We hear a lot about lens sharpness; but what does it actually mean? It’s not easy to quantify but for images to appear sharp, both sharpness and contrast are involved. However, you can’t measure either factor objectively and both are inter-related.
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Most people define sharpness by how clearly well-focused details appear. Contrast assessment is usually based on the perceived difference between the lightest and darkest tones. Unfortunately, subjective assessments are problematic because human vision is imperfect – and variable. While one observer may be able to perceive differences between 50 pairs of alternating lines in a millimetre, another may only distinguish 30 at the same viewing distance. To complicate matters, an individual’s perception can vary by as much as 10% at different times. Consequently, your eyes are a poor tool for evaluating the sharpness of any lens. To evaluate the resolving power of an optical system objectively, you must photograph an object that contains the maximum amount of sharpness plus the maximum contrast; in other words, a black and white grid. Test targets for evaluating resolution typically consist of a series of very fine sets of parallel lines arranged with different spatial frequencies, ranging from 100 line pairs per millimetre (lp/mm) to zero, which is one millimetre separation. In theory, a perfect lens should be able to transmit all the light that passes through it and resolve all the black and white line pairs – right up to 100 lp/mm – with neither blurring nor a loss of contrast. But even the most expensive lenses aren’t perfect; there’s always some diminution (or modulation) of contrast and, therefore, apparent resolution. The ability of an optical system to produce detailed, sharp-looking images is only loosely related to its measured resolving power, so other factors must be considered when evaluating lens performance. This is where MTF comes into play.
MTF The test target consists of sets of fine repeating lines that run sagittally (or parallel to the diagonal of the image format) and meridionally (at right angles to the sagittal lines) through the exact centre of the area that is photographed. The thinner the lines and the closer they are to each other, the more difficult it becomes for a lens to separate them and reproduce them sharply and with adequate contrast (in other words to ‘resolve’ them). 
The diagram above shows how resolution is measured by analysing sets of fine repeating lines at right angles to each other. The results of the analysis are combined into a modulation transfer function (MTF) that shows contrast at a specific spatial frequency, relative to low frequencies. If the optical system modulates (changes) the contrast by lightening the black lines or darkening the white ones it will degrade the ability to distinguish between them, thereby reducing the resolution of the system. No photographic lens can reproduce 100 line pairs per millimetre – but even the most basic lens can separate one line pair/millimetre.
MTF measurements show the percentage of contrast that remains between the black and white lines after they are projected through the lens. For a particular line frequency, an MTF of 0.8 means 80% of the original contrast remains. In other words, the lens reduces contrast by 20%.  A typical lens MTF graph from Canon. The black lines indicate measurements taken with the lens wide open; the blue lines show the lens at f/8. The MTF data for each lens is normally provided for two spatial frequencies: 10 lines/millimetre and 30 lines/millimetre, which are shown in different colours. For each spatial frequency, the MTF is usually plotted for two lens apertures, the maximum aperture and stopped down to f/8. The solid lines on the plot indicate the performance of the lens for the sagittal lines (parallel to the diagonal of the frame), while the dashed lines relate to the meridional lines (perpendicular to the sagittal lines). The closer the 10-lines/mm curve is to 1, the higher the contrast and the better the ability of the lens to separate the line pairs. The closer the 30-lines/mm curve is to 1, the better the resolving power and sharpness of the lens. In addition, the closer together the sagittal (S) and meridional (M) lines are to each other, the smoother and more natural the background blurring (bokeh) becomes. As you follow the lines from the left of the graph to the right, you track the distance from the centre of the image. In most graphs the lines will trend downwards as they approach the right hand side; a steep drop on the right side of the graph indicates edge softening. While you might think that high quality lenses should be able to record lines running in all directions equally well, almost all lenses will produce better results in the sagittal direction, particularly as the line sets become closer to the corners of the field of view of the lens. Performance generally decreases with distance from the centre of the field. This is why most MFT graphs show lines that tend to curve downward as they move left to right, tracking the lens’s performance from centre to corner of the frame. If the MTF graph for a lens shows the 10-line/mm curve to be greater than 0.6 it’s considered a satisfactory performer. Lenses for which the 10-line/mm curve is greater than 0.8 deliver excellent image quality. MTF graphs can also show up certain lens aberrations. A significant difference in MTF for the sagittal and tangential directions indicates an aberration such as astigmatism (where circular areas in the subject become increasingly oval in shape towards the periphery of the frame). Curvature of field is indicated when the MTF drops away from the centre, especially when using wider apertures with a small depth of field. (Interestingly, because high MTF figures mean fine detail, MTF analysis can also be used to estimate the amount of noise in a digital imaging system.)
MTF and Imatest Although MTF is typically expressed in line pairs per millimetre (lp/mm), the Imatest tests provide the results as MTF 50 frequencies per image height. MTF50 represents the point at which the contrast is half its original value. At this point, perceived image sharpness is most accurately determined because detail remains visible yet differences in responses from the imaging system are easiest to determine. In Photo Review’s lens tests we base our graphs on the line widths per picture height (LW/PH) figures in the Edge Profile (linear) graph. We use these measurements because they provide more scope for comparing cameras with different sensor sizes and aspect ratios as well as having a closer relationship to the measurements used in the past. This lets users compare old and new lenses. You don’t need to understand the maths behind MTF analysis; it’s enough to know that high spatial frequencies are correlated with fine image detail and the higher the LW/PH figure the sharper the image. Imatest also provides a guide in the form of an ‘ideal’ resolution in megapixels, shown circled in red in the diagram on this page. When this figure is half the sensor’s resolution (or higher), the camera can be seen as a good performer as far as resolution is concerned. When it’s lower, resolution is below expectations. 
Lens Manufacturers’ MTF Graphs  The graphs above are from a well-known specialist lens manufacturer and show the performance at the focal length extremities of an ‘all-in-one’ zoom lens ranging from 18mm to 250mm. In this case, the red lines show a spatial frequency of 10 lp/mm while the green lines show 30 lp/mm. The measurements have been conducted on shots taken with an APS-C DSLR camera. Note the decline in resolution towards the edges of the frame, shown by the downward trend in the green lines. In addition, different manufacturers use different analysers for measuring MTF. They also use different criteria as the basis of their published MTF graphs. Sometimes the frequency is expressed not in cycles or line pairs where black plus white count as one, but as lines per millimeter (black plus white count as two). The value of the latter is double that of the former, so the MTF values on which the graphs are based will be quite different. This can make it impossible to compare MTF plots from different manufacturers when comparing similarly-specified lenses. Leica provides the most comprehensive set of data, usually with separate graphs at three aperture settings: wide open and stopped down to f/5.6 and f/8. Each contains data for 5, 10, 20 and 40 lp/mm for both sagittal and meridional line sets. Canon’s MTF charts give results at two apertures: wide-open (the lower black pair), and stopped down to f/8 (the upper blue pair), with the lens set to infinity focus. MTF charts from Nikon and Sigma are based on the value at the maximum aperture of the lens; the red line shows the spatial frequency of 10 lines/mm and the green or blue line, 30 lines/mm. Olympus publishes MTF graphs for 60 lines/mm (the orange line) and 20 lines/mm (the blue line), which is equivalent to frequencies of 30 and 10 lines/mm when you account for the 2x crop factor relative to a 35mm lens. This is an article from Photo Review Magazine Dec-Feb 2010/11 Issue 46.
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