The simplest design that is reasonable for 35mm cameras is the triple configuration. Once the glasses are chosen, there are just enough variables (three powers, three shapes, and two separations) to correct all seven Seidel aberrations, as well as the focal length. The basic method used to flatten the Petzval field curvature in all anastigmats is the longitudinal separation of positive power from negative power. Increasing the separation lowers the relative ray height on the negative, thus will reduce the (negative) power contribution. The result is an effective net positive power without the undesirable excess of inward Petzval curvature. All anastigmats make use of this principle. Cooke triplet can be viewed as the trunk of the family tree of the airspaced anastigmats, while older anastigmats such as the Dagor, Sonnar, and the Biotar (double-Guass) types use thick meniscus components to separate positive convex surfaces from negative concave surfaces.
The choice of glass types is an important degree of freedom and has a significant effect on the characteristics of the triplet design. The glass for the positive elements should be a dense barium or lanthanum crown type; an index of 1.6 or more is almost essential. A triplet using an ordinary low-index crown glass (or acrylic plastic) for the positive elements is possible, but the result is poor unless the aperture or field (or both) is small. The other important factor in glass choice is the use of the relative difference in V values between the crown and flint elements as a means to adjust the vertex length of the triplet to its optimum value.Tessar
The Tessar, invented in 1902 by Paul Rudolph, is similar to the triplet. The difference is the cemented doublet replacing the rear singlet. Although Tessar is a modification of the Cooke triplet, it is actually a descendant of the double-meniscus anastigmat form. The Tessar performs better than the triple in COM3, AST3, PETZ3, and DIST3. The substitution of a new achromat doublet for a crown in the triplet is the equivalent of using high-index, high-V-value glass, and allows the possibility of utilizing the cemented surface of the doublet to control coma and oblique spherical aberration.
The Tessar design patent was held by Zeiss for two decades, and licensed to Rollei in Germany, Bausch & Lomb in the United States and to Krauss in France.
SonnarSonnar was introduced by Bertele (Zeiss) in 1931, at a time when antireflection coatings were not yet available. It can thought of as a triplet derivative with a meniscus component in the front air space. If the meniscus is made thick, it can have a field-flattening effect of its own. The Sonnar form makes use of this to eliminate the need for the center flint negative element. These lenses begin to look like the front half of a Biotar/double-Guass combined with the rear of a triple or Tessar. Given that the transmission of a single air-glass surface is typically about 95%, a lens with six air-glass surfaces can have a transmission of 0.95^6 = 0.73.
The Sonnar has proven incompatible in shorter focal lengths with SLR cameras due to the space taken up by an SLR's mirror. Therefore, the Sonnar type had a brief vogue as 35mm camera lenses of normal and long focal length, but they have been largely superseded by other constructions (e.g. double-Guass).
