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   Corona formation - Diffraction 

Light diffracted by a droplet.

The diagram illustrates how two points on a droplet surface can scatter light and act as sources of outgoing spherical waves.

The scattered waves overlap and interfere.

Where wave crests of the same sign coincide the light intensity is increased. Where the waves have opposite amplitudes they destructively interfere to give low intensity.

Scattered light from the whole droplet surface plus smaller contributions from reflected and transmitted waves combine to form a diffraction pattern - a corona.

A corona is produced by diffraction of light by small particles. Every point on the illuminated surface is a source of scattered outgoing spherical waves ( Huygens-Fresnel Principle ).   The outgoing waves mutually interfere to give regions of enhanced brilliance, constructive interference, and darkness destructive interference Interference or Diffraction? )
Scattering from only two points is shown on the diagram. Along the central axis, the incident light direction, the crests of the two scattered waves always coincide to form a region where the light is strong.

Moving away from the axis, there is a direction where the crests again coincide to give beams of enhanced brightness at an angle to the incident light. In between there is a region where crests of one wave coincide with those of opposite amplitude of the other. The two waves cancel and there is darkness in those directions.

There is a another coincidence of wave crests at a larger angle and the light intensity is again enhanced. With increasing angular distance from the axis there are alternating bright and dark regions, a diffraction pattern.

In reality, light is scattered from all around the droplet periphery and
other low intensity waves arise from reflection and transmission through the particle. The net wave amplitude at any point is the sum of the amplitude vectors, not intensities, of all the individual waves. The result is a very bright central region surrounded by less bright rings, a corona.

Corona formation, to a good approximation, needs no knowledge of the droplet interior because the surface scattered waves predominate. It could be water, ink or coal - the pattern is almost the same. It depends primarily on the droplet size, shape and the wavelength of the light.

There is no need for the droplet to be transparent nor even spherical. Small ice crystals, pollen grains and large dust particles all form coronae.
A white light corona is the sum of all the coronae contributions from each spectral colour.

The spacing of the cloud particles does not matter. Cloud particles are separated by 50 or more diameters and mutual interference as in a diffraction grating only takes place if the droplets are closer than two diameters as in condensation on a window pane. A corona is produced when each light ray reaching the eye has been scattered by a single droplet.   

If the corona is to be sharp with many rings, the cloud droplets must all be of similar size otherwise all the different size coronae produced by the droplets produce merely a blur.
The solution of one physics problem is often the solution of another one apparently quite unrelated. The diffraction pattern from a droplet is
almost the same as that from an opaque disc. In turn, the diffraction pattern from a disc is the same as that from a circular aperture of the same diameter (Babinet's principle). A telescope lens or mirror is just such an an aperture. A star seen through a telescope is a small disk surrounded (if the lens is good and the air steady) by one or two delicate rings. This is a corona, one for a 'droplet' the size of the telescope objective and only visible because it is magnified a few hundred times by the telescope optics, but a corona nonetheless. Large telescopes make sharp point-like stars. Small droplets make large coronae.