© Erwin Puts
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Chapter 5: image evaluation

5.1 Introduction

The reader should be aware, after reading chapter 1.1 and 1.2, that a photographic lens rarely delivers a perfect image of the object. There is always a certain magnitude of aberrations left in the optical system, that will degrade the quality of the reproduction. In the end there is only one valid criterion for the acceptance of the performance level of a lens, and that is user satisfaction. If a user is happy with the images (s)he sees, the lens is accepted and its performance is judged as sufficient.

This acceptance is purely based on personal considerations and so purely subjective.

From the individual viewpoint, this does not pose a problem. The personal judgment is most often also influenced by the subject matter and the content of a picture.

Again this is fine for any individual photographer. The acceptance of a certain performance level by personalized criteria, however, is hardly transferable to another person. If we want to make comparisons between lenses on more objective terms, we should disregard the content if the picture and look solely at the image structure as a technical issue of image recording. The optical designer too needs quantifiable criteria for image quality, as it is unknown who will buy the lens, in what circumstances it will be used and what the level of individual acceptance will be. The optical designer will ask this question: 'In what way will the image quality be degraded if a given amount of aberrations is present in the optical system?' And the second question would be: 'How can we interpret the results of our optical computations?'. There is not yet any direct link between the numerical results of a computation and the subjective interpretation of a picture by an observer. A number of criteria for image quality have been proposed during the long history of the photographic lens. The oldest one and still popular today is the resolving power, which defines in effect the smallest detail that can be detected or discriminated in an image. It is a very simple measure to use and interpret, which accounts for its popularity. Its elegant simplicity is deceptive, however, and it is a most dangerous and defective measure. It is specified in lines per millimetre and a lens that resolves 60 lines p/mm is considered 'better' than a lens that resolves 55 lp/mm. In all optical design programs and all books about optics, the Modulation Transfer Function is designated as the best single merit function for the assessment of image quality. And its use is increasingly adopted by manufacturers and magazines as a measure of optical performance. It measures the loss of contrast that occurs when the lens reproduces an object. If the test target is a chart with a black and white space, we say that the contrast is 100%, as the black part does not reflect any light and the white part will reflect 100% of the light falling on its surface. If the same pattern is imaged by the lens on a transparent screen, we can measure the contrast again and we would note that the white part now has received most of the light and the black part some light). The contrast has dropped or changed and in modern parlance we call this change a 'modulation'. The value might be 0.8 and this tells you that 80% of the original contrast of the object has been transferred to the image. Such a figure is intuitively unappealing as it does not relate to any photographic experience in the way the resolution figure does. I will explain the background of both measures, indicate the value and help you understand and interpret the data. Off record I will mention here that the MTF data are widely accepted in the optical industry as a representative measure of optical performance, but is a derived or secondary measure. The true nature of an optical system as far as the aberration content goes, is being evaluated with the ray intercept curves, the Strehl ratio, the point spread d function and the optical path differences.

 

5.2 Resolution

 

5.2.1 Resolving power.

On first sight it makes sense to look at the finest possible detail that a lens can reproduce, as a measure of optical performance. We certainly want to capture every aspect of the object in front of our lens. A well-known example is the proverbial portrait of a girl, where we would want to record every single hair of the eyelashes.

The image structure of an eyelash is representative of the idea of fine detail and looks like the test pattern we can find on the resolution test charts. There are many versions of this chart, and all are essentially the same. A pattern of alternating and equally spaced black and white stripes (bars or lines) of some length and width are grouped together in blocks of three or five bars. Every block has smaller dimensions than the previous one, representing a spatial pattern of higher frequency. Five bars with a width of 1mm occupy a space of 5mm, and five bars with a width of 0.2 mm each occupy less space and are said to have a higher frequency per millimetre. In the first case the frequency would be 1 line per millimetre and in the second case 5 lines per millimetre. See illustration. If we would wish to do a resolution test for a 50mm standard lens, we have to set up a camera in front of such a test chart at a certain distance, because we must know the 'magnification' of the lens in order to count the number of bars that are recorded on film. Let us assume that we use a 'magnification' factor of 50, that is we record on film the chart scaled down (reduced) with a factor of 50. The larger pattern would now be quite small on the negative, in fact 1/50 line per mm (or 50 lines per mm)and the smaller pattern would now be 250 lines per mm. These structures on the negative are too small to be seen with the unaided eye and we use a projection or an enlargement or a microscope to look at the patterns.

Ideally we should enlarge the negative 50 times to reproduce the original pattern. For the sake of argument, let us assume that the larger pattern is clearly identifiable and every bar can be individually recognized, but the smaller pattern is completely blurred and we do not see 5 individual bars, but an undifferentiated patch of grey colour. With this procedure we can say that this lens under these conditions resolves 50 lines per mm.

 

5.2.2 Resolution described.

Resolving power values specify the number of lines per millimetre that can be separated visually. The ANSI/ISO standard defines resolving power as "the ability of a photographic material to maintain in its developed image the separate identity of parallel bars when their relative displacement is small". Note that resolving power/resolution is a visual, not a measurable standard. Basically resolution is a very simple idea. It is based on the visual acuity of a human observer and here trouble starts. The ability of the eye to distinguish small objects that are very close together changes substantially depending on the shape of the object, on the illuminance level of the location where the observer resides, on the fatigue of the observer and many more. There is also an element of 'judgment' and psychology involved. Observer A may judge two objects to be detectable as separate, while observer B may judge the two objects too close together to be separate.

Figure 1 shows such a pattern of parallel bars and these patterns are used by all resolution charts in one version or another. Resolution then answers only this question. What is the minimum distance between two very small objects for them to be detected as separate entities. There is no rule that asks the observer to distinguish between 'just detectable' and 'clearly detectable'. In fact this difference is quite important.

 

Figure 77: 5.2.1.A bar chart

 

5.2.3 The shortcomings of the resolution test .

The process of photographing the bar test chart at a certain distance, developing the film and finding the smallest group of lines that can be distinguished is a relative straightforward operation. But here the trouble starts. First of all it is difficult to translate the raw numbers into meaningful and comparable figures. The test target elements consist of the groups of six bars in several sizes. The object spatial frequency is related to the image spatial frequency by the reduction ratio. Assume that the real test chart has six bars (three white and three black) over a distance of 10mm and you have chosen a reduction ratio of 100 times. Then the image resolution is 60 lines per mm. The groups of lines are always arranged in a vertical and horizontal direction and with almost all lenses you will note that the resolution figure for the horizontal and vertical lines is not the same. After exposing and developing the film optimally (a 1/3 stop will ruin the results) you need to study the negatives under again ideal photographic conditions. But you can never be sure that you focused absolutely spot on and so you have to repeat this series of pictures with focus settings that are changed by very small focus increments and decrements. Then you have to select the negatives with the best values. As your eye is not to be trusted here (due to physiological and psychological factors), the results are subjective and should be accepted with at least 10% margin. Even if you did everything right, the resulting figure of say 74 lines per mm will have to be interpreted as having a margin from 67 to 81 lines. Selecting which block has just discernable bars is a highly subjective act and two observers will differ here again by at least 10%. Even if the resolution figures would be related in meaningful way to the real optical performance of a lens, these four groups of margins, set up errors, focusing errors, interpretation errors, and individual judgments, will produce figures that have a latitude of 30% and more. A simple check in the magazines will tell you that the Summicron lens (7 element) as been credited with anything from 60 to 300 lines per mm as a resolution figure. Even when the test is done competently, the results are fully inconclusive if not wrong. A lens with an established resolving power of 100 lp/mm does not necessarily have higher image quality than a lens with under the same procedure has a resolving power of 80lmm. Resolution figures do not correlate well, if at all with real optical performance. This is a serious defect of the resolution test for photographic lenses. In astronomy and microscopy the concept of the resolution limit has more validity as here the ability to separate two closely spaced objects (like double stars in astronomy) is a more important criterion. It is best to relegate the resolution test to find the maximum number of lines a lens can resolve, to the dustbin of history and I have to strongly advice you, not to look at resolution figures as a serious tool for the evaluation of optical performance and not to try to do your own resolution tests, as there are too many unchecked variables involved.

 

5.3 Spatial frequency and contrast

 

5.3.1 Spatial frequency.

While the concept of the maximum resolution is of no relevance for photographic image quality, the basic idea of spatial frequency is not. The alternating pattern of black and white bars of equal width is used as a target to be imaged (recorded) by the lens to be studied. Sets of patterns with different spacings in a continuous range from 1 to 100 lp/mm are used as a target. The number of lines per mm are designated as frequency of N lines per mm, where N is any number between 1 and 100. Lower frequencies have the lower numbers. and higher frequencies the higher numbers. Lines/mm and line pairs/mm do not refer to the same measurements.

This is a very confusing, but relatively simple topic. A line is a black stripe of a certain width and length on a white background. Or a white stripe on a black background. We need the black-white contrast, as we are unable to detect a white line on a white paper. Assume we draw 10 black stripes on a white paper over a distance of 10cm. To be able to differentiate between any black line, there must be a small white space between two lines. We see a pattern of 10 alternating black and white stripes. Such a repeating pattern of black-white lines is called spatial frequency and has a clear analogy with the temporal frequency: the pattern in time of sounds and silence, as with the old mechanical ticking clock. The metronome, used in music training, is a device that can be set to different temporal frequencies of sounds, to help you stay tuned. These 10 black lines can be designated as having a spatial frequency of 10 lines over a distance of 10cm, or 1 line/cm. Over the distance of 10cm, we can distinguish 20 different lines, 10 black and 10 white. Engineers are down to earth people and they refer to this pattern as having 10 lines/mm, as they know that to see white, you need black. Normal people, like photographers, find this confusing and would say that there are 20 lines. To settle the matter, we define a black/white pair as a line pair and so our pattern can be described as having 10 lp/mm or 20 lines of alternating white and black colour or 10 l/mm (if we are engineers, assuming that a line is always a line pair). When dealing with photographic emulsions or optical aberration theory, a black-white pair indicates a wave pattern, a wave being a phenomenon that has a top and a trough. (Black equals the top of the wave and white the trough or the other way around). Such a top-trough combination is called a cycle and one line pair is identical to one cycle. Datasheets of film emulsions show MTF graphs as measured in cycles/mm.

 

Figure 78: 5.3.1 A lens MTF

 

Figure 79: 5.3.1.B film MTF

When reading resolution data, we should investigate what is referred to: single lines (black or white) or line pairs and who is talking. Leica MTF graphs and resolution data are always in line pairs and that is the convention I will follow in this book.

 

5.3.2 Contrast.

In chapter 1, I have drawn attention to the blur circle. To summaries, an object point is represented in the image as a disc of light with a core of high intensity (where most of the light will be concentrated) and a rim of diffuse light of diminishing intensity. If we represent this structure in a three dimensional diagram, the area of the disc on the x- and y- axis and the light intensity on the z-axis, we see an illumination mountain (Lichtberg in German). If we defocus, the area of the disc is enlarged and the intensity of the light in the core is reduced. That is logical, because the same amount of light energy from the object point is now spread over a larger area. This structure is called the point spread function and is defined as the light distribution in the image of a point. Literally the way (function) the light is spread out over the point.

 

Figure 80: 5.3.2 Illumination mountain

Contrast is defined as the difference in light intensity (luminance)between two areas.

If we have a black and a white area, the contrast is 100%, as all light is reflected from the white area and none of the black. A bright star against the deep black sky also has a 100% difference in contrast. If we take a Kodak grey card which has a reflectance value of 18% and hold it against a white background, the contrast has dropped significantly. The border between both areas is still quite visible. Would we juxtapose a grey card with 18% and one of 20% reflectance, we have great difficulty in detecting the border line.

 

Figure 81: 5.3.2 A ideal pattern high contrast

 

Figure 82: 5.3.2.B pattern as recorded by real lens

In an ideal lens/film system all light energy reflected from any white stripe (however small) would be concentrated on film in a corresponding white stripe. No light energy would reach the black stripe next to it. Again contrast would be 100% whatever the spatial frequency. But lens aberrations will spread out the light energy a bit and light scattering in the film emulsion will do the rest. So part of the light energy (aimed at the white stripe) will reach the black one, and is therefore lost for the white part. This scattering of energy will affect the high spatial frequencies to a higher degree as the distances between the white/black patterns become progressively smaller and the scattering relatively wider. In a real lens then we should find the maximum contrast or overall contrast at the low frequencies (1 or 5 lp/mm).

With higher and higher frequencies the contrast will inevitably drop. This contrast value at the finer spaced patterns we call the micro contrast, which is shorthand for contrast value at the higher frequencies. By now the reader should notice that contrast and resolution are more tightly coupled than has been suggested in the past.

Contrast and spatial frequency are related to each other through the point spread function. Note that the following example uses real optical data. An excellent lens will record an object point as a small circle of light with a diameter of 20 micron or micrometer. That is equivalent to 0.02 mm which is really small. Due to residual aberrations this circle is not of uniform intensity, but has the distribution as described above as a defocused blur circle. Specifically, the central core has a diameter of 8 micron and the surrounding diffused rim has a total diameter of 20 micron. We now take a spatial frequency of 100 lp/mm, that would amount to 200 alternating black and white bars on the negative. The dimension of every bar would be 0.005mm or 5 micron. But the smallest spot our lens can record is 20 micron! A white bar with a width of 5 micron cannot be represented with a circle of 20 micron.

It is clear that there are several white bars that will all fall within the space of one circle of light that ideally represents only one single white bar. The resulting image will be blurred and we are unable to detect the individual white bars. We could say the contrast is zero. If we want to see the individual bars there should be a one-toone relation between a bar and a image circle. When we use a spatial frequency pattern of 25 lp/mm, that is 50 lines in a millimetre, every white line now has a width of 0.02mm, that is exactly the diameter of the blur circle. All light reflected from a white bar is now recorded in one circle and between two white bars there is deep dark one, where there has been no light on the film. We see the alternating pattern quite clearly. Now for the tricky story. If we use a spatial frequency of 75 lp/mm, that is 150 lines in a millimetre, every white bar has a width of 0.0067mm or rounded 7 micron. The central core of the light circle will occupy the location of the corresponding white bar, but the rest of the blur circle will illuminate the black bars.

Now we have a pattern of white and grey bars, with a reduced contrast and it now much more difficult to see the pattern as clear as before.

Let us look at figures above. This is again an ideal pattern, showing from bottom to top spatial frequencies from 10 to 100lp/mm. Note the fuzzy edges at the 10lp/mm.

As a matter of interest, look at the 0 lp/mm bar (very bottom: a grey line, because there is zero contrast.) Note that the 100lp/mm are recorded with clarity because there is good contrast between the black and white lines. In print the 100lp/mm might be unresolved, Then look at the 80 or 70 lp/mm. The argument holds at every frequency. If we record this pattern by a Leica lens, we get figure xx. (Note: these pictures are computer simulations that are as realistic as possible. They show more clearly what happens). We now note that the lower contrast makes it very difficult to detect the spatial structures of the 70 lp/mm band. Even the 50lp/mm has a contrast loss. Most importantly and this is of utmost relevance, we see in figure 5.3.2B that a reduction in contrast does not lead to a higher resolution. If contrast drops so does resolution. These two figures prove that the old maxim that low contrast combines with high resolution and low resolution presupposes high contrast ,is simply not true.

If you want a high resolution that is detectable by the eye, you get it through a high contrast and a good acutance. There is no way that you will see a high resolving power without good contrast in the photographic world. In astronomy where astronomers are used to detect the faintest signals, a signal to noise ratio is used, which is the same as a spatial frequency to contrast ratio.

The size of the blur disc and the distribution of light within the area then determines the contrast of the higher spatial frequencies and their visibility. The same argument works for the lower spatial frequencies too. When the lens records a white line with substantial width against a black background, the definition of the border line is still made with these small discs of light. If the core coincides exactly with the borderline, the rim of diffused light will spill over in the dark side and generate a small edge of lower contrast. We do not see a sharply delineated edge, but a slightly blurred edge. It is evident from this mental and visual exercise that spatial frequency and contrast are related to each other by the dimension of the blur circle. And we argued and demonstrated that the higher spatial frequencies will be of lower contrast, depending on the size of the blur circle or as it is called the geometrical spot size.

 

5.4 The Modulation Transfer Function.

The reduction of contrast from object to image is called the modulation of contrast and the relationship between modulation and spatial frequency is graphically represented as the MTF graph, where the vertical axis depicts the level of contrast transfer, the horizontal axis the location of the image point in the film area and the lines of the graph represent the spatial frequency.

 

Figure : 5.4.A-MTF at different apertures

The value of the MTF graph, compared to the procedure for finding the maximum resolution of a lens, is its firm foundation in optical theory. The effect of aberrations is to increase the blur circle, change the shape of the circle to an irregular patch and change the light distribution over the patch of light. These effects are comparable to the defocus blur, described above. The effect of the aberration of field curvature or astigmatism is like a defocus, as the image plane is curved and not flat, and if you locate the (flat) image plane at a certain position along the optical axis, the point's being imaged at the curved surface, automatically appear as out-of-focus. The bigger size of the blur circle and its uneven light distribution reduce the contrast. There is then a direct relationship between the optical errors in a lens and the size and shape of the blur circle, or which is almost the same, its level of contrast. The logic is simple: a lens that is highly corrected will reproduce object points as very small circles with a focused (concentrated) light energy and thus a high contrast. If we can look at the performance of the lens over the whole image area from centre to corner (or axis and several field positions) for several spatial frequencies, we can infer from these values the state of the aberration correction and its related image quality. We need to study this performance not only for one aperture but for all apertures. Any MTF diagram gives the information for one aperture only. Quite often the validity of the MTF graph as an indication for optical performance is questioned. It is stated that real life objects are solid three dimensional structures and the test object for an MTF graph is a two dimensional flat pattern of alternating black and white bars.

Such an argument does not take into account that the image quality is based on the size of the blur size and its encircled energy. The representation of a three dimensional object is made possible through the concept of depth of field and this effect is related to the defocus blur, which is measured with the MTG graphs too. A solid object is reproduced in the flat image plane by a successive series of slices through the object, of which one slice is the focused one and all the others are more or less defocused. The image points in all slices are correctly defined and measured by the MTF graph as a series of blur sizes of growing size.

 

5.4.1 The generation of MTF graphs.

Two methods are being used to get these MTF figures. One method does measure the values by using equipment for the determination of the contrast transfer. An illuminated target, almost always a very narrow slit of 0.02mm is projected through the lens on a detector (a sensitive surface, nowadays a CCD chip) , and the brightness difference at the edges of the slit (illuminated and non-illuminated part) is recorded. This can be done because the scanning slit is much smaller than the target slit and we are able to record the brightness variation along the edge. Ideally we would see a square shape as the transition from dark to white is abrupt. Due to aberrations we see a slightly rounded off top with a gentle slope. (see Figure:).

 

Figure 83: 5.4.1.A two dimensional slice

 

Figure 84: 5.4.1.B broader base

These measured values are transformed by a mathematical technique of differentiation into the point spread function (the illumination mountain) and from there into the MTF graphs. The second method calculates the values from the optical data, describing the lens. The computer program calculates the spot diagram (see chapter 1.1) and the intensity distribution of the light over the blur disc. From these data the point spread function is derived. A line can be mathematically defined as an infinite number of points and from one spot we can generate a line spread function, which is a summation of an infinite number of PSF's. From the line spread function we can, through integration and Fourier Transforms, generate the MTF again. Theoretically both methods should deliver the same results. In reality they do not. The measured values may differ from the calculated values, because of production tolerances during manufacture. But more importantly, the calibration of the measuring equipment may be different. The results depend on the accuracy of the measurements, the quality of the white light used, the number of wavelengths used and their weighting, the defined focus location and several more variables.

Therefore it is very dangerous to compare results obtained by different tests, as all of these variables may be different and so results cannot be compared. 80% in one graph is not 80% in another one. With the calculated graphs, we have the same variability. Wavelengths used, weighting of wavelengths and other parameters generate different results. Again: a meaningful comparison is possible if you know that all parameters are identical. As these are not published, you should restrict yourself to a comparison between data from the same manufacturer and do not compare results between manufacturers. The published graphs by Leica are computer based graphs. As the production tolerances are very small, we can expect the results between the calculated and measured values to be quite close. Leica computes the values and then uses these values as an acceptance criterion when a lens is measured with MTF equipment.

 

5.4.2 The interpretation of MTF graphs

The interpretation of MTF diagrams is not easy. The graphs represent the spatial frequency of 5, 10, 20 and 40 line pairs/mm over the whole image area from centre (0) to the edge (21.6mm). The diagonal of the 35mm negative is 43.2mm and as a lens is symmetrical around the axis, we need only to look at one point on a line from centre to edge. Every spatial frequency is represented by two lines, a tangential one and a sagittal one to show astigmatism and field curvature. If the curves for both orientations (horizontal bars and vertical bar are wide apart, we may assume that the overall contrast is low and the fine details quite blurred. Generally the line for the 5lp/mm represents the contrast of the outlines of the larger object shapes and the lines for the 40lp/mm the ability to record very fine detail crisply, that is with clean (high contrast) edges. For general photography the lines of the 5 and 10 lp/mm are the most important. The higher the curves, the straighter the curves and the less difference between the tangential and sagittal lines the better the overall contrast and image quality. As example look at the figures here for an old Summarex 85/90mm lens a new Summicron 90mm lens. These differences are very visible in practical photography. One should be aware when comparing these graphs that a difference in contrast values of even 1 percent point is significant: a contrast transfer of 90% at 10 lp/mm is a visible degradation when compared to a contrast transfer of 92% at 10 lp/mm. When one looks at the higher frequencies, the margins are larger: 50% at 40lp/mm will deliver the same results as a lens with 55%, but not as good as a lens with 60%. Use the MTF graphs with caution. They are the best representation of image quality we currently have, but some optical and mathematical background is useful to prevent the observer to make the wrong inferences.

 

5.4.3 Tradeoff between contrast and resolution?

The relation between contrast and resolution is basically inverse. The real MTF graph generated for the Apo-Telyt-M 1:3.4/135mm for the on-axis position produces a downward slope, giving 100% contrast at 0 lp/mm less than 10% contrast at 400 lp/mm. Both of these extremes are only limiting values. More important is the midrange between 20 and 100 lp/mm. Leica lenses are optimised for maximum contrast at 20 lp/mm and this will automatically give the best results for the higher spatial frequencies. There is of course some trade-odd between contrast and resolution, but it is limited to a change of the distance of the flange focal length and the effective focal length. You cannot compute a lens that has high overall contrast and at the same time a low resolution. You will find in the literature many references to a dramatic trade-off between contrast and resolution, as with the Noctilux, a lens that is supposed to have been optimized for high contrast at wider apertures at the expense of a lower value for resolution. In fact the Noctilux 1:1/50mm has low medium overall contrast and low values for the 40 lp/mm too, indicating that contrast and resolution are related. Sometimes you will read or hear that Leica has optimized a lens for maximum contrast or maximum resolution. If one assumes a dichotomy, this is not the case. The Leica designers will optimise for a small size of the blur circle with as much light energy concentrated in the core as possible, given the state of the aberrations. And they will match the fixed location of the film plane to the selected position of the focal plane to maximize contrast. The story goes that Leica has made small changes in the life of the several Summicron 2/50 versions, specifically the Dual Range version where they are supposed to have slightly reduced the resolution to make possible a slight increase in contrast. Such stories are part of the many myths around the Leica products. There is no evidence at all to substantiate this statement and it is most certainly false. The idea behind this story is the quest for maximum resolution, which is irrelevant here and never was nor is part of the design criteria for the Leica lenses.

 

5.4.4 Are 40lp/mm enough

We have seen that high contrast and high resolution work together to get good clarity of very fine details. A perfectly sharp picture would have a contrast transfer of 100% at all spatial frequencies within visual range of the eye. In Figure 5 we can note that about 70 to 80 lp/mm are still resolved with good contrast and should be visible in a 20 to 30 inch enlargement. Every optical company produces MTF graphs that relate spatial frequency (resolution) to contrast. The highest spatial frequency that will be graphed is 40 lp/mm. This is kind of an industry norm. This figure is partly based on the research by Zeiss that showed that this figure of 40 lp/mm represented a limiting case for image quality. Many experiments by Zeiss, but also other optical companies and academic research institutes have clearly indicated that the higher spatial frequencies have no influence at all on the perceived image quality. The best image quality is assured when the contrast in the region from 5 to 40 lp/mm is as high as possible. Resolution figures from film companies indicate much higher resolution figures. A 100 to 150 lp/mm are quoted as maximum resolution (or to stay in the parlance of the emulsion characteristics: 100 to 150 cycles/mm (where a cycle = one linepair). There is a danger in referring to maximum figures without taking into account what they really mean. One of the films best known for best sharpness and resolution is Fuji Velvia. The official company specification sheets show a resolving power of 160 l/mm for a high contrast subject and 80 l/mm for a low contrast subject. Two remarks here. The high contrast subject is 1:1000, which is extremely high in practice and hardly ever encountered. So let us settle for an average between the two figures. That is 100 or 120 l/mm. But 100 or 120 lines/mm is identical to 50 or 60 lp/mm, quite close to the relevant spatial frequency figure for lenses. Looking at the MTF graph of the Velvia we see that the maximum spatial frequency in the graph is 60 cycles/mm (linepairs/mm) with a contrast transfer of 30%. All Fuji and Kodak films, even the most recent ones I checked on this and they all are close to this figure, So the optical industry and the emulsion industry are reasonable close in the maximum or limiting values for their products. There is one exception. Some black and white films (Kodak Technical Pan, Agfa APX25 and Ilford Delta100) can record spatial frequencies above 100lp/mm. If the utmost care and technique is lavished on these films and the photographic equipment (camera, tripod etc.) is up to the task we can record these finest structures. Can Leica lenses cope with this as they seem to be limited to 40lp/mm. Here again we should not be lured into a simplistic conclusion. Figures 4 and 5 show clearly that a lens covers the whole bandwidth from 1 to 100 lp/mm (and even more). The 40lp/mm as we have seen, are a very good measure for image quality if the contrast is high. But no lens will stop abruptly after the 40 lp/mm line. Lenses just go on recording finer and finer levels of details (higher and higher spatial frequencies) till the limit of film, lens or the lens/film-combination. Many current Leica lenses, among them the Apo-ElmaritMacro 2,8/100, the Apo-Summicron-M 2/90 ASPH, the Apo-Telyt 3.4/135 and the Summicron-R 2/180 and 2,8/180, can resolve 100lp/mm and more with high contrast. So the 40lp/mm norm does not indicate that a lens cannot resolve more than 40 lp/mm. It indicates that if a lens can handle a spatial frequency of 40 lp/mm with high contrast it is a lens very well corrected and certainly capable of recording higher spatial frequencies.

Measurements of the resolving power of the eye (and for once all scientists agree) give a maximum value of 10 lp/mm at a viewing distance of 25cm. (Values for a young child). When you grow older, the minimum viewing distance is larger and by definition the resolving power of the eye lower. Or the maximum spatial frequency we can detect is 10lp/mm. This maximum value is of theoretical nature as degrading circumstances always exist in practical situations. (A 100% contrast for instance will never be attained). So we need a lower value to be realistic. Again there is a remarkable consensus that a spatial frequency of 5 to 6lp/mm is realistic, but still in quite ideal circumstances. Now we are in for some number juggling. The unaided eye at a distance of 25cm can resolve 6 lp/mm, that is fine detail in textures. So every line has a width of 0.08mm. Where you read line, you may substitute point, so points smaller than 0.08mm in the print will not be detected by the eye. Think about this for a while. A 20x30 inch print on a wall is unlikely to be viewed at so close a distance as 25cm. Assume 75cm, which is reasonable if you would have a vies of the full picture area. But at this distance resolving power is reduced by 1/3, so we are left with 2lp/mm on the print or a point 0.25mm in diameter. Now a 20x30 inch enlargement for 35mm is even for a Leica quite demanding. That is an enlargement factor of 20 times. Accepting the 2lp/mm on the print at normal viewing distance as reasonable, we end up with a resolution figure of 2 times 20 (enlargement factor) is 40 lp/mm.

So the industry norm is a practical one, good enough for very big enlargements for exhibition prints. Now let us be very demanding. We want to record the finest textural details possible at a 20 times enlargement when looking at the print from a close distance, the 25cm. Then we need 6lp/mm times 20 (enlargement again) and we end up with 120 lp/mm on the negative, far above the 40lp/mentioned above.

We will see that for this requirement we need Technical Pan or equivalent films, and the very best of Leica lenses. But it can be done. Most films however break down at 50lp/mm, so we could not even record this level of detail on film, even if the lenses would allow us to do it. If we look at slides, we are in a very different position.

Assume we look at slides from a distance of 5 meters, which again is reasonable. At this distance, the eye can detect 0.3 lp/mm. The projection screen is 3 meters wide, which is quite a screen, which gives an enlargement factor of 85. Again 85 times 0.3 lp/mm gives us a maximum resolution of about 30 lp/mm, below the 40lp/mm norm.

 

5.4.5 The limitations of the MTF analysis.

While MTF diagrams are very important, they do not tell us all about a lens. Flare is not accounted for, as is colour transmission, close up performance (MTF data are measured or calculated for the infinity position), distortion and vignetting. The MTF graphs do give you a clear indication of the performance to be expected from a lens, but the personal situation and the material used are of decisive influence. If you take pictures with high speed film at shutter speeds of 1/8 of a second, you are less interested in the representation of the 40 lp/mm. But more in the flare characteristics. If you aspire high precision photography, the 20 and 40 lp/mm may be of prime importance. If you take pictures with a lens with very good MTF values and your results are disappointing, you should analyze your technique and try to find the weak spots. The MTF has one advantage: it is objective and value neutral. It is the user who has to find his own personal limits of performance. You should also be aware of the fact that lenses may be only compared with the same focal lengths. A 28mm lens may have a contrast value of 60% at 20 lp/mm, compared to 50% with a 90mm lens. As the reduction of the object is higher with a 28mm lens, the level of details that can be reproduced is also lower. To get a realistic comparison one should photograph an object at a distance of 2.8 meter for the 28mm and of 9meter with the 90mm. Than we have the same reproduction scale. As the MTF-data are all based on infinity, the observer should be aware of this.

© Erwin Puts
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