7.4 DESIGN OF AN APOCHROMATIC OBJECTIVE

Tracing paraxial rays in other wavelengths reveals only very small departures from the thin-lens system. These are caused by the small assumptions that were made in deriving Eq. (5-1b).

We must next achromatize for the zonal rays by use of the D – d method. For the Dn values, we use (ng – nC) because we are endeavoring to unite C, e, and g at a common focus. When this is done, the fourth curvature becomes 0.14697738, and the focal length drops to 9.7209. However, the spherical aberration is found to be þ0.35096, and we must bend the lens to the right to remove it. Repeating the design with c1 ¼ 0.6, and adding the marginal, zonal, and paraxial rays in all three wavelengths gives the spherochromatism curves shown in Figure 7.7a. Both the zonal aberration and the spherochromatism are clearly excessive, and so we adopt the device of introducing a narrow air space after the front element.

As this quickly undercorrects the spherical aberration, we return to the preceding setup, with the addition of an air space, and once more determine the last radius by the D – d method:

The spherochromatism curves are shown in Figure 7.7b, and the whole situation is greatly improved. This is about as far as we can go. Increasing the air space still further would lead to a considerable overcorrection of the zonal residual, and the result would be worse instead of better; however, if the air space is greatly increased, a different solution may be found as discussed later.

But first, it is of interest to compare this apochromatic system with a simple doublet made from ordinary glasses. An f/8 doublet was therefore designed using the regular procedure, the glasses being

The final doublet system is shown in Table 7.9. The spherochromatism curves are shown in Figure 7.7c.

Table 7.9

Prescription of f /8 Doublet Shown in Figure 7.7c

It is clear that the zonal aberration is negligible, the only real defect being the secondary spectrum. However, the effort to correct this in the three-lens apochromat has increased the zonal aberration and spherochromatism so much that it is doubtful if the final image would be actually improved thereby. An apochromat is useful only if some means can be found to eliminate the large spherochromatism that is characteristic of such systems.

7.4.3 Apochromatic Objective with an Air Lens

If the airgap is significantly increased and c2 and c3 are allowed to differ somewhat, an air lens is formed between these surfaces. By using a computer optimization program to achromatize the lens for g and C spectral lines, correct secondary spectrum using g and e spectral lines, correct marginal and zonal spherical aberration in the e spectral lines, and correct marginal spherochromatism for g and C spectral lines, diffraction-limited performance can be obtained. A representative lens is shown in Figure 7.8 that operates at f/8 and has the following prescription:

Figure 7.8 Layout of an f/8 apochromatic triplet objective lens having axial diffraction-limited performance and showing ray paths for axial, 1 , 2 , and 3 extraaxial object points.

The glasses used in this example are Schott N-FK51, N-KZFS4, and N-SF15, respectively. Figure 7.9 illustrates the achievable wide spectral bandwidth for this apochromatic triplet objective. Notice the characteristic shape of the central portion of the plot and the rapid chromatic undercorrection at each end of the spectral bandwidth.

The longitudinal meridional ray errors for light from 440 nm to 700 nm in steps of 20 nm is shown in Figure 7.10. The optimization criteria mentioned above yielded a highly corrected lens system. As can be seen, the marginal and axial chromatic error is negligible while some zonal aberration remains, although it is quite small. The spherochromatism comprises primary, secondary, and tertiary components having signs of minus, plus, and minus, respectively. Also, notice that the intercepts of the plots are wavelength dependent, which means that an amount of positive and negative zonal aberrations for each plot are wavelength dependent. The amount of positive and negative zonal aberrations for the e spectral line is essentially balanced (see arrow in Figure 7.10).

Does this apochromatic objective have excellent performance just on axis or does it have a useful field-of-view? Figure 7.11 presents the transverse ray fans for axial, 1 , 2 , and 3 extraaxial object points. The off-axis behavior will be discussed in later chapters, but recalling the discussions in Chapter 4, it is evident that (1) the lateral chromatic aberration grows as the field angle increases,

(2) negative coma is dominant at 1 with very slight negative linear astigmatism, and (3) linear astigmatism is beginning to become dominant by 3 . The