A lens that resolves fine detail does not necessarily produce a print that looks crisp, and a lens that looks crisp does not necessarily resolve the most detail. The two qualities are measured separately, and the gap between them is where much of a monochrome rendering is decided. The Modulation Transfer Function (MTF) is the single most useful tool for separating them, because it does not collapse a lens into one number. Instead it describes how faithfully the lens transfers contrast across a range of detail sizes — and in a black-and-white image, where tone carries everything, that distribution matters more than a peak resolution figure.

What MTF Actually Measures

MTF describes how much of an object’s contrast survives the trip through the lens to the image plane, as a function of spatial frequency. Contrast here is defined as modulation: for a pattern of light and dark, the modulation equals (I_max − I_min) / (I_max + I_min). A target with perfect black-and-white bars has a modulation of 1.0; after passing through the lens, the bars are rendered with reduced separation between light and dark, and the ratio of output modulation to input modulation is the MTF value at that frequency. The basic terms and mathematical relations are codified in ISO 9334. Mathematically the MTF is the magnitude of the Fourier transform of the lens’s point spread function — the image it forms of an ideal point — so the curve is a complete description of how the optic smears detail, not a sampled approximation of it.

Spatial frequency is given in line pairs per millimetre (lp/mm) at the film or sensor. Every real curve starts near 1.0 at very low frequencies and falls as frequencies rise, because finer detail is progressively harder to transmit. Where a given lens’s curve sits, and how fast it falls, is its fingerprint.

Low Frequencies Build Tone, High Frequencies Build Edges

The reason MTF is published at several frequencies is that each band describes a different visual quality. Leica’s datasheets, such as the one for the Summicron-M 35 mm f/2 ASPH., plot four: 5, 10, 20 and 40 lp/mm. The two low frequencies, 5 and 10 lp/mm, describe contrast across large object structures — broad areas of tone, the overall snap between a wall and a shadow. The high frequencies, 20 and 40 lp/mm, describe how finely textured detail is resolved and with what local contrast.

In a black-and-white image these map onto distinct perceptions. High MTF at low frequencies produces the sense of a “luminous” negative with deep blacks and clean separation between tonal masses; it is what the eye registers first as a print that “has presence.” High MTF at the higher frequencies, often discussed as microcontrast, governs whether fine texture — fabric weave, skin, the edge of a leaf — is rendered with crisp local contrast rather than a soft grey approximation. A lens can be strong in one band and weak in another, and the two failures look entirely different in a print.

Apparent Sharpness, Astigmatism, and the Monochrome Print

Apparent sharpness correlates more closely with low-to-mid-frequency MTF than with the highest resolvable frequency. In his Zeiss monograph How to Read MTF Curves, optical designer H. H. Nasse notes that contrast in the low-to-middle frequency range dominates the subjective impression of sharpness for normal viewing distances, while the very highest frequencies contribute detail that is often only visible under magnification. This is why two lenses with similar resolution limits can render with markedly different character: the one holding higher contrast through the low and middle bands reads as the sharper, more incisive lens.

MTF curves are also published in two orientations, sagittal (radial) and tangential (meridional). The separation between them indicates astigmatism — the lens focusing detail differently depending on its orientation — and a large gap shows as smeared, directionally inconsistent detail toward the frame edges. Because monochrome work strips away colour as a distraction, these structural tonal qualities — edge contrast, the cleanliness of fine texture, and the evenness of rendering from centre to corner — become the whole of what the eye reads. Interpreting a lens through its full MTF, rather than a single sharpness score, is the most reliable way to predict how it will translate a subject into tone.