Astigmatism - A General Overview

In optics, astigmatism is when an optical system has different foci for rays that propagate in two perpendicular planes. If an optical system with astigmatism is used to form an image of a cross, the vertical and horizontal lines will be in sharp focus at two different distances.

There are two distinct forms of astigmatism. The first is a third-order aberration, which occurs for objects (or parts of objects) away from the optical axis. This form of aberration occurs even when the optical system is perfectly symmetrical. This is often referred to as a "monochromatic aberration", because it occurs even for light of a single wavelength. This terminology may be misleading, however, as the amount of aberration can vary strongly with wavelength in an optical system.

                  

The second form of astigmatism occurs when the optical system is not symmetric about the optical axis. This may be by design (as in the case of a cylindrical lens), or due to manufacturing error in the surfaces of the components or misalignment of the components. In this case, astigmatism is observed even for rays from on-axis object points. This form of astigmatism is extremely important in ophthalmology, since the human eye often exhibits this aberration due to imperfections in the shape of the cornea or the lens.

                  

In the analysis of this form of astigmatism, it is most common to consider rays from a given point on the object, which propagate in two special planes.

The first plane is the tangential plane. This is the plane which includes both the object point being considered and the axis of symmetry. Rays that propagate in this plane are called tangential rays. Planes that include the optical axis are meridional planes. It is common to simplify problems in radially-symmetric optical systems by choosing object points in the vertical ("y") plane only. This plane is then sometimes referred to as the meridional plane.

The second special plane is the sagittal plane. This is defined as the plane, orthogonal to the tangential plane, which contains the object point being considered and intersects the optical axis at the entrance pupil of the optical system. This plane contains the chief ray, but does not contain the optic axis. It is therefore a skew plane, in other words not a meridional plane. Rays propagating in this plane are called sagittal rays.