The Physics
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Opus in profectus

# Aberration

## Summary

• For an ideal image-forming optical system…
• there is a one-to-one correspondence between points in the object space and points in the image space (that is, points map to points not circles, ellipses, or blobs) and
• straight lines in the object space correspond to straight lines in the image space.
• An aberration is a departure of an image-forming optical system from ideal behavior.
• Chromatic aberrations are caused by dispersion (the variation in the index of refraction of a medium with frequency).
• Longitudinal chromatic aberration (or axial chromatic aberration) occurs because image distance varies with frequency.
• Lateral chromatic aberration (or transverse chromatic aberration) occurs because image size varies with frequency.
• Geometric aberrations are caused by geometry (the shape of a lens or mirror). They are sometimes called monochromatic aberrations because they occur even for images formed with light of a single frequency.
• Spherical aberration occurs because the focal length of a spherical lens or mirror varies with distance from the principal axis.
• Distortion is any aberration where straight lines in an object are mapped to curved lines in an image.
• Barrel distortion occurs when the magnification of an optical system decreases with distance from the principal axis. The resulting image appears to be pushed outward at the center like the image was mapped onto the outside of a sphere (or a barrel).
• Pincushion distortion occurs when the magnification of an optical system increases with distance from the principal axis. The resulting image appears to be pushed inward at the center like the image was mapped onto the inside of a sphere (or the top of a pincushion).
• Mustache distortion occurs when the magnification of an optical system decreases then increases with increasing distance from the principal axis. It is a combination of barrel distortion near the center of the image and pincushion distortion near the edges. A horizontal line near the top of the image would appear to curve down near the center and up near the edges like a handlebar mustache.
• Coma is an aberration that results in wedge shaped, or comet-like flares in images of objects that are not on the principal axis. It occurs because rays that are not parallel to the principal axis do not converge at a point.
• Astigmatism is an aberration that causes lines in any two perpendicular directions to be in focus at two different distances.
• Third order astigmatism occurs in optical systems with rotational symmetry because rays that are not parallel to the principal axis do not converge at a point.
• Astigmatism also occurs in asymmetrical optical systems that have one radius of curvature when measured in the vertical plane and another different radius of curvature when measured in the horizontal plane.
• Field curvature is an aberration that results in a curved focal plane.