# Triplet Lenses

This is a continuation from the previous tutorial - achromatic doublet lenses.

In 1893, a new type of triplet lens for photographic applications was invented by the
English designer H. Dennis Taylor. He realized that the power of two lenses in contact of equal, but opposite, power is zero, as is its Petzval sum.

As the lenses are separated, the system power becomes positive since the negative lens contributes less power. The Petzval sum remains zero, since it does not depend upon the marginal ray height. In order to overcome the large aberrations of such a configuration, Taylor split the positive lens into two positive lenses and placed one on each side of the negative lens. A stop is often located between the negative and rear-positive lenses.

Figure 22 illustrates a typical triplet lens. The triplet can be used at reasonably large apertures ($$\gt{F/4}$$) and moderately large fields of view ($$\gt\pm25°$$).

The triplet has eight degrees of freedom which are the three powers, two airspaces, and three lens bendings. The lens powers and airspaces are used to control the axial and lateral chromatic aberrations, the Petzval sum, the focal length, and the ratio of the airspaces.

Spherical aberration, coma, and astigmatism are corrected by the lens bendings. Distortion is usually controlled by the airspace ratio or the choice of glasses. Consequently, the triplet has exactly the number of degrees of freedom to allow correction of the basic aberrations and maintain the focal length.

The design of a triplet is somewhat difficult since a change of any surface affects every aberration. The choice of glass is important and impacts the relative aperture, field of view, and overall length. For example, a large $$\Delta{V}$$ produces a long system.

It should be noted that a triplet corrected for third-order aberrations by using the degrees of freedom almost always leads to a lens with poor performance. A designer normally leaves a certain amount of residual third-order aberrations to balance the higher-order terms.

A few years later, Paul Rudolph of Zeiss developed the Tessar, which resembles the triplet, with the rear lens replaced by an achromatic doublet. The Tessar shown in Fig. 23 was an evolution of Rudolph’s anastigmats which were achromatic lenses located about a central stop.

The advantage of the achromatic rear component is that it allows reduction of the zonal spherical aberration and the oblique spherical aberration, and reduces the separation of the astigmatic foci at other than the design maximum field angle.

Performance of the Tessar is quite good and has generally larger relative apertures at equivalent field angles than the triplet. A variety of lenses were derived from the triplet and the Tessar in which the component lenses were made into doublets or cemented triplets.

The next tutorial discusses about symmetrical lenses