Page "Optical aberration" Paragraph 24

If rays issuing from O ( fig.

5 ) be concurrent, it does not follow that points in a portion of a plane perpendicular at O to the axis will be also concurrent, even if the part of the plane be very small.

With a considerable aperture, the neighboring point N will be reproduced, but attended by aberrations comparable in magnitude to ON.

These aberrations are avoided if, according to Abbe, the sine condition, sin u ' 1 / sin u1 = sin u ' 2 / sin u2, holds for all rays reproducing the point O.

If the object point O is infinitely distant, u1 and u2 are to be replaced by h1 and h2, the perpendicular heights of incidence ; the sine condition then becomes sin u ' 1 / h1 = sin u ' 2 / h2.

A system fulfilling this condition and free from spherical aberration is called aplanatic ( Greek a -, privative, plann, a wandering ).

This word was first used by Robert Blair ( d. 1828 ), professor of practical astronomy at Edinburgh University, to characterize a superior achromatism, and, subsequently, by many writers to denote freedom from spherical aberration.

Both the aberration of axis points, and the deviation from the sine condition, rapidly increase in most ( uncorrected ) systems with the aperture.