For the sagittal plane, the extreme rays are symmetric with respect to the central ray. Oblique astigmatism arises not from any asymmetry of the lens, but an asymmetry in the nature of the optical paths followed by rays in the tangential and sagittal planes. Similar treatments can be found in Pedrotti & Pedrotti, Sec 5-5 and Hecht, 2nd Ed Sec 6.3. This visualization of oblique astigmatism follows the treatment of Jenkins and White in their text "Fundamentals of Optics", 4th. Oblique astigmatism is an aberration of off-axis rays that causes radial and tangential lines in the object plane to focus sharply at different distances in the image space. But even spherical lenses that are perfectly symmetrical exhibit a type of astigmatism for light which approaches the lens from a point off the optic axis. The kind of astigmatism commonly encountered as a vision defect is a result of different lens curvatures in different planes. A more general type of astigmatism, which occurs for off-axis rays through any spherically ground lens, is called oblique astigmatism. But if the focal length of the lens is different for different planes of incident light, there will be no point where all the rays from the object reach a sharp focus. If the behavior of light from a point source object is examined, then for a perfect lens it should form a focused bright spot on the opposite side of the lens. Coma can also be corrected by an appropriately placed stop, but the placement and size of an optimum stop also depends upon the other aberrations. The appropriate separation of these two lenses can correct for coma at various object distances. That lens would not be optimum for other object distances.įor more versatile correction of coma, one can use a combination of two lenses, both of which are corrected for zero coma at infinite object distance. That encourages the picturing of this image as comet-like.Ĭoma is shape-dependent, so a lens shape can be found with zero coma for a given object distance. Hecht notes that a little more than half of the light in the image is in the roughly triangular region inside the large oval above, so the image fades as it expands away from the central focus. For positive coma, rays from an off-axis object through larger radii of the lens contribute a larger oval of light further from the principal focus.
Hecht, 2nd Ed in Sec 6.3 on aberrations gives a careful discussion of coma. More complete correction can be achieved by using a combination of lenses symmetric about a central stop. For a single lens, coma can be partially corrected by bending the lens. A lens with considerable coma may produce a sharp image in the center of the field, but become increasingly blurred toward the edges. Coma is an aberration which causes rays from an off-axis point of light in the object plane to create a trailing "comet-like" blur directed away from the optic axis (for positive coma).
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