Refractors: Astigmatism
 
A lens system which has been corrected for both spherical aberration and coma may not be free from aberration completely, especially when images are formed of objects which are at a considerable distance from the optic axis. Such images may suffer from astigmatism. The effect of astigmatism is illustrated in figure 1. The position of the focus depends on which section of the lens is used to form the image. The spread in the position of the image lies between two points which correspond to the image position for rays in the plane formed by the point object and the optic axis (i.e. the tangential plane) and to the image position for rays in the plane at right angles to this (i.e. the sagittal plane).

Figure 1. Points T and S represent the foci of rays passing through the tangential and sagittal planes of a lens; the spread of the astigmatic image lies between the points T and S.
Between these points there is a position where the smallest image can be found and again this image is known as the circle of least confusion.
By examining the images produced by objects with a range of distances from the optic axis, it is possible to record the surfaces on which the focus, T , of the rays of the tangential plane and the focus, S, of the rays of the sagittal plane lie. They are found to approximate to paraboloids of revolution.
A single achromatic combination is likely to exhibit appreciable astigmatism. However, the combination of two achromats at the correct spacing can provide a paraboloidal surface containing both the T and S images. This surface is known as the Petzval surface, after the investigator of this property