## How lens designs evolve

Most of us have seen dozens of diagrams of lens designs without any explanation of how to understand them. Figure 7.12 is an attempt to make lens diagrams comprehensible. It shows how nearly all modern lenses belong to four groups.

Looking at the historical development, you can see that the usual way to improve a design is to split an element into two or more elements. Thus the three-element Cooke Triplet gradually develops into the 11-element Sigma 105-mm f/2.8 DG EX Macro, one of the sharpest lenses I've ever owned.

The reason for adding elements is that every lens design is, fundamentally, an approximate solution to a system of equations describing the paths of rays of light. By adding elements, the designer gains more degrees of freedom (independent variables) for solving the equations.

But there are also other ways to add degrees of freedom. One is to use more kinds of glass, and many new types have recently become available. Another is to use aspheric surfaces, which are much easier to manufacture than even 20 years ago.

Perhaps the most important recent advance is that anti-reflection coatings have improved. It is now quite practical to build a lens with 20 or 30 air-to-glass surfaces, which in the past would have led to intolerable flare and reflections.

There have also been changes in the way designs are computed. Fifty years ago, designers used a whole arsenal of mathematical shortcuts to minimize aberrations one by one. Today, it's easy to compute the MTF curve (not just the individual aberrations) for any lens design, and by dealing with MTF, the designer can sometimes let one aberration work against another.

Manufacturers usually describe a lens as having "X elements in Y groups," where a group is a set of elements cemented together. How many elements are enough? It depends on the f -ratio and the physical size of the lens. Faster lenses need more elements because they have a wider range of light paths to keep under control. Larger lenses need more elements because aberrations grow bigger along with everything else.

Zoom lenses (Figure 7.13) need numerous elements to maintain a sharp image while zooming. In essence, the designer must design dozens of lenses, not just one, and furthermore, all of them must differ from each other only in the spacings between the groups! That is why zooms are more expensive and give poorer optical performance than competing fixed-focal-length lenses.

Triplet Family

Double Gauss Family

Telephoto Family

Cooke Triplet (H. D. Taylor, 1893)

Asymmetrical triplet (telephoto-like)

Zeiss Tessar (Paul Rudolph, 1902)

Zeiss Sonnar (1932) (modern T* 135/2.8 shown)

Olympus Zuiko 100/2.8 and 180/2.8 (1970s)

Nikkor ED IF AF 300/4 (1987) and ED IF AF-D 180/2.8 (1994)

Gauss achromat (1817)

Double Gauss (Alvan Clark, 1888)

Zeiss Planar (Paul Rudolph, 1896)

Nikkor-H Auto 50/2 (1964)

Fraunhofer achromat (1814)

Telescope with Barlow lens (1834)

Classic telephoto (1890s)

Retrofocus Family

Simplest wide-angle lens (simple lens with reducer in front)

Sigma 105/2.8 DG EX Macro (2004)

AngĂ©nieux Retrofocus 35/2.5 (1950)

Figure 7.12. Lineage of many familiar lens designs. In all these diagrams, the object being photographed is to the left and sensor or film is to the right.

Zoom principle: moving Barlow lens changes focal length of telescope

 r- \ -P- ) I I I 1

Adding positive element reduces focus shift when zooming

Canon EF 28-80/3.5-5.6 zoom lens (two sets of elements move separately)

Figure 7.13. A zoom lens is like a telescope with a variable Barlow lens. A simple, low-cost zoom is shown here; others have as many as 22 elements moving in six or eight independent sets.

### 7.6.2 The triplet and its descendants

Multi-element lens design began in 1729 when Chester Moore Hall discovered that convex and concave lenses made of different kinds of glass could neutralize each other's chromatic aberration without neutralizing each other's refractive power. The same discovery was made independently by John Dollond in 1758. Later, the mathematicians Fraunhofer and Gauss perfected the idea, and telescope objectives of the types they invented are still widely used.

Early photography led to a demand for lenses that would cover a wider field of view, and in 1893 H. Dennis Taylor designed a high-performance triplet for Cooke and Sons Ltd. (www.cookeoptics.com).

Modern medium-telephoto lenses are often descendants of the Cooke Triplet. The key parts of the design are a convex lens or set of lenses in the front, a set of concave lenses in the middle, and a convex lens at the rear. A particularly important triplet derivative is the Zeiss Sonnar, which originally used a very thick concave element with other elements cemented to it to minimize the number of air-to-glass surfaces. Lenses of this type were made in East Germany through the 1970s, and you can recognize them by their weight. The famous Nikon 105-mm f /2.5 telephoto is a Sonnar derivative with a thick element.

Around 1972, Yoshihisa Maitani, of Olympus, designed a very compact, lightweight 100-mm f /2.8 lens which is a Sonnar derivative with the thick central element split into two thinner ones. Other camera manufacturers quickly brought similar designs to market, and even the Sonnar itself has shifted toward thinner, air-spaced elements. Over the years, Sonnar derivatives have become more and more complex.

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