Atmospheric optical phenomena usually appear inparallel light, i.e., in the light from a distant sourcesuch as the Sun or the Moon. With the rainbowsand the 22° and 46° halos, for example, the drops orcrystals that give rise to the phenomena are arrangedon imaginary cone-shaped surfaces with the vertex inthe observer’s eye. When seen in divergent lightfrom a nearby source the phenomena become modi-fied to varying degrees, the drops or crystals formingrainbows, and the 22° and 46° halos in such lightbeing situated on the surface of an imaginary bodyformed by rotation of a circle segment around itschord, as shown in Fig. 1, with the terminal pointsbeing the light source and the observer’s eye. Thespindle-shaped forms in the figure represent Min-naert’s Cigar,1 recently reported in this journal,2 andthe apple-shaped forms ~spheroidal with a depressionat each pole! represent the rotatory bodies of therainbow–fogbow–dewbow complex.3–6 In dewbows,as well as the horizontal 22° and 46° halos ~for ex-mple, those formed in ice crystals on the ground orn the roof of a car!, the drops or crystals involved are
situated where the surface of the rotatory body isintersected by a horizontal plane that corresponds tothe ground or the car roof. Similar effects could alsoarise in connection with heiligenschein ~i.e., the col-rless bright area around the antipoint of a light
J. O. Mattsson [email protected]! and L. [email protected]! are with the Department of Physicaleography, Lund University, Solvegatan 13, Lund SE-223 62,weden.Received 17 November 2000; revised manuscript received 27
ource! and with related phenomena. These will bereated here.
2. Heiligenschein and Related Phenomena
Heiligenschein can arise in different ways, for exam-ple, by ~1! shadow hiding in and around the antipointf the light source or ~2! backscattering of light to-ard the observer from the foci of dewdrops or otherater drops ~rarely frozen transparent drops! on
eaves, etc. around the antipoint that act as small,ncomplete lenses. In ~1! a dry heiligenschein, alsoermed opposition effect, could arise. In ~2! a deweiligenschein is produced. Alternatively, thesehines could be termed spatial heiligenschein androplet heiligenschein. There is a third mechanismhat is strongest in the 180° direction, coherent back-cattering, which is an interferencelike component toiffuse scattering from granular surfaces such asand7,8; it is especially relevant for satellite image
interpretation.A spatial heiligenschein can sometimes be observed
on the bare soil of dry arable land, in corn fields andon stubble and, from the air, above wooded areas ~Fig.!. Because of the gradual decrease in the extent ofhaded surfaces and shadows as the antipoint of theight source is approached, the delimitation of thehine is rather diffuse. The bright area sometimesxtends beyond the antipoint, or is in other respectsodified as when it appears on a crop with vertical
talks or a stubble.Droplet heiligenschein is often seen as a bright
hine around the shadow of the observer’s head or theamera on dew-covered surfaces, which can some-imes be observed from the air. Inasmuch as themage-forming properties of drops of water are noterfect, light is not deflected by exactly 180°, and asresult a diffusely limited area with a bright white
hine is produced around the antipoint of the light
0 September 2001 y Vol. 40, No. 27 y APPLIED OPTICS 4799
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source. The phenomenon is particularly brightwhen small ~spherical! drops form a dense dew coveron a horizontal surface giving the plants a grayish-white velutinous appearance.9 This applies to cer-tain species of plants more than others, examplesbeing rape, clover, some species of cabbage and grass,and tulip.
These types of heiligenschein are usually producedin parallel light ~from the Sun or the Moon! but alson divergent artificial light. If the light source islose to but not behind the observer, a landscapeithout shadows, a so-called sylvanshine ~Fig. 3! orffects related to sylvanshine, will appear. More
Fig. 1. Water drops or ice crystals that cause some of the atmospof an imaginary body formed by rotation of a circle segment around~d! the primary rainbow. L denotes the light source and O repreangles, i.e., angles from the antisolar point. The phase angle equsource. All the points that correspond to the indicated angles ar
Fig. 2. Spatial heiligenschein on bare soil. Photograph taken byJ. O. Mattsson, near Malmo, Sweden, in 1972.
800 APPLIED OPTICS y Vol. 40, No. 27 y 20 September 2001
han one sylvanshine or related effect can sometimese observed simultaneously. The sylvanshine, ob-erved, explained, and named by Fraser,10 is a bright
white light that is retroreflected from certain speciesof trees or bushes when they are covered with dropsand a beam of light strikes them, for example, fromthe headlights of a car or from a flashlight. If thelight divergence is extensive as with flash-lamp pho-tography, the sylvanshine could appear in more thanone place at the same time. It is unaffected by theobserver’s shadow. An effect related to the sylvan-shine is shown in Fig. 4. Note that we are not dis-cussing phenomena that are simply the result ofuneven illumination.
3. Retroreflection and Light Divergence
Heiligenschein, sylvanshine, and related phenomenaare all manifestations of retroreflected light. Retro-reflection ~or catadioptric reflection! is the increase inreflection of electromagnetic energy in the directionopposite that of the incident radiation independent ofthe angle of incidence. There is usually a combina-tion of retroreflection and diffuse and specular reflec-tion. In our experience it appears to be reasonableto assume that retroreflected light reaches the ob-server or camera from points on a plane horizontalsurface when this light has a phase angle of 5° or less.
Parallel light from a distant source, e.g., the Sun orthe Moon, is retroreflected from an area on the plane
optical phenomena in divergent light are situated on the surfacehord: ~a! the 22° halo, ~b! the 46° halo, ~c! the secondary rainbow,the observer’s eye. All the angle values in the figure are phase
80° minus the scattering angle, which is the angle from the lightlized at the circle segments.
hericits c
sentsals 1
e loca
uWsp
lltc~obilltca
hrb
c
surface around the antipoint of the light source ~hei-ligenschein!. When the incident light is perpendic-
lar to the surface, the heiligenschein is circular.hen the light is obliquely incident the heiligen-
chein assumes the form of an ellipse although it iserceived as a circle.When the distance between the observer and the
ight source is decreased, light divergence could ateast theoretically give rise to certain optical effectshat have not been previously reported. Again, wean use the circle to give a geometric representationFig. 5!. Points with a phase angle of 5° are situatedn the surface of the imaginary rotatory body formedy rotation of the circle segment around its chord, asn Fig. 5. Points with a phase angle of less than 5°ie outside the body. After the relative positions ofight source L and observer O have been determined,he boundary of the retroreflecting region can be cal-ulated as phase angle v between the two vectors LRnd OR
cos v 5uLR z ORu
uLRu0.5 z uORu0.5 5 cos 5°. (1)
We place the origin of the coordinate system underthe light source at ground level ~i.e., footpoint of thelight source!, so that L 5 ~0, 0, zL!. This will not
Fig. 3. Sylvanshine from a silver spruce ~Abies alba! with myri-ads of dewdrops and fog drops. Flash-lamp photograph taken byJ. O. Mattsson at Ljunghusen, South Sweden, 26 November 1999,at 0.30 a.m MET.
20
affect the degree of generality. The observer standson the x axis some distance from the footpoint of thelight source or at its footpoint, giving O 5 ~xO, 0, zO!.Each point on the rotatory body, in three-dimensionalspace R 5 ~xR, yR, zR!, satisfies Eq. ~1!. However,
ere we are interested only in the intersection of theotatory body with the ground, which we assume toe flat and horizontal, i.e., R 5 ~xR, yR, 0!. The
points on the plane that retroreflect toward the ob-server lie on and outside the line of intersection.The appearance of the intersection can readily beapproximated on a grid.
Figures 6–10 show some examples of retroreflec-tional patterns calculated for planes of varying posi-tions and orientations. In all the calculations,except those for Fig. 9, we assume that both the lightsource and the observer are points. In Fig. 9 weallow the light source to be a cube centered at heightzL above the ground, i.e., L 5 ~DxL, DyL, zL 1 DzL!.Grid-point calculations of Eq. ~1! were made for eachof the eight corners of the light cube.
When the light source is placed in the zenith andnear the observer, the heiligenschein is circular, butlarger. Outside the heiligenschein is a circular beltwith a phase angle of more than 5° so that there is noretroreflection from the belt toward the observer.Outside this area again lies an area with a phaseangle of 5° or less. Inasmuch the distance from thelight source is greater, this area should display weak-ened retroreflection @Fig. 6~a!#. When the lightsource is located obliquely above the observer or cam-era the heiligenschein becomes extended @Fig. 6~b!#and, when the mutual positions of light source, ob-server or camera, and ground are altered, the nonre-troreflecting belt can be breached so that theheiligenschein merges into the outer retroreflectingarea @Fig. 6~c!#. The shape, size, and location of thezones depend on the mutual positions of the lightsource, the observer or camera, and the plane surface~Figs. 7–10!.
Note that the nonretroreflecting belt becomes nar-rower with decreasing distance of the light sourcefrom the observer or camera until it disappears com-pletely and the whole plane retroreflects at least intheory, resulting in a landscape without shadows or,alternatively, a phenomenon related to the sylvan-shine.
Drop-covered surfaces at some distance from theground or ground cover, as, for example, the upperparts of trees and bushes, will, of course, retroreflectfrom those points that are situated outside or on theimaginary surface of the rotatory body.
All the points on the surfaces of the imaginaryrotatory bodies represented in Fig. 5 form triangleswith points L and O. We regard the length of amedian from a point on the surface of one of theimaginary rotatory bodies to the opposite side ~thehord L–O! of the triangle, and perpendicular to this,
as being a useful measure of the relative sizes of therotatory bodies. If the chord has a length of one
September 2001 y Vol. 40, No. 27 y APPLIED OPTICS 4801
wwpbt
gltntstab
4
unit, the length of median m can be readily calculatedfrom the equation
m 5 0.5ytan~vy2!, (2)
here v is the phase angle. For the heiligenscheinith a phase angle of 5°, m is 11.45 units; for therimary rainbow, 1.30 units; for the secondary rain-ow, 1.05 units; for the 46° halo, 0.21 units; and forhe 22° halo, 0.10 units. The rotatory body of heili-
Fig. 5. Circle segments that, by rotation around their chords, formFor comparison of the size of the patterns and unlike the chords inthe phase angle for heiligenschein is less than 5° as well as the intsubsequent figures are included. For an explanation of the symb
802 APPLIED OPTICS y Vol. 40, No. 27 y 20 September 2001
enschein and associated phenomena in divergentight is thus much larger than the corresponding ro-atory bodies of the other atmospheric optical phe-omena shown in Fig. 5, which means that parts ofhe retroreflectional pattern could be situated a con-iderable distance from the light source and wouldherefore be only faintly illuminated. ~If we insteadssume a phase angle of less than 5° the rotatoryody should be even larger.! This could be one rea-
Fig. 4. Composite of flashlight images recorded from anairplane flying over Prasttomta, South Sweden, in the lateevening of 16 April 1968. Strong retroreflection from dewcharacterized open terrain. The figure illustrates an ef-fect related to the sylvanshine. As with the sylvanshinethe light source was close to the observer and camera, andthe retroreflecting area therefore extended over a largesolid angle. In contrast with the sylvanshine, the retro-reflection from the trees was minimal or nonexistent. Theshort sides of the image correspond to approximately200 m. The photographs were taken by the staff of anexperimental station belonging to the Swedish Defence Ma-terial Administration in Malmslatt, South Sweden.
maginary rotatory bodies of some atmospheric optical phenomena.all the chords here are the same length. The limit beyond which
tion lines that correspond to the horizontal surface in some of theee Fig. 1.
the iFig. 1ersecols s
d7r
son this retroreflectional pattern was not reportedpreviously. Another reason could be the diffuse de-limitation of the retroreflecting areas. Now that thephenomenon has been presented, it is perhaps lesslikely that the parts closer to the observer will escapenotice.
To reproduce some of the retroreflectional patternswe carried out some outdoor experiments with drop-covered boards scattered on the ground and illumi-
Fig. 6. Retroreflecting areas ~white! calculated for a plane hori-zontal surface ~e.g., the ground! illuminated by divergent light.An asterisk denotes the lamp ~a mathematical point!; a dot denotesthe observer. The lamp is situated 2.5 m above the plane surface;the observer’s eye level is at 2 m. The distance between thefootpoints of the lamp and the observer is ~a! 0 m, ~b! 0.12 m, ~c!0.15 m. The dark patterns in this and the following figures wereformed by analogy with transverse sections through an apple. Allthe measurements are in meters.
20
Fig. 7. Same as Fig. 6 but with the lamp 5 m above ground and2 m between the footpoints of the lamp and the observer.
Fig. 8. Same as Fig. 7 but with 5 m between the footpoints of thelamp and the observer.
Fig. 9. Same as Fig. 7 but with the lamp as a 0.23-m cube. Theistance between the footpoints of the lamp and the observer ism. The fact that the light source is not regarded as a point
esults in a diffuse delimitation of the pattern.
September 2001 y Vol. 40, No. 27 y APPLIED OPTICS 4803
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nated by a strong electric bulb a short distance away.When the positions of the boards were altered rela-tive to the light source, some nearby details of thepatterns were discernible although they were not suf-ficiently distinct to be photographed.
When the light comes from behind, the shadow castby the observer can partially obscure the heiligen-schein. This problem can be overcome to some ex-tent by replacing the observer by a small camera.
Retroreflection from spherical drops that rest di-rectly on a plane smooth surface without any hair orthick coating is most intense at a given angle of in-cident light, which, according to Mattsson and Cav-allin,11 is approximately 60°, although figurespresented by Lynch and Livingston7 support a valuef approximately 54°. The heightened oblique ret-oreflection can give rise to certain optical effects in
Fig. 10. ~a! Same as Fig. 7 but with 7.5 m between the footpointsof the lamp and the observer. ~b! The merging of the heiligen-schein and the outer retroreflecting area.
Fig. 11. How a retroreflec
804 APPLIED OPTICS y Vol. 40, No. 27 y 20 September 2001
this type of drop deposition. In parallel light as wellas in divergent light from a source not too close to theobserver, a particularly brilliant heiligenschein orpart of it can be seen when the active drops are illu-minated by light at this angle of incidence, when allother factors are disregarded. In the retroreflectingdrop deposition on a plane smooth surface illumi-nated by a light source close to but not behind theobserver, the increased brilliance takes the form of acircular belt, a retroreflection circle, of drops struckby light with the relevant angle of incidence. Alter-natively, the decrease in light intensity of the surfacewith distance from the nadir will be reduced within acircular belt where the angle of light incidence isoptimal ~Fig. 11!. For spherical drops the nadir ishe center of the circular belt with a radius of 60° ~or4°!. For distorted ~flattish! drops the values areigher than for spherical drops ~see Fig. 12!. Heres well, all other factors are disregarded.When the drops on the surface are larger and
herefore flatter, their nonsphericity would probablynhance the degree of brilliance of the heiligenschein.f the inclination of the board is altered, certain mod-fications result because the flatness of the drops isartially the result of surface tension, partially ofravity.These effects of intensified retroreflection in rela-
ion to the direction of incident light have not to ournowledge, been published before. However, gonio-hotometric measurements with laser light11 andutdoor experiments indicate their existence. Forhe experiments we used a horizontal waxed boardainted white, which had been sprayed with waternd obliquely illuminated from above by light from aandle. The board was photographed from a posi-ion close to the light source. By increasing the dis-ance between the board and the light source, a zonehat displayed strong retroreflection appeared wherencident light was approximately 70°. This zoneontrasted strongly with a drop-free track retained ascontrol on the board ~Fig. 12!, which agrees with
esults from goniophotometric measurements maden a dense cover of large, and consequently somewhatat, drops. The retroreflection was considerably re-
circle can be represented.
tion
teaodcfbntm
duced around the nadir and also decreased stronglywhen angle of incidence increased to more than ap-proximately 75°. Additional experiments of thistype including some with deposits of spherical drops~dew cover! are recommended.
The effects of heightened retroreflection in relationo the direction of incident light, as well as the otherffects of light divergence, can be seen under favor-ble circumstances, for example, in a horizontallyriented stand of vegetation, such as a field with aense cover of rape seedlings ~Brassica napus!. Re-ordings in the dark with a scanning laser beam couldacilitate their registration. Such recordings areuilt up at each point by retroreflected light. Inight-recorded laser images there is little or no con-amination of light from other parts of the scene, asight occur in flashlight images.
4. Final Remarks
Many observations of retroreflectional phenomena, inparticular the droplet variant of heiligenschein, aremade in divergent light from an artificial source suchas streetlights and lamps in parks. Geometric prop-erties of the phenomena in such light that have pre-viously been overlooked should be investigated indetail and fully documented.
Exactly how the heiligenschein and related phe-nomena are perceived, in both parallel and diver-gent light, is still not completely understood.However, we already know that the brilliance andluster of the phenomena are enhanced when ob-served from a vehicle in motion or when the ob-server changes position with respect to thephenomena. According to Greenler12 the effect ismore readily observed than photographed, becausemotion apparently blurs the structure of the back-ground so that it is easier to observe the light in-tensity effect. However, we ourselves believe thatthe reason the phenomena are enhanced when seenin motion is that the observer sees the changes inillumination of details of the ground or vegetationwhen the antipoint area of the light source passesacross them. The shine is also more readily per-
Fig. 12. Strong retroreflection from large drops that cover a boardin an outdoor experiment. Backscatter was strongest where lightincidence was approximately 70°, which could be estimated bycomparison with a drop-free track.
20
ceived when the rods of the eye are activated be-cause they are more sensitive than the cones andreact more rapidly.
When the illuminated parts of the stalks, or thewater drops, are viewed stereoscopically, how doesthis effect the perception of the heiligenschein lus-ter and what is the role of the glistening effect?We have found that the sheen becomes weaker andcan disappear when observed with only one eye.What happens when the distance between the eyesincreases as when one uses a mirror system or fieldglasses? These and other questions lend an addedincentive to the further study of the perception ofheiligenschein.
The study of heiligenschein and related retroreflec-tional phenomena also yields information of practicalvalue, for example, with respect to architecture,plant-surface properties, and soil texture, as well asdew distribution for use as a local climatic or archae-ological indicator.10,11,13–15 On a clear night pat-terns of dew could reveal the presence of patches ofcold such as a flow of cold air or cold-air lakes andeven disclose the location of wind-protected zones.Dew-free areas could indicate a warmer environmentsuch as thermal belts, zones exposed to counterradia-tion from buildings and trees, and sites exposed towind. The physical properties of the ground are alsoof significance for the surface temperature and for theformation of dew. Buried archaeological remainscould have an effect on the ground physics andthereby indirectly also on the formation of and thepattern of dew. The heiligenschein effect shouldalso be taken into consideration during the interpre-tation of air photographs and satellite images. Inastronomy the heiligenschein effect ~or opposition ef-fect as it is also termed! is used to retrieve informa-tion about the regolith.
The heiligenschein and related retroreflectionalphenomena can be investigated by flash-lamp pho-tography from the air or the ground, airborne regis-tration by ~circular! scanning with a laser beam, orvideoscanning of the antisolar or antilunar area froman aircraft.
Directed flashlight techniques as well as speciallight-amplifying and telelens techniques allow re-cordings to be made over extensive areas. Retrore-flectional studies of limited surfaces in the terrainand the use of physical models can also yield valuableinformation, for example, in connection with the mi-croclimate.
We thank three anonymous reviewers for sugges-tions that greatly improved the manuscript. We arealso indebted to Margaret Greenwood Petersson forchecking the language.
References1. M. Minnaert, “Een halo in de onmiddellijke nabijheid van het
oog,” Hemel Dampkring 26, 51–54 ~1928!.2. J. O. Mattsson, L. Barring, and E. Almqvist, “Experimenting
with Minnaert’s Cigar,” Appl. Opt. 39, 3604–3611 ~2000!.3. C. Floor, “Rainbows and haloes in lighthouse beams,” Weather
35, 203–208 ~1980!.
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4. C. Floor, “Optic phenomena and optical illusions near light- of Physical Geography, Lund University, Lund, Sweden, 1971!,
4
houses,” Z. Meteorol. 32, 229–233 ~1982!.5. J. O. Mattsson, “Concerning haloes, rainbows and dewbows in
divergent light,” Weather 53, 176–181 ~1998!.6. J. O. Mattsson, S. Nordbeck, and B. Rystedt, “Dewbows and
fogbows in divergent light,” No. 11 of Lund Studies inGeography Series C ~Lund University, Lund, Sweden,1971!.
7. D. K. Lynch and W. Livingston, Color and Light in Nature~Cambridge University, Cambridge, England, 1995!.
8. K. Muinonen, “Coherent backscattering by solar system dustparticles,” in Asteroids, Comets, Meteors 1993, A. Milani, M.Di Martino, and A. Cellino, eds. International AstronomicalUnion Symposium No. 160 ~Kluwer Academic, Dordrecht,The Netherlands, 1994!, pp. 271–293.
9. J. O. Mattsson, “Heiligenschein and retro-reflection from drop-covered surfaces,” No. 7 of Rapporter och notiser ~Department
806 APPLIED OPTICS y Vol. 40, No. 27 y 20 September 2001
in Swedish.10. A. B. Fraser, “The sylvanshine: retroreflection from dew-
covered trees,” Appl. Opt. 33, 4539–4547 ~1994!.11. J. O. Mattsson and C. Cavallin, “Retroreflection of light
from drop-covered surfaces and an image-producing device forregistration of this light,” Oikos 23, 285–294 ~1972!.
12. R. Greenler, Rainbows, Halos, and Glories ~Cambridge Uni-versity, Cambridge, England, 1980!.
13. J. O. Mattsson, “Dew as a climatic indicator,” SvenskGeografisk Årsbok 47, 29–52 ~1971!, in Swedish.
14. J. O. Mattsson, “Climatic information in night-recorded aerialphotographs with special regard to registrations made in retro-reflected light,” No. 23 of Rapporter och notiser ~Department ofPhysical Geography, Lund University, Lund, Sweden, 1974!.
15. J. O. Mattsson, “Images made by laser-scanner,” Svensk Lant-materitidskrift 64, 435–441 ~1972!, in Swedish.
