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Astigmatism

Astigmatism, similar to coma, is the aberration in the image formed by a lens, of object points off the axis. The differences between astigmatism and coma, however, is that in coma the spreading of the image takes place in a plane perpendicular to the lens axis and in astigmatism the spreading takes place along the lens axis. Astigmatism discussed in this article is different from the one treated in defective vision.

Fig. illustrates the defect of astigmatism in the image of a point B situated off the axis. Two portions of the cone of rays of light diverging from the point B are taken. The cone of the rays of light refracted through the tangential (vertical) plane BMN comes to focus at a point P₁ nearer the lens and the cone of rays refracted through the sagittal (horizontal) plane BRS comes to focus at the P₂ away from the lens. All rays pass through a horizontal line passing through P₁ called the primary image and also through a vertical line passing through P₂ called the secondary image. The refracted beam has an elliptical cross-section which ends to a horizontal line at P₁ and a vertical line at P₂. The cross-section of the refracted beam is circular at some point between the primary and the secondary images and this is called the circle of least confusion. If a screen is held perpendicular to the refracted beam between the points P₁ and P₂, the shape of the image at different positions is as shown in fig.

The focus of the primary images of all points in the object plane gives the surface of revolution about the lens axis and is called the primary image surface. Similarly, the locus of the secondary images gives the secondary image surface. The surface of best focus is given by the locus of the circles of least confusion. The primary and the secondary image surfaces and the surface of best focus are illustrated in fig. P₁ and P₂ are the images of the object point B. TPN and SPR are the first and the second image surfaces touch at the point P on the axis. Generally, the surfaces of the best focus is not plane but curved as shown. This defect is called the curvature of the field. The shape of the image surfaces depends on the shape of the lens and the position of the stops. If the primary image surface is to the left of the secondary image surface, astigmatism and a concave lens of suitable focal lengths and separated by a distance, it is possible to minimize the astigmatic difference and such a lens combination is called an anastigmat.