Anastigmat

ANASTIGMAT, a lens consisting of several lenses and possessing the property of producing a sharp, undistorted image even of those points that lie

Figure 1. Old form of spectacle lens.

far from the optical axis. Ordinary optical lenses suffer from a defect called astigmatism (see), which consists in the fact that images of points lying far from the optical axis are stretched into lines. Anastigmatic lenses are lenses in which 'oblique astigmatism' is to a certain extent eliminated. Biconvex and biconcave lenses, the most common even today for the correction of ametropic eyes, have a very major defect, because they provide good vision only when the eye looks perpendicularly through the center of the lens. However, when the eye rotates behind the lens, when one begins to look through the lens obliquely (see Figure 1), vision is severely impaired due to the resulting 'oblique astigmatism.' The further the eye moves from the center during this rotation behind the stationary lens, and the stronger the refractive power of the lens, the greater will be the degree of 'oblique astigmatism' and, consequently, the worse the vision will be. For a biconvex lens of 6 D, when looking through its edge, this astigmatism reaches a huge value of 4.81 D. A plano-convex lens of the same power will have a slightly smaller astigmatism: 2.13 D; however, it is still very large. Therefore, the task of modern optics is to find such forms of lenses that would provide good images even when looking through them obliquely; in other words, the center of rotation of the eye must be taken into account, which remains stationary during all rotations of the eye and is located approximately 25 mm from the back surface of the corrective lens. (The distance from the back surface of the lens to the apex of the cornea is, on average, 12 mm, and from the cornea to the center of rotation is 13 mm). Lenses in which 'oblique astigmatism' is eliminated, i.e., anastigmatic lenses, usually have the shape of convex-concave lenses (see Figure 2), and if the convex surface of the lens has a steeper radius, then the entire lens will act as a convex lens, equal in power to the difference between the refraction of the convex and concave surfaces; if the concave surface has a steeper radius of curvature, then the entire lens will act as a concave lens. Already periscopic lenses, one surface of which always has one

Figure 2. New form of spectacle lens.

and the same fixed radius of curvature of 40 cm, possess less 'oblique astigmatism': for the specified lens of 6 D, it will equal 1.48 D; of course, this value is still significant. Much better are the so-called 'semi-shell' lenses (Halbmuschelgläser), also having, similar to periscopic lenses, one fixed radius of curvature, but a steeper one - 9 cm; for a +6 D lens, the 'oblique astigmatism' at the edge will be only 0.15 D. However, only the 'punctual' lenses of Ostwald (flatter) and Wollaston (more curved) (see Figure 3) can be considered completely satisfactory; they do not have a fixed radius of curvature, and for each lens of the required refractive power, both radii of curvature are determined separately. For the same +6 D lens, the 'oblique astigmatism' at the edge will equal only 0.03-0.02 D. These lenses are produced by various firms under various names: 'Punctalgläser' by Zeiss, 'Isokrystar' by Busch, 'En-Gee Menisken' by Nitsche u. Günther, and many others. Such lenses can be manufactured up to -25 D and +7.5 D. Thus, the extreme limit

Wollaston

for concave lenses is quite sufficient. As for convex lenses, here this extreme limit will also usually be sufficient for cases of congenital hypermetropia; however, for the correction of aphakics, where stronger convex lenses are required, these lenses cannot satisfy, and one has to resort either to combinations consisting of several lenses—at least 2 (by the way, this system is little used) or to prescribe aspheric lenses (see).