Modular Transfer Function (MTF)

Preamble
If we are honest, as photographers interested in the photographic image, some of us are at least a little curious about how our lenses perform optically on a test bench. Of course, optical performance is not the be-all and end-all of image-making. There are a number of other considerations when choosing a lens: cost, handling, size, speed, weight, feel etc. But it is perhaps nice to know how a lens is evaluated and measured, and its optical characteristics judged.

For the past 25 years or so the accepted technique for evaluating optics impartially has been by Modulation Transfer Function (MTF). Let me say from the beginning that I am not a MTF expert: I am far from it. I am just someone who has come to understand MTF in a non-academic and limited way, and finds it a useful guide to a lens’ performance.

I trust the following helps to get you started in understanding MTF graphs. The article is not an in-depth technical critique or assessment of MTF function: there are plenty of websites by those far more qualified than me devoted to comprehensively explaining the science and methodology. Also, since I am solidly 35mm format, this is the format I am writing about in relation to MTF, and figs. 1 & 2 reflect this.

Optical Performance
In the ideal (and impossible) world of lens perfection a lens absolutely free of optical ‘errors’ is able to focus a very small point of light unadulterated by ‘errors’ onto the image plane (film or digital sensor) exactly and without any distortion or deviation from original. However, every lens no matter how well corrected, suffers ‘errors’ or aberrations, as they are properly called. These aberrations include coma, astigmatism, spherical and chromatic aberration.

Naturally I acknowledge that the characteristics of a film’s emulsion and a digital sensor’s design also impact on the images produced. Here, I am simply referring to lens analysis, and for sake of simplicity I disregard a film or sensor’s impact.

Taking our perfect point of light as a reference, every lens, due to its inherent aberrations, will distort or blur in some way this perfect point. Because of the lens’ aberrations its image will lose contrast compared to the original, rather as, in crude terms, the effect of an out of focus image of a point source has a halo or blur. In essence our perfect point of light is blurred, and because of this, it has lost contrast compared to the original. Depending on the lens’ characteristics its aberrations will vary from its centre to the edges and out to the corners of the image plane.

The MTF Graph
Simply put, when a lens is evaluated by imaging a black and white pattern using MTF, the drop in contrast is measured. The resulting MTF graph shows the total level of optical aberrations (the lens’ various combined ‘errors’) across the image plane travelling out from its centre to the edges. MTF charts show this for different apertures and for a lens’ ability to resolve increasingly fine detail.

Fig. 1 below shows the 35mm format to assist in visualising the MTF reference points recorded in the charts in fig. 2.

MTF Chart1

Okay, So How Does One Interpret A MTF Graph?
In fig. 2 below there are two charts (one for f2.8, one for f5.6). Taking one of the charts, the left vertical side shows (in %) the change in contrast from 0 at the bottom to 100 at the top, where zero (0) represents no contrast at all (pure black is grey, pure white is grey), and 100 is equivalent to maximum contrast (pure black is pure black, pure white is pure white). The in-between values indicate the percentage of white that is degrading or intruding into the black areas of the pattern, e.g. 50% shows that there is difference between the dark grey and light grey areas of 50%.

With acknowledgement to Leica Camera AG.

With acknowledgement to Leica Camera AG.

The horizontal scale shows half of the actual image area (in my example this is 35mm – 24x36mm). A 35mm lens projects – typically – a circular image of about 43mm diameter to cover the diagonal of a 35mm frame (43.2mm). You will see at the right-hand side 20, which is roughly half of the diagonal measurement in millimetres. Rounded, 20 is equivalent to the extreme corners of the image, 0 denotes the very centre of the image (the axis).

How Does All Of This Help Us?
In fig. 2 position 10, denotes approximately the short side of our 35mm frame (12 = half 24mm), 15, the long side (18 = half 36mm). By taking a vertical line from either of the horizontal points (0, 10, 15, 20) one can see at their intersections with the horizontal lines from the left the percentage at these points of a 35mm lens’ optical performance outwards from the centre (0) to the corners (20), judged by its loss of contrast caused by its aberrations.

The wavy blue and red horizontal lines are the lens’ actual MTF values: these vary from lens to lens and aperture to aperture. You will note there are four groups of blue and red lines (in pairs). The topmost blue and red pairs denote 5 lines per millimetre (lp/mm), second pair down 10 lp/mm, third 20 lp/mm and the bottom pairs 40 lp/mm. The blue lines represent a pattern with a radial (sagittal) axis (like in the direction of the spokes of a wheel radiating out from a hub) and the red lines the tangential (at an angle of 90° to the radial, as, say, in the ripples made by a stone dropped in a pond).

The 5 lp/mm pairs pretty much show the overall contrast of the lens. At 10 lp/mm finer details are examined, at 20 lp/mm it is the definition of critical fine detail, at 40 lp/mm the maximum resolution a lens can record is shown.

With the blue and red lines close together across the image (0-20) a lens is performing in an exemplary manner. The farther apart the pairs of blue and red lines the more aberrations are being recorded, such as coma and astigmatism, showing that the lens’ performance is being degraded.

Of course, for a portraitist, a degraded performance may be just the thing they are looking for, and they may consider it a good thing (some call it ‘character’). One might want a contrasty, sharp, well corrected centre area (0-10), not concerning oneself about the outer edge of the image (10-20). A photographer principally engaged with architecture or document copying may require a well corrected lens across the image plane from the centre to the edges (0-20). In this respect I am not suggesting one type of lens is better than another, it is all relative and for the individual to determine according to their needs and preference.

How To Read An Example
Fig. 2 shows the MTF graph for a Leica Elmar-M 50mm f2.8.

Wide open (f2.8) the four pairs of blue and red lines are spread between over 90% (5 lp/mm) to 60% (40 lp/mm) at the centre (0). This spread indicates medium contrast and good rendition of course to medium detail, with the recording of the finest details dropping off towards the edges and particularly at the corners (20). Overall at f2.8 across the frame the lens exhibits fine correction. In practice I find f2.8 more than adequate, especially for black and white.

Stopping down to f.5.6 the 5 to 40 lp/mm spacings at the centre (0) are closer together, 100% to 70%, denoting increased contrast, a reflection of the lens’ ability to define the finest detail across almost the full frame, as shown by the improvement in the lines straightness from left to right – the centre to the edges. At this aperture sagittal and tangential line pairs follow each other fairly closely, which is what one would wish to see: the closer the line pairs are together, the better are the corrections. I find the performance at f5.6 remarkable for such a simple optical design (4 elements, 3 groups.

Summary
Interesting though MTF charts are, one should not read too much into them, after all they are but an indication (nevertheless a valuable indication) of how a lens performs on the test bench, rather than its performance in real life. Using a lens in real life is a far better an indication of its optical qualities.

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