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In spherical aberration, rays of light from a point on the optical axis of a lens having spherical surfaces do not all

meet at the same image point. Rays passing through the lens close to its centre are focused farther away than rays

passing through a circular zone near its rim. For every cone of rays from an axial object point meeting the lens,

there is a cone of rays that converges to form an image point, the cone being different in length according to the

diameter of the circular zone. Wherever a plane at right angles to the optical axis is made to intersect a cone, the

rays will form a circular cross section. he area of the cross section varies with distance along the optical axis, the

smallest size !nown as the circle of least confusion. he image most free of spherical aberration is found at this

distance.

Coma,so called because a point image is blurred into a comet shape, is produced when rays from an off"axis object

point are imaged by different zones of the lens. In spherical aberration, the images of an on"axis object point that fall

on a plane at right angles to the optical axis are circular in shape, of varying size, and superimposed about acommon centre# in coma, the images of an off"axis object point are circular in shape, of varying size, but displaced

with respect to each other. he accompanying diagramshows an exaggerated case of two images, one resulting

from a central cone of rays and the other from a cone passing through the rim. he usual way for reducing coma is

to employ a diaphragm to eliminate the outer cones of rays.

Astigmatism,unli!e spherical aberration and coma, results from the failure of a single zone of a lens to focus the

image of an off"axis point at a single point. $s shown in the three"dimensionalschematicthe two planes at right

angles to one another passing through the optical axis are the meridian plane and the sagittal plane, the meridian

plane being the one containing the off"axis object point. Rays not in the meridian plane, called s!ew rays, are

focused farther away from the lens than those lying in the plane. In either case the rays do not meet in a point focus

but as lines perpendicular to each other. Intermediate between these two positions the images are elliptical in

shape.

Curvature of fieldand distortionrefer to the location of image points with respect to one another. %ven though the

former threeaberrations may be corrected for in the design of a lens, these two aberrations could remain. In

curvature of field, the image of a plane object perpendicular to the optical axis will lie on a paraboloidal surface

called the &etzval surface'after ()zsef &etzval, a *ungarian mathematician+. Flat image fields are desirable in

photography in order to match the film plane and projection when the enlarging paper or projection screen lie on a

flat surface. istortion refers to deformation of an image. here are two !inds of distortion, either of which may be

present in a lens- barrel distortion,in which magnification decreases with distance from the axis, andpincushion

distortion, in which magnification increases with distance from the axis.

pherical Aberration: this is the aberration affecting rays from a point on the optical axis;

because rays from this point going out in different directions pass through different parts of
http://www.britannica.com/EBchecked/topic/559630/spherical-aberrationhttp://www.britannica.com/EBchecked/topic/127208/comahttp://www.britannica.com/EBchecked/topic/127208/comahttp://www.britannica.com/EBchecked/media/62038/http://www.britannica.com/EBchecked/topic/39798/astigmatismhttp://www.britannica.com/EBchecked/media/62039/http://www.britannica.com/EBchecked/media/62039/http://www.britannica.com/EBchecked/topic/147238/curvature-of-fieldhttp://www.britannica.com/EBchecked/topic/166143/distortionhttp://www.britannica.com/EBchecked/topic/454658/Petzval-curvaturehttp://www.britannica.com/EBchecked/topic/54025/barrel-distortionhttp://www.britannica.com/EBchecked/topic/54025/barrel-distortionhttp://www.britannica.com/EBchecked/topic/460859/pincushion-distortionhttp://www.britannica.com/EBchecked/topic/460859/pincushion-distortionhttp://www.britannica.com/EBchecked/topic/127208/comahttp://www.britannica.com/EBchecked/media/62038/http://www.britannica.com/EBchecked/topic/39798/astigmatismhttp://www.britannica.com/EBchecked/media/62039/http://www.britannica.com/EBchecked/topic/147238/curvature-of-fieldhttp://www.britannica.com/EBchecked/topic/166143/distortionhttp://www.britannica.com/EBchecked/topic/454658/Petzval-curvaturehttp://www.britannica.com/EBchecked/topic/54025/barrel-distortionhttp://www.britannica.com/EBchecked/topic/460859/pincushion-distortionhttp://www.britannica.com/EBchecked/topic/460859/pincushion-distortionhttp://www.britannica.com/EBchecked/topic/559630/spherical-aberration


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the lens, then, if the lens is spherical, or otherwise not the exact shape needed to bring them

all to a focus, then these rays will not all be focused at the same point on the other side of the

lens.

Coma: this aberration affects rays from points off the optical axis. If spherical aberration is

eliminated, different parts of the lens bring rays from the axis to the same focus. But the

place where the image of an off-axis point is formed may still change when different parts of

the lens are considered.

Astigmatism: this is another aberration affecting rays from a point off the optical axis. These

rays, as they head through the lens to the point in the image where they will be focused, pass

through a lens that is, from their perspective, tilted. ven if neither spherical aberration nor

coma prevents them from coming to a sharp focus, if we consider the rays of light that are in

the plane of the tilt, and the rays of light that are in the plane perpendicular to that, these rays

pass through a part of the lens with a different profile. !o they may not be focused at the

same distance from the lens, even if they do come to a focus in each case.

Curvature of Field: even when light from every point in the ob"ect is brought to a sharpfocus, the points at which they are brought into focus might lie on a curved surface instead of

a flat plane.

Distortion: even when all the previous aberrations have been corrected, the light from points

in the ob"ect might be brought together on the image plane at the wrong distance from the

optical axis, instead of being linearly proportional to the distance from the optical axis in the

ob"ect. If distance increases faster than in the ob"ect, one has pincushiondistortion, if more

slowly, barreldistortion.

Distortion

#istortion represents the inability of a lens to create a rectilinear image of the sub"ect. It does not modify

the colors or the sharpness of the image but rather its shape. This distorsion happens because the focal

length of the lens varies over the $et%val surface &transverse magnification' and as parts of the image aremore magnified than others. #istortion occurs in two main effects : barrel and pincushion, also called

positive and negative distortion.

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