Category Archives: theory
On Sept 25th and 27th, 2014, I was traveling by plane from Dresden to Brussels and back, with stops at Frankfurt and Munich, respectively. As usual, I booked window seats to study sky phenomena. The sunward side was not very interesting, since these short-distance flights are carried out at heights below the cirrus clouds and therefore no sub-horizon halos can be observed (at least in autumn). On Sept 25th only a single 22° halo appeared in the cirrus clouds above the plane, whereas on Sept 27th ice crystal clouds seemed to be fully absent.
Accordingly, the viewing direction towards the antisolar point proved to be much more interesting. As most of the Atmospheric Optics enthusiasts I had seen glories and cloudbows before (especially when traveling to the Light&Color meetings in the US) but this time the conditions seemed to be especially favorable. I could observe an an almost textbook-like development of both phenomena right after piercing through an Altocumulus layer after the take off from Dresden (Sept 25th, 11:13 CEST):
From Debye series simulations (intensity sum of the p = 0 to p = 11 terms in order to prevent artifacts from the small-scale inter-p-interferences as present in the Mie results) a mean drop radius of about 8 µm with 0.5 µm standard deviation can be estimated (assuming a Gaussian drop size distribution):
This simulation was calculated for the original lens projection with added ad-hoc gray background. It is also available as a fisheye view centered on the antisolar point without background , together with the corresponding simulation for monodisperse drops (no spread in size) of 8 µm in radius .
Unsharp masking and saturation increase processing of the photograph reveals that the sequence of supernumeraries can be traced until they merge with the glory rings:
Over the next minute I mounted the fisheye lens to my camera in order to record a broader view. Unfortunately, some of the outer glory rings and inner supernumeraries had already vanished, indicating an increase in the drop size spread:
Note the smaller angular size of the plane’s shadow as the distance to the Ac layer had further increased. A well fitting simulation to this photo can be calculated by assuming again a mean drop radius of 8 µm and setting the standard deviation now to 1 µm:
For comparison, the fisheye simulation centered on the antisolar point was calculated for the 1 µm drop size spread as well . Furthermore, I recorded a video sequence showing the movement of both glory and cloudbow across the uniform Ac layer (11:15, ). When later the edge of the Ac field was reached, the glory showed an appreciable degree of distortion (11:18 CEST , processed version ).
On Sept 27th, not a uniform but a fractured Ac layer was present after the take off from Brussels. Nonetheless the glory appeared circular (12:34 CEST , processed version , video at 12:37 CEST ), with the exception of occasional larger disturbances in the layer (12:34 CEST ). The cloudbow was not as prominent as two days earlier. During the later part of the flight only occasional Cumulus clouds were present, which did not allow for further glory observations until the plane started descending when approaching Munich. At this point the angular size of the clouds became large enough again to act as suitable canvas for the glory (13:14 CEST  ). During the final passage through a Cu cloud I recorded a further video (13:15 CEST ). Remarkably, the angular size of the plane’s shadow varies rapidly (indicating the distance to the drops) whereas the the angular size of the glory remains rather stable (indicating the drop radius).
Photos and videos were taken with a Pentax K-5 camera equipped with either a Pentax 10-17 mm fisheye or Pentax-DA 18-55 mm standard zoom lens. A gallery view of my photos can be seen here .
Fraunhofer lines are dark lines in the sun’s spectrum. They are caused by resonant atomic absorption of the sun’s thermal continuum radiation by photospheric gases.
The lines provide clues to the chemical composition of the solar atmosphere, as well as its physical conditions like temperature, pressure, magnetic fields etc.
My rainbow photography dated 11.Oct.2013 showed some greyish bands in the yellow.
Are they traces of the strongest Fraunhofer lines or artifacts of the camera’s sensor being unable to profile intermediate colors?
Is it possible at all to obtain spectral lines in nature without a prism or grating?
Author: Michael Großmann, Kämpfelbach, Germany
In my last post I outlined several possibilities to explain the great brightness of the antisolar arc (AA) compared to the heliac arc (HA) in the Neklid display from Jan 30th, 2014. All of them were a bit off the main road of traditional halo science, but traditional arguments did not help to clarify what was observed, hence I had to look for something else.
Both the concepts of plate Parry crystals and trigonal Parry columns should yield weak traces of unrealistic (or better to say non-traditional) halos that might appear in a deeper photo analysis. Claudia Hinz provided me with a set of pictures from the display to unleash any kind of filters that would seem appropriate. Indeed it was possible to pin down traces of the Kern arc in some of the pictures after the initial application of an unsharp mask (1, 2), followed by high-pass filtering (1, 2) or, alternatively, by Blue-Red subtraction (1, 2). Note that the Kern arc was weakly present in the simulations for hexagonal, Parry-oriented plates. This, of course, must not be confused with the recently proven Kern arc explanation relying on trigonal plates in plate orientation. Finally, trigonal columns in Parry orientation are a third non-traditional crystal configuration giving rise to new halos. However, these do not yield a Kern arc.
Obviously, the Kern arc fragments in the photos are very feeble and the whole procedure reminds a bit of the search for higher order rainbows. It is mere guesswork to detect how far the arc stretches around the zenith, but doubtlessly it extends up to 90° and more in azimuth, thus being clearly distinguishable form the circumzenith arc. Nonetheless, one would feel safer with further evidence. Comparing the simulations for Parry columns and Parry plates, three more differences are discernible (apart from the changed AA/HA ratio):
1) For Parry plates, the upper suncave Parry arc does not show an uniform brightness, but appears brighter directly above the sun and loses some intensity towards the points where it joins the upper tangent arc.
2) The upper loop of the Tricker anthelic arc is suppressed for columns, but shows up for plates.
3) Some extensions of the upper Tape arcs appear between the Wegener arc and the subhelic arc.
At least the first two points can be answered in favor of the Parry plates, being visible even without strong filtering. However, I failed to detect any extended Tape arcs as “ultimate proof” so far. This might not surprise since they are, according to the simulation, comparable to the Kern arc in intensity and appear in regions of the sky where the crystal homogeneity was not as well developed as in the vicinity of the zenith.
Piecing the parts together, it seems evident that at Neklid the AA intensity was due to Parry-oriented hexagonal plates. Their traces were detectable, whereas nothing appeared that would hint on trigonal Parry columns. In contrast to this, Parry trigonals were responsible in Rovaniemi 2008. This implies that in nature at least two different mechanisms occur for AA brightening.
Finally the question remains how plates may get into a Parry falling mode. But as long as no one understands how symmetric columns do this (though we have the empirical evidence), we should be prepared for surprises. There might also be a connection to recently discussed details of the Lowitz orientation (2013 Light and Color in Nature conference, talk 5.1).
(photo by Claudia Hinz)
The antisolar (or subanthelic) arc (AA) was one out of the vast range of halo species occurring during the marvelous Neklid display observed by Claudia and Wolfgang Hinz on Jan 30th, 2014. This kind of halo seems to be exceedingly rare, since it has only been documented during the very best displays, mostly observed in Antarctica. On the other hand, the heliac arc (HA) is a, however not frequent, but well-known guest in Central Europe. Both of them are reflection halos generated by Parry oriented crystals and touch each other at the vertices of their large loops. Fisheye photos towards the zenith from Neklid shows both these halos in perfect symmetry and approximately similar intensity, at least regarding the upper part of the AA.
When trying to simulate the display (solar elevation 17.5°) using HaloPoint2.0, I noticed that the AA was rendered much weaker than the HA, which of course does not match the photographic data. To obtain the Parry effects (Parry arcs, Tape arcs, HA, AA, Hastings arc, partially circumzenith arc, Tricker arc, subhelic arc) I chose a population of “normal” (i.e. symmetrically hexagonal) column crystals with a length/width ratio of c/a = 2 in the appropriate orientation. Since both HA and AA are generated by this very same crystal population, their mutual intensity ratio cannot be influenced by adding plates, singly ordered columns, or randomly oriented crystals. This mysterious issue has also been noted by a Japanese programmer who came across the Neklid pictures.
Inclusions of air or solid particles within the ice crystals are an obvious hypothesis to explain this dissenting AA/HA intensity ratio, since they cannot be accounted for in the standard simulation software. However, a look into literature reveals that there are external and internal ray paths for the HA, but only internal paths for the AA ( p. 34-35). That means that inclusions will diminish the AA to a greater extent than the HA. In the extreme case with the interior totally blocked, no AA can arise but a HA is still possible due to external reflection at a sloping crystal face. Hence inclusions cannot explain the bright AA from the Neklid display. Air cavities at the ends of columns which are seen quite often in crystal samples will also inhibit the AA because an internal reflection at a well defined end face is needed for its formation.
Spatial inhomogeneities in the crystal distribution might serve as explanation as long as there is only one single photo or display to deal with, especially when the air flow conditions are as special as they were at Neklid. Maybe there were just “more“ good crystals in the direction of the AA compared to where the HA is formed, either by chance or systematically due to the wind regime. But surprisingly also the observations from the South Pole (Jan 21st, 1986 (Walter Tape); Jan 11th, 1999 (Marko Riikonen), also discussed here) show an AA/HA ratio somewhere in the region of unity as far as one can guess from the printed reproductions ( p. 30,  p. 58). Parts of the AA appeared even brighter than the HA in Finnish spotlight displays. All this implies a deeper reason for the AA brightening. It seems rather unlikely that in all these cases the inhomogeneities should have worked only in favor of the AA.
Hence the crystals themselves must be responsible for AA brightening. Non-standard crystal shapes and orientations are conjectures that can be tested easily with the available simulation programs. For a first try, one can assign a Parry orientation to plates instead of columns. Changing the c/a shape ratio from 2 to 0.5 while keeping all other parameters fixed results in a much brighter AA.
It is, however, commonly accepted that due to the air drag only columns can acquire a Parry orientation ( p. 42). Furthermore, some halos appear in the plate-Parry simulation which have not been observed in reality, e.g. a weak Kern arc complementing the circumzenith arc. At this stage the question may arise why only due to aerodynamics any symmetric hexagonal crystal (may it even be a column) should be able to place a pair of its side faces horizontally to generate Parry halos such as the HA and AA. Cross-like clusters or tabular crystals ( p. 42), from whose shapes one will immediately infer that rotations around the long axis are suppressed, seem much more plausible. Surprisingly, Walter Tape’s analysis of collected crystal samples shows that Parry halos are mainly caused by ordinary, symmetric columns. Parry orientations might be a natural mode of falling for small ice crystals, though up to now the aerodynamic reasons remain unclear. Nonetheless I tested if tabular crystals would give a bright AA. This was neither the case for moderate (height/width = 0.5) nor strong aspect ratio (height/width = 0.3). The AA was in both cases even weaker than in the symmetric standard simulation with which the discussion started.
Trigonal plates have been brought into discussion as possible crystal shapes being responsible for the Kern arc (see also  p. 102). Out of curiosity I tested how Parry oriented trigonal columns would affect the AA/HA intensity ratio. In contrast to symmetric hexagonal columns two different cases exist here, depending on whether the top or bottom face is oriented horizontally. As seen from the results, a sufficiently bright AA can be simulated using trigonal Parry columns with horizontal bottom faces, but the upper suncave Parry arc and the lower lateral Tape arcs at the horizon disappear. Obviously they have to, since a trigonal crystal in this orientation does not provide the necessary faces for their formation. On the other hand, the simulation predicts unrealistic arcs like the loop within the circumzenith arc. Choosing a trigonal Parry population with top faces horizontal will diminish the loop of the HA and wipe out the upper part of the AA as well as the upper lateral Tape arcs and add an unrealistic halo that sweeps away from the supralateral arc.
Is it possible to generate a realistic simulation of the Neklid picture with such crystals? Clearly this will require to add a second Parry population of symmetric hexagonal prisms. Doing so, a reasonable compromise can be achieved. In this case the hexagonal crystals produce the Parry arc, whereas the trigonal ones are responsible for the AA. Due to the triangular portion being small, the unrealistic halos become insignificant. However, the fact that a further degree of freedom (mixing ratio trigonal/hexagonal) has to be added to the set of initial simulation parameters is somehow dissatisfying.
The question lies at hand if this result might also be obtained by choosing a single Parry population of intermediate shapes between the symmetric hexagonal and trigonal extremes. This idea is further motivated through pictures of sampled crystals that, though being labeled „trigonal“, show in fact non-symmetric hexagonal shapes. The simulation for these shapes does indeed predict an enhanced AA compared to symmetric hexagons, but the lower lateral Tape arcs and the upper suncave Parry arc still appear too weak. This means that an additional set of symmetric hexagonal crystals is needed again to render these halos at the proper intensity.
Moreover, quite prominent unrealistic halos like the loop crossing the circumzenith arc appear in the simulation. If this assumption for the Parry crystal shape was right, this arc should be visible in an unsharp mask processing of the photos. Its absence hints that these crystals did not play a dominant role in the Neklid display. One could argue that the unrealistic halos may depend strongly on the actual crystal shape and might be washed out in a natural mixture of different “trigonalities“. However, the simulation tests indicate that even in this case the unrealistic halos remain rather strong, as long as one still wishes to maintain an AA at sufficient intensity.
As a conclusion, it can be stated that the intensity ratio between the heliac arc and the antisolar arc in the Neklid display as well as in Antarctic and Finnish observations has raised basic questions about the shapes of the responsible crystals. Simulations with symmetric hexagonal Parry columns, i.e. the standard shapes, render the AA to weak compared to the HA. Inclusions in the crystals and spatial inhomogeneities of the crystal distribution can be ruled out as the cause of this deviation. Plates in Parry orientation or a mixture of Parry oriented trigonal columns with horizontal bottom faces and hexagonal columns both result in a more realistic AA/HA intensity ratio. However, they introduce traces of unrealistic halos and are rather uncommon hypotheses: Plate crystals are not supposed to fall like this, and the existence of “true” trigonal crystals is doubtful. Moreover, the trigonal crystals need an accompanying set of standard Parry crystals to generate other halos like the upper suncave Parry arc.
So all in all the mystery of bright antisolar arcs cannot be regarded as solved at this stage. Since this halo species is very rare in free nature, it might be helpful to test perspex crystal models of different shapes in Michael Großmann’s “Halomator“ laboratory setup. Though the refractive index in perspex is higher than in ice, the basic relations between HA and AA stay the same. However the big challenge remains to collect and document crystals during such a display, e.g. with the methods described by Reinhard Nitze.
 W. Tape, Atmospheric Halos (American Geophysical Union, 1994)
 W. Tape, J. Moilanen, Atmospheric Halos and the Search for Angle x (American Geophysical Union, 2006)
I missed an important piece of information from Finland 2008: The idea of trigonal crystals making Parry halos was already pointed out by Marko Riikonen in an analysis of the Rovaniemi searchlight display. In that case, even one of the halos that I termed “unrealistic“ was observed in reality, thus strongly supporting the trigonal interpretation.
Only at very rare occasions, light refraction can be seen as impressive as in this example. The photo was taken by Hermann Scheer at the Meteorological Observatory on Mt. Hoher Sonnblick (3105m) in the Hohe Tauern mountains in Austria. A layer of ice and rime had formed on the glass sphere of the Campbell Stokes sunshine recorder. This layer split the sunlight up into its spectral colours. That is how impressive physics can be.
It was an ironic situation when during the night from 14th to 15th of July 2012 (at a weekend) a high number of observers and photographers were looking for a predicted aurora borealis and instead were confronted with a remarkable outburst of structured (or banded) green airglow. This phenomenon is well known and explored by professional geo-scientists but seemed to have slipped the attention of most amateur observers, including myself, up to then. Though it first seemed likely that the geomagnetic storm may have somehow triggered this event, later observations (e.g. July 23rd, 2012: http://www.polarlichter.info/airglow.htm) indicated that the traditional excitation mechanism (UV and X-Ray radiation from the sun) is capable of producing intense green airglow without the need for a geomagnetic anomaly.
Due to the fascination I felt during my own observation, I got interested in using the many available photographs from the July 14th/15th night for a height and position reconstruction. However, as I later found out from literature, the airglow height of 87-95 km (i.e. a quite thin layer, comparable to the NLC layer around 83 km) is already well established by professional measurements. It is remarkable that this value can in fact be reproduced by comparing amateur photographs from various locations in Germany by an un-biased analysis, which I want to present here.
The first task to do was to contact other observes via the well-known communication boards about atmospheric optics to gather suitable photographic material. Of course I had my own images at hand and intended to use them for this process, so I already had a list of time slots to find synchronous counterparts for. Even though I could find several pictures taken within a tolerance of < 1 minute with respect to my own photos, I had to drop most of them since a coarse analysis of the viewing directions yielded no overlapping fields of view. But through discussing my idea with several other photographers, I was able to identify other matching pairs independent from my own material. Finally, I ended up with two data sets (image pairs), 1 and 2, to work with:
1a) Frank and Sabine Wächter: July 15th, 00:55 CEST, 51° 12’ N, 13° 35’ E, 189 m above sea level (Meißen, Saxonia): https://dl.dropbox.com/u/8849406/Forum/AirglowBlog/1a.jpg
1b) Jens Hackmann: July 15th, 00:55 CEST, 49° 29’ N, 9° 55’ E, 333 m above sea level (Weikersheim, Baden-Württemberg): https://dl.dropbox.com/u/8849406/Forum/AirglowBlog/1b.jpg
2a) Franz Peter Pauzenberger: July 15th, 02:02 CEST, 49° 00’ N, 11° 30’ E, 518 m above sea level (Beilngries, Bavaria): https://dl.dropbox.com/u/8849406/Forum/AirglowBlog/2a.jpg
2b) Alexander Haußmann: July 15th, 02:01 CEST, 51° 32’ N, 13° 58’ E, 110 m above sea level (Senftenberg, Brandenburg): https://dl.dropbox.com/u/8849406/Forum/AirglowBlog/2b.jpg
For a detailed analysis, it is necessary to calibrate these photos, which means to precisely assign values for azimuth and elevation to each pixel. If the projection characteristics of the photographic lens are known, the positions of two stars in each picture are sufficient input for this purpose. However, the simple assumption of an ideal gnomonic (rectilinear) or equal-area projection (for ordinary and fisheye lenses, respectively) drastically limits the accuracy of the results. To overcome this, the projection characteristics for all four lenses were reconstructed by measuring the pixel distances of approximately 15 stars from the image center and compare these with the angular distance from the optical axis for each image.
After this calibration and assignment, longitude and latitude positions for each pixel can be calculated, allowing the projection of the photo onto a map if a certain height of the airglow layer is assumed. This method already proved to be very useful for the reconstruction of NLC positions (http://www.meteoros.de/php/viewtopic.php?t=8451). Since the goal is here to determine the layer height, this parameter is varied until the corresponding structures in both reconstructions of an image pair give the best fit. Indeed it was possible to find consistent height values for both data sets, 92 km for pair 1 (https://dl.dropbox.com/u/8849406/Forum/AirglowBlog/1.gif) and 93 km for pair 2 (https://dl.dropbox.com/u/8849406/Forum/AirglowBlog/2.gif). Here the traditional blink comparison technique was applied in a modern form using gif animations. It is fascinating to see how the airglow structures that look completely different in the original two photos of each pair coincide in the reconstruction on the map. Evidently, all non-airglow structures such as trees, background light, clouds, photographic violet aurora etc. have to be ignored in the reconstruction. It should be noted that more complex approaches (http://www.opticsinfobase.org/ao/abstract.cfm?uri=ao-51-7-963) are recently established in the professional field, allowing even to resolve finer structures within the thickness of the airglow layer.
Furthermore, these reconstructions show an undistorted view on the band structure of the green airglow layer. As already expected from the perspective view of the original photos, these bands are roughly aligned in the direction from West to East. Using the consistent height information obtained from the image pair comparisons, it is moreover justified to project a whole picture series from a single observation site onto the map in order gain insight in the airglow band dynamics. For this purpose I used a time lapse series that I took from July 14th, 23.16 CEST to July 15th, 01.20 MESZ at the Senftenberger See (51° 29’ N, 14° 01’ E), starting in the evening dawn and originally intended to capture the predicted aurora borealis (https://dl.dropbox.com/u/8849406/Forum/AirglowBlog/3.avi). Due to the weak contrast of the airglow at this stage, strong image processing is needed to separate the bands from the background. Though this finally results in a rather poor signal to noise ratio, it can clearly be seen that the airglow bands move in northward direction (https://dl.dropbox.com/u/8849406/Forum/AirglowBlog/4.avi), illustrating the recombination and/or matter transport dynamics in the mesopause region.
Author: Alexander Haussmann
My book “Polarized Light in Nature” is now online available.
The pdf can be downloaded from my site, www.guntherkonnen.com. Go to English/Articles and scroll down to the year of publication (1985). The size of the download is 24 Mb.
The Dutch version (1980) can also been downloaded from the site (18 Mb).
Direct access is also possible:
http://s3.amazonaws.com/gunther-konnen/documents/249/1985_Pol_Light_in_Nature_book.pdf?1317929665 (English version)
http://s3.amazonaws.com/gunther-konnen/documents/246/1980_Gepolariseerd_Licht_boek.pdf?1317928523 (Dutch version),
but these addresses may change in case my site migrates to another server.
Author: Günther Können, Netherlands
A slight-projector and a singel water drop shows a lot of bows. Here you can see the primary, secondary and tertiary bow.
The distance between the water drop an the projection backside (white paper) is 30 mm, waterdrop an light source has an diameter of 2 mm.
Photo taken on 28.07.2011 on my desktop 🙂
Author: Michael Großmann, Kämpfelbach, Germany
A rainbow is a product of millions of falling raindrops interacting with sunlight. A single reflection form the primary bow, a double reflection forms the secondary bow. However, under ideal conditions there can be many more orders of reflection. As shown above, five, six and even ten internal reflections can be observed. Moreover, it’s theoretically possible to detect twenty internal reflections, but the problem is to produce a perfectly spherical water droplet. The drops I used for this experiment were formed artificially. The light source is a 5 mW green laser pointer. Note that the bright spot at left center is the laser illuminated water drop.
The third and fourth order reflections aren’t shown here because they, along with the seventh and eighth order reflections, are positioned on the other side of the picture in the direction of the light source. The primary and secondary bows will be viewed in the direction you’re facing opposite the sun The fifth, sixth, ninth, and tenth order reflections are also in this direction. However, the third and fourth (as well as the seventh and eighth) order reflections can’t be seen because they’re behind you.
Under exceptional atmospheric conditions it may be feasible to see the third and fourth order bows if you’re facing the sun, but they’re quite faint. A third order bow, for instance, is one quarter as bright as a primary bow. A fifth order rainbow is only about one tenth as intense as the primary bow.
If you need more information about the experiments with high order bows, you can read this pdf.
Nikon D40X, focal length 18mm, 100 ISO, 2,5 sec. at f/6,3
Author: Michael Großmann, Kämpfelbach, Germany