Explanation for Rayleigh Criterion?

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Discussion Overview

The discussion revolves around the Rayleigh criterion, which pertains to the resolution of diffraction patterns in optics. Participants seek to understand the rationale behind the criterion and its implications for resolving closely spaced objects, such as stars, in various optical contexts.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions the underlying reason for the Rayleigh criterion, specifically why resolution occurs when the maxima of one diffraction pattern coincide with the first minima of another.
  • Another participant notes that individual eyesight variations affect the ability to resolve two 'Airy discs,' suggesting that the Rayleigh criterion serves as a general guideline rather than a strict rule.
  • It is mentioned that the Rayleigh criterion ensures a noticeable dip between two peaks, which is important for accurate peak height measurements.
  • A participant points out that the Rayleigh criterion is just one of several resolution criteria, indicating that other criteria exist with different justifications, such as the Sparrow and Johnson criteria.

Areas of Agreement / Disagreement

Participants express differing views on the applicability and interpretation of the Rayleigh criterion, with no consensus reached on its definitive rationale or superiority over other criteria.

Contextual Notes

Some participants highlight that the Rayleigh criterion is developed for continuous detectors and applies to mutually incoherent sources, suggesting limitations in its applicability to other contexts.

ameliatqy
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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?

Thank you for your help in advance!
 
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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.
 


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.
 


A picture is worth 1000 words:

rayc.gif

(From http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/raylei.html )
 


ameliatqy said:
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?

Thank you for your help in advance!

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
 

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