Aberration of Lens

Lenses are widely used in microscopes, telescopes, spectacles and other optical instruments. It is a transparent substance of plastic or glass which is bounded by two surfaces, one or both of which may be curved. The lens works on the principle of refraction. During the formation of images by lenses, it was assumed that objects are very small in size and objects are placed very close to the principal axis of the lens. But in actual practice, these assumptions are not satisfied. So, certain defects take place. Due to these defects, the images are blurred and distorted instead of being sharp and well-defined. These types of defects are called aberrations.

Different Types of Aberrations

The deviations from the actual size, position and shape of an image as calculated by simple equations are called aberrations produced by the lens. There are two types of aberrations:

• Monochromatic Aberration: The aberration which occurs when monochromatic light is used is called monochromatic aberration.

• Chromatic Aberration: The aberration that occurs due to the dispersion of light is called chromatic aberration. Chromatic aberration is generally produced by the variation of refractive index with the colour of light.

Monochromatic aberrations are further classified into three steps:

• Spherical Aberration

• Cometic Aberration

• Astigmatism Aberration

• Distortion and Curvature of Field

Spherical Aberration

The rays refracting from different regions of the lens do not come to the same focus but are focused at different points which are known as spherical aberration. As shown in the figure given below, light rays refract when passing through the lens.

The marginal rays come to a focus at a shorter distance along the principal axis, while the paraxial rays come to a focus at a longer distance. This creates different focal points along the same axis. The focal point with the “circle of least confusion” is shown in the above figure. The focal length for paraxial rays is greater than the focal length for marginal rays and the difference in focal length of the lens for paraxial rays and marginal rays are called longitudinal spherical aberration. In spherical aberration, a single-point image is not possible at any point on the screen. The image formed in spherical aberration would always be a circle.

There are three methods by which we can reduce spherical aberration:

• By using a plano-convex or plano-concave lens with a curved side facing the incident rays.

• By using suitable stops, we can reduce spherical aberration.

• By using a parabolic mirror and by using a lens of large focal length.

Cometic Aberration

When a point object is situated away from the principal axis of the lens, then the image formed has a comet-like appearance which is shown in the figure given below. So, the deviation of an image's shape from that object is known as comatic aberration or coma. The image is comet-shaped and hence the name is given as Coma.

This aberration is similar to spherical aberration because in both cases, the lens failed to bring all the rays from an object to focus at the same point. Cometic aberration arises due to the inability of the lens to focus the central and marginal rays at the same point. Another reason is that the linear magnification produced by different zones of the lens is different for a point object situated away from the principal axis. Each zone forms the image of a point in the form of a circle known as a comatic circle.

To avoid comatic aberration,

• We must follow the abbe’s sine condition to reduce comatic aberration.

\mu _{1}h_{1}sin\theta _{1}=\mu _{2}h_{2}sin\theta _{2}

Where \mu _{1} and \mu _{2} are the refractive indices of the object and image respectively. h_{1} and h_{2} are the lengths of the object and image for a particular zone. \theta _{1} and \theta _{2} are the angles made by the rays with the axis.

• By using stops of suitable diameters, we can minimise the comatic aberration.

Astigmatism Aberration

This aberration is similar to comatic aberration because, in both aberrations, the object lies off the principal axis. In comatic aberration, the spreading of the image takes place in a plane perpendicular to the lens axis and in astigmatism, the spreading takes place along the lens axis.

Astigmatism aberration occurs due to the large difference in the angle between rays and the principal axis.

• By using a suitable combination of a convex and concave lens, astigmatism aberration can be reduced.

• With the help of suitable stops, astigmatism aberration can be reduced.

• By using the toric lens, we can reduce this aberration.

Distortion and Curvature of Field

Distortion

Distortion is also a type of monochromatic aberration which describes how the magnification in an image changes across the field of view at a fixed distance. The inability of a lens to form a flat image of a flat object is called distortion. It arises due to the fact that the magnification produced by the lens for different parts of the object is different. Because the different parts of the object are having different axial distances from the lens and that is why different parts of the object are magnified differently. By using a suitable combination of thin lenses, the distortion formed by lenses can be minimised. It can also be minimised by using suitable stops.

Curvature of Field

The image of an extended object due to a single lens is not a flat one but will be a curved surface. This effect is known as the curvature of the field. The central part of the image will be well-focused but the outer part will not be well-focused and that is why we will get a blurred image. The curvature of the field is due to the different focal lengths of the lens for paraxial and marginal rays. By using suitable convergent and divergent lenses or by using stops, we can eliminate the curvature of the field.