Question

State and explain Rayleigh's criterion.

Answer 1

The Rayleigh Criterion. The Rayleigh criterion is the generally acceptedcriterion for the minimum resolvable detail - the imaging process is said to be diffraction-limited when the first diffraction minimum of the image of one source point coincides with the maximum of another.

Answer 2

When a point object is imaged using a circular aperture such as the lens or the iris of our eye, the image produced is not a point, rather a diffraction pattern. This is true, mainly when the size of the object is comparable to the wavelength of light.

A circular aperture creates a diffraction pattern of concentric rings that grow dimmer as we move away from the centre. These are known as Airy discs.

Consider the diffraction pattern for a circular aperture as shown in the figure below.

Rayleigh Criterion

It can be shown that, for a circular aperture of diameter D, the first minimum in the diffraction pattern occurs at

The accepted criterion for determining the diffraction limit to resolution based on this angle was developed by Lord Rayleigh in the 19th century.

“Rayleigh criterion for the diffraction limit to resolution states that two images are just resolvable when the centre of the diffraction pattern of one is directly over the first minimum of the diffraction pattern of the other.”