# Explanation for Rayleigh Criterion?

## Main Question or Discussion Point

Explanation for Rayleigh Criterion??

I just want to ask what is the reason behind Rayleigh criterion which states that items are just resolved when the maxima of a diffraction pattern coincides with the first minima of the other diffraction pattern. I have tried finding the answer but to no avail. Can anyone help?

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Philip Wood
Gold Member

Everyone's eyesight is different. Some people can probably resolve apart two 'Airy discs' if they are a little closer together than the RC, others might need them to be somewhat further apart than the RC. The RC is a handy 'rule of thumb', rather than having a strict optical basis. And, as a rule of thumb, it's very easy to use: you can simply say that two stars (or whatever) are resolvable (resoluble?) if they're separated by an angle of $1.22\frac{\lambda}{d},$ in which $\lambda$ is the wavelength of the light and d is the aperture diameter.

marcusl
Gold Member

This is a practical definition that ensures the presence of a noticeable dip between the two peaks, and makes the heights of the peaks correct since each is summed with zero from the other.

The Rayleigh criterion is just one choice for resolution, however--others exist as well, each with their own rationale.

Andy Resnick

I just want to ask what is the reason behind Rayleigh criterion which states that items are just resolved when the maxima of a diffraction pattern coincides with the first minima of the other diffraction pattern. I have tried finding the answer but to no avail. Can anyone help?

Perhaps it's worth noting that the Rayleigh criterion is not the only criterion for resolvability, it's simply the one developed during the era of film (continuous detectors) and applies to mutually incoherent (independent) sources. Two other important criteria in use today are the Sparrow criterion:

http://www.opticsinfobase.org/view_...eq=0&mobile=no&org=Cleveland State University

http://www.biomachina.org/courses/structures/082.pdf

And the Johnson criterion, which is appropriate for sampled imaging systems:

http://en.wikipedia.org/wiki/Johnson's_criteria