Optics 101

# Astigmatism in Optical Systems

An optical system that exhibits astigmatism focuses two orthogonal axes of light at two different distances. In other words, astigmatism is an optical aberration that causes rays to propagate in two perpendicular planes with two different foci.

The name of this aberration is derived from the Greek words ‘a’, meaning without, and ‘stigma’, meaning a spot or puncture.

Astigmatic aberrations are similar to comatic aberrations and are caused mainly due to the oblique angle of the light beam. Astigmatism occurs when the off-axis image of a point object appears as a line or an ellipse. The angle of the off-axis rays causes the line image to be either tangentially or sagittally oriented. As we move away from the center the detail, contrast, and size of the image will reduce.

## Occurrence of Astigmatism

Astigmatism occurs in the outer portions of the field of view in uncorrected lenses. Astigmatism mainly occurs in cylindrical lenses and in holograms. The tangential plane consists of the chief ray and the optical axis of the lens, while the sagittal plane is perpendicular to this plane and consists only of the chief ray.

In a system devoid of astigmatism, the chief ray will pass through the center of the aperture and exit through the pupil of the lens. In a system with aberrations, the tangential and sagittal planes are refracted slightly, and both the rays intersect the chief ray at different points, producing an elongated image.

## Types of Astigmatism

There are basically two forms of astigmatism, third order aberration, and non-symmetric axis aberration.

Third order aberration occurs for objects that are away from the optical axis, and for a light of a single wavelength. The extent of aberration depends on the angle between the rays from the object and optical axis of the system.

Astigmatism in systems that are not rotationally symmetric occur due to the misalignment of components. This aberration is observed mainly in telescopes.

## Correction of Astigmatism

Astigmatic errors can be corrected by proper design of objectives, such that there is proper spacing of individual lens elements. The shapes and refractive indices of lenses and the aperture sizes need to be appropriately chosen for correcting astigmatism.

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