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Thermodynamics

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Comatic Aberration

The effect of rays from an object point not situated on the axis of the lens results in an aberration called coma. Comatic aberration is similar to spherical aberration in that both are due to the failure of the lens to bring all rays from a point object to focus at the same point. Spherical aberration refers to object points situated on the axis whereas comatic aberration refers to object points situated off the axis. In the case of spherical aberrations, the image is a circle of varying diameter along the axis and in the case of comatic aberration the image is comet-shaped and hence the name coma. Fig. 1, illustrates the effect of coma. The resultant image of a distant point off the axis is shown in the side figure. The rays of light in the tangential plane are represented in the figure.

Fig. 2, illustrates the presence of coma in the image due to a point object situated off the axis of the lens. Rays light getting refracted through the centre of the lens (ray I) meets the screen XY at the point P. Rays 2, 2 ; 3, 3 etc. getting refracted through the outer zones of the lens come to focus at points Q, R, S etc. nearer the lens and on the screen overlapping circular patches of gradually increasing diameter are formed. The resultant image of the point is comet-shaped as indicated in the side figure.

Let 1, 2, 3 etc. be the various zones of the lens. Rays of lights refracted through these different zones give rise to circular patches of light 1’, 2’, 3’ etc. The screen is placed perpendicular to the axis of the lens and the at the position where the central rays come to focus. Like spherical aberration comatic aberration produced by a single lens can also be corrected by properly choosing the radii of curvature of the lens surfaces. Coma can be altogether eliminated for a given pair of object and image points whereas spherical aberration cannot be completely corrected. Further, a lens corrected for coma will not be free from spherical aberration and the one corrected for spherical aberration will not be free from coma. Use of a stop or a diaphragm at the proper position eliminates coma.

Coma is the result of varying magnification for rays refracted through different zones of the lens. For example, rays of light getting refracted through the outer zones come to focus at points nearer the lens. Hence the magnification of the image due to the outer zones is smaller than the inner zones and in this case coma is said to be negative. On the other hand if the magnification produced in an image due to the outer zones is greater, coma is said to be positive.

According to Abbe, a German optician, coma can be eliminated if a lens satisfies the Abbe’s since condition viz.

₁y₁ sin θ₁ refer to the refractive index, height of the object above the axis and the slope angle of the incident ray of light. Similarly, ₂, y₂ and θ₂ refer to the corresponding quantities in the image medium. The magnification of the image is given by y2/y1

Elimination of coma is possible if the lateral magnification y₂/y₁ is the same for all rays of light, irrespective of the slope angles θ₁ and θ₂. Thus, coma can be eliminated if, sin θ₁/sin θ₂ is a constant because ₁/ ₂ is constant. A lens, that satisfies the above condition is called an aplanatic lens.