of the sensor (e.g. Schneider datasheets).

The yaxis shows the contrast in percent. The xaxis shows the spatial frequency in cycles per mm, while different graphs show the contrast at different distances from the center of the sensor. (e.g. SILL datasheets).
The following diagram illustrates how the MTF of a lens affects an image, as it is projected onto a sensor.