12.1.3 Coma

Figure 12.2 Bending a meniscus lens (20 ). The abscissa value is measured from the anterior principal point in each case.

are measured from the front or anterior principal point in each case. The reference point for the parameter L can be the vertex of the first lens surface, the anterior principal point, or any other point the designer may select. In curve

(a) the lens is shown bent into a strongly meniscus shape, concave to the front where parallel light enters. There is a large amount of spherical undercorrection, leading to an S-shaped cubic curve, and the interesting region containing the maximum, inflection, and minimum points lies close to the lens. Placing the stop at the location denoted by a “tick mark” on the H0 L plot results in a flat tangential field (slope is zero) and no coma (zero curvature or inflection point). The distortion is negative since the Gaussian image height is 3.64.

In curve (b) of Figure 12.2, the lens is bent into such a weak meniscus shape that there is very little spherical aberration, with no maxima or minima. With the stop at the tick mark, the astigmatism is inward curving and the coma is positive. In curve (c) of the figure, a plano-convex lens with its curved face to the front is shown. There is now no coma and very little spherical aberration so that the curve is practically a straight line. The tangential astigmatic field is strongly inward curving. In the remaining graphs the lens is a meniscus with a convex side to the front, and now the interesting region has moved behind the lens, still on the concave side of the lens. Curve (d) in Figure 12.2 shows spherical aberration with no coma (inflection point) and some inward curving tangential astigmatic field. The final curve is for a stronger bending and shows stronger spherical aberration and a slight inward curving field. It will be noticed that all the graphs have about the same slope at L ¼ 0. This bears out the well-known fact that any reasonably thin lens with a stop in contact has a fixed amount of inward-curving field independent of the structure of the lens.

As a simple meniscus lens has only two degrees of freedom, namely, the lens bending and the stop position, it is clear that only two aberrations can be corrected. Invariably the two aberrations chosen are coma and tangential field curvature. The axial aberrations, spherical and chromatic, can be reduced as far as necessary by stopping the lens down to a small aperture; f/15 is common although some cameras with short focal lengths have been opened up as far as f/11. The remaining aberrations, lateral color, distortion, and Petzval sum, must be tolerated since there is no way to correct them in such a simple lens. Changes in thickness and refractive index have very little effect on the aberrations.

DESIGNER NOTE

In designing a landscape lens, one should choose a bending such that the H0 L curve is a horizontal line at the inflection point. This will ensure that the coma is corrected and the tangential field will be flat at whatever field angle was chosen for plotting the H0 L curve. Of course, the field may turn in or out at other obliquities.

12.2.1 Simple Rear Landscape Lenses

To meet the specified conditions, it is found that by interpolating between the examples shown in Figure 12.2 for a simple rear landscape lens, a front surface curvature of about –0.28 is required. With the thickness and refractive index used here, there is very little latitude. Solving the rear curvature to give a focal length of 10.0, we arrive at the 25 H 0 L curve shown in Figure 12.3. This curve indicates that the stop must be at B, a distance of 1.40 in front of the lens. At f/15 the stop diameter will be 0.667, and to cover a field of up to 30 the lens diameter

Figure 12.3 The H 0 L graph of a rear meniscus lens having a flat coma-free field (25 ).

must be about 1.80. Actually, because of excessive astigmatism, it is unlikely that this lens would be usable beyond about 25 from the axis. The lens system is

0.28

0.15 1.523

0.4645

with f 0 ¼ 10.0003, l0 ¼ 10.1445, LA0 ( f/15) ¼ –0.2725, and Petzval sum ¼ 0.0634. The astigmatism is shown in Figure 12.4 and has the values presented in Table 12.1.

If a flatter form were used, the spherical aberration would be slightly reduced and the tangential field would be inward curving. This would reduce the astigmatism, but the sagittal field is already seriously inward curving and flattening the lens would make it even worse. It therefore appears that the present design is about as good as could be expected with such a simple lens.

30°

20°

10°

0

–0.5 0

Figure 12.4 Astigmatism of a simple rear meniscus lens. The sagittal field is the solid curve and the tangential field is the dashed curve.