12.3 A PERISCOPIC LENS

It was found empirically very early in the development of photography that placing two identical landscape lenses symmetrically about a central stop removed the distortion and lateral color thereby giving a better image than could be obtained by the use of a simple meniscus lens alone. Such a lens was called periscopic.

To design the rear half of a symmetrical lens, we assume that there will be parallel light in the stop space, and now we can evidently ignore coma since it will be corrected automatically by the symmetry (in at least a single zone). Therefore we have to consider only the tangential field curvature, and by the H 0 L curve we can select a stop position to flatten the field, provided the lens bending is equal to or stronger than that used for a landscape lens, but we cannot use stop position to flatten the field if the bending is weaker than that of a landscape lens. This is because the H0 L curve doesn’t contain a place where the slope is zero. Also, the steeper the bending the closer the stop will be to the lens, resulting in a more compact system.

Using the thickness and refractive index employed in our previous designs, we will try a rear-meniscus lens with c1 ¼ –0.8. The structure is

with f 0 ¼ 9.99975, l0 ¼ 10.41182. The H0 L curve for a 20 obliquity is shown in Figure 12.6.

This graph tells us that our lens will have a flat tangential field if the stop is placed at a distance of –0.85 or –0.23 from the front lens surface. Naturally, we choose the nearer position, and we mount two similar lenses about a central stop located 0.23 from each of the facing surface vertices. The focal length now

H′

3.61

3.60

L

drops to 5.3874, and so we scale up the combined system to a focal length of 10 (scale factor = 10/5.3874; remember that the radius is scaled by this value, not the curvature). The resulting system is shown in Figure 12.7a.

0.51287

0.278 1.523

0.431

0.427

0.427

0.431

0.278 1.523

0.51287

20

10

–0.4 0

(a)

20

10

–0.4 0

(b)

Figure 12.7 Two periscopic designs. The sagittal field is the solid curve and the tangential field is the dashed curve.

with f 0 ¼ 10.00414, l0 ¼ 9.32841, stop diameter ( f/15) ¼ 0.620, LA0 ( f/15) ¼ –0.2959, Petzval sum ¼ 0.0562. Astigmatism and distortion are presented in Table 12.3.

The spherical aberration and field curvature calculated here are for parallel light entering the left-hand end of the system, but it was designed on the assumption that there would be parallel light in the stop. It is actually rather surprising that the aberrations for a distant object resemble so closely the aberrations of the rear half alone. It is clear from examination of Figure 12.7a that the tangential field is slightly too far backward, and it is therefore desirable to reduce the central air space slightly to flatten the field. Also, the scaling-up process has made the lens elements unnecessarily thick, and it would be worth going back to the beginning and redesigning the system with much thinner lenses.

It is of interest to compare this design with the original Steinheil “Periskop” lens, which was of this type. According to von Rohr,1 the specification was

0.5645

0.1316 1.5233

0.4749

0.6484

0.6484

0.4749

0.1316 1.5233

0.5645

with f 0 ¼ 10, l0 ¼ 9.2035, stop diameter ( f/15) ¼ 0.627, LA0 ( f/15) ¼ –0.355, Petzval sum ¼ 0.0615. Table 12.4 presents the astigmatism and distortion. The modified lens is shown in Figure 12.7b.

Table 12.4

Astigmatism and Distortion for Lens Shown in Figure 12.7b