Notes on MTF measurements

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Introduction

The de facto industry standard to quantify lens performance is the modulation transfer function (MTF). An explanation of MTF is beyond the scope of this article, but excellent texts are available elsewhere [1, 2]. The MTF can be computed theoretically for known lens designs, but there are always implementation losses and the performance of a real lens falls short of the theoretical ideal. A more realistic performance indicator is measured MTF. For decades the preferred measurement device has been the scanning-slit optical bench. However, such a system is not within reach of individuals and with the advent of digital cameras a new method has emerged. This method, which is popular among photo magazines and some enthusiasts on the internet, uses dedicated charts/targets and analysis software. Unfortunately there are disadvantages and pitfalls, which are rarely mentioned or even recognized, and lenses may be hailed or dismissed for the wrong reasons.


Considerations

An optical bench is a calibrated measurement device designed specifically for the job. Measurements are automated, reproducible, independent of the operator, and allow a lens performance evaluation at infinity focus. This is not true for MTF measurements by means of photographing test charts (ISO, USAF, Siemens star, etc.) or at least to a lesser degree. Drawbacks of target lens tests include:

The last point is an important one. The measured MTF is not lens MTF, but system MTF, where the system is the entire chain of operator, lens, anti-alias filter, sensor response, in-camera processing, and post-processing algorithms. There are many factors that influence the final MTF values. The operator is part of the chain and influences the outcome, for instance via his ability to achieve a parallel set-up of target and sensor. Autofocus, manual focus, live view, ... each method may yield different results. Some testers apply focus bracketing and simply use the image that yields the highest MTF value at a given position in the frame, an inelegant working method that is in glaring contrast with the calibrated optical bench and its standardized focus criterion. At the same time the system MTF can be seen in a positive light, because system MTF, including the operator, is what eventually determines the technical quality of a photographic image. An optical bench only provides the lens MTF.

One should be very careful with interpreting system MTF as an indicator of lens performance. Even relative comparisons between two lenses using the same camera, hardware and software settings, etc. should be judged with caution. For instance, differences between lenses may be reduced by digital sharpening algorithms or use of the luminance signal in the MTF analysis [2]. On the other hand, differences between lenses may be exaggerated by testing at relatively close focus. Documentation of the testing methodology and interpretation of the results are as important as the method itself. The following points can be used to assess the credibility of the magazine or site:

The first and last points in the above list are of particular importance. It is well known, to testers and readers alike, that lens performance is a function of the aperture. MTF measurements are therefore normally presented for several aperture settings. It is also well known that lens performance is a function of the position in the field. Corners may be much weaker than the image center. MTF measurements are therefore normally presented for several distances from the center, also known as image heights. It is less well known that there exists such a thing as sagittal and tangential lens performance, and that two MTF values are needed for each aperture value and image height. Finally, it is also less well known that lens performance is a function of the object distance, especially for lenses with a large maximum aperture and/or an asymmetrical design.


Image magnification

The MTF parameter space is large, certainly if also depth information at the sensor side is taken into account to reveal astigmatism/field curvature. Even manufacturers present a limited amount of information in their lens product Assuming that the chart is photographed so as to fill the frame, the dimensions of the chart together with the sensor size determine the image magnification. The object distance depends on the lens focal length. sheets. However, a minimum requirement to any MTF test report is sufficient documentation. For instance, there has to be mention of the object distance or image magnification. More often than not this crucial parameter is missing in the presentation of results. As a rule photo magazines do not bother to list the subject distance. Internet sites may provide the information, but you need to dig deep. However, it is also possible that you encounter vague statements concerning the use of different chart sizes to best suit the lens, without the actually employed size being mentioned in the presentation of results.

All lens aberrations depend on the object distance. A simple yet convincing illustration shows how curvilinear distortion may change from moderate moustache distortion at long range, to strong barrel distortion at close range. Distortion does not influence MTF, but other aberrations do and they also vary with distance. In addition, vignetting is a function of the distance.

Most photographic lens designs are optimized for peak performance at large distances. The reason is simply that this suits everyday use. For applications such as landscapes, seascapes, cityscapes and the like, it is desirable to have a flat field and good sharpness across the frame at infinity focus. When an 'infinity' lens is used at closer focus, the optical performance suffers most in the corners. There are many close-focus applications where this is not very objectionable, for instance portraits or pictures of animals or plants. The subject then is a three-dimensional object that is typically not placed in a corner.

User requirements are different for reproduction photography. For reproductions of paintings, documents, stamps, etc., the requirement is a flat field with uniform sharpness across the frame, but now not at infinity but at close to intermediate distances. Lenses optimized for infinity are not suitable for this task, but fortunately there exist dedicated lenses known as macro lenses. As expected, these perform less well at infinity. An elegant solution to combine the best of the two worlds is the use of floating elements. A lens design with floating elements has variable air spaces between two or more lens groups, which gives the designer more degrees of freedom for aberration control over the distance scale. Such a lens may perform fairly well both at close focus and at infinity. Some lenses branded as a macro lens even have their peak performance at infinity, but they are still very good at close focus.

The answer is simple. Testing at large distances requires an impractically large target and working space.

Since many lenses are optimized for large distances and lack variable air spaces, they are not suitable for reproduction photography. The question arises, then, why target MTF measurements tests these lenses as if they were reproduction lenses. It appears that the employed target width is typically in the regime from 1 and 1.5 m (information that is remarkably difficult to find). This corresponds to a magnification between 0.036 and 0.024 on a full-frame sensor, which is not the macro regime but not close to infinity either.


Case study

How big is the difference in MTF performance between image magnifications? The answer depends on the lens under consideration, but can be substantial. As a case in point, Figs. 1 and 2 show MTF curves from a design study of two 2.8/25 retrofocus lenses that lack floating elements. These lenses were not taken into production and the MTF is theoretical, but that does not matter for the comparison. Furthermore the data are not MTF50 curves, but MTF curves as a function of distance from the optical axis for three spatial frequencies: 40, 20, and 10 line pairs per millimeter (lp/mm). The highest curves are for 10 lp/mm, the lowest for 40 lp/mm. The solid curves are sagittal MTF, and the dashed curves tangential MTF. For the interpretation of such graphs the reader is referred to [1]. In the present study we adopt the simple viewpoint that higher is better. The purpose is not to analyze and interpret each graph in detail, but to show how lens performance can differ between image magnifications.

Lens A in Fig. 1 is designed for a high performance at infinity focus, which corresponds to an image magnification m=0. Graphs are also shown for m=0.025, which corresponds to a subject distance of about 1 m and which is in agreement with typical magnifications of target MTF measurements. Comparison of curves shows that the sagittal MTF is not degraded much by reducing the focus distance from infinity to 1 m. In fact, at F/5.6 the rendering of sagittal details is even more uniform across the frame. However, the overall lens performance is dragged down substantially by the tangential MTF. Starting at 10 mm from the image center, the curves drop rapidly and render corner performance much worse than at infinity focus.

MTF of lens A.

Figure 1. MTF for lens A, a 2.8/25 lens optimized for m=0 (infinity focus). Data courtesy of Carl Zeiss.

In contrast to lens A, lens B is designed for a high performance at m=0.025. Fig. 2 shows curves at F/5.6 for three values of the image magnification, m=0, m=0.025, and m=0.050. Unsurprisingly, the best lens performance occurs at m=0.025. Infinity focus noticeably lowers the performance for lens B at 20 and 40 lp/mm, and so does the close focus of m=0.050. It is again the tangential MTF that suffers most from the refocusing. Candidate causes for a large separation between sagittal and tangential MTF are lateral chromatic aberration (the achilles heel of the retrofocus design) and astigmatism. The question arises again which MTF (sagittal, tangential, or an average value) is being published in target MTF reports. The presence of the graph for the full aperture of F/2.8 at m=0.025 illustrates that the impact of focus distance can be as big as the impact of the aperture.

MTF of lens B.

Figure 2. MTF for lens B, a 2.8/25 lens optimized for m=0.025. Data courtesy of Carl Zeiss.


Concluding remarks

A low-cost lens MTF test has emerged by means of target reproduction photography and dedicated image analysis software. The method is valuable in that it yields measurements of system MTF. One can only admire the efforts that testers put in, because this illustrates how difficult it is to get the most out of your equipment also in everyday photography. Unfortunately the methodology also has serious disadvantages. Since system MTF is measured and not lens MTF, the results are difficult to interpret. Moreover, the method yields lens ratings for reproduction photography, which for many lenses is not the intended application. The effect of object distance or orientation (sagittal or tangential) on MTF can be as big or bigger than the effect of lens aperture or image height. Test reports that include information on magnification and/or orientation should be taken for what they are. Test reports that lack the information should be dismissed.



© Paul van Walree 2011–2016


References


[1]   H. H. Nasse, How to read MTF curves?, Carl Zeiss Camera Lens Division (2008).
[2]   H. H. Nasse, How to read MTF curves? Part II, Carl Zeiss Camera Lens Division, (2009).