Corona (atmospheric optics)

Lunar court or lunar corona

Full moon with multicolored corona

A corona ( Latin corona "wreath, crown") or courtyard is a luminous phenomenon around the moon or sun, which is caused by the diffraction of light on the water droplets of clouds - in contrast to the rainbow or halo effects , both of which are caused by refraction . In the case of a corona, often only a white disc with a reddish border can be seen, which is called aureole. Under favorable conditions, the aureole is surrounded by several colored rings.

The diameter of the aureole around the sun or moon has an angular extent between 2.5 ° and 8 °, the angular diameter of the outer rings can be up to 15 °. The diffraction effect that creates the corona need not necessarily be caused by water droplets. In rare cases, ice crystals or other aerosols can also cause corona , for example a pollen corona .

Such a corona is an effect of atmospheric optics , in contrast to the solar corona , which is the atmosphere of the sun that is only visible during a total solar eclipse .

Colloquially, the term " moon court " is also used for a 22 ° halo around the moon.

Appearance and appearance

A faint aura around the rising sun

Corona around a street lamp, generated by a steamed-up pane

If clouds move in front of the sun or moon, under certain conditions luminous disks form around the respective light source, which are sometimes still surrounded by colored rings. The scientific name for this luminous phenomenon is corona, the bright disc in the center of the corona is called aureole. In everyday language this is often called the courtyard and the colored rings are also called wreaths. However, the terms are not always used in this way and, another source of confusion, halos are also referred to as wreaths in older texts .

Coronas can usually be observed around the moon, less often around the sun. This is not because they occur less frequently around the sun, but because the light of the sun outshines the corona phenomenon and, in addition, you should generally avoid looking into the sun (and should also avoid it because of the danger to the eyes) . In order to observe solar coronas, sunlight must therefore be weakened - by using filters or by observing the phenomenon in a mirror image, on a body of water or a window pane. Under favorable conditions, coronas around planets or stars can also be observed.

Usually only the aureole around the moon can be seen - a white disc, the edge of which changes into yellow and red. The moon itself is often outshone by the aureole. If it can be seen, the difference in size between it and the aureole is immediately noticeable: While the disc of the full moon can be seen at an angle of about 0.5 °, the diameter of the aureole, depending on the size of the drops (see influence of the Drop size ), an angular extent of typically 2.5 ° to 8 °. Aureoles are more or less pronounced in almost all types of clouds that are not too thick , which is why they occur comparatively frequently. Corons appear particularly often in altocumulus clouds and thin layer clouds .

Under favorable conditions, colored rings are attached to the aureole (see influence of the wavelength ), whereby the colors blue, green, yellow and red can be seen from the inside out. Up to four ring systems were observed. The outer ones lack blue, otherwise the colors are similar to those in the innermost ring system. Corons can have very different dimensions, the angular diameter of the outermost rings can be up to 15 °. When clouds pass through, the corona can change - the diameter can grow or shrink, rings appear or disappear again, depending on how the drop sizes change.

You can also observe or create artificial corona, for example by looking at a lamp through a fogged window or fog.

Emergence

The corona as a diffraction image

For comparison: halo (above), corona (below). In addition to the more intense colors of the corona, the difference in size is particularly noticeable.

Corons are a diffraction phenomenon and must not be confused with the halos around the sun or moon - these are created by refraction of light in grains of ice in high clouds and have a larger diameter (mostly 22 °, more rarely 46 °) and a different color sequence. Coronas are created by the diffraction of sun or moonlight by water droplets - so clouds must be present if you want to observe a corona. On the other hand, these clouds must not be too powerful, since the moon or sunlight must be able to penetrate them.

Light is an electromagnetic wave . In order to understand diffraction effects, the simple beam optics are no longer sufficient, but the wave properties of the light must be taken into account. The diffraction of the light waves on an obstacle deflects the light from its original direction. Superpositions of the diffracted waves can in turn cause interference phenomena , the so-called diffraction patterns. How these diffraction patterns look depends, among other things, on the shape of the diffractive object. Water droplets are spherical and therefore form a circular obstacle for the spreading light. Therefore, the diffraction pattern of a water drop corresponds approximately to that of a circular disk. According to Babinet's theorem, this in turn corresponds to a good approximation to that of a circular aperture of the same diameter: a light disc , the central image with the greatest intensity, and concentric light and dark rings, the intensity of the light rings decreasing outwards. While the central image corresponds more or less to the original direction of propagation of the light (the deflection angle is around 0 °), the larger the deflection angle, the larger the diameter of the rings. The diameter of the diffraction rings depends on the drop diameter and the light wavelength . The larger the wavelength and the smaller the diffractive water droplets in the cloud, the wider the rings.

The diffraction rings are the lines of intersection of the cone shells with the plane of the screen.

The diffraction images of all water droplets in a cloud are perceived by an earthly observer as a single system of concentric rings around the light source (the corona), which corresponds to the diffraction image of a single drop on a screen. This comes about as follows:

The diffraction pattern of a single drop on a screen - i.e. in a certain plane perpendicular to the original direction of propagation of the light - consists of concentric rings. These rings are the intersection lines of the cone shells , into which the light is diffracted, with the plane of the screen. First of all, each drop creates its own diffraction pattern and its own cone coats of diffracted light. (For reasons of clarity, only one cone envelope is shown in the illustration; in fact, each diffraction ring naturally has its own cone envelope. It should be noted that the central diffraction disk is not a cone envelope, but a cone.)

The corona is created by the light that falls into the eye (dark red arrows). The viewing angle is decisive for the expansion of the rings.

All cone shells of a certain diffraction ring have the same opening angle - assuming uniform droplet size - this corresponds to the deflection angle . Of the diffracted light from all these cone shells, however, an observer can only perceive that which falls into his eye. The observer does not see most of the light waves at all because they pass his eye (figure on the left; light red arrows). ${\ displaystyle \ phi}$

The light perceived by the observer comes from a circular area

For example, if a drop bends red light in such a way that a maximum is created at a deflection angle of 3 °, and if the drop is in such a position in the cloud that the red light deflected by 3 ° hits the eye of an observer, the observer sees red at the point of the drop, also at a viewing angle of 3 ° (picture left). The angle of deflection or opening angle of the cone shells and viewing angle are the same, since they are alternating angles with respect to the original direction of propagation of the light. It does not matter how high the drop is in the cloud, because the viewing angle at which the drop perceived as red appears is always the same, since the deflection angle is the same (provided the drop size is uniform). However, an equal viewing angle means that both drops seem to be at the same distance from the center of the corona phenomenon. So both are part of the same red ring. ${\ displaystyle \ phi}$ ${\ displaystyle \ phi}$

In the figure on the left this is shown for drops on the right and left side of the corona. In order to obtain the complete circular corona, this image must be rotated around the original direction of light propagation (image on the right).

A great many water droplets are required for a corona to develop; however, the light is only diffracted once on a drop because the drops in the clouds are very far apart. It can therefore be neglected that light that has been diffracted by two or more water droplets one after the other also enters the viewer's eye.

The aureole corresponds to the main maximum, the ring systems to the secondary minima of the diffraction pattern of an individual drop.

Influence of the wavelength

Artificially created corona with the help of bear moss spores. Bottom left: red LED ; bottom right: blue LED; above: white LED.

The ring diameter depends on the wavelength - the larger the wavelength, the stronger the diffraction, i.e. the greater the deflection of the light from the original direction.

The main maximum lies in the center for all wavelengths (i.e. around the deflection angle 0 °), which is why all colors here overlap to form white and create a white aura. However, the first minima in each case - which form the edge of the main maximum, i.e. the bright central diffraction disk - are at a different deflection angle for each wavelength. Since blue light has the smallest deflection angle and red light the largest, the area of the central main maximum is smaller for blue light than for yellow and red light. The yellow and the red main maximum protrude beyond the area in which all the colors add up to white and create the yellow-reddish outer edge of the aureole. Therefore, at first glance, the impression arises that the sequence of colors in the corona begins with red. In fact, however, every ring system begins with an inner blue color ring.

The secondary maxima also have a different position for each wavelength. Since red light is more strongly diffracted, it forms diffraction rings with a larger diameter than blue light (assuming the same order of diffraction or the same ring system). The originally white moon or sunlight is split up in this way by diffraction and deflected into cone coats of individual colors for each drop.

The cone coats of blue light have a smaller opening angle, so they hit the eye at a smaller viewing angle. Light shown by dashed arrows does not hit the eye.

The blue light that an observer perceives comes from drops further inside than the red.

Since the angle of vision at which a corona ring of a certain color is seen is equal to the deflection angle, this means that the blue ring is seen at a smaller angle than the red ring of the same ring system. The droplets that create the blue ring are therefore further inside than those that cause the red ring (figure on the left). In the three-dimensional picture, the smaller deflection angle of the blue light means that its cone surface lies within that of the red light (figure on the right).

Of course, the red light is also diffracted by the drops perceived as blue. Due to the larger deflection angle, red light that emanates from the blue drops does not hit the observer's eye. The same applies to the blue light that emanates from the drops perceived as red.

The observer perceives the red light from the external drops and the blue light from the internal drops. He therefore sees a red ring on the outside and a blue ring on the inside.

In 1824, Joseph von Fraunhofer was the first to quantitatively describe the coronas as a result of the diffraction of light on many small objects. The Fraunhofer diffraction equation can be used to describe the intensity as a function of the deflection angle to a good approximation:

{\ displaystyle I (\ phi) = I (0) \ left ({\ frac {2J_ {1} ({\ frac {2 \ pi} {\ lambda}} R \ sin \ phi)} {{\ frac { 2 \ pi} {\ lambda}} R \ sin \ phi}} \ right) ^ {2}}

In the equation denote: = intensity; = Wavelength; = Deflection angle; = Radius of the diffracting obstacle (here the droplet radius); = Bessel function of the 1st type and 1st order (here:) . is the so-called circular wave number , a characteristic of the wave.

{\ displaystyle I}

{\ displaystyle \ lambda}

{\ displaystyle \ phi}

{\ displaystyle R}

{\ displaystyle J_ {1} (x)}

{\ displaystyle x = {\ tfrac {2 \ pi} {\ lambda}} R \ sin \ phi}

{\ displaystyle {\ tfrac {2 \ pi} {\ lambda}}}

The intensities depending on the deflection angle for different wavelengths and a droplet radius of 10 μm

{\ displaystyle \ phi}

The graphic on the right shows the intensities calculated using the above equation as a function of the deflection angle for different wavelengths and a drop radius of 10 μm, normalized to the intensity for . In addition, the resulting position of the aureole (including the yellow-reddish border) and the first ring system was sketched with colored bars. The positions of the first minima are found for blue (440 nm) at around 1.5 ° and for red (650 nm) at around 2.3 °. The first secondary maxima are around 2 ° (blue) and 3 ° (red). ${\ displaystyle \ phi}$ ${\ displaystyle I (0)}$ ${\ displaystyle \ phi = 0}$

Usually only one ring system can be observed, only under extremely favorable conditions do you see several (up to four). This is because the intensity decreases rapidly. In addition, the secondary maxima of the different wavelengths become wider with increasing order and therefore fall more and more on top of each other, which means that the colors mix more and more to white.

The diffraction theory is only suitable for describing corona, however, if the droplets are large (from a radius of about 10 μm). If they are small, must have the exact theory of Gustav Mie be used. This not only takes into account diffraction, but also all interactions that take place between the light wave and the obstacle, including reflections and the light passing through the drop.

Influence of the droplet size

The diameter of the rings also depends on the size of the diffracting obstacles, in the case of the corona, on the size of the water droplets in the clouds. Large droplets create small coronas, small drops create wide coronas. So the larger the corona, the smaller the droplets the cloud through which the light shines through. With the help of the equation given above from the diffraction theory, the dependence of the intensity distribution on the drop size can be shown (see figure). For blue light (440 nm) the first minimum is found for a drop radius of 10 μm at around 1.5 °, for a drop radius of 20 μm at around 0.8 °.

The intensities as a function of the deflection angle for different drop sizes

{\ displaystyle \ phi}

Not only does the radius of the rings increase with decreasing drop size, but also the distance between the maxima and minima and thus the width of the rings. The graph shows the intensities as a function of the deflection angle for two different drop sizes, normalized to the intensity for , calculated according to the diffraction theory. The position of the aureoles - including the reddish border - is sketched for both droplet sizes, as well as the two most widely spaced colors blue (440 nm) and red (650 nm) of the first ring system. The angle difference between blue and red in the first secondary maximum is, for example, about 0.8 ° for a drop radius of 10 μm, and only about 0.3 ° for 20 μm. ${\ displaystyle \ phi}$ ${\ displaystyle I (0)}$ ${\ displaystyle \ phi = 0}$

The most visible coronas are generated with drop radii between 5 and 20 μm (for comparison: rainbows are created with drop sizes in the millimeter range, as found in raindrops). The moon and sun are not point-like light sources, but have an angular diameter of about 0.5 °. The diffraction rings produced therefore have a width of approximately the same angular distance (with a point-like light source, the diffraction rings would be thin circular lines). So that the color splitting is even visible, the distance between two rings of neighboring colors must be greater than 0.5 °. Since the color splitting is smaller, the larger the droplets are, no more ring structures can be seen for droplets with radii of more than about 30 μm. Drops that are too small (less than 5 μm radius) cause a large color splitting, but also wider rings for each color. Since the light is distributed over a larger area, the intensity decreases accordingly, and the contrast and thus the visibility against the background decrease.

The droplet size within the cloud must not be too different. Each drop size creates its own ring diameter, which is why if the drop radii are too broadly distributed, rings of different colors eventually overlap and the ring pattern disappears. Since the droplet size in clouds is never completely uniform, different colors always overlap. The colors in coronas are therefore not pure colors.

Deviations from the circular shape occur when different areas of the clouds contain drops of different sizes.

If the drop size changes over time, the expansion of the rings changes accordingly. For example, if a rainy area approaches, the droplets grow rapidly and the corona narrows. As the size of the droplets also becomes more uneven, the colored rings disappear and the corona changes into a white disk.

If only an aureole can be seen, the droplets in the cloud are therefore mostly of a non-uniform size. Since such clouds are more frequent than those with a uniform (and suitable) drop size, coronas consisting only of aureoles can be observed more frequently than those with colored rings.

If different areas of a cloud consist of droplets of different sizes, the corona “frays”, as each cloud area creates its own ring diameter.

Determination of the drop size from the ring radius

Lunar corona into which the lunar disc recorded at the same focal length (colored black) was copied

For a specific wavelength, the position of the first minimum can be determined using the above equation from diffraction theory. In the above equation, a minimum of the intensity is equivalent to a zero of the Bessel function . Their first zero for is included . The following applies: ${\ displaystyle J_ {1} (x)}$ ${\ displaystyle x> 0}$ ${\ displaystyle x = 3 {,} 83}$

{\ displaystyle x = {\ frac {2 \ pi} {\ lambda}} R \ sin \ phi = 3 {,} 83}

Resolved according to the drop diameter : ${\ displaystyle 2R}$

{\ displaystyle 2R = {\ frac {3 {,} 83} {\ pi}} \ cdot {\ frac {\ lambda} {\ sin \ phi}} = 1 {,} 22 \ cdot {\ frac {\ lambda } {\ sin \ phi}}}

In the equations: = angular position of the first minimum; = Wavelength of the diffracted light; = Radius of the drop.

{\ displaystyle \ phi}

{\ displaystyle \ lambda}

{\ displaystyle R}

This equation can be used to estimate the size of the causing drops from the observed ring diameter. This takes advantage of the fact that the outer edges of the red rings are roughly at the position of the yellow minima, as Joseph Fraunhofer found out. If you solve the equation for the droplet diameter , set = 571 nm (yellow light) and determine the angular extent of the red border of the aureole of an observed corona, you get an estimate for the size of the droplets that have generated this corona. ${\ displaystyle 2R}$ ${\ displaystyle \ lambda}$

A practical problem is the determination of the angular extent of an observed corona. One way to solve this problem is to compare the extent of the corona with that of the lunar disk, which is about 0.5 °. In the photo shown, the lunar disc taken at the same focal length was copied into the corona (and colored black). The extent of the first red ring can now be estimated by measuring to a value of around 3.3 °. (It should be noted that the deflection angle only corresponds to half the ring diameter, i.e. around 1.7 °.) This results in a drop radius of around 12 μm.

Diffraction on other particles

With the help of bear moss spores , corona was generated around a lamp

It does not have to be water droplets that diffract the light - even if this is the case with the vast majority of coronas. Pollen grains, aerosols (such as after volcanic eruptions) or ice crystals are also possible. Ice crystals, however, do not have a spherical shape, but rather create the diffraction pattern of a gap as elongated needles. However, since the ice needles are aligned completely irregularly in the clouds, the lines of the slit diffraction images add up to form rings. The halos mentioned above are also created by grains of ice. However, since coronas require ice grains up to a maximum of 30 μm, but halos only occur from crystal sizes of at least 20 μm, both phenomena rarely occur simultaneously.

Pollen corons can be elliptical or diamond-shaped, since non-spherical pollen often - when falling in air - prefer a certain orientation. After volcanic eruptions there is a lot of dust in the atmosphere, which can also cause coronas. Since these aerosols with a diameter of 2-3 μm are smaller, the aureole is correspondingly larger, with radii of 13 ° –20 °. They are called Bishop's rings , after Rev. Sereno Edward Bishop (1827-1909), who first described them in 1883 after the eruption of the Krakatau volcano .

In the experiment, coronas can be created using Quetelet's rings by dusting a pane of glass with fine particles, such as bear moss spores, and illuminating them from behind.

Coronas and the weather

Most coronas are formed by diffraction from water droplets. But since clouds consisting of water droplets - in contrast to mixed clouds, which consist of water droplets and grains of ice - usually do not bring with them any or at best drizzle, peasant rules such as these emerged:

Is the ring near the sun or the moon

the rain spared us,

but the ring is wide

he has rain in his company.

The second half of this rule relates to the halo, which on the one hand is wider than a corona and on the other hand can be observed more easily around the sun, but less often around the moon. A halo arises in thin, high ice clouds ( cirrostratus ), which are one of the harbingers of a storm depression.

Note: In mixed clouds, due to the different saturation vapor pressure above ice and above water, the ice grains can grow very quickly (at the expense of the water droplets) until they begin to fall and precipitation occurs. Depending on the temperature, hail falls or the grains of ice melt into raindrops on their way down.

literature

Michael Vollmer: Play of light in the air. Spektrum Akademischer Verlag, Heidelberg 2006, pp. 193-215, ISBN 3-8274-1361-3
Kristian Schlegel: From the rainbow to the northern lights. Spectrum Akademischer Verlag, Heidelberg 2001, pp. 61–65, ISBN 3-8274-1174-2
Les Cowley, Philip Laven, Michael Vollmer: Colored rings around the moon and sun. In: Physics in Our Time. Vol. 36, Issue 6, Wiley-VCH, Weinheim 2005, pp. 266-273

Individual evidence

↑ Photo of an aureole around the planet Venus
↑ Aureole around the star Sirius
↑ ^a ^b ^c ^d ^e Michael Vollmer: Lichtspiele in der Luft , Spektrum Akademischer Verlag, 2006, pp. 193–215, ISBN 3-8274-1361-3
↑ ^a ^b ^c ^d ^e ^f Les Cowley, Philip Laven, Michael Vollmer: Colored rings around the moon and sun , In: Physics in our time. Vol. 36, Issue 6, Wiley-VCH, Weinheim 2005, pp. 266-273
↑ Simulations of coronas with different drop sizes (in English)
↑ Photo of a pollen corona
^ Photo of a Bishop ring
↑ Horst Malberg: Peasant rules. Springer Verlag, Heidelberg 1993, pp. 56-60, ISBN 3-540-56240-0

Web links

Commons : Korona - collection of pictures, videos and audio files

This version was added to the list of articles worth reading on March 26, 2010 .

[1] Photo of an aureole around the planet Venus

[2] Aureole around the star Sirius

[lichtspiele-3] Michael Vollmer: Lichtspiele in der Luft , Spektrum Akademischer Verlag, 2006, pp. 193–215, ISBN 3-8274-1361-3

[farbige_ringe-4] ↑ ^a ^b ^c ^d ^e ^f Les Cowley, Philip Laven, Michael Vollmer: Colored rings around the moon and sun , In: Physics in our time. Vol. 36, Issue 6, Wiley-VCH, Weinheim 2005, pp. 266-273

[5] Simulations of coronas with different drop sizes (in English)

[6] Photo of a pollen corona

[7] Photo of a Bishop ring

[8] Horst Malberg: Peasant rules. Springer Verlag, Heidelberg 1993, pp. 56-60, ISBN 3-540-56240-0