Figure 13.15 Ray fans (a) for on-axis and (b) and (c) for 5 mm off-axis. Ordinate scales are0.1 mm. Solid curves ¼ F light, short dashed curves ¼ d light, and long dashed curves ¼ C light.

designer is often faced in practice with the design of an entire system rather than just simply a lens. In the example relay lens given by Altman and Kingslake, they designed it as part of an overall system. The lateral color of the system was well corrected for all zones. To accomplish this, the eyepiece was allowed to have moderately large residual undercorrected lateral color, which was matched by opposite lateral color in the rest of the system. The objective lens was well corrected since a color-free image was desired at the reticle.

In this particular system, the prism system needed to be placed between the reticle and the relay lens, which made correction more difficult than if the prism system had been placed following the relay lens. To achieve a balance in the lateral color, they found it necessary to make the rear element of the relay lens from a very-high dispersion dense flint glass and the front lens from a very-low dispersion crown glass. It also required the refractive index of these outer lenses to be markedly different, which caused serious zonal spherical aberration, spherochromatism, and coma; however, the novelty of the use of the meniscus elements in each negative triplet provided a means to achieve excellent correction. Reading of their patent is encouraged by those interested in further design details.

13.5DOUBLE-GAUSS LENS WITH AIR-SPACED NEGATIVE DOUBLETS

The basic Gauss lens that was shown in Figure 13.10 can be improved by replacing the negative lenses with air-spaced negative doublets and the rear positive element with a cemented doublet as illustrated in Figure 13.16.12 This 100-mm focal length lens is well corrected at f/2 operating at unity magnification. The purpose of this lens was for printing on a film that is sensitive to a particular wavelength of blue light, say 435.8 nm. Consequently, chromatic correction was

Figure 13.16 Unity-magnification Double-Gauss lens with air-spaced negative doublets.

not of particular importance except that it was desirable to achromatize the lens for blue and green light where the green light was used for alignment of the system. A typical structure is as follows:

66.300

17.42 1.75510 47.2

192.96

2.23

46.049

108.97

2.36

352.51

10.06 1.69873 30.1

33.510

Stop

5.460

5.460

33.285

12.15 1.61633 31.0

252.60

2.18

133.01

4.63 1.69680 56.2

50.695

0.51

138.25

10.95 1.68235 48.2

37.751

1.41 1.62032 60.3

79.381

The principal invention of this lens structure is the use of a pair of negative doublets, located about a central stop, with each having a strong negative air lens (see Section 7.4.3). All of the elements in this lens use high refractive index glasses and large thicknesses to simplify correction of aberrations by using weaker surfaces. Examination of Figure 13.17 shows that the spherical aberration is undercorrected and that the axial image quality can benefit by moving the image plane slightly toward the lens by an amount of 85 mm.

The astigmatic field curves in Figure 13.18a show that they intersect at 5, which implies that this is essentially the limit of the useful field-of-view. These field curves are also inward curving, which is advantageous to enhance the off-axis resolution since the axial refocus is inward toward the lens. Figure 13.19a presents the axial ray fan after refocus. Inspection of this plot shows that the spherical aberration contains at least third-, fifth-, seventh-, and ninth-order spherical aberration.

The off-axis ray fans, when refocused is invoked, are shown in Figure 13.19b and Figure 13.19c. Figure 13.18b illustrates that the distortion is triflingly small. The patent suggests that this lens can resolve over 400 lines per mm

M

Z

Figure 13.17 Longitudinal aberration focused at the paraxial focal point; the abscissa is in lens units.

Figure 13.18 Field curvature and distortion. The abscissa for the field curve (a) is in lens units and distortion (b) is in percentage points.

Figure 13.19 Ray fans (a) for on-axis and (b) and (c) for 5 off-axis when lens has been refocused by 0.085 mm with respect to the paraxial focus. Ordinate scales are 0.01 mm.

(200 line-pairs per mm). Figure 13.20 shows the MTF for a diffraction-limited f/ 2 lens, the axial MTF, and the MTF for an object 5 off axis. It is evident that the lens is nearly diffraction-limited on-axis with excellent sagittal off-axis performance and somewhat degraded tangential off-axis performance at the edge of the field of view.