Modulation Transfer Function, universally abbreviated to MTF, is a comprehensive and mathematically rigorous method of measuring and expressing the resolving power and contrast reproduction capability of an optical system - such as a photographic lens - or a photographic recording medium such as film or a digital image sensor. It is widely regarded as the most complete and meaningful single measure of optical and imaging system performance available, providing far more detailed and useful information about real world image quality than simple resolution figures alone can convey.
The fundamental concept underlying MTF is the measurement of how faithfully an optical system or recording medium reproduces contrast across a range of spatial frequencies - that is, across patterns of alternating light and dark lines of progressively increasing fineness. In the real world, any photographic subject can be understood as a complex mixture of spatial frequencies, from broad, low frequency tonal transitions such as smoothly graduated skies and out of focus backgrounds, through medium frequency elements such as facial features and moderately detailed textures, to the finest high frequency details such as hair, fabric weave, and intricate surface texture. A perfect optical system would reproduce all of these spatial frequencies with equal fidelity, transferring the full contrast of the original subject at every level of detail to the recorded image. In practice, all real optical systems and recording media fall short of this ideal, with contrast reproduction declining progressively as spatial frequency increases and fine detail becomes harder to resolve.
MTF is measured by presenting the optical system with a series of test targets consisting of alternating black and white line pairs of known spatial frequency - typically expressed in line pairs per millimetre - and measuring the contrast of the reproduced image of each target. The contrast of the input target is always one hundred percent - the lines are pure black and pure white - while the contrast of the reproduced image will be reduced by the optical system to a degree that increases with spatial frequency. The ratio of output contrast to input contrast at each spatial frequency, expressed as a value between zero and one or as a percentage, is the MTF value at that frequency. Plotting these values across a range of spatial frequencies produces the characteristic MTF curve, which graphically represents the complete contrast transfer performance of the system from the coarsest to the finest spatial frequencies it is capable of resolving.
MTF curves are typically measured and plotted at multiple aperture settings to show how performance varies with the aperture used, at different positions across the image field to reveal the relationship between centre and edge performance, and for both sagittal and tangential orientations of the test target to reveal any astigmatism or difference in resolution between lines running in different directions. The resulting family of MTF curves provides a comprehensive optical portrait of the lens or system under test, allowing informed comparison between different lenses and systems and revealing not only the maximum resolving power at the limit of resolution but also the contrast with which medium and coarse detail is rendered - a quality that has a profound influence on the perceived sharpness and microcontrast of the final image and is often of greater practical significance than the absolute resolution limit alone.
MTF data is published by most major lens manufacturers for their lens products, and is also independently measured and published by camera and lens review organisations and technical publications. For photographers evaluating lenses or comparing optical systems, MTF curves provide a valuable objective basis for assessment that complements but goes considerably beyond the subjective impressions of sharpness and detail rendering that practical test photographs alone can provide.