A lens spec claiming it "resolves 50 line pairs per millimeter" tells you almost nothing about how the image will actually look. It says the lens can distinguish that many fine lines at some threshold of contrast — nothing about whether contrast at 20 lp/mm, the frequency range that actually reads as "sharp" to a viewer, is any good at all. A Modulation Transfer Function chart is the answer to a different, better question: not whether a lens can resolve a frequency, but how much contrast survives at every frequency, all the way from coarse detail to fine.
What the Chart Actually Plots
MTF plots contrast retention on the vertical axis, from 0 (no contrast left — a flat gray) to 1.0 (contrast fully preserved), against spatial frequency on the horizontal axis, measured in line pairs per millimeter. No real lens holds a flat line at 1.0 across the chart — contrast retention falls as spatial frequency rises, because finer detail is harder for any optical system to reproduce faithfully. Where that curve sits at a given frequency is the actual answer to "how sharp is this lens at this level of detail," which a single cutoff number can't distinguish: a lens can resolve a high frequency technically while still reproducing it at contrast so low the result looks soft.
Why the Chart Shows Two Curves, Not One
MTF charts plot two curves per frequency: sagittal and meridional (also called tangential), corresponding to two perpendicular orientations of the test pattern. In a lens with no astigmatism, they'd sit on top of each other. In practice they diverge, and the size of the gap is a direct readout of how much astigmatism the lens has at that point in the frame.
Astigmatism is a field aberration — it's near zero at the center and grows toward the corners, and it causes light from the sagittal and meridional planes to focus at slightly different distances. One orientation lands in sharper focus than the other at the same focal plane, which means the same corner of the frame reads differently sharp depending on the direction of detail in the scene. A wide, close sagittal/meridional pair means the corners will look reasonably crisp regardless of orientation; a wide gap means corner detail running one way will look noticeably softer than detail running the other way — a distinction a single resolution number has no way to represent at all.
Why the Chart Changes Between Apertures
The aperture a lens is tested at changes which failure mode dominates the curve, which is why MTF charts are typically shown wide open and at several stopped-down apertures rather than just one.
Wide open, lens aberrations — spherical aberration, coma, field curvature — are at their worst, because the full width of the elements is in play, including the outer zones where those aberrations are strongest. Stopping down masks those outer zones, so aberration-driven contrast loss falls and the MTF curve rises. Stop down far enough, though, and a different effect takes over: diffraction, a wave phenomenon in which light bends around the aperture's edges and spreads into an Airy pattern — a bright center surrounded by faint rings — that grows larger as the aperture opening shrinks. Past a certain point that spreading itself becomes the dominant source of contrast loss, and the curve falls again. The aperture where a lens's MTF curve peaks — commonly cited as roughly two stops down from maximum on many full-frame lenses, though the exact point is specific to each design — is the point where aberration loss has fallen enough and diffraction loss hasn't yet risen enough for the two to cross.
Why This Predicts Sharpness Better
A lens's line-pair resolution rating is a single point on a curve MTF shows in full. Two lenses can share an identical rated resolution while one holds far more contrast at every frequency below that ceiling — the difference between an image that reads as crisp and one that reads as merely acceptable lives in that difference, not in the shared number at the top. Corner performance is where this matters most for anything shot edge-to-edge, like landscape or architectural work: a lens with excellent center MTF and a wide sagittal/meridional split in the corners will still disappoint there, in a way its rated resolution figure gives no hint of. For how a lens's coating layers relate to a different part of what shows up in its optical signature, see our piece on Zeiss T coating.
A resolution figure is a claim about a ceiling. An MTF chart is a record of what actually happens on the way there. You can see how a lens's optical signature carries into a final grade in the Cineon studio.