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# 4: Optical Aberrations

• 4.1: Introduction to Optical Aberrations
We have hitherto made the assumption that a lens or a curved mirror is able to form a point image of a point object. This may be approximately true if the depth of the mirror or the thickness of the lens is small compared with other distances, and if the angle that all rays make with axis of the mirror or lens is small, and if we are using monochromatic light. Usually none of these conditions is satisfied exactly, and consequently the image suffers from several aberrations.
• 4.2: Spherical Aberration
Spherical aberration is found in optical systems that use elements with spherical surfaces.
• 4.3: Astigmatism
In Greek, stigma means a mark - in particular the mark made by the prick of a pointed instrument. An ideal optical instrument produces an image of a point source, which is also a point. If the image is not a point, then it is astigmatic. However, the use of the word astigmatic to describe an image of a point source that is not also a point is restricted to the kind of optical aberration described in this section.
• 4.4: Coma
Coma, like astigmatism, is another aberration that appears off axis, near the edge of an image field.
• 4.5: Curvature of Field
In designing a lens or lens system, the problems of astigmatism and curvature of field are often closely related. For example a meniscus lens tends to suffer from astigmatism, and there is a focal surface for the tangential image, and a focal surface for the sagittal image, and the tangential and sagittal surfaces curve in opposite senses.
• 4.6: Distortion
The magnification of an image is image distance divided by object distance, and image distance is different off-axis than on-axis, so the image magnification varies with distance from the axis. If this distortion is quite small, it may not be noticed in ordinary pictorial photography, but if one is using a photograph for precise positional measurements (for example, in astrometry) it is necessary to correct for the distortion.

Thumbnail: Coma. Image used with permission (CC BY-SA 3.0; HHahn).