What is the Rayleigh criterion for resolution?

The Rayleigh criterion for resolution is a measure that defines the minimum distance at which two light sources can be resolved.

The Rayleigh criterion is a fundamental concept in physics, particularly in the field of optics. It was established by the British physicist Lord Rayleigh, and it provides a quantitative measure of the ability of an optical system to resolve detail in the object that is being viewed. The criterion states that two light sources can be considered as just resolved when the centre of the diffraction pattern of one is directly over the first minimum of the diffraction pattern of the other.

The resolution of an optical system, such as a microscope or telescope, is limited by the wave nature of light. When light from two separate points enters an optical system, it is diffracted, and the resulting diffraction patterns can overlap. If the overlap is too great, the two points cannot be distinguished from each other and are said to be unresolved. The Rayleigh criterion provides a way to calculate the minimum separation at which the two points can be resolved, based on the wavelength of the light and the size of the aperture through which the light is entering.

The formula for the Rayleigh criterion is θ = 1.22 λ / D, where θ is the minimum angular separation between two points that can be resolved, λ is the wavelength of light, and D is the diameter of the aperture. This formula shows that the resolution improves (i.e., the minimum resolvable angle decreases) as the wavelength of light decreases or as the aperture size increases.

In practical terms, the Rayleigh criterion is important in many areas of science and technology. For example, it sets the limit for the smallest details that can be seen in microscopic images, or the finest details that can be made out in astronomical observations. Understanding and applying the Rayleigh criterion is therefore crucial for designing and using optical instruments effectively.