Introduction | ISO sensitivity | Noise | Color sensitivity | Resolution | Distortion | Light transmission | Vignetting | LCA

Modulation Transfer Function (MTF)

Resolution is extracted from the MTF curve and reports a specific point on that curve, so let’s start with a practical measurement experiment to help describe what MTF is. If we look at a series of black and white stripes with varying spatial frequency and fixed contrast (same reflectance ratio between black and white, independent of the spatial frequency), we can see that the image of high-frequency stripes has a lower contrast than that for low-frequency stripes. For very high frequencies, the image eventually becomes (almost) uniform, with an intermediate level between black and white, which our eyes perceive as a shade of gray.

The MTF precisely describes the contrast attenuation: for each spatial frequency, the MTF plots the ratio of the output modulation versus the test object modulation.

A MTF curve is represented above. The x-axis represents the spatial frequency in line pair per mm (here on the image sensor). The maximal attainable frequency on the sensor is called the Nyquist frequency and corresponds to alternating dark and bright lines one pixel wide. The y-axis (the MTF value) represents the contrast restitution for the corresponding spatial frequency. This value is between 0 and 100%, meaning complete obliteration or perfect restitution of the frequency, respectively.

The value of the MTF at frequency 0 is always 100% since a flat field is considered to have been reproduced perfectly, with no intensity loss. Attenuation due to lens transmission is measured separately.

MTF depends on light wavelength, field position, spatial orientation, focal length and aperture value.

The first dependency is a consequence of light dispersion (with lens refraction depending on the wavelength). Since the different wavelengths are integrated by the color channels of the camera, the DxOMark resolution score displays the resulting MTF on the red, green, and blue channels.

DSLR lenses usually have a radial symmetry, which means that field dependency can be summarized by the MTF at different distances to the image center.

For the DxOMark resolution score, we compute MTF in horizontal and vertical directions by examining the spatial response of the camera to a perfect edge. This measurement follows ISO standard 12233.

Any difference in MTF between the horizontal and the vertical directions is a sign of astigmatism.

What is resolution?

The resolution of a camera is defined by the size of the smallest detail that the camera can optically discriminate. ISO standard 12233 defines the limiting resolution as the first frequency such that the contrast attenuation is 95% (hence a MTF value of 5%). In practice, this value is very small and is also sensitive to measurement noise. For DxOMark scoring, we chose a threshold value equal to 20%. As an example, a lens (mounted on a given camera body, as resolution depends on both the lens and the sensor) with a DxOMark resolution score of 40lp/mm will attenuate the contrast of a detail at 40lp/mm down to 20%.

Because of field aberrations (such as field curvature), the value of the limiting resolution depends on the field position. DxOMark displays maps of the limiting resolution for each focal length and aperture value.

Presentation of results

We map the limiting resolution on a color scale as a function of focal length and aperture value. We make measurements for several field positions.

We map the limiting resolution in the image on a color scale, and make measurements for several focal lengths and aperture values.

We plot the limiting resolution as a function of the radial field position, taking into consideration horizontal and vertical directions.

We make measurements for several focal lengths and aperture values.

We plot MTF as a function of the spatial frequency for the different channels, expressing frequencies in lp/mm on 24x36mm.

We make measurements for several focal lengths, aperture values, and field positions.