The aberrations of the third order are: (1) aberration of the axis point; (2) aberration of points whose distance from the Aberra- axis is very small, less than of the third order - the tions of deviation from the sine condition and coma here fall together in one class; (3) astigmatism; (4) curvature of the field; (5) distortion.
These anastigmatic lenses, which are manufactured up to X 40, are chromatically and spherically corrected, and for a middle diaphragm the errors of lateral pencils, distortion, astigmatism and coma are eliminated.
The image is greatly affected with astigmatism; but this is of little consequence, if y in (8) be small enough.
The correction of astigmatism is in many cases a matter of considerable difficulty, but the results to vision almost always reward the trouble.
Airy, the astronomer, about 1827, corrected his own astigmatism by means of a cylindrical lens.
If measures are made by placing the image of a star in the centre of the disk of a planet, the observer may have a tendency to do so systematically in error from some acquired habit or from natural astigmatism of the eye.
(4) After eliminating the aberration on the axis, coma and astigmatism, the relation for the flatness of the field in the third order is expressed by the " Petzval equation," I 1 = o, where is the radius of a refracting surface, n and n' the refractive indices of the neighbouring media, and / the sign of summation for all refracting surfaces.
The same holds for the errors depending upon the angle of the field of view, w: astigmatism, curvature of field and distortion are eliminated for a definite value, w*; " zones of astigmatism, curvature of field and distortion " attend smaller values of w.
(2) Largest field of view; necessary corrections are - for astigmatism, curvature of field and distortion; errors of the aperture only slightly regarded; examples - photographic widest angle objectives and oculars.
Photog., 1891, 5, p. 225; 18 93, 7, p. 221), cemented objectives of thin lenses permit the elimination of spherical aberration on the axis, if, as above, the collective lens has a smaller refractive index; on the other hand, they permit the elimination of astigmatism and curvature of the field, if the collective lens has a greater refractive index (this follows from the Petzval equation; see L.
To eliminate distortion and astigmatism when the centre of rotation of the eye coincided with the point where the principal rays crossed the axis.
In astigmatism, owing to differences in the refractive power of the various meridians of the eye, great defect of sight, frequently accompanied by severe headache, occurs.
To), and does not influence the definition at the (primary) focus, although it may introduce astigmatism.'