14.5 DESIGN OF A TESSAR LENS

The Tessar14 resembles the Protar in that the rear component is a newachromat cemented doublet, but the front component is now an air-spaced doublet rather than a cemented old-achromat. The cemented interface in the front component of the Protar was very strong, leading to a large zonal aberration, but the separated doublet in the Tessar gives so much less zonal aberration that an aperture of f/4.5 or higher is perfectly feasible. From another point of view, the Tessar can be regarded as a triplet with a strong collective interface in the rear element; this interface has a threefold function: It reduces the zonal aberration, it reduces the overcorrected oblique spherical aberration, and it brings the sagittal and tangential field curves closer together at intermediate field angles. Although sometimes it is mentioned that the Tessar was derived from the Cooke Triplet lens (Section 14.6) invented by Taylor, its actual genesis is the Protar being that Rudolph invented both the Protar (1890) and Tessar (1902) as explained in the Tessar patent specification.

14.5.1 Choice of Glass

It is customary to use dense barium crown for the first and fourth elements, a medium flint for the second, and a light flint for the third element. Possible starting values are therefore as shown in Table 14.11.

Table 14.11

Initial Selection of Glasses for Tessar Design

14.5.2 Available Degrees of Freedom

Because of the importance of the cemented interface in the rear component, it is best to establish it at some particular value, say 0.45, and leave it there throughout the design. Since there is no symmetry to help us, we must correct every one of the seven aberrations, and also hold the focal length, by a suitable choice of the available degrees of freedom; this makes the design decidedly

14.5.3 Chromatic Correction

Assuming that this is a reasonable starting system, we next trace an f/4.5 marginal ray in e light and find the (D – d) Dn contribution of each lens element, as shown in Table 14.12. We could, of course, adjust the two components to make both totals separately zero, but it is then found that the lateral color HF0 – HC0 , calculated by tracing principal rays at 17 , is strongly positive. Since lateral color takes the same sign as the longitudinal color of the rear component, we must have a considerable amount of negative D – d sum in the rear and an equal positive sum in the front component.

We will therefore try to increase the negative sum in the rear component by choosing a glass for element (d) with a higher dispersive power, that is, a lower V number. Such a glass is SK-8 with ne ¼ 1.61377, Dn ¼ nF – nC ¼ 0.01095, and Ve ¼ 56.05. The slight alteration in refractive index requires a small adjustment of the system, giving Setup B:

with f 0 ¼ 10, l0 ¼ 8.851896, Ptz ¼ 0.025. An f/4.5 marginal ray gives LA0 ¼ þ0.30981 and the D – d values shown in Table 14.13.

This sum is quite acceptable so far as longitudinal chromatic aberration is concerned. We must next check for lateral color. Tracing principal rays at 17 in F and C light tells us that the lateral color is þ0.000179, which is also acceptable, so that now both chromatic aberrations are under control. Fortunately chromatic errors change so slowly with bendings that our future efforts at correcting spherical aberration, coma, and field curvature by bending the three components do not greatly affect the chromatic corrections.

Table 14.13

Setup B Chromatic Aberration Contributions

14.5.4 Spherical Correction

Because elements (a) and (b) are working at about the minimum aberration positions, we cannot hope to correct spherical aberration by bending them. Thus we are obliged to control spherical aberration by bending the rear component, that is, by changing c5. This will be done by a series of trials at every Setup from now on.

We arbitrarily require LA0 to be about þ0.098; this will yield a zonal residual of about half that amount, giving excellent definition when the lens is stopped down, as it will almost always be in regular use. We then vary c1 and c3 to correct the OSC and Xt0 by means of a double graph (Figure 14.21). The aim point will be at zero for both these aberrations.

Correcting the spherical aberration of Setup B by adjusting c5 gives Setup C, shown in the following table:

0.18 1.51354

0.45

0.62 1.61377

0.2632877

with f 0 ¼ 10, l0 ¼ 9.035900, Ptz ¼ 0.02499, LA0 ¼ 0.09724, OSC ¼ –0.01778. A principal ray traced at 20 through the stop emerges from the front of the lens at 17.3070 , with the following fields:

Figure 14.21 This double graph shows the effects of bending the first two elements of a Tessar at 17 field angle. (In each case the Petzval sum and spherical aberration have been corrected first.)

The distortion is negligible, showing that the choice we made of u40 ¼ –0.05 is about right, and we will continue with that value in what follows. The negative OSC is, however, much too large, and the tangential field is much too backward-curving.