M

Z

P –0.004 0 0.004

Figure 10.2 Broken-contact aplanat.

DESIGNER NOTE

It is worth noting that the air space in this lens has the form of a negative element, the equivalent of a positive glass lens that undercorrects the spherical aberration. Increasing the airgap will increase the zonal aberration noticeably, while decreasing it at this separation will reduce the zonal aberration only slightly. A broken-contact lens of this type requires the utmost care in mounting, and particularly in centering one element relative to the other.

In a large lens it is best to mount each element into a separate metal ring, using push–pull screws to secure and adjust the separation to give the best possible definition. For a small lens, the air space is too narrow for a loose spacer to be used, and it is best to mount the two elements on opposite sides of a fixed metal flange with separate clamping rings to hold them in place.

10.2 PARALLEL AIR-SPACE TYPE

As an alternative to the broken-contact type just discussed, we may prefer to keep the two inner radii equal to save the cost of a pair of test plates, and vary the air space to correct the spherical aberration. Then if the coma is excessive, we can correct it by bending the whole lens.

As before, we start at the maximum of the bending curve, with c1 ¼ 0.15 and ca ¼ 0.5090, giving c2 ¼ c3 ¼ 0.3590. In Section 10.1 our starting setup had an air space of 0.01, giving LA0 ¼ 0.10566 and OSC ¼ 0.00062 (Setup A in Figure 10.1). If we increase the air space to 0.04, with the usual D – d solution for the last radius (Section 5.9.2), we obtain Setup B:

LA0 ¼ 0:01466; OSC ¼ 0:00305

We next apply a trial bending of 0.01 to the entire lens, with the 0.04 air space, and we get LA0 ¼ 0.00646 and the OSC ¼ 0.00201 (Setup C). These values are plotted on a double graph with spherical aberration as abscissa and OSC as ordinate, as before (Figure 10.3). Evidently a further bending by 0.0198 should bring us close to the aim point. Actually this bending gave LA0 ¼ 0.00014 and OSC ¼ 0 (Setup D).

As the zonal aberration of this air-spaced lens is liable to be strongly overcorrected, we prefer to have a small negative value for the marginal aberration. Since our trial change in air space gave @LA0/@(space) ¼ 4.0, we try increasing the air space by 0.0001. This gives the final setup as follows for trim diameter ¼ 2.2, f 0 ¼ 10.1324, l0 ¼ 9.7012, LA0 ¼ 0.00017, LZA ¼ þ0.00666, OSC ¼ 0. It should be noted that the overcorrected zonal aberration is now 1.6 times as great as in the broken-contact design, and this is the principal reason why the previous type is generally to be preferred (Figure 10.4). However, the air space is now wider, which may be of help in designing the lens mount. Nevertheless, the LA0 is very sensitive to changes in the airgap. Figure 10.4 shows the excellent state of zonal chromatic correction. The prescription for the final design is as follows.

Figure 10.4 Spherochromatism of a parallel air-space aplanat.

The spherical aberration for the parallel air space aplanat shown in Figure 10.4 almost entirely comprises primary and secondary (thirdand fifthorder) contributions. The spherochromatism for each the C and F also has the same general shapes. If now the first surface of this aplanat is made aspheric to reduce the spherical aberration in d light, a dramatic reduction can be obtained as illustrated in Figure 10.5. Notice that the spherical aberration contributions now contain a tertiary (seventh-order) term. This is a nice example to illustrate that the inclusion of an aspheric surface can cause remarkable variation in spherochromatism. Overall, the image quality of the lens with the aspheric first surface is superior. Also, as you should expect, the zonal chromatic correction is unchanged as is the zonal secondary color.

M

d

F

Z

C

Figure 10.5 Spherochromatism of a parallel air-space aplanat with aspheric first surface.

10.3 AN APLANATIC CEMENTED DOUBLET

In Section 9.3.5 it was pointed out that the bending of a cemented doublet that yields zero OSC almost coincides with the bending for maximum spherical aberration. Consequently, if we can find two types of glass for which the spherical aberration curve just reaches zero at the top of the bending parabola, this peak bending will also be very nearly aplanatic.

Some guidance as to likely types of glass can be obtained by calculating the spherical G sums, and plotting the thin-lens bending curve as in Figure 7.2, relying on the fact that the true thick-lens curve coincides closely with the approximate thin-lens graph shown there. A few trials along these lines indicate that the spherical aberration curve will be bodily lowered if we increase the V difference between the glasses or if we reduce the n difference between them.

Since we have only three degrees of freedom in a cemented doublet, which must be used for focal length, spherical aberration, and OSC, it is clear that we must leave the final choice of glass until the end in order to secure achromatism by the D – d method. Since there are more crowns than flints in the Schott

catalog, we will adopt some specific flint and try several crowns to see how the chromatic condition is operating. Taking as our flint Schott’s SF-9 with nD ¼ 1.66662 and VD ¼ 33.08, we select three possible crowns, and with each we adopt an approximate value of ca ¼ 0.3755 for f 0 ¼ 10.

Thus we find by a series of trials the value of c3 that corrects the spherical aberration at f/5. The whole lens is then bent, again by a series of trials, to eliminate the OSC. Then the D – d sum of the aplanat is found for the marginal ray; finally we find, also by the D – d method, what value the crown VD should have to produce a perfect achromat. Repeating the process with each of the three crowns enables us to plot a locus of possible crowns on the glass chart (Figure 5.5), and if this locus happens to pass through an actual glass, that glass will be used to complete the design. Figure 10.6 is a magnified portion of the glass chart containing this locus.

Figure 10.6 Locus of crown glasses for a cemented doublet aplanat, using SF-19 as a flint.

Our three trials give the results shown in Table 10.1. Even without plotting a curved locus on the blowup of the glass chart as shown in Figure 10.6, we can see that the third selection, SK-11, gives a close achromat with our chosen flint. The final design after solving the last radius to give a zero D – d sum is as follow: