Figure 11.20 Spherochromatism of f/2.8 triplet objective.

is not a straight line indicates the presence of spherochromatism; this is shown plotted in the ordinary way in Figure 11.20. The tilt of the 20 curve at the principal-ray point (Figure 11.19) indicates the presence of lateral color, of amount about 0.0018. The lateral color found by actual ray tracing was HF0 – HC0 ¼ 0.00168, which is in excellent agreement considering the difficulty in graphically determining the exact tangent to the curve at the principal-ray point.

11.6 THE SYMMETRICAL PRINCIPLE

A fully symmetrical (holosymmetrical) system is one in which each half of the system, including the object and image planes, is identical to the other half, so that if the front half is rotated through 180 about the center of the stop it will coincide exactly with the rear half.

Such a fully symmetrical system has several interesting and valuable properties, notably complete absence of distortion and lateral color, and absence of coma for one zone of the lens. These are the three transverse aberrations, with the contributions of the front component being equal and opposite to the contributions of the rear. The two half-systems also contribute identical amounts to each of the longitudinal aberrations, but now the contributions have the same sign and add together instead of canceling out.

The reason for this cancellation of the transverse aberrations can be seen by consideration of Figure 11.21a. Any principal ray in any wavelength starting out from the center of the stop and traveling both ways to the object and image planes will intersect those planes at the same height above and below the axis, giving a magnification of exactly 1.0 over the entire field. Thus distortion and lateral color are automatically absent.

To demonstrate the absence of coma, we must trace a pair of upper and lower oblique rays in the stop both ways until they intersect each other at P

(a)

P′

Figure 11.21 Transverse aberrations of a holosymmetrical system. (a) Distortion and lateral color and (b) coma.

and P0 (Figure 11.21b). We then add a principal ray through the center of the stop at such a slope that it passes through P. Symmetry will then dictate that it will also pass exactly through P0. Hence, this one zone of the lens will be coma-free, although one cannot draw any similar conclusion for other zones of the lens. It should be noted that if there is any coma in each half of the lens, the principal ray in the stop will not be parallel to the parallel upper and lower oblique rays initially placed there. The symmetry principle is a powerful tool for the lens designer, but its limitations must be kept in mind.

DESIGNER NOTE

If the lens is symmetrical but the conjugates are not equal, then the distortion will be corrected only if the entrance and exit pupils, where the entering and emerging portions of the principal ray cross the axis, are fixed points for all possible obliquity angles.22 Similarly, lateral color will be absent if the entrance and exit pupils are fixed points for all wavelengths of light. These two conditions are often referred to as the Bow– Sutton condition. No corresponding conclusions can be drawn for coma, but it is generally found that coma is greatly reduced by symmetry, even though the conjugate distances are not equal. The point to notice is that if distortion and lateral color must be well corrected over a wide range of magnifications, as in a process lens used to copy maps, then the designer must concentrate on correcting the spherical and chromatic aberrations of the principal rays rather than on correcting the primary image, stopping the lens down if necessary to maintain the image quality. Stopping the lens down, of

course, has no effect on the aberrations of the principal ray.