14.5.5 Correction of Coma and Field

To plot a double graph, we make a trial change of Dc1 ¼ –0.05 from System C and then restore everything to its original value (i.e., Setup D). We then return to Setup C and now change c3 by 0.05, which gives Setup E. These changes are shown in Figure 14.21. Following the usual procedure with a double graph, and making several small adjustments, we finally come up with Setup F:

( f/4.5) ¼ 0, Ptz ¼ 0.0250. The results are shown in Table 14.14.

The aberration graphs are shown plotted in Figure 14.22. As a check on the coma we next trace a number of oblique rays entering parallel to the principal ray at 17.19 and draw a meridional ray plot (Figure 14.23). It will be seen that the two ends of this graph sag somewhat, but the middle part of the curve is straight. This is an indication of the presence of negative higher-order coma, and it cannot be usefully corrected by the deliberate introduction of positive OSC. A much better method of removing it is to introduce some vignetting. If we limit the clear aperture of each surface to the diameter of the entering f/4.5 axial beam, we shall cut off the ends of the ray plot in Figure 14.23 to the marks

Table 14.14

Astigmatism and Distortion for Setup F

30°

T

S

Z

10

Figure 14.23 Meridional ray plot of Tessar Setup F. Rays SS are through top and bottom of the stop. Rays VV represent vignetted limiting rays.

VV shown, and we shall thus remove almost the entire higher-order coma without seriously reducing the image illumination. Figure 14.24 shows the lens apertures so reduced and the path of the limiting oblique rays VV.

The astigmatic fields shown in Figure 14.22 cross rather too high and the field is a little backward-curving. We shall therefore return to the double graph of Figure 14.21 and establish a new aim point at OSC ¼ 0 and Xt0 ¼ –0.04, which is by chance very close to Setup E. After making several small adjustments in c1 and c3, and of course correcting the spherical aberration each time by c5 and the Petzval sum by d20 , we arrive at the following solution G:

We must now study the effect of changing the cemented interface c6. This was arbitrarily set at 0.45, and we will next repeat the entire design with c6 ¼ 0.325. The resulting lens is decidedly different from the previous design, as shown in the following table:

with f 0 ¼ 10, l0 ¼ 9.20712, LA0 ( f/4.5) ¼ 0.08714, LZA ( f/6.4) ¼ –0.03475, OSC ( f/4.5) ¼ 0, P (D – d) Dn ¼ –0.0000707, lateral color (17 ) ¼ –0.00121. The results are shown in Table 14.16.

These aberrations are shown in Figure 14.26. The field is a little narrower than before but quite satisfactory. It should be noted that both of the color aberrations

418 Unsymmetrical Photographic Objectives

Table 14.16

Astigmatism and Distortion for Second Tessar System

30°

T S

Z

10

Figure 14.26 Aberrations of second Tessar system.

are negative; to rectify this requires a small increase in the V number of the glass used for the rear crown element, say to SK-1, which has ne ¼ 1.61282 and Ve ¼ 56.74, or SK-19 with ne ¼ 1.61597 and Ve ¼ 57.51. The lens designer should always be mindful of the impact glass choice can have on a design.

The chief matter requiring study is the meridional ray plot in Figure 14.27, which should be compared with the previous graph in Figure 14.23. It is immediately clear that the change from c6 ¼ 0.325 to 0.45 has had the effect of raising the lower end of the curve and depressing the upper end. That is, strengthening c6 has introduced some undercorrected oblique spherical aberration to the existing negative higher-order coma, with an improvement in the overall quality of the lens. The lower end of the curve needs cutting off more than the upper end, but obviously we cannot cut it back beyond the marginal ray aperture.

The best way to improve this Tessar is to raise the refractive indices, preferably above 1.6 in all elements. It is doubtful if changing the thicknesses would have any significant effect.