# Symmetrical Lenses

This is a continuation from the previous tutorial - triplet lenses.

In the early 1840s, it was recognized that lenses that exhibit symmetry afford various benefits to the lens designer. The first aberration acknowledged to be corrected by the symmetry principle was distortion. It can also be shown that coma and lateral color are necessarily corrected by a symmetrical lens construction.

Although the principle of symmetry implies that the lens be operated at a magnification of $$-1$$, the degree to which the aberrations are upset by utilizing the lens at other conjugates is remarkably small. This principle forms the basis of most wide-field-of-view lenses.

One of the earliest symmetrical lenses was the Periscopic (Periskop) lens invented by C. A. Steinheil in 1865. Figure 24 shows an F/11 Periscopic lens constructed from the landscape lens discussed previously.

Symmetry corrects for coma and distortion, while the spacing of the lenses and their shapes are selected to produce a flat tangential astigmatic field. Since the stop position for the landscape lens was chosen to yield a flat tangential astigmatic field, essentially no change in the lens separation is necessary even though the Periscopic lens is being used at infinite conjugates.

No correction for spherical aberration can be made. When used at other than unit magnification, some optical improvement can be achieved by making the stop slightly asymmetrical and/or having a different shape for the front or rear lens. This lens has continued to find application throughout this century.

By 1966, Dallmeyer in England and Steinheil and von Seidel in Germany both invented the Rapid Rectilinear lens that could be used at apertures of up to F/6.

The lens has two cemented achromats about a central stop. Use of the doublet allows correction of the axial chromatic and spherical aberrations. Glass selection is of importance in the design. Typically, the $$\Delta{n}$$ between the glasses should be large while the $$\Delta{V}$$ should be relatively small.

The positive lens is located nearest the stop and has the lower refractive index. A notable characteristic of the lens is that the aberrations are reasonably stable over a broad range of object distances.

It should be noted that vignetting is often used in these and other lens types to control the higher-order aberrations that are often observed at large field angles. Although a loss in illumination occurs, the gain in resolution is often worthwhile.

The airspaced dialyte lens comprises four lenses symmetrically arranged about a central stop. The rear portion of the lens is an achromatic doublet that has five degrees of freedom (an air space, two powers, and two bendings) which may be used to control the focal length, spherical aberration, axial chromatic aberration, astigmatism, and the Petzval sum.

With a like pair of lenses mounted in front of the stop, the symmetry corrects the coma, distortion, and lateral color. When used at infinite conjugates, the resultant residuals of the aberrations can be controlled by deviating somewhat from perfect symmetry of the air spaces about the stop.

Lenses of this type can provide useful performance with apertures approaching F/4 and fields of view of about $$\pm20°$$ or so.

The next tutorial discusses about double-Gauss lenses