12.4 ACHROMATIC LANDSCAPE LENSES

12.4.1 The Chevalier Type

In this type, a flint-in-front lens of slightly meniscus shape is used, with stop in front and the concave side facing the distant object.

As an example we will use the following glasses:

(a)Flint: nd ¼ 1.62360, V ¼ 36.75, Dn ¼ 0.01697

(b)Crown: nd ¼ 1.52122, V ¼ 62.72, Dn ¼ 0.00831

For a focal length of 10, we find using Eq. (5-4)

ca ¼ 0:2269; cb ¼ þ0:4634

Assuming an equiconcave flint as a starter and establishing suitable thicknesses (actually those used here were too thick), we solve the last radius by the D – d method and find the focal length to be 10.515. After scaling down to a focal length of 10 we have

with f 0 ¼ 10.00, l0 ¼ 10.4510, LA0 ( f/15) ¼ –0.162, Petzval sum ¼ 0.0667. We next trace a set of oblique rays through the upper half of the lens at 20

to locate the stop position for zero coma (Figure 12.8). This gives the values shown in the table on the next page.

H′

3.58

3.57

Figure 12.8 The H0 – L curve of a Chevalier achromat (20 ).

The inflection point of this graph is at L ¼ –1.67, and because the graph is S-shaped, the tangential field will obviously be backward-curving (see Section 12.1.2). Performing Coddington traces at several obliquities produces data for Figure 12.9 (see Table 12.5).

Unfortunately, it is not possible to flatten the tangential field in a lens of this type at the same time as eliminating the coma. The concave front face and the dispersive interface both contribute overcorrected astigmatism of about the same amount, and bending the lens merely increases one contribution while reducing the other. Using modern barium crown glass with a flint of the same index, one could make an achromatic lens that would behave like a simple landscape lens so far as the monochromatic aberrations are concerned, with the interface then being merely a buried surface. Another possibility is to depart

30°

20°

10°

Figure 12.9 Astigmatism of a Chevalier achromat. The sagittal field is the solid curve and the tangential field is the dashed curve.

Table 12.5

Astigmatism and Distortion for Lens Shown in Figure 12.9

from strict achromatism by weakening the cemented interface, but the high cost of such a lens over that of a single element would be scarcely justified.

12.4.2 The Grubb Type

In 1857 Thomas Grubb2 made a lens that he called the aplanat, consisting of a meniscus-shaped crown-in-front achromat. The spherical aberration was virtually corrected by the strong cemented interface, and as a result the user had to accept either the coma or the field curvature since both could not be corrected together. The Grubb lens eventually led to the “Rapid Rectilinear” design discussed in Section 12.5.1.

12.4.3 A“New Achromat” Landscape Lens

Since the cemented interface in the “old” Chevalier achromat has the effect of overcorrecting the astigmatism at high obliquities, it is evident that we could reverse the effect if we were to use a crown glass of higher refractive index than the flint glass (a “new achromat”). Furthermore, this combination of refractive indices has the effect of reducing the Petzval sum, but it will be accompanied by a large increase in the spherical aberration.

The design procedure for a new achromat is entirely different from that for an old achromat, because now we leave the achromatizing to the end and solve the outside radii of curvature for Petzval sum and focal length. We select refractive indices such that there are a variety of dispersive powers available for achromatizing after the design is completed. Two typical refractive indices meeting this requirement are

(a)Flint: 1.5348 (available V numbers from 45.7 to 48.7)

(b)Crown: 1.6156 (available V numbers from 54.9 to 58.8)

As a first guess we will aim for a Petzval sum of 0.03 on a focal length of 10. We must also guess at a likely interface radius and lens thicknesses. This gives the following as a starting system.

0.551

0.1 1.5348

0.164

0.4 1.6156

0.5687

with f 0 ¼ 9.9998, l0 ¼ 10.8865, Petzval sum ¼ 0.030. The large thickness helps to reduce the Petzval sum without using very strong elements (see “A Thick Meniscus” in Section 11.2.2).

In plotting the H 0 L graph, we use a larger obliquity angle than before because new achromats tend to cover an exceptionally wide field. The graph shown in Figure 12.10 represents the curve for 25 , and we see that the inflection falls at L ¼ –0.326. The astigmatic field curves are also shown and indicate that they suffer higher-order astigmatic and Petzval terms. As was mentioned in Section 11.2.1, the longitudinal distance from the Petzval surface to the tangential focal line is three times as great as the corresponding sagittal astigmatism when considering primary (Seidel) aberrations.

In a like manner, when the secondary or fifth-order Petzval occurs, the

longitudinal distance from the secondary Petzval surface to the tangential focal line is five times as great as the corresponding sagittal astigmatism.3,4,5

The field focus locations can be written as

zt ¼ ½ð3AST3 þ PTZ3ÞH2 þ ð5AST5 þ PTZ5ÞH4&=u0

H′

4.53

4.52

L

40°

30°

20°

10°

0

–0.5 0 0.5

Figure 12.10 Tentative design of a new-achromat lens. The sagittal field is the solid curve and the tangential field is the dashed curve.

It is evident that the collective interface should be made stronger to move the field inward, and a smaller Petzval sum would also be desirable. Hence for our next attempt we try c2 ¼ 0.25 and Petzval sum ¼ 0.027. The changes listed in the following table give the system that is shown in Figure 12.11.

with f 0 ¼ 9.99996, l0 ¼ 10.91516, Petzval sum ¼ 0.027, LA0 ( f/15) ¼ –0.50, and stop position ¼ –0.102. The astigmatic and distortion behavior are shown in Table 12.6.

Assuming that this is acceptable, the last step is the selection of real glasses for achromatism. A few trials, using the D – d method, indicate that the following Schott glasses would be excellent:

(a)LLF1: ne ¼ 1.55099, Dn ¼ 0.01198, V ¼ 45.47

(b)N-SK4: ne ¼ 1.61521, Dn ¼ 0.01046, V ¼ 58.37

40°

30°

20°

10°

Figure 12.11 Astigmatism of a new achromat, later form. The sagittal field is the solid curve and the tangential field is the dashed curve.