Telephoto Zoom Lenses with Donders-type Afocal System
Nikon
70(80)-200mm f/2.8 and 200-400mm f/4.

 

This article follows on the page Focal Length and Magnification.
It contains nine Flash animations, requiring a 1200-pixel-wide display.

 

Fig. 01: Zoom-Nikkor AF-S 80-200 mm f/2.8D IF-ED.

 

-o---0---o-

 

Summary:

I  –   Presentation.
II  –   Brief history.
III  –   Working principle of the zoom with Donders-type afocal system.
IV  –   The Zoom-Nikkor 80-200mm f/2.8 ED Ais.
V  –   The Zoom-Nikkor AF 80-200mm f/2.8D ED.
VI  –   The Zoom-Nikkor AF-S 80-200mm f/2.8D IF-ED and Zoom-Nikkor AF-S VR 70-200mm f/2.8G IF-ED.
VII  –   The Zoom-Nikkor AF-S VR 70-200mm f/2.8G II.
VIII  –   A few words about the maximum magnification of this type of telephoto zooms.
IX  –   The Zoom-Nikkor 200-400mm f/4 ED Ais.
X  –   The Zoom-Nikkor AF-S VR 200-400mm f/4G IF-ED.

Annex I  –   Brief presentation of the Zoom-Nikkor 50-300mm f/4.5 ED Ais.

 

o---0---o

 

I  –  Presentation.

Among high-grade long-focal-length lenses used by wildlife photographers, some are telephoto zooms like the Nikkor AF-S VR 70-200mm f/2.8G or the Nikkor AFS VR 200-400mm f/4G. On both zooms, the zooming works according to the same principle: a Donders-type* afocal system mounted in front of an ordinary photographic lens. The direct ancestors of these lenses appeared for the first time on the Nikon’s catalog in the early 80’. But before them, several telephoto zooms, like the Nikkor-ED 180-600mm f/8, and even the huge Nikkor-ED 360-1200mm f/11 paved the way.

* Franciscus Cornelis Donders (1818-1889): Dutch medical scientist (ophthalmologist). He invented a variable-magnification three-component telescope.

Fig. 02: Field angle variation of the Zoom-Nikkor AF-S VR 70-200mm f/2.8G IF-ED.
Main subject located 9 m (9.8 yd.) away from a 24x36 mm sensor camera
(height at the shoulders ≈ 0.8 m ≈ 31.5 inches).

On this type of zoom, the zooming does not cause any change of the lens-barrel length. That’s an important characteristic: these zooms are quite big, and they remain big whatever the focal length setting. On the earliest models, focusing did lead to a slight lengthening of the optical system, because this function was ensured by the displacement of the external front elements of the lens. Today, as focusing is performed by internal components, no change occurs on the overall length of the lens. Therefore, these bulky, sturdy, made-in-one-piece zoom lenses are of high rigidity (key to longevity) and provide excellent sealing against external agents.

Like the first Pierre Angenieux’s 20-80mm zoom patented in 1955, the Nikon's 70(80)-200mm f/2.8 and 200-400mm f/4 belong to the so-called “mechanically-compensated” zooms category. Yet, while Pierre Angenieux’s lens does not include a true afocal unit, the mentioned Nikon lenses do use such a system which perfectly suits low range zooms (ratio of maximum focal length to minimum focal length R < 4).

Fig. 03: Optical system of the first Pierre Angenieux’s mechanically compensated zoom
(20-80 mm f/2.5, patented in 1955).

As we’ll see, on these Nikon’s lenses, the working principle of the zooming didn't change over time, while their focusing system went through several important evolutions.

 

o---0---o

 

II  –  Brief history.

Regarding the 70(80)-200mm f/2.8.

1982. Very first Zoom-Nikkor 80-200mm f/2.8 ED marketed. Large-sized and heavy lens: 231 mm (9 inches) long, 99 mm (3.9 inches) diameter, and 1.9 kg (4.2 lb.). A push-pull rotary ring controls zooming and focusing. External front elements perform the focusing. This lens disappeared from Nikon's catalog only three years after its release. This is the only manual-focus 80-200 mm f/2.8 ever marketed by Nikon.

1987. First non-motorized autofocus model: the Zoom-Nikkor AF 80-200mm f/2.8 ED (elements ensuring the focusing driven by a motor placed inside the camera). Focusing is still carried out by the external front elements driven by a push-pull rotary ring.
 
1992. First mechanical update of the previous model (optical system remains the same).

1997. Second mechanical update of the 1987’ model (optical system remains identical). The push-pull ring is given up for good on this type of telephoto zoom. Since then, two different rotary rings control zooming and focusing.

1998. Release of the Zoom-Nikkor AF-S 80-200mm f/2.8 IF-ED. This model marks two major evolutions:

2003. Release of the Zoom-Nikkor AF-S VR 70-200mm f/2.8G IF-ED. It is an evolution of the previous model (optical systems closely related): the focal-length range is extended to 70-200 mm, and an optical image stabilization system (VR) is integrated to the lens. The focusing is still performed by the shift of only the internal part of the front group.

2009. The release of the Zoom-Nikkor AF-S VR 70-200mm f/2.8G II marks a new deep evolution: for the very first time, the focusing is no longer carried out by any front-element shift. It is the compensator (third group) that insures the focusing.

Regarding the 200-400mm f/4.

1983. First Zoom-Nikkor 200-400mm f/4 ED marketed. This lens descends from a series of several long-focal-length telephoto zooms (up to 360­-1200mm) that paved the way. Although slightly shorter than the current model, it is also larger in diameter and weight: 144 mm (5.7 inches) and almost 3.7 kg (over 8 lb.). Very expensive, it remained an unattainable dream for most wildlife photographers who, however, used to consider it as the lens of every situation. It disappeared from the Nikon's catalog in 1988.
 
2003. Nikon makes a stir releasing a modern version of this telephoto zoom lens now including autofocus and stabilization: the Zoom-Nikkor AF-S VR 200-400mm f/4G IF-ED is launched.

2010. Update of the previous model: upgraded stabilization system, and improved optical coating (Nano Crystal).

 

o---0---o

 

III  –  Working principle of the zoom with Donders-type afocal system.

Afocal attachments are described on my page Focal Length and Magnification. It shows how an afocal converter can change the focal length of a lens, and how a simple reversal of such an attachment, in one way or another, offers two different magnifications (Figure 4).

Fig. 04: Afocal system reversible by rotation.
Mouse out: positive lens on the front (telephoto).
Mouse over: negative lens in front (wide-angle).

Well, a Donders-type afocal system works according to the same principle...

But how to change from a two-magnification reversible afocal system, to another one allowing continuous focal-length variation?

Simply by "splitting" one of the afocal-system components (positive or negative) into two sub-components...

Indeed, a two-lens assembly with a given power can replace any single lens of same power. Figure 5 (bellow) shows how a couple of cemented lenses, one positive (#1) plus one strongly negative (#3), can replace the single negative element #2 of our experimental afocal system: the focal length of the single lens #2 and the focal length of the cemented assembly #1 + #3 are equal.

Fig. 05: Characteristics of lenses used in the experimental systems.

Note

Figure 6 compares the previous two-element afocal system (on top) and the new three-element afocal system (bottom). Both are equivalent. The lenses #1, #1a and #1b are identical. The lens #3 is more divergent than the lens #2.

Fig. 06: Two equivalent afocal systems.

So, our new afocal system now includes three elements instead of two, yet its features remain unchanged, and it can still be reversed by rotation, in one way or another, just as could be done with the two-lens system. Of course, the elements #1a and #3 do not have to be actually cemented together. Thus, the new system acquires a major interest: the reversal of the afocal system is now possible without rotating it, simply sliding the negative lens #3 from the front toward the rear and vice versa (Figure 7). Thus, going from a negative-positive afocal attachment (wide-angle) to a positive-negative one (telephoto) is now much easier.

Fig. 07: Three-element afocal system including a floating intermediate element.

What happens when the negative lens #3 stands in an intermediate position?

Between the two extreme positions of the negative lens #3, the focal length of the whole system varies continuously. But…

On the page Focal Length and Magnification (§ 2.1) we saw that to make a two-lens afocal system, the second focal point of the first lens must be coincident with the first focal point of the second one: the optical gap (Delta) must be zero. Now, in the new three-lens afocal system, the first component is a compound one, and it includes a movable element. Obviously, the position of the second focal point of this compound unit depends on the position of its moving part. Figure 8 (bellow) and the attached animation show that, when the lens #3 stands in any intermediate position, the second focal point of the compound unit (F'1a+3) is no longer coincident with the first focal point of the second component (F1). Consequently, the afocal feature of our system is only effective when the lens #3 occupies one of the two extreme positions. These are the only cases where the light rays (incoming from an infinitely distant object) reaching the master lens are actually parallel. In all other cases, the light beams reaching the master lens tend to be slightly divergent, and consequently the master lens focuses further aft, as if the object had come closer. Conclusion: with such a system, the back focal length varies with the focal length of the whole system.

So, the whole system (afocal attachment-plus-master lens) described above is not a zoom; it would be a so-called “varifocal lens” that requires a focusing adjustment after each focal-length change.

Fig. 08: Optical gap (Delta), focal length, and image shift
with regard to the displacement of the negative lens #3.

Such an afocal system (three components, variable angular magnification) constitutes a so-called “Donders telescope”. This example shows a perfectly symmetrical Donders telescope (first and third element identical, symmetrical intermediate element). When the negative lens is half way between its extreme positions, the angular magnification of the afocal system is G = 1, then the focal length of the master lens is unchanged. In practice, the systems included in the telephoto zooms are non-symmetrical systems (see further).

Note

To make a true zoom it is imperative to solve this image-shift problem. And to do so, the afocal feature of the system must be maintained regardless of the negative-lens position (#3): the optical gap must remain zero.

All that is necessary to maintain a zero optical gap is to shift the rear positive element #1b in order to make its first focal point move accordingly with the second focal point of the compound unit. Coordinating the movement of the rear lens #1b with the shift of the negative lens #3 in order to respect the previous condition cancels the image shift induced by the change of focal length: the rear-lens movement “compensates” the image shift (Figure 9).

Fig. 09: Axial stabilization of the image by the controlled shift of the rear positive element #1b.

In cases like the example above, the lens #1a would be called “front element”, the intermediate negative lens #3 would be called “variator”, while the rear lens #1b would be the “compensator”. The variator and the compensator move in different ways. They are mechanically driven by means of a cam, hence the expression "mechanical compensation”.

Figure 9 highlights two important points:

Finally, with the help of only three lenses and a 50mm lens, we’ve created a 25-100mm zoom lens. Obviously, the optical performance of such a simplistic designed lens would be marred by numerous aberrations. That’s the reason why the above computations are made at small aperture, and no oblique light beam is shown. For best performance, each component (front, variator, compensator and master lens) must be well corrected from aberrations, and also help to correct other components aberrations. To do so, all zoom components are compound ones, made of several lenses, out of different types of glasses. While it significantly complicates the optical system diagram, it offers much higher performance (Figure 10).


 
Fig. 10: Comparison between the diagram of our experimental zoom
and the one of a real zoom lens (Zoom-Nikkor AF 80-200mm f/2.8D ED).

On this type of telephoto zoom lens, focusing can be achieved in different ways by moving:

Since any movement of the object induces an image shift proportional to the focal length of the whole system, the first way mentioned above, although possible in absolute terms, is not interesting in practice: such a system would require to adjust the focusing after each change of the focal length. To my knowledge, this focusing method is only used on projection-device lenses (and some small autofocus point-and-shoot-camera lenses).
 
Through the clearance between the afocal system and the master lens, the light rays are parallel. Consequently, moving away from the sensor only the master lens allows focusing without appreciable effects on the system performance: that's the second focusing method mentioned above. But again, focusing adjustment is necessary after each change of the focal length (because, for a given object distance, the image location depends on the focal length of the whole system). Such a system used to be commonly offered on some motion-camera zooms with a "macro" position setting: for a given focal length (usually the shortest, because it is the one that offers the largest clearance between the compensator and the master lens), the master-lens forward shift allowed very close focusing.
 
Year after year, on the Nikon's 80-200mm f/2.8 and 70-200mm f/2.8 telephoto zoom lenses, the last three methods listed above have been used in the order they appear here. Regarding the 200-400mm f/4 we’ll see that things are a little different.

Now let's see the working of these lenses...

 

o---0---o

 

IV  –  The Zoom-Nikkor 80-200 mm f/2.8 ED Ais.

This is a push-pull-ring zoom lens: one single ring is used to zoom (by translation) and focus (by rotation). The solutions adopted for the design of this lens are simple. In return for some concessions (bulk), these solutions allow excellent performance across the whole focal-length range.

By way of example, here are the calculated focal lengths of the four units of this telephoto zoom lens:

And the focal lengths of the afocal-system combinations in both extreme positions of the variator:

Contrary to our experimental system, on this telephoto zoom the front-group focal length is different from the one of the compensator (dissymmetrical system). Therefore, the full displacement of the variator is not equivalent to a reversal of the afocal system, and the angular magnification of the afocal system set to ”telephoto” is not equal to the reciprocal of the angular magnification when it is set to "wide-angle".

We can determine the focal length of the zoom on both variator extreme positions as follows...

When the variator is on the front:

When the variator is on the rear:

The ratio of the extreme angular magnifications is the zoom ratio (R):

The front group alone ensures the focusing: a 17.85 mm forward shift allows focusing from infinity to 2.5 m (8.2 ft.). This focusing system offers a major advantage: only the afocal system is involved in the focusing process (the master lens remains fixed). Therefore, once carried out, the focusing does not change with the focal length. That's why this focusing system has been used almost exclusively on this type of zoom for years.

When the front group moves forward to focus:

Fig. 11: Zoom-Nikkor 80-200 mm f/2.8 ED Ais set to its minimum focal length.
Effect of the focus distance on the effective focal length.
Mouse out: infinity focus.

Mouse over: minimum focus (2.5 m).

This increase in the focal length is due to the fact that, while the front group shifts forward to focus on a close object, the space between itself and the variator lengthens. Now, this is precisely what occurs when the variator moves backward (toward the right) in order to increase the focal length. To a certain extent, the same cause produces the same effect.

For a given forward movement of the front group, the increase in the focal length is clearly stronger when the variator is on the front (wide-angle) because then the relative lengthening of the space is much more important than when the variator is far away on the rear (telephoto). In some cases (see further), depending on the respective powers of the different components, it may happen that the long-focal lengths decrease; but the short-focal lengths will always increase when the object gets closer.

Fig. 12: Zoom-Nikkor 80-200 mm f/2.8 ED Ais.
Zooming system.

On this type of telephoto zoom, the translational motion imparted to the push-pull ring is directly transmitted to the variator: the displacement of the ring is exactly equal to that of the concerned lens group. On the other hand, a cam provides coupling with the compensator.

On this particular zoom, the front-group focal length is long (f’f > 190 mm) and its aperture is relatively small (f/2.7). This explains the excellent performance of this zoom lens at long focal length settings. In return, the lens is cumbersome because:

 

o---0---o

 

V  –  The Zoom-Nikkor AF 80-200 mm f/2.8D ED.
 
First evolution of the optical system: the compactness.
 
Three versions of this famous telephoto zoom lens followed one another sharing the same optical system. The first two have a single push-pull rotary ring to control the zooming and the focusing, while the latest includes two rings: one for the zooming, the other one for the focusing. The optical system of these lenses is very close to that of their manual focus predecessor and, again, the front group alone ensures the focusing.

However, the specification has increased:

Fig. 13: Zoom-Nikkor AF 80-200 mm f/2.8D ED set to its minimum focal length.
Effect of the focus distance on the effective focal length.
Mouse out: infinity focus.

Mouse over: minimum focus (1.5 m).

These requirements impose a significant reduction in the front-group focal length. The latter is then reduced to f’f ≈ 123.5 mm (against 191.44 mm on the previous model). Thus, a front-group shift of only 13.22 mm, allows focusing from infinity to 1.5 m (4.9 ft.) instead of 2.5 m (8.2 ft.) on the previous model. The stroke of the variator is also significantly reduced: less than 40 mm, i.e. a third of the focal length range. Finally, the optical length (front lens-to-image plane) of this zoom is only 230 mm (instead of 260 mm on the previous model), when set to minimum focus distance. The focal length of the master lens is virtually unchanged: f’m ≈ 113.00 mm.

The angular magnification of the afocal system of this telephoto zoom ranges from Gmin ≈ 0.72 to Gmax ≈ 1.73 for an overall focal length ranging from 80.9 mm to 196 mm (when set to infinity focus).

Yet, reducing the front-group focal length implies a proportional increase in its aperture. It is now over f/1.6 (instead of f/2.7 on the previous model); this complicates the control of aberrations on long-focal-length settings (afocal system including two more elements all in all). We’ll see that a significant reduction in the front-group focal length is not without consequences on the maximum magnification of zooms (see § VIII)...

Fig. 13bis: Zoom-Nikkor AF 80-200 mm f/2.8D ED
Zooming system.

Note that the variation of the angle of view with respect to the variator displacement is almost perfectly linear.

An animation showing the working of the one-ring model (1992, same optical system) can be seen at the bottom of the page Appendix (the location and size of the entrance and exit pupils are also shows). Unlike the very first model (Ais), the translational motion imparted to the push-pull ring of this telephoto zoom (27,6 mm) is different from that of the variator (39,8 mm): the latter is then led by a cam as well as the compensator.

 

o---0---o

 

VI  –  The Zoom-Nikkor AF-S 80-200mm f/2.8D IF-ED and AF-S VR 70-200mm f/2.8G IF-ED.

Second evolution of the optical system (excluding the stabilization of the “VR” model): focusing by moving only the internal part of the front group.

The Zoom-Nikkor AF-S 80-200mm f/2.8D IF-ED (Figure 1and 13ter, below), and its direct stabilized descendant, the Zoom-Nikkor AF-S VR 70-200mm f/2.8G IF-ED, are both two-ring telephoto zooms whose optical systems substantially differ only by the stabilization group of the last model (incorporated into the master lens). The afocal systems of both lenses are very close.

Fig. 13ter: AF-S VR 70-200 mm f/2.8G IF-ED and AF-S 80-200mm f/2.8D IF-ED compared.

One way to increase the performance of any autofocus system is to reduce the mass of the moving parts. To meet this demand, Nikon developed a new afocal system whose front group is composed of two convergent sub-units, the first being fixed and the other one movable (Figure 14).

Fig. 14: Zoom-Nikkor AF-S VR 70-200 mm f/2.8G IF-ED set to its minimum focal length.
Effect of the focus distance on the effective focal length.
Mouse out: infinity focus.

Mouse over: minimum focus (1.5 m).

Moving forward the second sub-unit of the front group ensures the focusing, hence the expression "internal front focusing”.
 
By bringing the two front sub-units nearer, their global focal length decreases. In the process, the second focal point of the whole front group shifts forward as if the front group physically moved forward as a whole. Thus, a forward shift as small as 9.72 mm of the second sub-unit produces an 8.04 mm shift of the second focal point of the whole group in the same direction, reducing the focus distance from infinity to 1.5 m (4.9 ft.). In return, the front group is now longer, just as the telephoto zoom (optical length ≈ 258 mm).

To keep relatively small dimensions of the whole optical system, the focal length of the front group has been reduced again: it is now only f’f ≈ 99.12 mm on infinity focus (f’f ≈ 96.51 mm on minimum focus).

Advantages:

Note

Drawbacks:

As seen on the two previous telephoto zooms, the forward shift of the rear part of the front group (which is in a way equivalent to a shift of the entire front group) induces an increase in the focal length throughout the zooming range. Even though the provided magnification on short focus distances incites most users to think different.

Fig. 15: Zoom-Nikkor AF-S VR 70-200 mm f/2.8G IF-ED.
Zooming system.

Note the strong asymmetry of the oblique beam with regard to its chief ray (dotted line crossing the optical axis at the center of the stop) and, consequently, the strong difference between both axial and oblique apex-angles of the cones of illumination (vignetting).

 

o---0---o

 

VII  –  The Zoom-Nikkor AF-S VR 70-200 mm f/2.8G II.

Third evolution of the optical system: the internal focusing by the compensator shift.

The patent 2009/0086321A1 (Keiko Mizuguchi) describes the optical system of this lens but offers no examples corresponding to the model actually produced. Since this study is based on the data taken from this patent, the following calculated results may not accurately match the characteristics of the real lens, but the working of the system and the way the quantities vary are fully representative.
 
Reminder

 
The focusing system adopted on this lens uses that power of the compensator to control the position of the image plane. To achieve this fourth-generation telephoto zoom, the role of the compensator has just been extended. It is therefore a return to a four-group system with characteristics that remain stable regardless of the focus distance (in the previous case the front-group characteristics change with the focus distance). Here, the front-group focal length is fixed (f’f ≈ 94.57 mm) as well as its aperture (f/1.4).
 
Working principle: we know that when the object gets closer, the image shifts backward beyond the second focal point of the lens; moving the compensator backward allows bringing back the image forward, as it is done during a zooming.
 
This focusing system offers at least three advantages:

Fig. 16: Nikkor AF-S VR 70-200 mm f/2.8G II zoom-type. Zooming system.
Mouse out: minimum focal length (f' ≈ 71.4 mm).
Mouse over: maximum focal length (f' ≈ 196.0 mm).

But it also offers two drawbacks…

The first one has no consequences for the photographer but it explains why this system has not been used before: to ensure the focusing on a given object distance, the compensator shifting depends on the focal length. Likewise, during a zooming, the compensator shift now depends on the focus distance. Thus, mechanically, this system is more complicated than the previous ones. For example, when the lens is set to the shortest focal length, a 2.41 mm compensator shift moves the focus plane from infinity to 1.4 m (4.6 ft.). The same focus-distance range requires a 14.55 mm shift when the lens is set to the longest focal length.

The second drawback has not gone unnoticed: the compensator shift induces a substantial reduction in the focal length when the telephoto zoom is set to short focus distances. Why?

Because moving the compensator backward to focus on close objects, increases the space between itself and the variator. Now, we know that any increase in the distance between these two units induces a reduction in the focal length of the entire system: this is precisely what occurs when the variator moves forward in order to decrease the focal length. Again, to a certain extent, the same cause produces the same effect. This is also the reason why the focal-length variation on Figure 8 (no-compensation system) is different from the one on Figure 9 (compensated system).

Fig. 17: Nikkor AF-S VR 70-200 mm f/2.8G II zoom-type set to its minimum focal length.
Effect of the focus distance on the effective focal length.
Mouse out: infinity focus.

Mouse over: minimum focus (1.4 m).

 

o---0---o

 

VIII  –  A few words about the maximum magnification of this type of telephoto zooms.

The maximum magnification is reached at the longest focal length and minimum focus distance.
 
The maximum magnification of this type of lens depends on many factors: the effective focal length of the entire system (of course), but also the focal length of the front group as well as the characteristics of the other groups and how they interact on each other. Therefore, two zoom lenses of different designs set to the same effective focal length and same focus distance will provide different magnifications if the second-focal-point shift they induce is different. Remember that the displacement of the second focal point determines the magnification on the lens (see Focal Length and Magnification).

Figure 18 illustrates the foregoing… The Zoom-NIkkor 80-200mm f/2.8 ED Ais (top) and Zoom-Nikkor AF-S VR 70-200 mm f/2.8G IF-ED (bottom) are both focused on the same distance: 2.5 m (8.2 ft.). On this focus distance, the maximum focal length of the AF-model is f’ ≈ 199.5 mm and the maximum focal length of the Ais-model is f’ ≈ 202.5 mm. So, I slightly zoomed out the latter to get f’ ≈ 199.5 mm on both lenses.

One can see that, although similar configurations, the position of the cardinal points of both zooms is different. Consequently, the magnification of the Ais-model (with longer front-group focal length) is 6.6% greater than the one of the AF-model *. This difference in the magnifications would have been even more important on closer focus distances (but the Ais-model can’t focus closer than 2.5 m).

* The front-group focal length is f’f ≈ 191.44 mm on the Ais-model, and only f’f ≈ 97.67 mm on the AF-model (on this particular focus distance).

Fig. 18: Magnification comparison between two different optical systems;
same focal lengths, same focus distances (2.5 m – 8.2 ft.)

Figure 19 highlights the influence of the front-group focal length (ensuring the focusing) on the magnification of the four Nikon telephoto zooms set to minimum focus. One can see that when the zooms are set to their shortest focal length, their magnification is in accordance with the typical magnification of a thin-single-lens system. By zooming-in (toward the long focal lengths), the zooms with shorter focal-length front group are those whose magnification deviates the most from their typical magnification curve. With a front-group focal length f’f ≈ 191 mm, the magnification of the 80-200mm Ais is almost in line with the typical curve.

The AF-S 70-200mm VR II (compensator-shift focusing) shows a very different magnification curve (red colored on the graph). Here, the second-focal-point shift of the zoom is proportionally higher in the early range of the focal length. Thus, the magnification is higher than the typical values on short focal lengths, and then becomes lower than the typical values when the focal length increases.

Fig. 19: Minimum-focus-magnification comparison between four Nikon zooms
with regard to their effective focal length.

As mentioned earlier, the focal length of the front group is not the only factor influencing the magnification curve of this type of zoom. The Tamron SP AF 70-200mm f/2.8 Di LD [IF] Macro is an internal-front-focusing zoom (like the Nikon 70-200mm VR I). With a front group whose focal length varies from f’f ≈ 106.23 to f’f ≈ 108.37 mm depending on the focus distance (rather close to the Nikon’s), this lens shows a very different magnification curve (Figure 20). When the focus distance is set to 1.5 m (4.9 ft.) the magnification is still almost in line with the typical curve, then the curve arches at intermediate focal lengths and bends a lot when the focus distance is set to 0.95 m (3.1 ft.).

Fig. 20: Tamron SP AF 70-200 mm f/2.8 Di LD [IF] Macro.
Focal length and magnification.

Note how the focal length range decreases with the focus distance:

Fig. 21: Two telephoto zooms with Donders-type afocal systems,
including very different focusing systems:
- shifting front group on the Zoom-Nikkor AF 80-200 mm f/2.8D ED (background),
- shifting compensator on the Zoom-Nikkor AF-S VR 70-200 mm f/2.8G II (on Kirk Lens-Plate).

 

o---0---o

 

IX  –  The Zoom-Nikkor 200-400mm f/4 ED Ais.

Like the Zoom-Nikkor 80-200mm f/2.8 ED Ais released the year before, the very first Zoom-Nikkor 200-400mm f/4 (released in 1983) is a push-pull-rotary ring zoom. Besides, Mr. Yoshinari Hamanishi designed both lenses. Again, the solutions adopted for the design of this lens are simple, and the manual shift of the entire front group ensures the focusing.

Nikon does not reveal the location of the lens aperture-stop. I placed it in front of the master lens because this is the most natural aperture-stop location on this type of zoom. But it remains a personal hypothesis. However, other locations inside the master lens would be possible; and it would not affect the following.

Here are the calculated focal lengths of the four units of this telephoto zoom lens:

Extreme angular magnification of the afocal system: Gmin ≈ 0.91 to Gmax ≈ 1.82.
Zoom ratio: R = Gmax / Gmin = 1.82 / 0.91 ≈ 2.

The power balance of the different groups is very different from that of the 80-200 mm:

Fig. 22: Zoom-Nikkor 200-400mm f/4 ED Ais set to its minimum focal length.
Effect of the focus distance on the effective focal length.
Mouse out: infinity focus.

Mouse over: minimum focus (4 m).

Under such conditions, the focal length of this telephoto zoom set to minimum focus (4 m – 13.1 ft.) varies in a very different way from shorter focal-length zooms (see graph Figure 19).

Fig. 23: Zoom-Nikkor 200-400mm f/4 ED Ais.
Zooming system.

The small difference appearing between the apex-angles of both cones of illumination, axial and oblique, indicates very slight vignetting.

 

o---0---o

 

X  –  The Zoom-Nikkor AF-S VR 200-400mm f/4G IF-ED.

This new version of the 200-400mm is very different from the previous one. Not only because of it includes two rings instead of a single one, but above all because its optical system is much more sophisticated. Mr. Susumu Sato designed this lens, as well as its “little brother” the Zoom-Nikkor AF-S VR 70-200mm f/2.8G IF-ED released the same year (2003). Both lenses include an image stabilization system (triplet incorporated into the master lens), but the focusing system of the 200-400mm is different from any telephoto zoom we've seen before: the “afocal internal focusing system” (one more afocal system!). Nikon uses this internal focusing system on all its telephoto lenses (from 180mm to 600mm), but this is the only zoom that has it. This system is presented on my page Mise au point (still in French).

Given the important size of the front elements of such a telephoto zoom, the afocal focusing system allows a much greater reduction in the mass of the moving parts. Although it is more complex as far as the optics is concerned, it still allows keeping the mechanical simplicity of the classical internal front focusing system (focusing independent of the focal length).

Like the previously studied telephoto zoom lenses, the optical system of this one includes a three-component afocal system placed in front of a master lens. But here, the front group includes its own afocal system ensuring the focusing (Figure 24). Thus, the front group of this zoom constitutes, by itself, a true internal focusing telephoto lens whose focal length is f’ ≈ 299 mm and aperture is f/3.0 (on infinity focus).

The calculated focal lengths of the four groups of this zoom are:

The angular magnification of the afocal system ranges from Gmin ≈ 1.28 to Gmax ≈ 2.46 (always greater than G = 1) for an overall focal length ranging from f’ ≈ 204 mm to f’ ≈ 392 mm, when the system is set to infinity focus.

Fig. 24: Zoom-Nikkor AF-S VR 200-400 mm f/4G IF-ED set to its minimum focal length.
Effect of the focus distance on the effective focal length.
Mouse out: infinity focus.

Mouse over: minimum focus (2 m).

When set to the minimum focus distance (2 m – 6.6 ft.), the behavior of the focal length is reminiscent of the previous model, but the deviation from the nominal curve (infinity) is much stronger, and there is a slight decrease in the focal length at the end of the range. Thus, when set to minimum focus, the focal length range is only 85 mm (from f’ ≈ 250 mm to f’ ≈ 335 mm, R ≈ 1.34).


 
Fig. 25: Zoom-Nikkor AF-S VR 200-400 mm f/4G IF-ED.
Zooming system.

The magnification curves with respect to the focal length of both 200-400mm set to their respective minimum focus distance, are very different. The influence of the afocal internal focusing system of the VR model is obvious. Note that the magnification of the lens increases continuously even when the focal length stops increasing, and also when it slightly decreases at the end of the range (f’ ≈ 334.6 mm). There, is the only point where the magnification is in accordance with the typical value of a 335mm lens.

Fig. 26: Minimum-focus-magnification comparison between the two Nikon’s 200-400mm
with regard to their effective focal length.

Conclusions

At short focus distance, the magnification of this type of zoom, with front focusing system or internal front focusing system, is truly representative of their effective focal length only when set to shorter focal lengths. Beyond, the relationship between the magnification and the focal length is never simple, and only the definition of the optical system allows accurate calculations.

With compensator-shift focusing zooms (70-200 VR II), or zooms with afocal internal focusing system (200-400 VR), no simple relationships connect magnification and focal length, and again, only the definition of the optical system allows accurate calculations.

P.T., September 9, 2010.
Last update, February 6, 2011.

 

o---0---o

 

References:

 

o---0---o

 

Annex I  –  Brief presentation of the Zoom-Nikkor 50-300mm f/4.5 ED Ais.

True afocal systems seem to be not suitable for zoom ratios greater than about R ≈ 4. Beyond this value, the telephoto zooms with constant overall length and constant aperture include non-afocal systems (convergent). To my knowledge, such photographic lenses are not so numerous in photography (much more common in the film and video field).


 
Fig. 27: Zoom-Nikkor 50-300 mm f/4.5 ED Ais.

Until the late 1990s, Nikon used to propose a 50-300mm zoom lens (R ≈ 6) with constant aperture (f/4.5) including a convergent system in front of a master lens. Compared with the telephoto zoom lenses previously seen, the structure of the master lens is very different. The first element (negative) of the master lens converts the convergent light beams emerging from the compensator into almost parallel light beams. The three following elements create the real image on the sensor. The compensator displacement curve is very different from the curves previously seen.

Fig. 28: Zoom-Nikkor 50-300 mm f/4.5 ED Ais.
Zooming system.
 

Heavy and bulky, this type of zoom has never been adapted to the autofocus…

 

-o---0---o-

 

Top of the page - Back to Appendix

Other subjects :

Fisheyes (in English)
Focal length and Magnification (in English)
La mise au point (in French)
Pupilles et ouvertures (in French)
AF-S VR 300 mm f/2.8G (in French)
Fluorine et verres ED (in French)