Airy Diffraction Pattern from a Circular Aperture

What you are seeing: if you shine a perfectly collimated monochromatic light beam through a small round hole and catch the light on a screen far away, you do not get a sharp shadow of the hole. You get a bright central spot surrounded by faint concentric rings: the Airy pattern. It is one of the most fundamental diffraction phenomena and sets the resolution limit of every telescope and microscope.

For a circular aperture of radius $a$, the intensity in the Fraunhofer far field is $$I(\theta) / I_0 = \left[\frac{2 J_1(x)}{x}\right]^2,\quad x = \frac{2\pi a}{\lambda}\sin\theta,$$ where $J_1$ is the first Bessel function of the first kind. The first dark ring sits at $x_1 \approx 3.8317$, corresponding to angular radius $\theta_1 = 1.22\,\lambda / D$ with $D = 2 a$ the diameter. This is the Rayleigh resolution criterion.

Below: 2D intensity heatmap on the left (use the gamma slider to bring out faint rings), 1D radial intensity profile $I(x)$ on the right with the first five $J_1$ zeros marked.