Many vision-system designers understand basic image-distortion effects and how to correct them, but they may need to account for the modulation transfer function (MTF) of a lens, too. The MTF describes how a lens affects contrast information and thus how “sharp” an image appears. So, if you plan to measure edge locations, part placements, or dimensions, pay attention to the MTF of the lens.

These bands show how five MTF values affect images of the same black-to-white (b/w) pattern. Many tests use alternating b/w bars, but this test used b/w patterns created by a swept-sine function. Courtesy of Norman Koren.

Unfortunately, no one manufactures perfect lenses, so all images show some gray at a black-white transition. But wide lines still provide an MTF of 100% because the centers of the alternating lines appear pure black or pure white. As the lines get narrower, images lose contrast, and the black and white lines blur and appear grayer. Still-narrower black and white lines appear all gray, and you can no longer distinguish between them. Because no contrast information gets to the image sensor, the MTF now equals 0%. As an analogy, think of a swept square wave that passes through a low-pass filter. At low frequencies, the signal looks pretty good, but at high frequencies, the signal disappears.

Some lens suppliers provide plots of MTF values. A typical plot shows the MTF vs. spatial frequency at the center of an image (on axis). Some plots may show the relationship between the MTF and the distance from the lens’ central axis. The MTF decreases as the off-axis distance increases. The lens aperture setting—its f stop—can affect the MTF, so you need to learn the test conditions that were used to create the MTF charts. When you look at MTF plots, make sure you know the units for the lines, or spatial-frequency, axis. Vendors will specify lines per millimeter or line-pairs per millimeter. Ten line pairs equals 20 lines. If you cannot obtain an MTF plot, run a program such as Imatest (www.imatest.com) that will perform MTF and many other lens and image tests.

According to the Luminous Landscape photography Web site (see “For Further Reading”), the larger the MTF value at 20 lines/mm, the better the contrast-reproduction capability of a lens. The larger the MTF value at 60 lines/mm, the better the lens’ resolving power and subjective sharpness. Generally, a lens with an MTF above 80% at 20 lines/mm will produce an excellent image. Consider a lens with an MTF between 79% and 60% as just satisfactory.