The way a zoom lens works

The secret of a Variogon, i.e. of a vario- or zoom lens, is that it cleverly takes advantage of a number of basic optical laws, and by appropriately correcting the aberrations which arise in connection with them, makes it possible to achieve good imaging quality. To this end, there are three essential preconditions: adequate computer programs, high-performance computers, and above all, the optical-physical know how. 

The zoom lenses of today are very complex, both in their construction and their mode of operation. For that reason, to better understand how the traditional Variogon lens, its main principle of operation is described below. All zoom lenses, however, have the property of projecting the image to be depicted exactly onto a fixed local imaging plane, be it the surface of the film or the plane of an image sensor, while the focal length is being changed.

The principle of design of a Variogon of the traditional type of construction is easy to understand. The essential factor is that the image is not projected directly onto the film, but arrives there only after several intermediate virtual images have been created. 

The first lens group creates an image of the subject like any other lens. Only this part of the optical system is adjusted for the distance from the subject, not the entire lens, as is often customary. From this first image, a second group of lens elements creates a second image; it is only the third group of lens elements that creates the final image.

Fig. 1:  Schematic representation of the basic structure of a Variogon lens

Because the second group is shifted, the image ratio from the first to the second intermediate image is changed, and with it the size, too, of the subject as it finally appears on the sensitive medium (Fig. 1). But at the same time, this means that the focal length of the entire system has been changed. With the axial shift, however, the position of the second and third realized image has changed. So that the user does not have to re-focus after every change in the focal length, another lens group is brought into play. Its function is to restore the sharpness simultaneously with the change in the focal length.  

The variation in focal length can be realized basically in two ways. In one case, the two lens groups are controlled mechanically in such a way that both carry out specific, but different, movements ( mechanical compensation ), in the other case, both lens groups are moved together; then, by a clever choice of the optical values of both components, one can keep the position of the image constant; to be sure, in this second case, in theory not entirely strictly, but in practice with sufficient precision ( optical compensation ).  

Fig. 2 : 2: Mechanical compensation for the change in the focal distance. above: The motion of the second lens changes the focal length, that of the first keeps the sharpness constant. below: The second lens element consists of two parts; by means of their relative movement, the sharpness is kept constant.

Fig. 2 shows schematically the principle of mechanical compensation which is used in all traditional Variogon lenses. In it, the lens groups - here represented by one or two lenses - are indicated by Roman numerals l, II and III, the images by Arabic numbers 1, 2 and 3.. The curves which are drawn in the diagram give the position of the lenses with different focal lengths, above with the shortest ones, below with the longest ones. 

In the upper part of Fig. 2, the movement of Lens II changes the focal length, that of Lens I keeps the positions of images 2 and 3 constant. In the lower portion of Fig. 2, Lens Group II is split (IIa and IIb); here the change in the distance of the two lenses serves to retain the image. 

Fig. 3:   Practical demonstration using the Variogon 2.8/10-40 mm. In the practical demonstration in Fig. 2, one part of the lens group has negative refractive power and the intermediate images are virtual images.

As a practical example of the principle illustrated in Fig. 2, the Variogon 1:2.8/10-40 is shown in cross-section. The individual elements are indicated with Roman numerals. 

In some cases, the third group of lens elements is divided in such a way (lIla and IIIb in Fig. 3) that the rays between them are parallel. Then one can imagine the entire lens in this position as separated into a supplementary lens without focal length and the main lens. Lenses without focal length function to a certain extent like Galileo's telescope , which, depending on which end one looks into, makes the image larger or smaller. When the supplementary lens enlarges, the focal length of the combination is lengthened, and vice versa. The supplementary part of the Variogon is such that one can change its enlarging property constantly, and hence the focal length of the lens can be adjusted as desired.

Variogon 2,8/10-40 mm,

Fig. 4: Variogon 2,8/10-40 mm

Variogon zoom lens