Focus on Pictures

 

Extension tubes and magnification

There are various way of obtaining larger images of objects by adding elements to the lens-camera combination:

We will here only consider how extension tubes affect image size. For a better understanding we need to to consider how an image is formed by a lens.

How an image is formed

Positive lens producing and imageFigure 1 illustrates in simplified form how an object O is depicted as image I by a positive, i.e. a converging lens.

dO and dI represent the distance from object to lens, and from lens to image, respectively.

Let f be the focal distance, with fO at the object side, and fI at the image side, where fO = fI. If we regard the lens as a thin lens (where the path of the light through the lens itself contributes to very little change in the direction of the light rays), then
1/dO + 1/dI = 1/f.

Any light traveling from the object in parallel with the optical axis is deflected through fI. Any light passing between object and fO is deflected and emerges from the lens in parallel with the optical axis. Where the deflected lines intersect, the image is 'in focus', i.e. sharp, in the focal plane.

It follows that a lens with a small focal length produces a smaller image of a distant object than one with a long focal length. Magnification is image size/object size: SI/SO.

If the distance between object and image is very large, i.e. orders of magnitude larger than the focal length of the lens, we designate this as infinity, when f = dI. In that case all light reflected by the object travels almost in parallel with the optical axis, and the image size is very small. If we subsequently put the same object, say, at a distance equal to the focal length in front of the camera-lens combination, we need to increase the distance between lens and focal plane to obtain a sharp image. The lens must be moved forward. It follows that, in order to focus at increasingly smaller distances from the front element of the lens, we need to extend the light path between lens and focal plane. Extension in any camera is achieved by moving the lens package forward. The above example also illustrates the rule of thumb: adding extension equal to the focal length produces an image as large as the object: magnification 1:1.

It follows from the above that any lens can in principle be used to obtain larger images simply by adding extra extension between camera and lens, using either extension tubes of fixed length or bellows equipment. There is an issue here. Lens designs are such that any defraction errors (chromatic abberation, pin or cushion formation, etc.) are minimised; usually the distance between object and lens is large compared to the focal length. The use of extension tubes may lead to high magnifications, when this situation is reversed: in macro work, when magnification may go up beyond 1:1, the distance between object and lens becomes smaller than that between lens and image. In that case there is definitely something to be gained by reversing the lens, using a 'reversing ring', because that best mimicks the way the lens should normally be used for obtaining the highest quality image.

Macro lenses

Dedicated macro lenses not only have a helical focusing mount that allows much greater lens travel, i.e. move the entire lens package forward, but are also optically optimized so as to minimize diffraction anomalies. Most will allow to take pictures at 1:1 magnification. For example, the Minolta 50mm macro f 2.8 can achieve a 1:1 magnification at an object-image distance of 20 cm. This implies a distance between image and lens of 10 cm, and 10 cm between lens and object. The extension then is 5 cm, illustrating the rule of thumb that an extension equal to the focal length results in 1:1 magnification.
In many macro lenses the focal length diminishes with working distance. Take the Minolta 100mm macro f 2.8. It produces a 1:1 image at a distance of 35.2 cm. If we assume extension equal to focal length, the minimum working distance ought to be 40 cm. In fact, the 35.2 working distance is compatible with 88mm focal length. The 100mm macro lens therefore achieves 1:1 magnification by a combination of lens travel and shortening focal length ('internal focusing').

Extension and magnification factor

Experimentally the influence of extension tubes on magnification factors was studied as follows:

 
Magnification
  Minolta 100mm macro f 2.8 Minolta 50mm macro f 2.8
Extension tube mm
Lens 35.2 cm
Lens 50 cm
Lens 20 cm
Lens 25 cm
0
1.000
0.361
1.000
0.397
12
1.126
0.455
1.231
0.626
20
1.191
0.533
1.383
0.786
32
1.333
0.647
1.623
1.004
36
1.374
0.691
1.697
1.077
48
1.514
0.806
1.982
1.318
56
1.566
0.896
2.113
1.474
68
1.697
1.018
2.309
1.736
Max. ratio 1.697 2.820 2.309 4.441

If you plot the data shown in the table you will see a linear increase in magnification with added extension. As you will appreciate from the table the lens with the shorter focal length has the greatest proportional increase in magnification (Max. ratio = magnification at tube extension 68 mm divided by that at extension 0).
The shorter focal length also yields larger maximum magnification, but at the expense of such a small working distance that lighting the object becomes a significant problem. The larger working distance with the longer macro lens is definitely an advantage in practice.

It goes without saying that, as one focuses at smaller distances, depth of field goes down to millimetres or fractions thereof, so that one has to apply small lens openings. Also, with such a diminished field of view, small movements of the object become large movements in the image plane. Add to this your own movements when you handle the camera, and you will understand why you will end up with many a picture that is not as sharp as you expected. Don't put the blame on back-focus or front-focus of your camera too quickly. A tripod and remote shutter release help to minimise camera movement, a flash helps in applying a small lens opening and short exposure time. However, when chasing bugs a tripod is often not that handy.

I did worry a little bit about attaching a lens with 68mm extension tube to the camera. The 100mm lens is fairly heavy, and its excentric placement makes for considerable stress on the camera; the extension tubes + 100mm macro lens weigh in at 0.78 kg. So one does well to support this combination one way or another when making photographs.

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