Editing Optical aberration (section)

===Aberration of lateral object points (points beyond the axis) with narrow pencils — astigmatism===
{{Main|Astigmatism (optical systems)}}
{{For |Astigmatism of the eye|Astigmatism}}

[[File:ABERR2.svg|right|frame|'''Figure 2''']]

A point {{mvar|O}} ('''Figure 2''') at a finite distance from the axis (or with an infinitely distant object, a point which subtends a finite angle at the system) is, in general, even then not sharply reproduced if the pencil of rays issuing from it and traversing the system is made infinitely narrow by reducing the aperture stop; such a pencil consists of the rays which can pass from the object point through the now infinitely small entrance pupil.  It is seen (ignoring exceptional cases) that the pencil does not meet the refracting or reflecting surface at right angles; therefore it is astigmatic (Greek {{Transliteration|grc|a-}}, privative; {{Transliteration|grc|stigmia}}, a point).  Naming the central ray passing through the entrance pupil the ''axis of the pencil'' or ''principal ray'', it can be said: the rays of the pencil intersect, not in one point, but in two focal lines, which can be assumed to be at right angles to the principal ray; of these, one lies in the plane containing the principal ray and the axis of the system, i.e. in the ''first principal section'' or ''meridional section'', and the other at right angles to it, i.e. in the second principal section or sagittal section.  We receive, therefore, in no single intercepting plane behind the system, as, for example, a focusing screen, an image of the object point; on the other hand, in each of two planes lines {{mvar|{{prime|O}}}} and {{mvar|{{pprime|O}}}} are separately formed (in neighboring planes ellipses are formed), and in a plane between {{mvar|{{prime|O}}}} and {{mvar|{{pprime|O}}}} a circle of least confusion.  The interval {{mvar|{{prime|O}}{{pprime|O}}}}, termed the astigmatic difference, increases, in general, with the angle {{mvar|W}} made by the principal ray {{mvar|OP}} with the axis of the system, i.e. with the field of view.  Two ''astigmatic image surfaces'' correspond to one object plane; and these are in contact at the axis point; on the one lie the focal lines of the first kind, on the other those of the second.  Systems in which the two astigmatic surfaces coincide are termed anastigmatic or stigmatic.<ref name=EB1911/>

[[Isaac Newton|Sir Isaac Newton]] was probably the discoverer of astigmation; the position of the astigmatic image lines was determined by Thomas Young;<ref>Young, Thomas (1807), ''A Course of Lectures on Natural Philosophy.''</ref> and the theory was developed by [[Allvar Gullstrand]].<ref>Gullstrand, Allvar (1890) ''Skand. Arch. f. Physiol.''; and (1901) ''Arch. f.  Ophth.'', 53, pp. 2, 185.</ref><ref name="gullstrand1900"/><ref name=EB1911/>  A bibliography by P. Culmann is given in Moritz von Rohr's ''Die Bilderzeugung in optischen Instrumenten''.<ref name=vonRohr>{{cite book |first=Moritz |last=von Rohr |author-link=Moritz von Rohr |title=Die bilderzeugung in optischen Instrumenten vom Standpunkte der geometrischen Optik |location=Berlin |date=1904}}</ref><ref name=EB1911/>