How is the Rayleigh criterion connected to the Abbe limit?
Nicholas Hunter
Answered question
2022-11-05
Answer & Explanation
Lena Gomez
Beginner2022-11-06Added 14 answers
And Rayleigh limit given by
where lambda is the wavelength and NA the numerical aperture of the light collecting lens.
The factor 1.22 comes from the definition of Bessel function of 1st kind,the fact that 1st minima of the diffraction pattern appears at 1.22 units from the central zero.
Rayleigh criterion is thus a modification of the Abbe Resolution limit. The Rayleigh criterion states that in order for 2 closely placed PSF to be resolved, the central maxima of one should lie exactly at the first minima of the second one. Since the Airy pattern is defined by the Bessel function, the minimum separation between the 2 patterns should be 1.22λ/2NA instead of just λ/2NA considering that the first minima will be at 1.22 times the unit from the central maxima.
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