Editing Optical aberration (section)

====Aberration of elements, i.e. smallest objects at right angles to the axis====
If rays issuing from {{mvar|O}} ('''Figure 1''') are concurrent, it does not follow that points in a portion of a plane perpendicular at {{mvar|O}} to the axis will be also concurrent, even if the part of the plane be very small.  As the diameter of the lens increases (i.e., with increasing aperture), the neighboring point {{mvar|N}} will be reproduced, but attended by aberrations comparable in magnitude to {{mvar|ON}}. These aberrations are avoided if, according to Abbe, the ''sine condition'', {{math|1= sin ''{{prime|u}}''{{sub|1}}/sin ''u''{{sub|1}} = sin ''{{prime|u}}''{{sub|2}}/sin ''u''{{sub|2}}}}, holds for all rays reproducing the point {{mvar|O}}. If the object point {{mvar|O}} is infinitely distant, {{math|''u''{{sub|1}}}} and {{math|''u''{{sub|2}}}} are to be replaced by {{math|''h''{{sub|1}}}} and {{math|''h''{{sub|2}}}}, the perpendicular heights of incidence; the ''sine condition'' then becomes {{math|1= sin ''{{prime|u}}''{{sub|1}}/''h''{{sub|1}} = sin ''{{prime|u}}''{{sub|2}}/''h''{{sub|2}}}}. A system fulfilling this condition and free from spherical aberration is called ''aplanatic'' (Greek {{Transliteration|grc|a-}}, privative; {{Transliteration|grc|plann}}, a wandering).  This word was first used by [[Robert Blair (astronomer)|Robert Blair]] to characterize a superior achromatism, and, subsequently, by many writers to denote freedom from spherical aberration as well.<ref name=EB1911/>

Since the aberration increases with the distance of the ray from the center of the lens, the aberration increases as the lens diameter increases (or, correspondingly, with the diameter of the aperture), and hence can be minimized by reducing the aperture, at the cost of also reducing the amount of light reaching the image plane.