5.2 Spherochromatism of a Cemented Doublet

inside the paraxial focus for d light while the C light focus lies to the outside. This should be evident since the refractive index is progressively greater for C, d, and F light thereby increasing the optical power of the lens ðfl ¼ ðnl 1Þðc1 c2ÞÞ. The longitudinal axial chromatic aberration is given by L0ch ¼ LF0 LC0 (see 5.2.3) and transverse axial chromatic aberration6 is given by L0ch tan u0. A simple converging lens that is uncorrected for aberrations, as shown in Figure 5.1, is said to have undercorrected aberrations. If the sign of an aberration of the optical system is opposite to that of a simple converging lens, the lens system is said to be overcorrected. When a specific aberration is made zero or less than some desired tolerance, the lens system is said to be corrected.

5.2SPHEROCHROMATISM OF A CEMENTED DOUBLET

Consider a cemented doublet objective lens, as illustrated in Figure 5.2. The prescription of this lens, repeated from Section 2.5, is as follows:

If we now trace through it a marginal, zonal, and paraxial ray in each of five wavelengths, we obtain Table 5.1, which shows image distances expressed relative to the paraxial focus in D light.

Figure 5.2 A cemented doublet objective.

These data may be plotted in two ways. First we can plot the longitudinal spherical aberration against aperture, separately in each wavelength (Figure 5.3a); and second, we can plot aberration against wavelength for each zone (Figure 5.3b). The first set of curves represents the chromatic variation of spherical aberration, or “spherochromatism,” and the second set represents the chromatic aberration curves for the three zones. On these curves we notice several specific aberrations.

5.2.1 Spherical Aberration (LA0)

This is given by L0marginal l0paraxial in brightest (D) light. It has the value 0.0081 in this example, and is slightly overcorrected.

5.2.2 Zonal Aberration (LZA0)

This is given by L0zonal l0paraxial in D light. It has the value –0.0175, and is undercorrected. The best compromise between marginal and zonal aberration

for photographic objectives is generally to secure that LA0 þ LZA0 ¼ 0, but for visual systems it is better to have LA0 ¼ 0.

5.2.3 Chromatic Aberration (L0ch)

Figure 5.3 Spherochromatism ( f ¼ 12). (a) Chromatic variation of spherical aberration;

(b) chromatic aberration for three zones.

If no zone is specified, we generally refer to the 0.7 zonal chromatic aberration because zero zonal chromatic aberration is the best compromise for a visual system. Photographic lenses, on the other hand, are generally stopped down somewhat in use, and it is often better to unite the extreme colored foci for about the 0.4 zone instead of the 0.7 zone suggested here.