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Chapter 4:

Part 2: Some advanced topics in optical design and manufacture

4.1 Apochromatic correction

The notion 'Apochromat' has been introduced around 1880 by Ernst Abbe. He used it for optical systems, that were very well corrected for chromatic aberrations.

The Greek word 'achromat' means no-colour and 'apochromat' means no-colour traces. We know already that the refractive index of glass changes with the wavelength. This spreading of the light is known as dispersion and we can see it in nature quite often when looking at a rainbow. The smaller the wavelength, the higher the refractive index and the closer the focus is to the lens. Within the visible spectrum about 200 different colours can be identified and named. The scientist Fraunhofer gave the more important of these spectral colours a letter for easy recognition. If we only have one glass element, we have to choose which colour we will use to locate the sharpness plane on the optical axis. It is customary nowadays to select the E or D(d) line as the primary or reference wavelength for optical analysis.

When the focal length of a lens is computed, the D or E line is used. All monochromatic aberrations are also computed with this wavelength as the reference.

Table: Some wavelengths and their spectral source

Wavelength	Designation of Fraunhofer line	Spectral source	Name of Color
706.52	R	Helium	Dark red
656.27	C	Hydrogen	Red
589.29	D	Sodium(doublet)	Orange yellow
587.56	D or d	Helium	Gold yellow
546.07	E	Mercury	Green
486.13	F	Hydrogen	Pure blue
435.83	G	Mercury	Violet-blue

All colours (with the exception of the primary wavelength) will have different focal points and also different enlargements of the object point. The focal length is a direct measure of the magnification of the object. A 200mm lens will give images four times as big as a 50mm lens. All deviations from the reference wavelength are known as chromatic errors. Errors in the difference from the focal length are called longitudinal chromatic aberrations and errors in the magnification are called lateral chromatic aberrations. These chromatic errors are the result of the dispersion of the glass. As every glass type and wavelength has different values, we need to find a simple way to identify and compare glass. We can measure the average dispersion over a range of wavelengths and use this number for comparison. That is what Abbe did, when he introduced the Abbe-number. Take the reference wavelength (Dline) and subtract 1 from its value. Then take the difference between the extremes for visual light (F-line minus C-line). Divide these two numbers and we have the Abbe- Number.

V = [ND - 1] / [NF - NC] These values range from 20 to 85. Crown glass has high dispersions and flint glass has low dispersions. The value of 50 or 55 is usually given as the demarcation line between both types. But these indications have only historical meaning. Glass can be identified by its Abbe-Number or a name, often from the Schott catalogue (SF2 of BK7) or by a glass number. This is a six digit number where the three first digits are the most significant digits of [ND - 1] and the last three digits are 10 times the Vnumber.

The famous 'Noctilux'-glass from the past was designated as '900403': an Abbenumber of 40,3 and a very high refractive index of 1.900 for the Fraunhofer Dline.

By suitable selection of glasses with dispersion characteristics that are mutually complementary, the designer can match a crown and a flint glass, such that two colours are focused to the same focal length. Often the C and F lines are chosen, as these lines correspond to the visual spectrum for which the eye is most sensitive.

Such an achromat has much reduced chromatic errors, but they are not gone. The residual errors are called secondary spectrum. The designer can carefully try to match special glass types in order to bring three different colours (now C and F and d) to a common focus and this type of lens is called an apochromat or apochromatically corrected lens. The negative definition of this type of lens, is a lens where the apochromatic error is not corrected. This error can be explained as follows: the overall dispersion does not tell you how the individual wavelengths are refracted. We might assume that there is an orderly pattern in the dispersion range. If we construct a graph with on the vertical axis the index of dispersion and on the horizontal axis the wavelength, we do not see a straight line, but a curved one, which has a different shape for every glass type. So the dispersion in the blue part of the spectrum relative to the red part is different for a crown glass and a flint glass. This phenomenon is known as partial dispersion, and is responsible for the apochromatic error. The designer can try to match two curves for two wavelengths but the rest of the spectrum will be out of synch and generate colour fringes and contrast loss over the whole image area. The apochromatic error will be enlarged when using telephotolenses, as the idea of a telephoto lens is the magnification of the object. With this enlargement, the colour errors will be enlarged too, as aberrations are linearly related to the focal length. The first Leica lens with apochromatic correction was the Apo- Telyt-R 1:3.4/180mm. The apochromatic correction is now introduced in the 90mm focal length, and there is no reason why to stop there. When stringent demands for colour correction are formulated, even the 50mm lens (and shorter) could become a target for this type of correction. The lens designer needs to find glasses with a characteristic pattern for the partial dispersion that is not normal, or abnormal. We saw that the normal partial dispersions do not allow for the best correction. Such glasses can be found on the glass-map and are called abnormal-dispersion glass or anomalous-dispersion glass. Such glass is very difficult to employ. Leica designers are well acquainted with these glasses, however, which explains the high level of the apochromatic correction of Leica lenses. You will see the apochromatic error at the edges of a dark-white border. On one side the edge is red and on the other side blueviolet.

Or as a green band on one side and a reddish-violet band on the other side.

These phenomena indicate two different types of chromatic error. Both can be unrelated, so one can be corrected and the other not or only partially. There is no agreed upon definition of what constitutes a 'true' apochromatic correction. Leica will designate a lens as an apochromat as both errors are corrected at full aperture, and over most of the image field. For this type of correction you need to employ these special glasses with abnormal-partial dispersion. It is also possible to reduce the apochromatic error to a small value, when using normal glasses. Then we have a lens with a very small secondary spectrum, which looks like an apochromat, but is not.

Every manufacturer has its own correction philosophy.

4.2 Can lenses be corrected for black & white emulsions only?

In the Leica community, you can often hear an assertion, that is as persistent as it is untrue. The older lenses, it is sometimes stated, are corrected and optimized for black& white photography. This statement, presumably, originates form the idea that colour corrections were not needed in the past, as colour film was unknown or not yet invented. When we photograph a scene with monochromatic film (black & white), we must realize that all colours of the spectrum are recorded as grey values on film. All wavelengths will be involved in the process of image formation. Red and blue light (the extremes of the visual spectrum) will be focused at the same locations by the lens, irrespective of the film used. The film will record the blue and red part of the light, coming from an object point, as grey tones. The apochromatic error, as we saw before, will image an object point with a red band on one side and a blue-violet on the other side. In B&W emulsions, that will be recorded as different shades of grey. So in fact, B&W film is the more demanding medium as it is very difficult for the eye to detect small differences in grey values. In addition I may add that the quality of light involved in black and white photography is always composed of all wavelengths, and will involve all residual aberrations.

4.3 Aspherics

Many of the aberrations, that I have discussed, are related the spherical form of the surface of the lens. It seems logical to assume that a non-spherical form, like an ellipse or a parabola, could be used to correct some of these errors. An aspherical lens surface is defined negatively, that is any surface that is not spherical or planar (flat) is called a-spherical. A hyperbola and an ellipsoid are examples of aspherical surfaces. An intuitive visual example would be the shape of an American football or a cylindrical lens. One of the basic aberrations of a spherical shape is the spherical aberration, whose name is aptly chosen. The principle of the use of aspherical surfaces to correct this inherent optical error, is not new. Kepler (1611) proposed its use and Descaters (1637), developed the necessary theory. But an aspherical surface is very difficult to make and it is easier and much more economical to restrict the manufacture of lenses to spherical shapes. If you look at figure (xx) you will see a classical lens shape, with two spherical surfaces with a radius of curvature of 20 (in this case). The rays do not converge to a common focus, as the definition of the spherical error has it. In the next figure I have introduced a certain asphericity to the first surface and now we see that the rays do focus in a much narrower band. The amount of departure from the spherical is small. In this particular case, it is about 0.1mm. In order to understand this number, assume that we start with a spherical surface with a diameter of 25mm, and the distance from the centre of the lens to the rim or edge is 12.5mm. The surface has a certain curvature and when we draw a line from the top of the surface to the axis, it will intersect the axis at a specified location.

If we give this lens an amount of asphericity, and repeat the act of drawing the line, we will now find that this new line intersects the axis 0.1mm way from the first (spherical) location. See picture. To get a rough understanding of the dimensions involved, you should reflect for a moment on the length of a millimetre. Divide this small space into 1000 equal parts. That is the length of a micrometer. The world of optics is really a cosmos of microscopically small dimensions. A wavelength has a mean length of 0.5 micrometer. For precision optics, it is required to stay within tolerances that are a quarter of a wavelength. The amount of asphericity, a small as it seems, is large, when compared to the required precision of a spherical surface, which may deviate only 0.1 micrometer. Luckily, Leica can produce lens elements that are so accurate, because if they could not , the whole idea of an asphere would be useless.

Figure 70: 4.3.A- spherical lens

Figure 71: 4.3.B- aspherical surface.

Note perfect point The above is an example of the use of aspherics to correct simple aberrations. The true power of the asphere (as the surface is commonly referred to), is the correction of higher order aberrations. I noted in chapter 1.1 that every surface of a lens (optical system) has its unique aberration content and the use of an asphere adds simply an additional component to the errors already present. The fascinating idea is that the asphere changes the mixture of aberrations at that surface and so helps correct higher order aberrations by introducing new ones. It is also evident, that the introduction of large errors on one surface and compensating them on other surfaces, demands a high precision in alignment and positioning of the lens elements.

As noted so often in these pages, mechanical precision and tight manufacturing tolerances are a necessary condition for high quality Leica optics. Wide aperture lenses and or compact lenses with aspherics are very demanding to manufacture as the requirements for tight tolerances grow exponentially. You pay for this production quality, even if you do not realize it.

Figure 72: 4.3.A CNC grinding

It is often assumed that the use of one or more aspherical surfaces does automatically enhance the optical performance of a optical system. That is not true.

Optical designers, employing the usual array of glass types, number of elements, curvatures of surfaces etc, might create masterpieces, but also lenses of modest performance. And there are indeed on the market now lenses with aspherical surfaces, where the optical role of these surfaces is less evident. To be useful, an asphere can be integrated into an optical system only if the correction of the higher order aberrations is required. If you have a lens, where mainly the third-order aberration are corrected, an asphere would be of no great help. Aspherics will be employed to enable the designer to build in an elegant way high quality optics in a compact format and with less weight. There is a rule of thumb that every aspherical surface replaces one lens element. As illustration, compare the six element Noctilux 1.2/50 with two aspheres with the current Summilux-R 1.4/50 with 8 elements, which is of higher overall optical quality. They can be used to correct aberrations, like spherical aberration and distortion (spherical aberration of the pupil), as in the Tri-Elmar. They can also be employed to get wider apertures and wider angles of field with a high level of correction (as with the Summilux 1.4/35 asph). The application of the aspheres is not restricted to these examples and can be used for many optical and/or mechanical purposes. The first economical large scale production of aspherical surfaces will be found in the Kodak Disc camera (1982), which used a glass lens, that could be pressed into shape. The classical way to give a lens surface its desired shape is grinding and polishing. The aspheric surfaces used in the Noctilux 1.2/50, were polished into shape manually with the help of specially constructed equipment. The failure rate of this process was high and abandoned after a few years. At the other extreme we have a manufacturing process where a plastic (Acrylic) lens is injection-moulded in a special mould. The fabrication of such a mould is very expensive and only feasible if large quantities of a lens are needed, say 50.000 pieces a year, as you can make about 200/day in this manner. The second method is compression molding where a lens blank is pre-machined close to the required shape and then the lens is put between the moulds and the whole assembly is heated. Leica does not use plastic elements or hybrid (glass-plastic) elements in their lenses. There are now two methods to produce aspherical surfaces. The first one, is the technique of direct precision molding of finished glass elements. It is basically the same technique as the blank pressing of components, where the mould and the glass are both heated and pressed into shape. The precision molding technique is a joint development of Leica, Hoya, and Schott and can be used to manufacture high precision surfaces. The limitation of the technique is not the accuracy of the aspherical surface, but the restriction to a few glass types and to glass of a diameter of about 20mm. Aspherical surfaces, formed with this technique can be found in many of the wide-angle lenses for the M-system. The current technique at Leica is the employment of computer-controlled polishing and grinding equipment, so-called CNC- machinery. (CNC=Computer based Numerical Control). The computer is fed with the necessary data, like surface specifications and tolerances and will then automatically 'operate' the tool. In this case every lens element is individually produced. There are no restrictions to diameter of the element, type of glass or level of precision, which allows the designers to explore even more exciting possibilities. The Apo-Summicron-M 1:2/90mm ASPH is the first lens with an asphere, manufactured with these new tools. The accuracy that can be attained when using this type of machinery is in the area of 0.1 micrometer, which means that the precision of classical spherical surfaces is now within reach, offering even more possibilities for correction of aberrations. Leica uses interferometers to check the correct asphericity. A compensation system is employed that adapts the spherical wave front as generated by the interferometer to the aspherical shape. A new method is the use of holograms to check the lens surface: Leica uses nowadays the CGH technique (Computer Generated Holograms).

4.4 Vignetting and the cos4-effect.

The simple explanation of vignetting is the mechanical obstruction of oblique rays. It is customary for photographic optics, and Leica lenses are no exception, that a 50% drop in illumination occurs at the edges of the frame. In many circumstances this drop will go unnoticed, especially if the change is very gradually. Mechanical vignetting can be reduced, but at the cost of a much bigger lens. But even that will not solve the problem, because the throat diameter of the lens is fixed. The free diameter for the rays is less than the full diameter suggests. In the case of the R, the mechanical linkage of the automatic diaphragm asks space that will block some of the rays and in the case of the M it is the coupling of the rangefinder mechanism that will reduce the free space. Vignetting is often used by the designer to improve the image quality in the field. Full illumination of course, is always a design aim and should be balanced against other requirements. Generally the designer ensures that the maximum diameter of the aperture stop is sufficient for all central rays to pass through the system and uses the vignetting to block some off axis rays to improve the performance. The worst aberrations are the oblique tangential rays in the outer zones. And exactly these can be clipped off when some vignetting is allowed. In lenses with a very wide angle of view, we note a second type of loss of light in the corners. I hinted at this phenomenon when discussing the field curvature. All light energy from an object point has to pass, as a cone of light, through the aperture stop.

The physical stop is the device we see when we look through the lens and count the aperture blades. In optical theory however, the aperture stop is less important. Why? Well, the aperture stop is located somewhere in the optical system and there are lens elements before and after the stop. These lens elements will deliver an image of the aperture stop and these are called, the entrance pupil and exit pupil respectively. The light rays that exit from the lens, are optically coming from the exit pupil. If we now take a point on the optical axis, and look from that location into the lens, we see the exit pupil and all rays coming from there form the cone of light. The solid angle (remember: we are in three dimensional space!) subtended by the exit pupil is the area of the exit pupil divided by the square of the distance from the pupil to the centre of the film plane. From an off axis point, let us say at the corner of the film plane, the distance to the exit pupil is clearly greater. The difference between the two distances is greater by a factor equal to 1/cos è and the increased distance will reduce the illumination in the corner by a factor of cos2 è. Now from the corner location the exit pupil is no longer circular, but we look at it obliquely and so is more ellipsoid. The projected area of the exit pupil is reduced by a factor about equal to Cos . The illumination at our corner point is reduced by cos3 è. But we are not yet ready. From our location at the edge of the frame we look at the exit pupil along the axis of the cone of light. But the film plane makes an angle with that cone of light and we have to add yet another factor of Cos to the equation, which now gets the familiar form of cos4 è. This phenomenon is very bad for wide angle lenses as we will see: a wide angle lens with an angle of 60o has a drop in illumination of cos4 30o = 0.56 and a wide angle lens with an angle of 90o has a drop of cos4 45o = 0.25, that is two stops loss. The cosine-fourth effect then is the sum of four different cosine factors. In wide angle lenses, this effect can be reduced by an optical construction, that the apparent size of the exit pupil increases for off-axis points or to introduce barrel distortion to offset the drop in illumination.

4.5 Coating and lens flare

When light strikes a glass surface, some of the light is reflected and lost for the process of image formation. Less light energy will reach the film emulsion and the transmittance of the lens is reduced. More importantly however, some of the light is not bounced back out of the lens system, but will stray into the lens elements and create veiling glare and ghost images. Specifically the veiling glare is a bad phenomenon (it works like a soft focus filter) as it will reduce overall contrast and especially will considerably lower the contrast of very small details, giving them a fuzzy look. The official definition of 'flare' is: non-image forming light, more or less evenly distributed on the film plane. You can easily see this phenomenon for yourself if you compare two pictures taken in exactly identical situations, one with a lens prone to image degrading flare (like the Summilux 35mm at full aperture) and one which has good flare control (like the Summilux-ASPH 35mm). In the first image the deep shadows are lighter (more deep grey than ink black), very fine subject detail can not be detected (which the ASPH easily shows) and the overall contrast is lower, where the ASPH has brilliance and deep saturated and clear colours (in the small subject areas that is). The ASPH also suppresses light fringes around the small subject outlines in strong backlighting and side lighting, where the older lens exhibits strong halo around the subject outlines. The second way to show the image degrading by flare is measuring the deep shadows with a densitometer. You will then find that the older lens has actually a higher reading in the deep shadows than the ASPH, which you could interpret (wrongly) that the older lens is better in the area of light transmission. Ghost images or secondary images, like the well-known round or hexagonal images of circle of the closed aperture blades, can be suppressed by effective reflection control, but they will occur and always unexpectedly at your best picture. When you are taking important pictures, you really should give the topic of reflections some analysis and precautions. Look at the angle, the sun or light source is making with the lens, see if light rays enter the lens directly and try to shade them off. Current Leica lenses are quite effective in the reduction of flare, but they are not immune to it.

Figure 73: 4.5.A coating

The principle of reduction of the reflected light is simple. If you add a thin layer of some substance to a glass surface, there will be two additional boundaries that the reflected ray has to transverse. It is possible to design the thin layer such that the reflected rays from the upper and lower boundary cancel each other before exiting the surface. This is called destructive interference. Optical coatings are thin films of various substances, often magnesium fluoride, zinc sulphide, hafnium oxide and many others with exotic names. Every substance has its own index of refraction. We habitually speak of single layer and multiple layer coatings, assuming that the latter have superior properties. As usual in optics, there is more than meets the eye. The optical thickness of a coating is different from its physical thickness, as we have to account for the index of refraction. All references to the thickness of a thin layer are in fact to the optical thickness. It can be calculated that to be effective the thickness should be a quarter or a half of the wavelength. Since interference effects produce colours, just as in oil droplets on wet pavements, we might be able to judge the thickness of a layer by looking at the colour. If a single layer film has an optical thickness of one-quarter of a wavelength, any wave reflected from the second (bottom) surface will be one half of a wavelength out of phase with light reflected from the first (top) surface and both will cancel. We have however to take into account the index and it can be proved that to be effective a thin layer needs to have an index that is the square root of the index of the glass, on which the layer is deposited. The reflectivity of a coated surface will change with the wavelength. It is clear that the quarter wave coating only works for one specific wavelength. For all other wavelengths the layer is more or less thick than this quarter-wave thickness. A single layer coating does function therefore more or less efficiently in a broader region than only the specified wavelength. Often a coating will try to reduce the reflection for the yellow light as this is the most visible to the human eye, and that gives the characteristic purple colour of single layer coatings. The efficiency of a coating depends on index of refraction of the glass and of the layer, light transmission properties of the layer, angle of the incident light. All these components have to be looked at before one can make comments on a coating. With more layers of different properties, one can broaden the effectiveness of the coating over a wider range of wavelengths. It is possible to reduce the reflection over the visual spectrum to 0.2%, compared to 4% for an uncoated surface. Current Leica lenses are all coated with a multi-layer coating and sometimes the surfaces of the cemented glasses are coated when research has indicated its effectiveness, a not too common practice. The most common method of depositing a layer to glass is the thermal evaporation coating. The coating material is heated in a vacuum chamber as is the glass that will be coated. The length of time and the temperature control the thickness of the layer.

If the glass surface itself is not absolutely smooth, irregularities will occur that diminish locally the effectiveness of the layer. Here we seen another hidden quality aspect. Leica takes great care to ensure that the glass surface is polished to a very low level of roughness, as this alone will degrade image quality. The cleaning of the lens, before the application of the layer has to very thorough. Leica uses often ultra-sonic cleaning procedures and sometimes a glass needs to be coated within hours after being cleaned as otherwise the air would already affect the surface. This coating technique does not deposit a really smooth, amorphic layer, but the surface is covered with a structure, consisting of rows of pillar like stakes, like rows of nails with the tip pointed upwards. Heating, cooling, depositing are time consuming and glass does not like the heating-cooling cycle. A new method has been introduced at Leica, developed jointly with Leybold: the plasma ion assisted deposition (IAD), where the growth of the pillar like structures is reduced and a much smoother surface area can be generated. The process uses a much lower temperature and in essence consists of a bombardment of ions onto the surface to be coated where atoms are set free that attach themselves to the substrate and form an amorphous layer.

4.6 The use of filters.

This topic will divide the Leica users in two camps, one stating that any filter will degrade the optical quality of the lens and the other one asserting that a filter will do no harm and will in addition protect the surface of the front lens. Filters are often an indispensable tool for the photographer. Many B&W pictures can be enhanced by the employment of filters to give a more natural grey value to the basic spectral response of the emulsion. A green filter will differentiate more between several green hues and an orange filter will enhance contrast. And slide film often needs a colour correction or colour balancing filter. So if the use of filters is unavoidable, what are the restrictions, if any? In addition the question most often posed is if it is a sensible act to have a UV filter permanently attached to the lens. The answer is simple, but has to be developed in two steps. IF a filter has absolutely plane surfaces (and I mean optically plane), then the degrading effects can be neglected in all but two situations.

It is not to be assumed than any filter can be qualified as optically plane, without any defects or surface irregularities.

1. If the lens is a wide aperture one and/or a wide angle one, the oblique rays will certainly degrade the image quality of the lens, when a filter is put in front of the lens. There are two additional surfaces, which will inevitably deflect a very small part of the rays.

2. If the lens is used in high contrast situations or when strong light sources are in or close to the main subject, you can expect secondary images and some veiling glare. I will be practical here. Whenever the situation is not very demanding I will use a UVfilter for protection purposes. Just to make sure. I am aware that the front surface is quite scratch resistant, but there is always that nagging doubt that some nasty particle will scratch my lens. And if I use lenses with longer focal lengths, even in some high contrast situations, I will leave the filter on. But when the degrading factors accumulate (example: 24mm lens and a contre-jour situation or 90mm with light sources in the image area) I will remove the filter. There are no hard and fast rules here. None of the extreme positions (never a filter, always a filter) corresponds to the reality of filter use and image degradation. It is up to the individual user to choose carefully when to use or not use a filter. In most normal situations the theoretical image degradation of a filter can be neglected and is most certainly less than a slow shutter speed. Take a picture with 1/250 with a filter and 1/15 without and there is really no contest. The slower shutter will have more negative effect on the image quality than the filter. The use of a filter will have some effect on the lens performance, but one should carefully reflect if this element in the imaging chain is the most crucial for the picture to be made. If the use of a filter is required there is no option but to use the best filter quality you can find. The situations outlined above, that will magnify the degrading effect of a filter, should be taken into consideration when making the picture. If you habitually use a filter for protection purposes, you should remove it under the specified conditions. Current lenses have quite resistant coating. But every one has to make his own choices here.

4.7 Wide apertures and the geometric flux.

From a modern perspective a lens transmits light energy from an object to an image plane. If we take a picture with, let us say, 1/125 of a second, all light energy reflecting or originating from the object is integrally captured on film in a fraction of a second. The lens or optical system is in fact just a tube that transmits the light energy. This phenomenon is designated as the geometrical flux or in German 'Geometrischer Fluss'. In analogy: through a water pipe with a certain diameter, only a certain amount of water per time unit can pass through. If you need a larger flow of water, you have to increase the diameter of the pipe. The length and diameter of the pipe then do determine the energy that can flow through it. The strength of the aberrations is also dependent on this dimension of the pipe. The Apo- Summicron-R 1:2/180 is twice as voluminous as the Apo-Elmarit-R 1:2.8/180. The dimensions for the 2/180 are 176 x 116 (length and width) and for the 2.8/180 are 132 x 76. Simple calculations of the tube volume gives 32.053 and 15.750, that is the Summicron is twice the pipe volume of the Elmarit, which is correct, given the fact that the Summicron is twice as sensitive. This relationship with tube diameter and length also explains why the Vario-Elmarit-R 1:2.8/35-70 ASPH is twice the volume of the Vario-Elmar-R 1:4/35-70mm. If you prefer to reduce the dimensions, you will have to perform some elaborate optical juggling which often degrades the image quality. A 2/50mm lens seems to be a piece of cake to design, but a 2/35 is much more difficult as a wider tube is needed for the passage of the light energy and a 1.4/35 is twice as problematic and four times as problematic as a 2/50 design. Now aberrations do not conform to a simple extrapolation pattern. Some aberrations grow exponentially when the tube dimensions grow geometrically. There is much truth in the statement that it is easier to correct a lens when the physical dimensions may be allowed to grow beyond the minimally required optical relationships. Aperture and field angle are intimately related, as far as aberrations are concerned.

The following table illustrates the dependency.

Aberration	Aperture = r (radius)	Field (angle of view) = w
Spherical aberration	R^3	No influence
Coma	R^2	W
Field curvature	No influence	W^2
Astigmatism	No influence	W^2
Distortion	No influence	W^3
Chromatic aberration	No influence	W

This table tells you that the spherical aberration grows by a factor of 8 if the aperture doubles and that distortion grows by a factor of 8 if the angle of field doubles. A 2/50mm can be approximately be corrected as well as a 2.8/25mm, but coma is reduced by a smaller aperture, but at the same time enlarged by the wider angle of field. And while spherical is reduced, distortion grows disproportional and the balance may re-introduce some other aberrations. How this works out in practice is part of the designers' chemistry. The smaller the physical volume, the more difficult the correction. The law of the geometrical flux is always true. The improved correction of the higher order aberrations at the wider apertures demands a very high accuracy in matching of parts and assembly of components. It does not make sense to calculate an improved version of a lens and then specify production tolerances that nullify the advances made. It is not an over statement, that a large part of the price you pay for a Leica lens, has been invested in the performance at the wider apertures. It is really counter-productive to stop down to very small apertures, as image quality will degrade visibly, when enlarging the negative 10 times or more.

4.8 Vario lenses.

The basic idea of a vario-lens (in Leica parlance and zoom lens by many other manufacturers) is the possibility of different magnifications in one optical system, without changing the distance from object to film plane. A lens with a fixed or single focal length there is only one magnification ratio for the object at a certain distance from the film plane. Assume we take a picture of a person with height 1.70 meter and we want to have this person fill the frame of the negative without turning the camera, the magnification will be 24mm/1700mm = -0.014. If we want a different magnification, to get a more detailed recording of the face we have to move closer to the person and refocus. If we take a simple lens and move it towards the object, we get a larger image and when we move it away from the object, the image becomes smaller. This would be a variable-power (or vario or zoom) system, manually operated, but is shows the principles. An uncompensated single lens vario system, as outlined above, can only have two magnifications where the image is focused sharply. We will have to add more lens elements and a compensation shift of some of the other lenses in the system to get more points of focus. A real-life zoom lens consists of at least two groups of lens elements. If we change the distance between the two groups, we alter the effective focal length and thus the magnification. If we now use a mechanical device to slightly shift the location of one of the groups, during the zooming action, we can preserve the final focus position. This compensation movement is unfortunately not a simple linear change in distance, but a non-linear one and needs a cam arrangement, with a rather complex shape of the cam. In the early days of zoom lens design, such a mechanical compensation could not be manufactured with the required precision and an optical solution was searched for. The optical compensation employs two more lenses or lens groups, which are linked together and also move together and in relation to the other lenses of the system. Such a system is simple to manufacture and all early zooms are optically compensated. The early zooms had a remarkable property that is almost lost today: the constant aperture over the full range. Also the exit pupil was a constant, and as the older cameras had no Autofocus and Auto-exposure to compensate automatically for focus changes and illumination differences, that was a bonus. But these demands stressed the design optically and generally the earlier zooms were optically not that good. As the lens elements had to be located at specific positions, the designer was restricted in the ability to correct the system over the whole zoom range. In fact the correct focus could not be held and was replaced by a focus within the depth of field parameters. And last but not least, those systems were physically large. When the problem of the accuracy of the machining of the cam arrangement was solved, most zoom lenses became and are of the mechanical compensation type.

A modern vario lens consists of three optical groups, the basic optical unit, that defines the general properties and where resides the bulk of the aberration correction, the unit that adjusts the magnification (the compensator for constant back focal length) and the unit that adjusts the focus position (the variator for focusing movement).

Figure 74: 4.8.A 105-280 See picture 4.2/105-280.

Some earlier lenses had two groups, only a variator and a compensator unit, which as a whole also functions as the basic unit. See 3.5/35-70mm. When the designer can employ many lens elements and is relatively free to move lens elements, a macro function can be built-in too, as with several current Leica Vario lenses. The Vario- Elmarit-R 1:2.8/35-70mm ASPH is a special case, as here the non-linear cam movement has been replaced by a linear movement, with the same possibilities but easier manufacture. Generally a designer will correct the vario-lens for three positions, the extremes and the geometrical mean of the extreme positions, on the assumption that the intermediate positions will be corrected automatically. Here much sensitivity and feeling of the designer is expected in order to create a really excellent lens. As we noted in chapter 1.1, the more lens elements you have, the more possibilities for aberration correction you have. But it is easy to lose track of all combinations. It is a hallmark of good design to accomplish more with less elements: most Leica vario lenses are within the 9 to 11 range, where the competition uses 16 to 20 elements.

Figure 75: 4.8.B 4/35-70

Figure 76: 4.8.C 2.8/35-70

The obsolete idea that vario lenses can never be as good as fixed focal length lenses is presumably based on earlier experiences of optically corrected zoom lenses. It is however not possible to work from pre-conceived notions. The Vario-Apo-Elmarit- R 1:2.8/70-180mm as example has better imagery than the fixed lenses from 80 to 135mm focal length, but is at 180mm not as good as the Apo-Elmarit-R 1:2.8/180mm. The same statement applies to the Vario-Elmar 4/35-70 and Vario- Elmarit 2.8/35-70 ASPH, when compared to the same range of focal lengths and comparable apertures.

4.9 Bo-ke, unsharpness and circle of (least) confusion

When we record a three dimensional (or solid) object with our Leica, we will have to accept that the image will be flat. The solid object will be represented on the film plane, that is in itself extremely thin and for all purposes can be considered dimensionless. The film emulsion has a thickness of 3 to 10 micrometer, but we can neglect this. It is, by the way, interesting to note that a film like Agra APX25 (one of the best to explore the Leica lens quality) has an emulsion 'thickness' of 3 micrometer. This is ten times smaller than the diameter of the circle of confusion, that is fixed at 1/30mm or 30 micrometer. Assume we take a picture of a person at two meters in front of the camera. Focusing on the eyes, will ensure that the focus plane, the vertical slice through that solid object will be sharply recorded on the film plane. All object points, in front and beyond that focus plane will be defocused or unsharp, and the more so as the distance from the focus plane becomes larger. Most photographers will have had the experience of a slightly defocused picture. But when looked at from a larger distance, the picture looks acceptable sharp to most viewers.

Or the other way: we have enlarged a picture to a 20x30cm print and find the image sharply rendered. Then we try a bigger enlargement, say 40x50cm and now we are heavily disappointed, as all object points are blurred a bit. These experiences allow us to remark that the eye will regard image points as sharp points when the viewing distance and/or the diameter of the point is below a certain limit. We know (see chapter 1.1) that a very small object point, like a star will be recorded on film, not as a point, but as a small patch of light, with a core of high intensity of light energy and a series of concentric bands or rings of ever diminishing intensity. The core is surrounded by a blurred edge, but we will not see a blurred disc of light but a sharp point of light. Unless we enlarge sufficiently and are able to discern the pattern of irregular light distribution. The ability of the eye to see 'clearly', is simply stated the ability to differentiate detail at some distance from the eye. If we do an eye test, we are asked to identify letters or shapes of ever smaller dimensions. When we can no longer identify a letter as a 'V' or an 'O', we are beyond our minimum visible resolution. It has been established that this happens when the eye subtends an angle of 1' (minute) of arc. Using an angle means that the resolution limit is dependent on the viewing distance and the size of the object. Using this criterion and the normal viewing distance of 25 cm, it has been established that any object, smaller than 1/16mm (0.0625mm) will be seen by the eye as a single point. And two small objects, separated by at least 1/16mm, will be identified as two single objects. When two objects are closer together, say 1/50mm the eye will only see one (bigger) object and not two smaller ones. These figures are obtained under ideal laboratory conditions, so it is reasonable to use lower figures for the photographic practice. Often the figure of 1/6mm (0.1667mm) has been proposed, which translates to 6 lines in a millimetre or six points on a line, one millimetre long, every point having a diameter of 0.1667mm. All these figures are related to the print that we are looking at. What does this mean for the dimensions of the points on the film plane. Let us assume, that we will enlarge a negative 5 times. Then we have to divide the diameter of our smallest visible point by 5, thus 0.1667/5 = 0.0333mm. As long as points on the film are smaller than 0.033mm, we will see them clearly as a point. If we use an excellent lens, with very well corrected aberrations, the points in the plane of sharp focus may be as small as 0.005mm. If we defocus a bit, these extremely tiny points become blurred and larger, let us say twice as large, that is 0.01mm. That is still below the limit of 0.033mm and even these unsharp patches will be seen by the eye as sharp points. If the true (sharp) focus plane would be located at a distance of 2 meters, that is the plane we are focusing on, we have image points of dimension of 0.005mm. The object plane at a distance of 1.90meter, will be defocused (out of focus) and generate larger image points of dimension 0.01mm, but still within the limit of minimum visible resolution. An object plane at 1.70meter will have defocused image points of 0.03mm and now we start seeing a defocus blur. The same reasoning can be applied to all object planes behind the plane of sharp focus. In this example, we will be able to se all object points that are located in the object from 1.80meter to 2.20meter as acceptably sharp points and we say that the depth of field in this case is 40cm. The position of best focus is of course 2meter, but all points within the sharpness limit, calculated here as extending from 1.80 to 2.20meter are seen as sharp. The depth of field (DoF) is related to the limit of minimum visible resolution, which in photography is called the circle of (least) confusion (CoC). The enlargement factor we have used (5 times) to calculate the CoC of 0.03mm has been established long ago when films and optics were in their infancy. If we enlarge 10 times, which we will often do with our small Leica negatives, we will quickly notice that this CoC is too large and that the DoF shrinks considerably. It is not well known that the DoF extension (distance before and after the sharpness plane) only depends on the reproduction factor. That is, when two objects are photographed such they are of equal magnification, irrespective of the focal length, the DoF is identical. In practical terms, an object taken with a 35 mm at 3.5 meter and the same object taken with a 180mm at 18 meter will have identical DoF. So if we wish to compare the unsharpness impression of two different lenses, or make any general statements. we should take care to compare pictures taken at equal magnifications.

The idea of bo-ke Most discussions of the concept of Depth of Field are based on the unsharpness criterion of 0.03mm and argue from there. It makes more sense, and in my view is more correct too, to interpret the DoF as a result from defocus blur. A more appropriate definition of the depth of field is this: the range of defocus within which the image appears to be correctly focused. This is what we do when we use zone focusing or the hyperfocal distance. Or even when we try to focus accurately and assume that we have a safety margin for some defocus or out-of-focus range. Any out-of-focus point will be represented as a defocused blur disc and we know, at least by experience, that any defocus decreases image quality as it blurs out fine detail, reduces contrast and makes sharp edges fuzzy. The shape of the blur disc is that of the aperture stop and its diameter is dependent on the size of the aperture stop and the distance between the in-focus and out-of-focus planes. We are familiar with the shape of the aperture stop when we see a circular or hexagonal out-of-focus spot in the fore- or background of the image, indicating the number of blades in the aperture stop. Less blades give a hexagonal shape and more blades a circular shape. Apart from this easily recognized phenomenon, you can note that the out-of-focus objects gradually become blurred when they are located farther away from the plane of focus. The change from focus to out-of-focus blur patterns is not gradual, but depends on many factors, such as the structure of the out-of-focus image itself and the distance from the plane of focus. It is therefore not easy to make comparisons between the shapes and structures of out-of-focus images between different lenses.

Generally one can assume that a blurred fore- and background will help to set the main object, correctly focused, clearly apart and also gives a clue of depth. The outof- focus shapes have been studied recently and the character of these shapes is designated by the Japanese word 'bo-ke'. 'Bo-ke' originally means being obscure.

The Japanese often use this word to express absent-mindedness or dotage of the elderly. The word itself has no positive connotations. A lens which is interpreted as having good bo-ke has a certain level of image degradation, that retains the original shapes and details of the out-of-focus object planes. One might say that the difference between the in-focus and out-of-focus images is relatively small, which provides a very smooth transition from focus to defocus. The concept of bo-ke is a subjective one and it is a matter of personal opinion if a certain kind of out-of-focus blur is pleasant or not. The concept of bo-ke has been interpreted as a criterion of image quality and a discriminating characteristic of lenses. The artistic interpretation and emotional connotations of an image are beyond the scope of this book. What I can discuss is the fact that there are indeed differences in the way lenses reproduce the out-of-focus planes. The presence of aberrations decreases the ability to detect a defocus, as the result of aberrations is a loss of contrast, blurring of sharp edges and of fine details, just as the effects of defocus, we described above. A lens that shows less image degradation in the out-of-focus areas, (has good bo-ke) must be, therefore a lens with a higher level of residual aberrations. Some Leica lenses are described as having good and bad bo-ke. The older lenses invariably get high marks for good boke and the current lenses get low marks. As we noted, the higher the optical correction of a lens, the more easier it is to detect the image degradation of the outof- focus areas and that is interpreted as bad bo-ke. New or recently redesigned Leica lenses are more highly corrected than older lenses and therefore have a steeper transition from focus to defocus areas. A lens in case is the Summicron-M 1:2/35mm (3) from 1979, which is credited with very good bo-ke and the current Summicron-M 1:2/35mm ASPH, which is supposed to have a different kind of boke.

The aberrations still present in the older version do indeed decrease the effect of the out-of-focus blur .The use of aspherical surfaces has no direct relation to the perceived presence of good bo-ke. It is the level of aberration correction which is instrumental, and not the use of aspherics. A lens without aspherics, but highly corrected, as several apochromatically corrected lenses, exhibit the same bo-ke fingerprint. When one stops down, the differences between the definition of the inand out-of-focus areas of several types of lenses do diminish of course, but do not disappear. It is a matter of optical progress that the new designs have a more easily recognizable out-of-focus blur and that a defocus is more visible. The definition of the in-focus part of an object is the most important part of a picture. Leica designers use all their creativity and expertise to design wide aperture lenses with outstanding in-focus imagery. A more pronounced out-of-focus area helps to concentrate the visual attention to the correctly focused plane. See examples in the colour section.

Colour slide 4a shows previous type of correction, 4c shows current type of correction. Slides Girl a and Girl b, show real pictures. Both at aperture 1:2 and identical situations. Note the smoother background of the older lens. Generally the older Leica lenses exhibit out-of-focus blurs that are quite soft and retain the outlines of object shapes. The shift from in-focus to out-of-focus is gradual and smooth.

Current lenses have a more abrupt transition and the out-of-focus blurs have a different character, notably a cleaner definition of the defocus rings, which breaks up the structure of the outlines.