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# circular aperture

 Definition/Summary This entry describes diffraction of a wave when it passes through a circular aperture.

 Equations The far-field (Fraunhofer) diffraction pattern for a circular aperture of radius r has a power per area (irradiance) given by: $$I(\theta) = I(0) \left( \frac{2 J_1(k \ r \ \sin\theta)}{k \ r \ \sin\theta} \right)^2$$ The angular radii of the first 4 dark rings in the diffraction pattern occur at $$k \ r \ \sin\theta \ \approx \ 3.8317, \ \ 7.0156, \ \ 10.173, \ \ 13.324$$ where the numbers are the zeros of $J_1$ Equivalently, in terms of wavelength the zeroes are at $$\sin\theta \ \approx \frac{\lambda}{r} \ \cdot \ 0.610, \ \ 1.12, \ \ 1.62, \ \ 2.12, \ \ 2.62, \ \ . . .$$ Angular radius (angle between the central axis and the 1st dark ring) of Airy disk: $$\theta_{Airy} \ = \ 1.22 \ \frac{\lambda}{d}$$ Airy disk radius for an imaging system: $$r_{Airy} \ = \ 1.22 \ \lambda \ \frac{f}{d}$$

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 Breakdown Physics > Classical Optics >> Diffraction