This makes coma very visible even in small amounts. The usual effect of coma is to cause all image points near the edges of the field to blur outward: the effect is exceedingly unpleasant, giving the impression that the image is flying apart. Thus coma must be reduced to the minimum in any lens which is to be considered well-corrected.

Luckily, the correction of coma is not difficult: it is done in much the same way as the correction of spherical aberration, by combining two lenses having opposite coma tendencies. It is quite possible to correct both coma and spherical aberration with the same pair of lenses (though some zonal residuals will necessarily remain), and a lens corrected for both spherical aberration and coma is called "aplanatic."

Astigmatism. This is probably the most serious and most stubborn aberration of large-aperture lenses. Because it cannot be corrected in lenses made of ordinary crown and flint glasses, early landscape lenses, Rapid Rectilinears, and portrait lenses were all. limited to apertures of 1/8 or smaller. Astigmatism is the tendency of a lens to focus off-axis rays to two separate positions; lines radial to the lens axis are focused in one plane, and lines tangent to the field are focused in another plane. This effect grows more serious with larger lens apertures and with wider angles of view, hence it is not much of a problem in telescope objectives, but exceedingly important in camera lenses.


With the new Jena glass types, and a proper choice of curvatures, the astigmatic difference between radial and tangential lines is minimized, but a new aberration appears; the combined images fall upon the surface of a sphere rather than in the flat plane we require. Curvature of field and astigmatism are thus closely tied together, and correction of the two aberrations must be done in one operation.


Curvature of Field. The formation of images on a spherical surface rather than on a flat plane is characteristic of lenses of any aperture; however, stopping down tends to minimize the effect simply because of the increased depth of field (and depth of focus). The effect is most serious when the lens has a large aperture and also an extended field. Therefore, it must be corrected even in simple box-camera lenses; here the flattening is accomplished simply by making the lens of meniscus shape and putting the diaphragm in front of the lens, which has its concave side facing the subject. Unfortunately, this tends to increase the astigmatism and coma of the lens; however, in lenses working at I/li or thereabouts the problem is not serious, and in box cameras, the other aberrations tend to swamp it out.

Another method of handling the box camera problem is to make the lens of meniscus shape, but with its convex side facing the subject, and the diaphragm behind. This construction is mainly used to make the camera more compact; the astigmatism is slightly improved but the field is severely curved. This is compensated by the simple mechanical means of curving the film path to approximately the same degree.

In large-aperture lenses, astigmatism and field curvature are the most serious problems; their corrections are bound up and must be effected together. The exact type of correction used depends upon the intended use of the lens. The most obvious would be to try to get the astigmatism and field curvature in opposite directions so that the plane of best focus would lie between them. Unfortunately, this does not produce a completely flat field, because of zonal residuals, but it is useful where a small aperture and a wide field are required, as in the case of extreme wide-angle lenses. In ordinary camera lenses, some field curvature is tolerated to secure a better correction of astigmatism.



is possible that rays from some intermediate zone will still fail to come into the same plane. This condition is known as "zonal spherical" aberration and is sometimes more serious than a simple undercorrection of primary spherical aberration.

Ordinary spherical aberration tends to cause the out-of-focus rays to surround the sharply focused points with a small halo. The effect on the image as a whole is to cover the entire image area with a haze of scattered and out-of-focus light. This tends to reduce the contrast of the image, but because the scattered light is much less bright than the sharply focused rays, it does not tend to damage the image definition very much. The effect is most visible with large aperture lenses on reflex cameras; the residual spherical aberration is seen as a haze that is most severe at full aperture, tending to disappear as the lens is stopped down.

This haze, containing as it does little of the available light, can often be minimized by the simple expedient of underexposing slightly. This is what is done in the case of the ordinary box camera; the single lenses used in these cameras have a considerable amount of spherical aberration, but since most box cameras are used on the verge of underexposure anyway, it has little effect on the image. Obviously, the use of faster-than-usual films in a box camera can seriously degrade the quality of the image.

When a lens is corrected to bring the extreme marginal ray to the same focus as the paraxial one, then the residual error is usually in the form of a zone of spherical aberration at about 0.7 of full aperture. If, though, the 0.7 ray is brought to the same focus as the paraxial ray, then there are two zones of residual spherical aberration, one at the margin, the other about halfway between the axis and the 0.70 point. These zones are opposite in direction and usually are only about half as serious as the single zone of residual spherical aberration resulting from a union of the marginal and paraxial rays. Since the zonal spherical aberration tends to cause a focus shift as the lens is stopped down, it is evidently desirable to reduce its effect to a practical minimum in this manner, This is especially important in the case of single-lens reflexes with automatic diaphragms, where focusing is always done wide open, and the lens is stopped down at the instant of exposure.

The use of paraboloidal curves to eliminate spherical aberration has been tried in a few very expensive lenses. Because of the great cost of grinding these special curves, it is not likely that any great use will be made of them in ordinary camera lenses. Aspheric curves of this type can be used quite easily and inexpensively in projection systems, however, in the condenser lenses, which focus the light on the film or slide. In such projectors, spherical aberration in the condenser system produces a serious unevenness of illumination on the screen. But since the condenser is not expected to produce a sharp image (it is only required to focus the lamp filament in or near the projection lens), high optical quality is not required. Usually, simple molded and fire-polished lenses are used in condenser systems, and it is easy enough to mold such lenses into a roughly paraboloidal shape. Often this reduces a condenser system to a single lens.

Coma. Unlike spherical aberration, coma appears only in off-axis image points. The marginal rays have a different focal length from the paraxial rays, and since focal length determines the size of the iniage, points near the margins are spread out into a fan-shaped pattern by failure of the marginal and paraxial rays to intersect. This pattern is generally somewhat comet-shaped, from which the aberration takes its name.

Coma differs from spherical aberration in another way; most of the light is scattered into the tail of the patch, rather than into the sharply focused point.



By this time it must be clear that the aberrations are mostly interdependent. Astigmatism and field curvature must be worked on together; however, to eliminate astigmatism completely introduces a large residual of spherical aberration. Which to minimize, then, depends upon which is considered more serious. Generally, spherical aberration does not seriously degrade the definition of tbe lens; it merely scatters the out-of-focus light into an overall haze, which reduces only the contrast of the image. On the other hand, astigmatism distorts the shape of the image points very seriously; circles of confusion become ellipses and in extreme cases, lines. This is destructive of definition, and it is generally considered best to minimize astigmatism as far as possible, even at the expense of admitting some spherical aberration.


Distortion. Distortion is a lens fault in which the magnification in the outer parts of the field is different from that at the center. If the marginal magnification is too great, the corners of a square object will be extended outward, causing the well-known "pincushion" distortion. The image as a whole will be too large, since the magnification increases with the distance from the axis. If the marginal magnification is too small, then the image will be bent inward, particularly at the corners, causing the equally well-known "barrel" distortion.

Distortion must be eliminated in the design of the lens; it is not affected in any way by stopping down. One way of correcting distortion is to make the lens system symmetrical in form, with the diaphragm in the middle, as in the well known Rapid Rectilinear lens. This has other benefits: it not only corrects distortion, but coma and lateral color as well. This cancellation is only complete for object-image ratios of 1:1 but is very large at other magnifications as well. It is possible to cancel the three aberrations for other object-image ratios by making the lens system hetni-symmetrical.; that is, the lens shapes are symmetrical, but the sizes are in the ratio of the desired object-image distance. Again, the correction will be best at the ratio designed for, but usefully large at others.

if the lens is of asymmetrical design, like the Tessar, distortion is corrected in other ways. it cannot always be eliminated completely, and for that matter, it is not always desirable to eliminate all traces of distortion. For instance, in lenses of fairly wide angle, used on miniature cameras where subject matter seldom contains any straight lines, some barrel distortion is often designed into the lens. This residual is generally considered to improve lens performance because the lower magnification at the edges of the field increases the corner illumination noticeably.

A large amount of barrel distortion is required in lenses of the "fisheyc" type, where the field of view is nearly 1800. With such a field of view, obviously, a lens having a flat field would also have a field of 180' in the image plane, and one would require a plate or film of infinite size to include the entire image. By designing these lenses with very severe barrel distortion, the image is caused to take the shape of a circle that contains the entire 180' field of view in a relatively small image area, although objects at the margins of the picture are far smaller than their true geometrical size. It is possible to compensate for the distortion of such a lens by printing negatives from it through the original fisheye lens mounted in an enlarger. The entire negative cannot be printed at one time, but sections of the image not too close to the margins can be printed with nearly rectilinear rendition in this way.

Other cases include telephoto lenses having positive front components and negative rear elements; these almost always have some distortion, though by careful design it can be reduced to a very small amount. Zoom lenses likewise suffer from distortion, which is likely to vary as the focal length is changed.



In one case the distortion went from barrel to pincushion through the normal zoom range; this lens was free from distortion at one focal length setting only.

Process lenses for photomechanical work must not have any appreciable distorti~; this applies also to wide-angle lenses for architectural work and lenses for aerial mapping. In all three cases, either symmetrical or hemisymmetrical construction is used.

Chromatic aberration. Up to this point, it has been tacitly assumed that the characteristics of the lens are the same regardless of the color of the light. This, of course, is not so. The refractive index of glass varies with wavelength; it is greatest for the short wavelengths (blue, violet) and least for the long wavelengths (orange, red). Thus the actual focal length of a simple lens will vary with color~shortest for blue, longest for red. That is, the image of a blue object falls closer to the lens than that of a red object, and it is impossible to focus both at the same time. The effect is extremely important and must be corrected in all but the simplest, most primitive systems. Achromats (lenses designed to bring two colors to the same focus) were even used in box cameras until quite recently

It is not well known among photographers that it is possible to combine two lenses made of the same type of glass to produce an achromatic combination; this is done by careful choice of the separation between the two lenses. At one particular spacing, the chromatic error of one lens will exactly cancel that of the other, and since the two glasses are alike, their variation in index is the same at every wavelength. Hence cancellation is complete at all wavelengths, and a very high order of chromatic correction can be attained in this manner. Unfortunately, the method does not admit of correction for other aberrations, and so it is used only for special purposes such as microscope and telescope eyepieces.

The more common method of correcting chromatic aberration is to use two different types of glass, having different refractive indexes but fairly similar dispersions (difference in index at different wavelengths). If a combination is made of the two glasses, one positive, the other negative, the chromatic errors will be canceled, but the combination will still have power because of the difference in refractive indexes.

The proper choice of glasses and adjustment of the powers of the two lenses will result in a pair of colors being brought to focus in the same plane. Which pair is chosen depends upon the use to which the lens is put one pair is used for visual purposes, such as telescopes, microscopes, and projectors; another pair for photographic purposes. There are also special types of achromatism for work in the infrared and ultraviolet.

It must not be assumed, however, that br~ging two colors to a focus will automatically bring all other colors to focus in the same plane - if this were the case, there would be no need for the different types of achromatism mentioned. Colors lying between the chosen pair will come to a focus somewhat closer to the lens, and those outside the pair will fall beyond the focus of the chosen colors. This error is called '~secondary spectrum and in the case of camera lenses is usually small enough so that it may be ignored except for very critical work. In fact, in such lenses, the exact type of achromatism is not very critical; any error in correction will merely result in some other pair of colors being brought to a common focus at the prescribed distance. Furthermore, the residual error will not have any great effect on the sharpness of the image. As in the case of spherical aberration, the out-of-focus rays arc simply superimposed on the focused ones, causing a colored halo that reduces only the contrast of the image. But for critical work, such as color photography with large cameras,




color separation work in photomechanical processes, and color mapping, the residual color error, or secondary spectrum, must be minimized if it cannot be completely corrected.

O'ie way of diminishing the secondary spectrum is to use certain special types of glass which have better characteristics than the usual ones for this type of correction, and can diminish the secondary spectrum to as little as 1/3 to 1/5 its normal value. The special glasses required for this type of color correction tend to be unstable, however, and so · they are used only in certain apochromats, where simple symmetrical construction is important.

A material frequently used in place of glass for the correction of high-aperture microscope objectives is fluorite (calcium fluoride). This material has a very high refractive index and a low dispersion, and lenses made from it have very low secondary spectra. However, until recently, the only source of fluorite was certain mines where it was found in the form of natural crystals; these were seldom big enough for anything except microscope objectives. Recently, a method has been found to grow fluorite crystals artificially, and a new lens, the 3OOmm Canon 1/5.6, contains two fluorite elements.

There is, however, another way to handle this problem, and that is to make a lens of three different types of glass and bring three different colors to a focus in the same plane. This method is employed in the so-called "photovisual" telescope objective, but is seldom used in camera lenses. For one thing, it is very difficult to find three glasses that have a set of dispersion and refraction ratios different enough to make this correction possible. For another, the final result is merely to bring a third color into focus, but colors between and outside the three are still out of focus, and this "tertiary spectrum" is often just about as bad as the secondary spectrum of an ordinary achromat.

In general, though, the problem is simply not that serious; secondary spectrum in camera lenses does not seriously degrade their performance, and a designer, if troubled by other aberrations, may sometimes allow large tolerances in achromatism.

Lateral Color. Lateral color, or chromatic difference of magnification signifies a difference, not of focus, but of image size, in various colors. This aberration is far more serious than simple axial chromatic aberration because it results in serious color fringes surrounding the outlines of objects. In color-separation work, it causes the three negatives to be different in size and impossible to bring into register. Even in black-and-white work, lateral color seriously degrades the sharpness of images, especially where the subject matter contains objects of a variety of colors.

Years ago, when most photography was done on films sensitive only to blue, the error was not considered serious; in essence, all photography was being done with light of a very restricted range of wavelengths. However, this explains why some old lenses that produced very sharp images years ago no longer do so; the lens has not deteriorated, but the use of panchromatic and color films brings to light the lateral color error which was in the lens all the time.

Lateral color must be eliminated in the design of the lens; it is independent of lens aperture and cannot be diminished by stopping down. This makes it just as serious in small lenses as in big ones. Luckily, there are several effective ways of correcting for lateral color.

The simplest method of correction is merely to make the lens symmetrical in form; the lateral color of the two elements is opposite in direction and is totally cancelled. This construction is generally used in process apochromats for photomechanical work.



In unsymmetrical systems of separated components, lateral color is corrected by making each component of the lens separately achromatic, rather than by depending on the color error of one element being corrected by an opposite error in the other. This is not difficult to accomplish, and most high-quality modern lenses are made in this manner. This criterion is important, though, for it explains why the addition of supplementary lenses, which are usually uncorrected, may degrade the definition of a lens quite seriously. Whereas stopping down will eliminate the other faults of lens attachments, such as spherical aberration, it will not affect lateral color. For this reason, some very high-grade close-up lenses are made as two-element achromats, as are many of the "tele-extenders" now being offered.

Nevertheless, it must be remembered that all the corrections of a lens are bound together, and all should be carefully balanced in the original design. Obviously, the better the correction of the prime lens, the more the addition of a partly-corrected attachment will affect it. This is not to say that these attachments are useless; it is only to point out that they are never as suitable as a good prime lens for critical work.

Aberrations and Focal Length. In designing a lens, the various dimensions are taken only as ratios; that is, the designer may begin a lens design with a focal length of "10" and a diameter of "2", producing an aperture of 1/5.0. All curvatures, thicknesses, and spacings are given the same way, as simple numbers. The unit is not specified; it may be inches, centimeters, millimeters, or in the case of telescope objectives, feet or meters. The unit is decided on at the stage in design where the aberrations are being evaluated; if the lens is measured in centimeters, then the aberrations will come out in centimeters. If we use inches, then all dimensions and aberrations will be in inches and all will be two and one-half times larger.

It follows from this that all units may be used, or for that matter, any arbitrary unit, such as half-inches or quarter-feet. That is, if a good design exists for a three-inch lens, and a six-inch lens is wanted, it is not necessary to make a new design. All that is necessary is to double all the dimensions of the original lens ~nd we have a new lens of the same aperture ratio and double the focal length. But in this case we also double the size of all the aberrations, and this is the key to the usefulness of this fact. If the three-inch lens had aberrations that were just barely tolerable, then the six-inch lens would have aberrations twice as big, and it would not be satisfactory.






On the other band, if we have a satisfactory lens of three-inch focus and want a lens of one-inch focus, we have only to divide all its dimensions by three to secure the new design. In this case, of course, all the aberrations will also be reduced by a factor of three. In essence, making the lens smaller has actually improved it.

This explains why very good large-aperture lenses can be supplied at moderate cost for Smm movie cameras, whereas for larger cameras the lenses require much better and more expensive construction. The current popularity of zoom lenses on Smm movie cameras is based on this simple fact. These same lenses, if enlarged to the required size for a l6mm camera would be considered quite inferior, and with further enlargement for 35mm cameras would be quite worthless. Larger zoom lenses for 35mm cameras are more complex in construction, more highly corrected, and more expensive.






Lens Types

There are literally hundreds of types of lenses on the market, ranging from the simplest single-element box-camera lenses to very complex high-speed anastigmats; in addition, there are numerous specialty lenses such as telephotos,



wide-angle lenses, zoom lenses, and others. It is not possible in the limited space fo Ir ~inI1tnc thp co~a ~ t~ available here to discuss all these types; many lens structures simply defy classification, and anyway, there are many books that tabulate and illustrate the

internal construction of camera lenses.

Actually, it 'S not really important to know the internal structure of a lens; in most cases this gives little clue to the purpose or performance of the objective. If a lens is an unsymmetrical four-element Tessar or a symmetrical four-element Gauss-type anastigmat, it is not likely that the user wilt find any real difference in performance. The choice of structure is mainly made by the designer for reasons of his own. In most cases, performance depends more on how well the design has been carried out than on what arrangement of elements has been chosen.

In the past, the number and arrangement of elements were used by the designer as starting points, to save a good deal of preliminary design work. He would choose, for example, an existing Tessar design of good performance, and most of his work consisted of attempting to improve its performance by minor changes in the types of glass and shapes of the elements.

Computer lens design has changed all that. In early attempts at computer designing, the computer was used simply to carry out the classical calculations of the various aberrations, just as the designer had done with his pencil and paper. It was soon discovered that this was unnecessary. The use of aberration theory began originally to save the labor of extensive ray-tracing; however, the computer can trace 1,000 rays per surface per second, and at this rate, it appears better to ignore all the classic aberrations and~go directly to ray tracing.

The new programs, therefore, merely choose a group of rays and trace them through the lens formula, to determine bow small an image spot results. After each pass, curvatures, thicknesses, or spacings are changed, and another set of rays is traced. The computer is programmed so that changes are made only as long as an improvement results; when changing a given surface ceases to produce an improvement, the computer automatically goes on to the next surface. This is repeated until no further improvement happens overall; then the computer stops and prints out the design of the lens as it appears at that point and gives an evaluation of the resolution and other performance factors.

If the design is satisfactory, the designer can accept it; if not, he may change one or more of the glass types and try another run. In any case, because of the huge speed of this system, it is no longer necessary to use any existing lens design as a starting point; the computer can start from nothing more than a number of flat plates of glass and end up with the same design, passing the existing design on the way.

As an example, the computer was given the following set of glass plates, in the order crown-flint-crown. The curve on the last surface gives the necessary power to the system, and decides the final focal length; all other surfaces were

( U ¾



flat. What came out of the computer was in no way unusual; it was a typical triplet anastigmat. What was unusual was that the entire design run took just































four minutes; the same lens would have taken weeks or months to design by pencil-and-paper methods.

The example is, of course, trivial; the design which evolved is a well-known one. The reason, of course, is that the problem is a simple one. With only three elements and two glass types involved, the final result would have had to come out the way it did. This type of anastigmat has been studied for years and almost all the useful solutions to the problem are known. Given three elements of two types of glass, however, there are at least four arrangements possible. Two of them are not likely to be useful-crown-crown-flint or flint-flint-crown would tend to a highly unsymmetrical design. The crown-flint-crown combination is the well-known one, used for years. The remaining possibility-flint-crown-flint-opens a question as to why it had never been tried. It appeared that this arrangement had been explored to a limited degree, and it seemed to result in excessive distortion. Thus it did not seem to justify the amount of labor which would go into a thorough study.

In computer design, though, at 1,000 rays per second, one can carry out an extensive study of a lens design in a very short time. Furthermore, new variables can be added, and these may bring up new answers not previously contemplated. One of these is the thickness of the glass elements. In manual designing, thickness was chosen merely to ensure that the desired diameter could be attained with the most extreme curvature likely to be found; in the computer program, thickness was put into the system as an additional variable, and safeguards were provided to prevent an element from coming to a sharp edge at too small a diameter.

With this type of program, a computer run on the combination flint-crown-flint came up with the rather remarkable construction shown here. The thick-




nesses of the elements are quite extreme, especially the center crown element. The result is, however, a wide-angle lens of unusual performance; it has a field of view of 110 and a fixed aperture of f/S. Because of its extreme angle of view, it is not possible to put a diaphragm between the elements; the V-shaped groove in the center element acts to stop the lens down to its normal and fixed f/S. This lens is now being manufactured as the Zeiss Hologon f/S. In a focal length of lSrnm it covers a 35mm double frame with excellent definition, it is free from distortion, and because of a special property of its exit pupil, it gives better than normal corner illumination.

Still, this is a simple case. Years ago, designers tried to improve on the simple triplet by splitting the front and rear crown elements into achromatic doublets (below); it was reasoned that with five elements, or ten surfaces, better correction





could be attained. Sometimes It was, sometimes the more complicated



not perform any better than the simple triplet.

A IS-minute computer run on this set of glasses, with freedom to vary

thicknesses as well, resulted in the rather startling design shown below. An old-time designer would not even have tried such a construction; by former standards the curves are excessively deep and would have been expected to lead to excessive astigmatism.










Nothing of the sort has happened; the correction attained with this construction is very high, and the lens is an excellent performer. At an aperture of f/2.8, it is currently made as the Zeiss Planar and the Schneider Xenotar; the design has been carried to an aperture off/2.0 in the Wray Unilite.

It is hard to classify this design; it certainly bears little resemblance to the triplet from which it was denved, especially as all semblance of symmetry is gone. The lesson to be learned from this is that cross-sectional diagrams of lenses really convey no useful information to the practical photographer; the only way to judge a lens is by its performance in actual picture-taking.

The Telephoto Lens

If a negative and positive lens of equal power are placed in contact with each other, they neutralize one another and have no more power than a piece of flat glass. If these two tenses are separated, the combination develops a focal length, long at first, gradually shortening as the space increases. When the separation is equal to the focal length of the positive lens, the focal length of the combination is the same as that of the positive lens alone. But, more important, as the components are separated, the principal point moves away from the lens in the direction of the subject. Since, however, focal length is defined as the distance from the principal point to the focal plane, we find that the back focus of the combination is much shorter than its equivalent focal length. Thus we can make a lens of long focus but short extension, and such a combination is called a telephoto lens.

Early telephoto lenses were made of a positive combination, similar to a rapid rectilinear lens, and a fairly well corrected negative rear component composed of two or three elements. Many of these were mounted in such a manner that the spacing between the two main components could be varied, and thus the focal length of the combination could be changed to suit the job at hand. This variation of focal length, however, went hand-in-hand with a change in back focus, so the lens had to be refocused for every new adjustment. In addition, its aperture changed with every setting, and complicated tables were needed to determine what f/stop was actually in use at any time.

This construction was not very well corrected, and it was taken as an axiom at the time that a telephoto lens could not produce as sharp an image as a normal objective. Still, it had some usefulness. Furthermore, since the front element was usually a more-or-less common camera lens of the Rapid Rectilinear type, many manufacturers offered rear elements only, known as "telenegative" components, which could be used with whatever camera lens the


























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photographer happened to have. In a way, these tele-negative elements were similar to the "tele-extenders" currently popular with users of 35mm single-lens reflex cameras. However, we know by now that adding any kind of partly-corrected lens system to one that is fully corrected can only upset the corrections of the system as a whole. Thus these devices are useful only for relatively non-critical applications.

It was eventually realized that a telephoto lens had to be designed as a single unit, for a single, fixed magnification if good performance were to be attained. Furthermore, the magnification had to be kept fairly low, simply to

avoid ending up with either a very bulky lens, or one of too small an f/number

-. to he of much use. Only by designing the lens as a unit can the distortion be kept to manageable amounts; the combination of a positive front and negative

rear combination is subject to a good deal of distortion unless special pains are taken to minimize this particular aberration.

With the general popularity of small cameras, the need for telephoto lenses has diminished; for the magnifications usually used, it is easier and better to use a normal camera lens of the appropriate focal length. Even for very long focal lengths, prime lenses are preferred. For one thing, when a lens of 400 mm focal length is used on a 3Smm camera, the field of view is so narrow that a simple two-element achromat will often perform as well as a much more complicated objective. In this way we can make large but lightweight long-focus lenses of moderate aperture and excellent performance.

The small camera has another problem; it is lacking in room for short back-focus lenses of the wide-angle type. Like most optical systems, however, the telephoto lens is reversible; if we put the negative element in front and the positive in the rear, we have what is known as a "retrofocus" lens, which has a short focal length and a long back focus. In this way we can make wide-angle lenses with ample clearance behind them to allow for the mirror and shutter of the single-lens reflex camera. Such lenses are also essential for use with turret-type motion-picture cameras.


Zoom Lenses

Variable focal length telephoto lenses have been known for over half a century, but these earlier lenses could not be considered "zoom" lenses because they did not meet two important criteria. A zoom lens must remain in focus as its focal length is varied, and it must retain the same relative aperture at all focal lengths.

To meet the first criterion, there are, obviously, two possibilities. The first is mechanical compensation-some kind of linkage between the focusing movement and the focal-length movement, such that the distance of the whole lens to the film is changed as the lens is adjusted from one foqal length to another. The difficulty with such a system, which was actually used in some early zoom lenses, is that it becomes hopelessly complicated if we also wish to adjust this linkage to focus on objects at different distances. These early lenses, therefore, were fixed focus; they were designed for a single distance, such as 25 feet, and then other distances were focused upon by the use of supplementary lenses placed in front of the whole system.

The second method is that used in. all modern zoom lenses: it is.. known as optical c6mpensation. In these lenses, there are two groups of moving elements, such that one adjusts the focal length and the other maintains a constant focal distance. Such lenses can be focused by the common method of separating the seCtions of the front element.

This system is only approximate at best. It is actually impossible for such a system to be in focus for more than two settings, and the problem that re583

mains Is simply to minimize the error at intermediate positions. If this can be done so that the focusing error is no greater than the normal depth of focus of a lens of similar focal length and aperture, then we can consider it fully corrected for most purposes.

This focusing error is proportionate to the size of the lens as a whole. Thus large zoom lenses for television cameras are exceedingly difficult to make and extremely expensive. Smaller zoom lenses for 3Smm motion-picture and still cameras are practical, and not too expensive, but their definition seldom equals that of a good prime lens for the same camera. In the case of 8mm cameras, the errors become small enough so that zoom lenses are commonly provided on all but the least expensive of these cameras, and zoom objectives are commonly provided for the Smm projector also.

The second criterion, that a zoom lens retain its relative aperture at all focal-length settings is obviously necessary if the lens is to he used on movie cameras, where the focal length is generally changed during the filming of a scene. This is not, however, a difficult problem; since the lens has been designed for a constant back focus, all that is necessary is to maintain a constant diameter of the exit pupil, and the diaphragm markings will be true at any focal length. This is accomplished by placing the diaphragm in the back part of the lens system, behind the moving sections; thus its size as seen through the back element of the lens does not vary in size with a change of focal length setting. If, then, the front elements are made large enough so that the image of their aperture is never smaller than the diaphragm aperture at its largest settings, the diaphragm will control the aperture of the entire lens at any focal length setting, and its aperture will not change regardless of magnification.


Afocal Converters

When a camera has a permanently mounted lens, it is sometimes desirable to have an attachment made that will shorten or lengthen the focus of the main lens without changing its back focus.

If a positive and a negative lens are separated by a distance equal to the difference between their focal lengths, rays that enter parallel (as from an object at infinity) emerge parallel, or apparently still coming from an infinite distance. Thus these combinations can produce an enlarged or reduced image of an object without affecting the focus of the lens over which they are used. Essentially, the combination of a negative eyepiece and positive objective is a Newtonian telescope, and it is well known that reversing such an instrument reduces the size of the image instead of enlarging it. Thus it is possible to make such a device act either as a telephoto or a wide angle lens, and in a few cases it can even be made reversible so it will serve either purpose.

There is a temptation to use ordinary binoculars in this manner, and in fact, attachments are sold to fit a pair of binoculars to a camera lens. While binoculars are fairly well corrected for their intended purpose, the achromatism is visual, not photographic, and definition will suffer.

However, if an afocal converter is made specifically for a given camera lens, with full corrections, it can work very well indeed. Some telephoto attachments are sold for twin-lens reflexes, which perform quite well; also a wide-angle converter fQr the Kodak Cine-Ektar lens was sold for some time and used by professionals with excellent results.

One point in this construction is that the ratio of diameters of the front and rear elements must be the same as the magnification (or reduction) of the lens attachment. If this is the case, then the exit pupil is as large as the entrance pupil of the camera lens, and there is no change in f/number settings.



· 1




t - I

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r 1

s a I


ra I




r 1-








The camera diaphragm numbers then retain their value and can be used for exposure control in the normal way. However, the focusing scale on the camera lens can no longer be used when a converter is attached; focusing movements are the same as if the prime lens had the new focal length.

Obviously, to make such an adapter reversible, both front and~rear elements must be very large, as either one will have to be used as front element. This makes the whole thing quite bulky and difficult to mount and corrections for focusing distances closer than infinity cannot be the same in both directions. For these reasons, few such attachments are marketed, though there is one available for motion picture projectors. its magnification is quite low, however; used with a two-inch projection lens, it produces focal lengths of either 1½ or 2½ inches, depending on which way it is turned.

The main reas~ the afocal converter is not more popular is simply that it is large and bulky, but more important, if it is not to damage the corrections of the prime lens, it must itself be fully corrected, which requires four elements at least. Such a lens will not cost much less than a prime lens of the same size.

Simple Lens Attachments; Diopter Measure

Small changes in focal length can be accomplished by adding a thin lens to an existjng combination. If the added element is thin enough, it has little effect on the corrections of the system, and this provides a useful means to extend the usefulness of certain lens systems.

For many years a simple lens of about three-foot focal length was sold as a "portrait attachment"; it was intended for use on box cameras to focus them -.for the closer distance required for head-and-shoulder pictures. Since a box camera Jens is substantially uncorrected to begin with, and since a lens having a focal length of three feet and a diameter of no more than an inch will be very thin and almost fiat, such a setup worked quite satisfactorily. However, there is often a requirement to make a similar adjustment in focal length of better-corrected systems, and the usual expedient is to use simple spectacle lenses.

Opticians who work mainly with thin lenses use a special system of measurement. When two thin lenses are placed in contact, the combined focal length (f) is given by the following formula:

1 1 1



This is not an easy formula to evaluate, but if lenses are marked with their "powers," where "power" is defined as



then the formula reduces to nothing more than

D= D1 + D2

and one can combine lens powers by simple addition or subtraction. The question of units is simple: if the focal length of the lens is given in meters, then the power D is in diopters. Thus a lens having a focal length of one meter has a power of one diopter, if its focal length is two meters, the power is 0.5 diopter, if the focal length is ½ meter, then the power is 2 diopters, ¼meter is 4 diopters, and so on.*

~Pecause the powers of lenses are given in diopters, some writers in the amateur press have been referung to them as "diopter lenses''. This terminology is careless and should be stamped out.






If one places a thin positive lens over the camera lens, and the latter is focused on infinity, then the combination is now focused at a distance equal to the focal length of the thin tens. Knowing the focal length of the attachment (which can be deduced from its power as explained above), we can do closeup copying and portraits by the use of such simple positive attachments.

It must be emphasized that the term "thin lens" means, in theory, a lens which is infinitely thin; any thickness causes the appearance of aberrations. Where the lens is substantially equivalent to a true thin lens, the added aberrations will be small and are easily compensated by simply stopping down the lens; however, the use of strong positive lenses, such as +3, +4 or +5 (or combinations of lower-powered lenses of equivalent strength) will definitely degrade the definition of the main lens except at extremely small apertures.

A few high-quality supplementary lenses of +1, +2 and +3 diopter strength are offered for high grade work; these are doublets, corrected mainly for chromatic aberration, but probably having some spherical and coma correction as well. These are definitely superior to simple spectacle l~ses for their intended purposes.


The formulas for combined focal length, field size, and wide-angle work apply only when the separation between the close-up lens and the camera lens is very small compared with the focal length of the camera lens. For this reason, they do not apply precisely to 3Smm cameras and they do not apply at all to movie cameras.

The following quantities, except "5" must all be expressed in meters. The answer will be in meters.

P5 = focal length of closeup lens = l/D

D = power in diopters (1+, 2+, 3+) of closeup lens

U = distance from closeup lens to subject

5 = focusing scale setting in feet

Fe = combined focal length of camera lens and closeup lens

F = focal length of camera lens

W = field width

w = negative width


Subjeet Distance

Distance for Infinity Setting

u - F_ - I for two closeup lenses = 1

D D1+D2



Distance for focusing scale set at "5" feet



~+-t28\; *

*8.28/si, "power of focusing scale." This is equivalent to the power of a closeup lens ~hkh would cause the same change of focus. For example, chang,ng the focusing scale setting from infinity to 8 feet is equivalent to adding slightly more than one diopter to the power of the closeup lens ~sed.







'Eq r

'U I

p p

It, I


'U I

Flu I Fc=~ I U

I + ED

Field Size


For Infinity Setting:

To find S and D for given u:

_ -D--3-2-8


Take highest whole number of D (1, 2, 3) that is not larger than i/U. Solve for S.

Combined Focal Length

wE S F

For Front-Element Focunng~ Lens at 5 feet:


E~D + 3.2~8 f




For Unit Focusing~ Lens at 5 feet:
































Field height is proportional to negative height.


For Wide-Angle Use with view-type cameras and lens-to-film distances shorter than when the lens is set on infinity.

Width of Field with close-up lens = Width of field without X (I + ED) close-up lens

















t Open the hack of your camera and look at the lens while adjustina the focus. lithe rear lens element moves. your lens is unit focusing; if it doesn't move, your lens is front-element focusmg.





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Tel: 905-625-9261