H′

Principal ray

3.25

UR

L

3.15

3.10

LR

tan U′

Figure 12.19 The meridional ray plot for the final system at 17.9 field angle.

Assuming that the sagittal coma is one-third the tangential coma, the equivalent OSC becomes –0.00096, which is small enough to be neglected, especially since a lens of this type is unlikely to be used at a field as wide as 17.9 . See Sections 4.3.4 and 9.3.

Although we have regarded this as a portrait lens, it has seldom been used in this way, but it could very well be used at or near unit magnification as a relay lens in a telescope, in which case the coma and distortion would automatically vanish due to symmetry (Section 11.6).

12.5.3 Long Telescopic Relay Lenses

In many types of telescopes and periscopes, an erector system working at or near unit magnification is inserted between the objective and eyepiece to give an erect image. This erector often consists of two identical spherically corrected doublets mounted symmetrically about a central stop, the stop position being chosen to give a flat field exactly as in the Rapid Rectilinear lens, except that now we often need a long system rather than a short one.

As was pointed out in connection with the design of the Rapid Rectilinear in the beginning of Section 12.5.1, the greater the amount of coma in the rear lens the smaller the stop shift required to give a flat tangential field, and the shorter the relay will be. For a long relay, we therefore need a spherically corrected lens with a very small amount of coma, and hence we select a design in which the graph of spherical aberration against bending rises only a little way above the abscissa line. Furthermore, whatever lens we use for the rear component of

This is important since, when a field lens is employed, it must have positive power and will adversely impact the field curvature.

The main relay in a submarine periscope consists of a pair of highly corrected aplanatic objectives spaced apart by a distance equal to two or three times their focal length, the field angle being then less than 1 . In this case the astigmatism is negligible so long as the tangential field is flat. Coma is corrected by the symmetry in the usual way.

12.5.4 The Ross “Concentric” Lens

This is the classic example of a symmetrical objective consisting of two deeply curved new achromats surrounding a central stop. It was patented by Schroeder in 1889, with the structure of the rear half, after scaling to a focal length of 10, according to von Rohr6 as follows:

with f 0 ¼ 10, l0 ¼ 10.5961, Lpp ¼ þ0.6166, Petzval sum ¼ –0.00618. The glasses are assumed to be light flint No. 26 and dense barium crown No. 20 in Schott’s catalog of 1886. The nearest "modern" Schott glass for No. 26 is LLF-6 and for No. 20 is SK-8.

Tracing a fan of rays entering at –20 gives the H0 – L curve shown in Figure 12.22a. Clearly the stop position for a flat tangential field should be at about L ¼ –0.237 (point A), but von Rohr’s specification places it at B, where L ¼ –0.194, resulting in a slightly backward-curving field. (Incidentally, measurements made on an actual Concentric lens did not agree with this specification in any respect.) The front principal point is at C.

After combining two of these lenses together and scaling to a focal length of 10, the spherical aberration at f/15 was found to be an unacceptable value of0.65, so that the lens should not be used at any aperture greater than about f/20 (spherical aberration decreases to about 0.27; see Eq. (6-12)). The fields with the preferred air space (0.868), and with that given by von Rohr (0.768), are also shown in Figure 12.22b. The unusual backward-curving sagittal field is, of course, due to the Petzval sum being negative. It is remarkable how great an effect a small change in the central air space has on the two fields.