Resolution and Rayleigh's Criteria

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SUMMARY

The discussion centers on Rayleigh's Criteria for resolution in optical systems, specifically the formula θmin=1.22 [λ/D]. The use of radians in the calculations is emphasized, as the approximation sin(θ)≈θ is valid only when θ is expressed in radians. The factor 1.22 is specifically applicable to circular apertures, while a square aperture uses a numerical factor of 1. The conversion of the constant to degrees results in a value of 69.9°.

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  • Understanding of Rayleigh's Criteria in optics
  • Familiarity with the concept of angular resolution
  • Knowledge of trigonometric functions, particularly sine
  • Basic understanding of aperture shapes in optical systems
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prettykitty
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When working problems using Rayleigh's Criteria:

θmin=1.22 [λ/D]

Why do the answers come out in radians?
I'm sure it has something to do with the aperture being circular but I don't understand why.

Thanks!
 
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You can change the units in the formula to degrees if you wish, in which case the constant 1.22 becomes 69.9°. Radians are the preferred unit in mathematics, however. The look direction in an optical system involves the quantity sin(\theta), and \theta is very small when determining resolution. We can use the approximation sin(\theta)≈\theta in deriving the Rayleigh criterion. That approximation is valid as written only for \theta in radians.
 
prettykitty said:
When working problems using Rayleigh's Criteria:

θmin=1.22 [λ/D]

Why do the answers come out in radians?
I'm sure it has something to do with the aperture being circular but I don't understand why.

Thanks!

The factor 1.22 is due to a circular aperture- for a square aperture, the numerical factor is 1.
 

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