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An optical mirage is a phenomenon associated with the refraction of light in the gaseous (cloud-free) atmosphere. During mirage a visible image of some distant object is made to appear displaced from the true position of the object. The image is produced when the light energy emanating from the distant source travels along a curvilinear instead of a rectilinear path, the curvilinear path, in turn, arises from abnormal spatial variations in density that are invariably associated with abnormal temperature gradients.
The visible image of the mirage can represent shape and color of the "mirrored" object either exactly or distorted. Distortions most commonly consist of an exaggerated elongation, an exaggerated broadening, or a complete or partial inversion of the object shape. Frequently, mirages involve multiple images of a single source. Under special conditions, refractive separation of the color components of white light can enhance the observation of a mirage. Atmospheric scintillation can introduce rapid variations in position, brightness, and color variations of the image.
When both the observer and the source are stationary, a mirage can be observed for several hours. However, when either one or both are in motion, a mirage image may appear for a duration of only seconds or minutes.
Although men have observed mirages since the beginning of recorded history, extensive studies of the phenomenon did not begin till the last part of the 18th century. Since that time, however, a large volume of literature has become available from which emerges a clear picture of the nature of the mirage.
The comprehensive body of information presented here is based on a survey of the literature, and constitutes the state-of-the-art knowledge on optical mirages. The report provides a ready source of up-to-date information that can be applied to problems involving optical mirages.
In essence, the literature survey yields the following principal characteristics of the mirage:
The contents of this report are based on a survey of literature on atmospheric refraction in general and on optical mirages in particular. The survey began with the review of such basic sources of information on atmospheric optics as Meteorologische Optik, by Pernter and Exner, Physics of the Air, by Humphreys, The Nature of Light and Colour in the Open Air,
In category 1, descriptive accounts of mirages go back in time to 1796, when Joseph Huddart observed superior mirages near Macao. (Earlier accounts can be found in Meteorologische Optik.) Numerous recent observations of abnormal atmospheric refraction can be found in The Marine Observer. The two "classical" observations most frequently quoted as having "triggered" a long series of investigations on optical mirage are the observations of Vince and Scoresby. Vince (1798) from a position on the sea shore observed multiple images of ships, some upright and some inverted, above the ocean horizon; Scoresby (1820) observed elevated images of ships and coastal lines while navigating near Greenland. Both observations were carefully documented and results were read before bodies of the Royal Society.
Proposed theories of the mirage (category 2) are basically of three types, that are best represented by the respective works of Tait (1883), Wegener (1918), and Sir C. V. Raman (1959). Tait (in his efforts to explain the observations by Vince and Scoresby) considers a vertically
Comparisons made between observation and theory (category 3) indicate that the two are compatible - i.e., abnormal light-refraction phenomena are associated with anomalous atmospheric-temperature structure. Many investigations (category 4) are concerned with determining the effects of light refraction on optical measurements made in such fields as surveying and hydrography. Corrections for refraction based on average atmospheric conditions have been computed (category 5). Of specific interest to meteorologists are the attempts to develop inversion techniques for obtaining low-level temperature structure from light-refraction measurements (category 4). The temperature profiles that can be obtained do not have the desired resolution and accuracy. During the last decade, literature on atmospheric scintillation has become extensive due to its importance to astronomy, optical communication, and optical ranging. A selected number of recent papers are presented in category 6.
The publications categorized below represent a cross section of the various endeavors that have resulted from the Earth's atmosphere having light-refraction properties. The body of information is fundamental to the contents of this report. In addition to the listed literature, many other sources of information on atmospheric optics were consulted in its production. They are referenced throughout the text, and are compiled in a bibliography at the end of the report.
CATEGORIES |
1. Descriptive 2. Theoretical Models 3. Theory vs. Observation 4. Application 5. Average values 6. Atmospheric Scintillation |
BACK TO SECTION 2
|
A. General B. Optical Refractive Index C. Snell's Law of Refraction D. Partial Reflections E. Spatial Variations F. Meteorological Conditions |
A clear picture of what causes refraction is obtained by means of Huygen's principle which states that each point on a wavefront may be regarded as the source or center of "secondary waves" or "secondary disturbances," At a given instant, the wavefront is the envelope of the centers of the secondary disturbances. In the case of a travelling wavefront the center of each secondary disturbance propagates in a direction perpendicular to the wavefront. When the velocity of propagation varies along the wavefront the disturbances travel different distances so that the orientation of their enveloping surface changes in time, i.e., the direction of propagation of the wavefront changes.
Practically all large-scale effects of atmospheric refraction can be explained by the use of geometrical optics, which is the method of tracing light rays -- i.e., of following directions of energy flow. The laws that form the basis of geometrical optics are the law of reflection (formulated by Fresnel) and the law of refraction (formulated by Snell). When a ray of light strikes a sharp boundary that separates two transparent media in which the velocity of light is appreciably different,
The group refractive index is given by
For a gas, the refractive index is proportional to the density rho of the gas. This can be expressed by the Gladstone-Dale relation:
Conditions: 5455 Å, 15°C | |
P, mb | n |
---|---|
1,000 | 1.000274 |
950 | 1.000260 |
900 | 1.000246 |
Conditions: 5455 Å, 1013.3 mb | |
T, °C | n |
---|---|
0 | 1.000292 |
15 | 1.000277 |
30 | 1.000263 |
Conditions: 1013.3 mb, 15°C | |
Lambda, Å | n |
---|---|
4,000 | 1.000282 |
5,000 | 1.000278 |
6,000 | 1.000276 |
7,000 | 1.000275 |
8,000 | 1.000275 |
T(°K) | 273 | 283 | 288 | 293 | 298 | 303 |
e/P | 0.006 | 0.012 | 0.017 | 0.023 | 0.031 | 0.042 |
Table 1 shows that the optical refractive index of the atmosphere is a relatively small quantity and that its largest variations with temperature, pressure and wavelength are of the order of 10-5. Such small changes in the refractive index correspond to relatively small changes in the direction of optical-energy propagation. Hence, an optical image that arises from atmospheric light refraction cannot be expected to have a large angular displacement from the light source.
Figure 1: Snell's Law
Click on Thumbnail to see Full-size image.
Mirages arise under atmospheric conditions that involve "total reflection." Under such conditions the direction of energy propagation is from dense-to-rare, and the angle of incidence exceeds the critical angle such that the energy is not transmitted through the refracting layer but is "mirrored." The concept of total reflection is most rigorously applied by Wegener in his theoretical model of atmospheric refraction (Wegener, 1918).
Snell's law can be put into a form that enables the construction of a light ray in a horizontal layer wherein the refractive index changes continuously. Introducing a nondimensional rectangular phi ,z coordinate system with the x-axis in the horizontal,
When the ordinate of the nondimensional coordinate system is to represent height, z must represent a quantity az', where z' has units of height and a is the scale factor.
By introducing more complicated refractive-index profiles into Eq. (3), the paths of the refracted rays from an extended light source can be obtained and mirage images can be constructed. Tait and other investigators have successfully used this method to explain various mirage observations.
Application of Eq. (3) is restricted to light refraction in a plane- stratified atmosphere and to refractive-index profiles that permit its integration.
This result can be applied to atmospheric layers of known thickness and refractive index distribution; the most convenient model is that in which
Atmospheric layers with
As dictated by Snell's law, refraction of light in the earth's atmosphere arises from spatial variations in the optical refractive index. Since
or
(°C/100m) |
CURVATURE OF LIGHT RAYS ("/km) |
---|---|
-3.4 | 0 |
-1.0 | 5.3 |
-0.5 | 6.4 |
0 | 7.5 |
+6.9 | 22.7 |
+11.6 | 33.0 |
The temperature increase through a low-level inversion layer can vary from a few degrees to as much as 30°C during nighttime cooling of the ground layer. During daytime heating, the temperature can drop by as much as 20°C in the first couple of meters above the ground
At any given location, the frequency of occurrence of large temperature lapses is directly related to the frequency of occurrence of warm sunny days. Fig.2 shows the average distribution of normal summer sunshine across the United States (Visher, 1954). More than seventy percent of the possible total is recorded in a large area extending from the Mississippi to the West Coast. Consequently, low-level mirages associated with large temperature lapses may be rather normal phenomena in this area. Distribution for summer and winter of the frequency of occurrence of temperature inversions <150 m above ground level are shown for the United States in Fig. 3 (Hosler, 1961). The data are based on a two-year sampling period. Figure 4 shows the distribution across the United States of the percentage of time that the visibility exceeds 10 km (Eldridge, 1966). When Figs. 3 and 4 are combined it is seen that large areas between roughly the Mississippi and the West Coast have a high frequency of extended horizontal visibility and a relatively high frequency of low-level temperature inversions. These meteorological conditions are favorable for the formation of mirages. On the basis of the climatic data shown in Figs. 2, 3, and 4 it can be concluded that at some places a low-level mirage may be a rather normal phenomenon while in other places it may be highly abnormal. An example of the sometimes daily recurrence of superior mirage over the northern part of the Gulf of California is discussed by Ronald Ives (1968). Temperature inversions in the cloud-free atmosphere are often recorded at heights up to 6,000 m above the ground. These elevated inversions usually arise from descending air motions, although radiative processes can be involved when very thin cirrus clouds or haze layers are present. Narrow
Values of astronomical and terrestrial refraction computed for
average atmospheric temperature structure are well documented. The
angular difference between the apparent zenith distance of a
celestial body and its true zenith distance (as observed from a
position near sea level) is zero at the zenith but gradually
increases in magnitude away from the zenith to a maximum of about 35
mm. of arc on the horizon. Thirty-five minutes of arc is very nearly
equal to the angle subtended by the sun's or moon's disc (30 mm.), so
that when these heavenly bodies appear just above the horizon they
are geometrically just below it. Figure 5 shows average values of
astronomical refraction as a function of zenith angle. The very large
Terrestrial-refraction angles have been computed as a function of
zenith angle and altitude of the luminous source (Link and Sekera
1940; Saunders, 1963). Depending on height, refraction angles
computed with reference to sea level vary from <5 sec. of
arc at a zenith angle of 5° to <12 min. of arc at a
zenith angle of 86°. Above 42 km refraction is negligible.
The importance of the seemingly small astronomical and terrestrial
refraction on visual observations can be evaluated as follows.
Resolving theory and practice have established that the human eye
(which is a lens system) cannot resolve, separate clearly, or
recognizably identify two points that subtend an angle to the eye of
less than 1/16° = 3.75 min. (Tolansky 1964; Minnaert,
1954). Under standard atmospheric-temperature conditions, angular
deviations due to astronomical and terrestrial refraction that are
larger than 3.75 min. occur when distant light sources are less than
about 14° above the horizon (zenith angle larger than about
76°. Hence, the effects of systematic atmospheric refraction
on visual observations of a distant light source (point source) which
is less than about 76° from the zenith can be considered
negligible because the average human eye cannot clearly separate the
source from its refracted image. However, when the luminous point
source is located at about 14° or less from the horizon, the location
and appearance of the source as seen by a distant observer are those
of its refracted image. Close to the horizon, refraction becomes
large enough to affect the visual observations of
When a luminous source is near the horizon, (i.e., near the
horizontal plane of view of its observer) the optical path length
through the atmosphere is maximum. In this case, systematic
refraction is at a maximum and the visual effects can be large when
layers of anomalous vertical temperature gradient are present. There
are, however, important practical limitations as to how much the
apparent position of a refracted image can differ from the true
position of the source. Limits in the viewing geometry can be
determined by Snell's law using limiting values of the optical
refractive index.
Observations indicate that a temperature change of 30°C across
relatively thin (<1 km) layers of temperature inversion or
temperature lapse approximates the maximum change that can be
expected (Ramdas, 1951). Thirty degrees Centigrade correspond to a
refractive-index change of about 3x10-5 (Brunt, 1929).
Combining this maximum change in the optical refractive index with
the range of values listed in Table 1, the following limits are
suggested as the range of the refractive index (n) that can be
expected in the lower cloud-free atmosphere.
It is evident that the presence of a layer of large temperature
gradient is necessary but not sufficient for mirage formation. A
remaining requirement is the presence of light that illuminates the
layer at grazing incidence. The incident light can originate from
a
physical source such as sun, moon, or planet, or it can be skylight
or sunlight reflected from the ground.
Whether the mirage is observed or not depends on the position of the
observer with respect to the light source and the refracting layer.
The planar geometry involved in a mirage observation can be
illustrated by applying Eq. (3):
The preceding discussion applies only to the case where the observer
is located within, or at the boundary of, the mirage-producing layer,
If the observer is some distance above or below the mirage-producing
layer, mirages of much more distant objects may appear.
From the above, it is evident that principal characteristics of the
optical mirage are the small elevation angles under which the
phenomenon is observed (<1°) and the large distances
(tens of kilometers) between observer and "mirrored" object that are
possible. The geometry of the mirage explains why many observations
are made on or near horizontally extensive, flat terrain such as
deserts, lakes, and oceans and frequently involve images viewed
through binoculars (oases, ships, islands, coastal geography).
Furthermore, the above geometry illustrates that the duration of a
mirage observation is critically dependent on whether or not the
source and observer are in relative motion. For example, when the
light source is moving in such a way that the angle of illumination,
Thetao, oscillates around the critical angle, a
stationary observer located at A in Fig. 7 may see a mirage image
that alternately appears and disappears.
It has been recognized that systematic refraction of the light from a
single source can lead to multiple mirage images the shapes of
which can be complicated. The early observations by Vince (1798) and
Scoresby (1820) included sightings of completely or partially
inverted images of a single distant ship. From a coastal position on
the English Channel, John Parnell (1869) observed five
elevated images, all in a vertical line, of a lighthouse on the
French Coast. All five images had different shapes. During their
observations in Spain, Biot and Arago (1809) observed up to four
elevated images of a distant (161 km) light signal. The images
disappeared and reappeared intermittently and at times joined to form
a narrow vertical column of light which subsequently separated into
two parts, the lower part appearing red and the upper part appearing
green. The above observations resulted from abnormal atmospheric
light-refraction the observed images were distant, and in most cases
detailed descriptions were made with the aid of binoculars.
Practically all theoretical and experimental investigations of
optical mirages (e.g., Wollaston 1800; Hillers 1914; R. W. Wood 1911)
have been concerned with demonstrating the number and shape of
observed images. Tait's theoretical treatise and Wollaston's
laboratory experiment can be considered classical examples. Tait's
terrestrial-refraction model represents a horizontally stratified
atmosphere, and a vertically finite refracting layer with a
continuous change in refractive index. Under these assumptions the
paths of light rays are represented by the solution to the
differential equation:
Apparent vertical stretching (elongation, towering) of a luminous
object due to refraction is illustrated in Fig. 9. For the sake of
clarity, height and elevation angles are exaggerated. A horizontal
refracting layer is assumed that is 10 meters thick and through which
the refractive index (n) decreases with height (z) from
1.00029 to 1.00026 according to the relation
Many examples of image inversion, vertical stretching, and shrinking
due to abnormal atmospheric refraction are given in The Marine
Observer.
Tait's theoretical approach, the emphasis on the refractive-index
profile, is basic to many other theoretical investigations of the
mirage. For example, Wilhelm Hillers (1913) shows how two refracted
images of a single light source can be formed when the profile in the
refracting layer is such that the refracted rays are circular. Fig.
10 shows the
Tait's approach cannot be applied indiscriminately to all mirage
phenomena because integration of Eq. (3) is restricted to a selected
range of refractive index profiles. Furthermore, the effect of the
earth's curvature is excluded so that only mirage phenomena
associated with not-too-distant objects can be considered. Hence,
Tait's model cannot explain mirage observations associated with
extraterrestrial sources such as the sun or the moon.
Alfred Wegener (1918) has developed an atmospheric refraction model
that explains distorted images of the sun, moon, planets, or stars
that are often observed near the horizon. Wegener assumes a
spherically stratified atmosphere and reduces the refracting layer to
a refracting boundary or surface of total reflection. Wegener
demonstrated that when the refracting boundary lies above the
observer and the sun is on the horizon, the boundary refracts the
solar light rays in such a way that the observer views two separate
images of the solar disc, a flattened upper image and a distorted
lower image. Fig. 11 shows the successive form of the two images for
a setting sun or moon in the presence of a 7°
temperature-inversion layer 50 m above the observer* as computed by
Wegener. The degree of deflection of the incoming light rays and
consequently the degree of distortion of the solar disc depends on
the refractive-index change or temperature change across the
reflecting boundary. When the temperature change is small, only a
single distorted image of the solar disc appears. When the change
across the boundary is
Wegener's model is not restricted to luminous sources outside the
earth's atmosphere. It can be applied to distant terrestrial objects
such as mountains from which emitted light rays are at grazing
incidence to the top of the refracting boundary. Wegener's model of
atmospheric refraction illustrates the characteristics that are basic
to many spectacular risings or settings of sun, moon, or planet.
Following are three accounts of such abnormal atmospheric-refraction
phenomena as given in The Marine Observer.
The atmospheric-refraction models of Tait and Wegener quantitatively
explain the basic characteristics of the most commonly observed
mirage-images. Other theoretical investigations are available that
discuss various special aspects. For example, the theory of the
superior mirage by Odd Haug explains the appearance of up to four
images from a single source. Wilhelm Hillers treats the special case
of a lateral mirage, i.e., the refraction of light when the
refractive-index gradient is horizontal, as may be the case along a
wall heated by solar radiation. Koji Ilidaka and Gustav Forster
discuss the theory of refraction when the surfaces of constant
density in the atmosphere are somewhere between horizontal and
vertical. Together, these theoretical models explain adequately the
varying ways in which a mirage image can appear to an observer.
Currently, there is no single model with a numerical solution
to all aspects of the mirage.
M/V. Australind. Captain J. F. Wood. Port Said to Bremen.
Observer, Mr. D. Ewan, Chief Officer.
27th April, 1950, 1546-1549 G.M.T. The accompanying sketches picture
the sequence of shapes assumed by the sun as a result of refraction.
After Clearing the horizon the sun slowly regained its normal
proportions and at an altitude of 1½° no refraction was
apparent. No land was visible near the phenomenon. Wind N, force 4.
Barometer 1020.3 mb, air temp. 58°F. Sky cloudless.
Position of ship: Latitude 38° 04'N., Longitude 9° 24'W.
(Reproduced from The Marine Observer, Vol. 21, No. 152, p. 80,
April 1951)
A recent theoretical and experimental investigation of the optical
mirage is presented by Sir C. V. Raman (1959). Sir C. V. Raman
demonstrates that multiple, inverted images of a single object can
arise from interference and focussing of the incident and reflected
wavefronts near the boundary of total reflection. Raman's work, which
is entirely based on wave theory, suggests the interaction of
wavefronts within a refracting layer as a mechanism in mirage
formation.
The occurrence of focussing and interference in situations that give
rise to mirage, examined specifically by Raman, is also evident from
various investigations based on geometrical optics. For example,
the crossing of light rays mentioned in connection with image
inversion implies interference of wavefronts at the points of
intersection.
The visual effects from focussing and interference must be considered
in particular when plane-parallel radiation (radiation from a very
distant source) is incident on a layer of total reflection. In this
case, there is a constant crossing of light rays within a relatively
narrow region of the refracting layer, as illustrated in Fig. 12 (for
the sake of clarity, height and elevation angles are exaggerated). In
Fig. 12, a circular collimated light-beam of diameter A is incident
on the lower boundary of a temperature-inversion layer at angle equal
to or exceeding the critical angle for total reflection. Interference
of the incident and reflected wavefronts occurs in a selected layer
near the level of total reflection. This layer, shaded in Fig. 12,
has a maximum thickness B, which is dependent on A. In
the absence of absorption, the amount of radiant energy, flowing per
unit time through Pi·A2 equals that flowing
through Pi·B2. When B is less than
A, the energy density at B is larger than at A,
so that the brightness of the refracted light beam increases in the
layer of interference.
An example of the ratio of A to B can be Given with the
aid of Eq. (3). It is assumed that the optical refractive index
through the inversion layer varies from
Observations of the brightening phenomenon must be considered rare in
view of the selective location of its occurrence within the
temperature-inversion layer and the requirement of plane-parallel
incident radiation. Upper-level inversions seem most likely to
produce the phenomenon. Some photographs showing apparent brightening
of "spike" reflections on the edge of the setting sun are shown in
O'Connell (1958, c.f., p. 158).
Microscopic effects due to interference of wavefronts within the area
of brightening are illustrated in Fig. 13. Wavefronts are indicated
rather than light rays. Unless absorption is extremely large, light
rays are normal to the wavefront. A train of plane-parallel waves is
assumed incident on the lower boundary of a refracting layer in which
the refractive-index decreases with height. When the angle of
incidence equals the critical angle, the incident waves are refracted
upon entering the refracting layer and are totally reflected at the
upper boundary. The crests and troughs of the waves are indicated by
solid lines and dashed lines, respectively. At the upper boundary,
the wavefronts of the incident and reflected waves converge to a
focus. The focus is called a cusp. The upper boundary of the
refracting layer resembles a caustic,
Currently, the focussing and interference effects are the least
explored and consequently the least discussed of the various aspects
associated with optical mirage.
Due to the wavelength dependence of the optical refractive index,
systematic refraction of white light leads to a separation of the
composing colors. Visible effects of color separation are most
frequently associated with astronomical refraction. In this case,
the light enters the atmosphere at an upper boundary where n
approaches unity for all wavelengths. At an observation site near sea
level n is wavelength-dependent, so that from the upper
boundary of the atmosphere to the observation site the individual
color components are refracted at different angles. The basic
composing color of white light may be assumed to be red (24%), green
(38%), and blue-violet 38%); the red is refracted less than the
green, while the green is refracted less than the blue-violet. The
visual effects of color separation depend on the zenith
The diameter of the light beam from a given extraterrestrial source
decreases with respect to an earth-bound observer, with increasing
distance from the zenith, as illustrated in Fig. 14. Thus, when the
zenith angle increases, the apparent diameter D of the
light source decreases rapidly to a minimum value on the horizon. Hence,
the chance of having a light source of diameter less than D is
greatest on the horizon. Therefore, color separation is observed
most frequently on the horizon, when the light source is reduced to
a bright point like a star or a minute portion of the solar or lunar
disc. A prominent example of the visible effects of color
separation is the so-called Green Flash. This phenomenon is
sometimes observed when the sun disappears in a clear sky below a
distant horizon. The last star-like point can then be seen to change
rapidly from pale yellow or orange, to green, and finally, blue, or
at least a bluish-green. The vividness of the green, when the sky is
exceptionally clear, together with its almost instant appearance
and extremely short duration, has given rise to the name "green
flash" for this phenomenon.
In terrestrial refraction the composing colors of white light are
very seldom separated to the extent that the effects can be observed
with the naked eye. When the wavelength dependence of the refractive
index is put back into Eq. (4),
Hence, for a given temperature inversion, the refractive index
(n) decreases somewhat faster with height (z) for
Lambda = 0.4µ
(blue) than for
Lambda = 0.7µ
(red), so that the blue rays are refracted more than the red rays.
However, the difference is generally too small to be resolved by the
eye. Only under very special conditions can a visible effect be
imagined. For example, when a 100-m-thick inversion layer is assumed
to be associated with a
Delta·T = 30°C,
the change of the refractive index for blue light and red light is
respectively,
When the optical refractive indices at the lower boundary of the
inversion are
(corresponding to P =1013.3 mb and T = 15°C), values at
the upper boundary are
When white light is incident at the lower boundary of the inversion
at an angle Phio such that
then the blue rays are totally reflected by the inversion layer but
the red rays are transmitted. Hence, for
S.S. Strathnaver. Captain I. M. Sinclair. Australia to London.
Observer, Mr. J. C. Vint, Supernumerary 2nd Officer.
6th December, 1957 at 2105 S.M.T. The accompanying sketch illustrates
the
M.V. Drina. Captain F. J. Swallow. Las Palmas to Buenos Aires.
Observer, Mr. W. M. Wheatley, Chief Officer.
28th January, 1956. At sunset the sun, when half a diameter above the
horizon, became lemon-coloured, although the shape remained normal.
The final visible segment of the sun turned to a vivid electric blue.
Visibility excellent. The sky after sunset was colourful with great
clarity of cloud shapes and colours. Cloud 3/8 Cu and Ac.
Position of ship: 18° 28's., 38° 28'w.
Note. The name of this phenomenon at sunset or sunrise is the
"green flash ", green being the colour most usually seen. It would
not be practicable to name it according to the colour observed, as
these comprise various shades of green and blue, also purple or
violet. We have had more observations of blue, purple or violet
flashes in recent years. While these colours are admittedly much less
frequently seen than various shades of green, it does appear that
they are not as rare as was form ly supposed; a probable explanation
of this is that more observers are now watching for the phenomenon.
M.V. Gloucester. Captain D. A. G. Dickens, R.N.R. Jeddah to
Suez. Observer, Mr. R. E. Baker, Chief Officer.
19th February, 1956. Abnormal refraction was observed as the sun set,
apparently shaped as shown in the sketches. The green flash was seen
all the time the upper half of the sun was disappearing,
approximately 30 sec; not only the detached pieces appeared green but
the edges of the main body as well.
Position of ship: 22° 08'N., 38° 25'E.
S.S. Pacific Northwest. Captain F. H. Perry. Panama to Los
Angeles. Observer, Mr. W. P. Crone, 4th Officer.
29th January, 1956. Half a minute before setting at bearing 262°
Venus appeared to turn bright red, becoming orange again just before
setting. At the moment of setting at 0345 G.M.T. there was an emerald
green flash of sec duration. This observation was made with the aid
of
binoculars. Cloud 2/8.
Position of ship: 24° 55'N., 112° 44'W.
(Reproduced from The Marine Observer. Vol. 27. No. 175, p. 15,
Jan. 1957)
M.V. Cambridge. Captain P. P. O. Harrison. Wellington to Balboa.
Observers, the Master, Mr. P. Bower, Chief Officer, and Mr. L. Money,
4th Officer.
2nd May, 1957. When the sun rose at 0700 S.M.T. a green flash was
plainly seen. There was a bank of cumulus whose base was one sun's
diameter above the horizon and as the sun disappeared behind the
cloud a red flash occurred lasting fully 3 sec.
Position of ship: 38° 51'S 175° 1O'W.
(Reproduced from The Marine Observer, Vol. 28, No. 180, p. 77,
April 1958)
S. S. Sirsa. Captain N. Maguire. Rangoon to Cochin. Observer,
Mr. J. Richardson.
3rd December, 1950, 1755 G.M.T. Jupiter on setting showed a red spot
on the side nearest to the horizon. The spot was visible through
binoculars and telescope but not to the naked eye. The sky was clear
in the vicinity and the phenomenon was visible from the time that the
planet was 20° above the horizon.
Position of ship: 7° 40' N, 77° 47' E.
Note. When abnormal refraction is present the light of stars
or planets near the horizon tends to be elongated into a short
spectrum with the red nearest the horizon and the green and blue
farthest from the horizon. Many varieties of phenomena result,
especially in the case of the bright planets Jupiter and Venus; these
are more often seen with binoculars than with unaided vision. At
times the planet may appear double, one red and one green, or the
colour of the planet may change from red to green. In cases of
extreme refraction the planet may be seen to "swim" out with a
lateral motion, accompanied by changes of colour, usually from red to
green, with momentary returns to the normal colour of the planet. The
green flash of sunrise or sunset is an example of the same thing; the
uppermost green image of the sun limb is visible for a fraction of a
second after the sun has set.
(Reproduced from The Marine Observer, Vol. 21, No. 154, p.
214. Oct. 1951)
Thus, unusual color effects that can be observed with the unaided eye
can be associated with mirage phenomena. Occurrence of these effects,
however, must be considered unusual in view of the special set of
circumstances required for their development.
Scintillation defines the rapid variations in apparent
brightness, position, or color of a distant luminous source when
viewed through the atmosphere. If the object lies outside the earth's
atmosphere, as in the case of stars and planets, the phenomenon is
termed astronomical scintillation; if the luminous source lies within
the atmosphere, the phenomenon is termed terrestrial scintillation.
Scintillation occurs when small-scale (meters or less)
inhomogeneities in atmospheric density interference with a
propagating wavefront for a short duration of seconds or minutes.
Such inhomogeneities are generally associated with turbulance and
convection. Turbulence and convection are most apparent in
atmospheric layers close to the earth's surface where they develop
under proper conditions of solar heating, wind velocity, and terrain.
However, they can occur also at high levels in the atmosphere.
Scintillation has been found associated with atmospheric layers near
the tropopause (30,000 to 40,000 feet).
Fluctuations in position are often referred to as "shimmer",
"dancing", or "wandering", and involve the apparent jerky or
continuous movement of an image about a mean point. Observations of
this phenomenon are not as common as observations of intensity
fluctuations. Under standard atmospheric conditions, position changes
vary from 1" to 30" of arc, and such displacements can hardly be
observed with the naked eye. Only under abnormal atmospheric
conditions are apparent position changes manifest. Their occurrence
is most probably in the case of point sources, i.e., sources having
no apparent diameter. Position changes of a planet like Venus or
Jupiter do occur, but actual observations are limited to very unusual
atmospheric conditions when the changes in direction of the
planet's light rays are so large as to be of the same order of
magnitude as the apparent diameter (0.5 to 1.0 minutes of arc).
In the case of an extended luminous source, a slow or rapid
"pulsation" can be observed. This contraction and expansion of the
image usually results in apparent changes of the image size.
Occasionally, pulsation of the solar or lunar limb can be observed
during setting or rising.
In general, the effects of scintillation are minimum when the
luminous source is viewed near the zenith, and maximum when the
source is viewed near the horizon. When terrestrial light sources are
involved, the scintillation increases with distance and is highly
dependent on the meteorological conditions.
The many detailed discussions of scintillation encountered in the
literature are primarily concerned with the application of optical
instruments to astronomy, optical communication, and optical
ranging.
The luminance or brightness, B, in e.g. lumens/m2 , of an
extended object or optical source is invariant with distance except
for losses due to scattering or absorption along the propagation
path. Except under conditions of heavy fog, clouds, or smog,
absorption is small compared to scattering, and may be neglected. If
the scattering coefficient per unit length, O , is constant,
attenuation of a light source of intrinsic brightness B is given by
where R is the distance of range travelled by the light from the
source to the point of observation. The portion of brightness lost by
scattering out of the path is given by
this loss represents light that is scattered in all directions by the
molecules of air and aerosol particles present in the propagation
path. Secondary scattering is neglected.
The quantity Sigma·R is often called the optical depth
of an atmospheric layer, although it is a dimensionless quantity.
Thus for thin layers where Sigma·R is small, the
scattered light flux, F, in e.g. lumens, is
where F is the light flux incident on the layer.
hence,
which, in the case of a small scattering volume where E and
Beta'(Phi) may be considered nearly constant over the entire
volume, reduces to
The units of Beta'(Phi) are typically lumens scattered per
unit solid angle per unit volume per lumen incident light per unit
area; I(Phi) then is expressed in candles, a unit of light
intensity equal to one lumen per steradian. The volume scattering
function is normalized by
hence for an isotropic scatterer, for which
The volume scattering function relative to an isotropic scatterer is
conveniently defined as
The relative volume scattering function for very clear air has maxima
at
respectively, and a minimum of
Industrial haze, or smog, has a strong maximum at
and a minimum at
with a weaker secondary maximum at
As an example of a scattering situation, consider a very clear
atmosphere with a total vertical optical depth of 0.2; this is about
twice the optical depth of a standard atmosphere of pure air
(Middleton, (1952). The linear scattering coefficient, Phi,
for this atmosphere will be about
2x10-5 m-1 near the ground. Assume that a
haze layer one meter in thickness and with an optical depth of 0.02
exists at 100 m above
To an observer on the ground, the additional extinction of light
caused by the presence of the haze layer, amounting to only 1.6% of
the incident light from a source near the zenith, would not be
perceptible except possibly very close to the horizon. However, light
scattered out of an intense beam by the haze layer could be easily
visible. Assume that a fairly powerful light source is aimed straight
up from the ground; taking as typical values, e.g., for an automobile
sealed beam unit, an intensity, Io, of
3x104 candles (30,000 candlepower) and a beam width of
6°, the light flux Fo incident on the layer at
h = 100 m is 236 lumens, neglecting attenuation in the
air below the layer. The beam solid angle, wo, is
7.85xl0-3 steradians. The incident illuminance,
Eo, on the layer is
where the illuminated area,
A = woh2,
is 78.5m2. The scattering volume, v, is
78.5m3 since the layer is one meter thick, and the
intensity of the scattered light is
If an observer is located 100 m from the light source, he will
observe the scattered light at a distance of ~140 m and a
scattering angle, Phi, of 135°. The apparent source of the
scattered light will appear to be elliptical, roughly 4° wide and
3° high, and will present an area normal to the observer,
An, of 62.6 m2. The value of
f(Phi) for a strongly scattering medium at
Phi = 135° is about 0.2; therefore the light
Is scattered toward the observer is approximately
7.5x10-2 candles, and the apparent brightness, B,
of the scattering volume will be
At this background brightness, data given by Middleton (1952) show
that the contrast required for 50% probability of detection for an
object of 3°-4° diameter is about 5.7x10-2; thus
the image hypothesized in this example would have a brightness about
20 times greater than the minimum detectable, and would no doubt be
easily visible as a pale, glowing, elliptical object.
In contrast, the air immediately above and below the haze layer with
Increasing the background brightness to
10-2 c/m2, corresponding to a bright,
moonlit night, would decrease the contrast of the scattered image to
1.2x10-1, which is about six times the minimum detectable
contrast at that background brightness and the image would therefore
still constitute a fairly obvious (object). Perception of light
scattered from the rest of the beam under this increased background
brightness, with
The level of background brightness for which the contrast of the
image in this example would be reduced to the point where there is
only a 50% probability of detection by an observer looking in the
right direction is roughly 10-1 c/m2; this
value corresponds to the brightness of a clear sky about 1/2 hour
after sunset.
Thus, scattering of light from sources of small beam width by
localized haze layers in the lower atmosphere may cause the
appearance of diffuse, glowing patches of light, moving with movement
of the light source, that could easily be interpreted as a UFO by an
observer unfamiliar with such phenomena. Data given by Middleton
(1952) show that with common light sources and under average
nighttime sky conditions, the main beam
During the last decade, active interest in optical mirage appears to
have waned. The reasons for the apparent decline are believed to be
two-fold. Firstly, on the basis of simple ray-tracing techniques,
the mirage theories satisfactorily explain the various large-scale
aspects of observations. Thus no disturbing contradictions between
theory and observation have been found. Secondly, although
atmospheric refraction remains of great interest to astronomy,
optical communication, and optical ranging, the phenomenon of the
mirage has so far failed to demonstrate a major use.
At the present time, there is no single theoretical model that
explains all the aspects, both macroscopic and microscopic, of the
mirage phenomenon. The absence of such a model must stand as evidence
that shortcomings remain in current knowledge. These shortcomings are
most eloquently discussed by Sir. C. V. Raman (1959), who suggests
and actually demonstrates that any approach to explain the phenomenon
must be based on wave-optics rather than ray-optics. The theory of
wave-optics, as applied by Sir. C. V. Raman, suggests the presence of
some intriguing aspects of the mirage that arise from the
interference and focussing of wavefronts in selected regions of the
refracting layer. Raman's experimental studies reveal that when a
collimated pencil of light is incident obliquely on a heated plate in
contact with air, the field of observation exhibits a dark region
adjacent to the plate into which the incident radiation does not
penetrate, followed by a layer in which there is an intense
concentration of light and then again by a series of dark and bright
bands of progressively diminishing intensity.
Further theoretical and experimental investigations are warranted in
order to determine to what extent the brightening and brightness
variations that arise from interference and focussing can add unusual
effects to observations of phenomenon associated with abnormal
refraction in the atmosphere.
When an unusual optical phenomenon is observed in the atmosphere, its
positive identification as a mirage cannot be made without a
physically meaningful description of what is seen and a complete set
of meteorological and astronomical data. The required "hard" data are
practically never available for the specific place and time of
observation, so that the descriptive account remains the only basis
for identification; in this case, successful identification depends
on a process of education. Thus, the casual observer of an optical
phenomenon can establish the likelihood that his observation is a
mirage only by being aware of the basic characteristics of mirage and
the physical principles that govern its appearance and behavior.
The conditions required for mirage formation and the principal
characteristics of mirage images, as described in this report, are
summarized below. The summary presents a set of standards by which to
interpret the nature of an optical observation in terms of a specific
natural atmospheric phenomenon.
Optical mirages arise from abnormal temperature gradients in the
atmosphere. A temperature decrease with height (temperature lapse)
exceeding 3.4°C per 100 m or a temperature increase with height
(temperature inversion) is most commonly responsible for a mirage
sighting.
Large temperature lapses are found in the first 10 meters above the
ground during daytime. They occur when ground surfaces are heated by
solar radiation, while during nighttime they can occur when cool air
flows over a relatively warm surface such as a lake. When the
temperature decreases with height more than 3.4° per 100 m
over a
horizontal distance of 1 kilometer or more, an observer located
within the area of temperature lapse can sight an inferior mirage
near the ground (e.g., road mirage, "water" on the desert)
Layers of temperature inversion ranging in thickness from a few
meters to several hundred meters may be located on the ground or at
various levels above it. In areas where they are horizontally
extensive, an observer can sight a superior mirage that usually
appears far away (beyond 1 kilometer) and "low in the sky." The
strength of the inversion determines the degree of image-elevation;
the stronger the inversion, the higher the image appears above the
horizon. Layers of maximum temperature inversion (30°C) are
usually found adjacent to the ground.
The geometry of illumination and viewing in the case of optical
mirage is determined by the spatial variations of refraction index
that occur in the cloud-free atmosphere, and by Snell's law of
refraction, which relates these variations to changes in the
direction of propagating wavefronts. The spatial variations in
refractive index are associated with layers of temperature inversion
or temperature lapse. Variations of 3x10-5, corresponding
to temperature changes of 30°C, are considered near maximum. As
a
consequence of Snell's law and the small changes in the atmospheric
refractive index, an optical mirage develops only when a temperature
inversion layer or a layer of large temperature lapse is illuminated
at grazing incidence. The requirement of grazing incidence implies
that the source of illumination must be either far away, i.e., near
the horizon, or very close to or within the layer of temperature
gradient. Therefore, both terrestrial and extraterrestrial sources
can be involved. Because of the distance factor, the actual source of
illumination may not be visible. Its location, however, must always
be in the direction in which the mirage image is observed, i.e.,
observer, image and "mirrored" source are located in the same
vertical plane.
Another consequence of Snell's law and the small spatial changes in
refractive index is that noticeable refractive effects are not likely
beyond an angular distance of approximately 14 degrees above the
horizon and that a superior mirage image is not likely beyond an
angular distance of 1 to 2 degrees above the horizon. Hence, mirages
appear "low in the sky" and near the horizontal plane of view. An
optical image seen near the zenith is not attributable to mirage.
Because of the restricted geometry between observer, mirage image,
and source of illumination, the observed image can often be made to
disappear abruptly by moving to higher or lower ground. Furthermore,
when mirage
A mirage can involve more than one image of a single object.
Observations of up to four separate images, some inverted and some
upright, are encountered in the literature. When multiple images
occur they all lie in a single vertical plane or very close to it.
The apparent shape of a mirage can vary from clearly outlined images
of an identifiable object such as a distant ship, landscape, or the
sun or moon, to distorted images that defy any description in terms
of known objects (e.g., Fata Morgana). Apparent stretching either in
the vertical or in the horizontal plane is common.
During daytime, a mirage can appear silvery white ("water" on the
ground), or dark when projected against a bright sky background, or
it can reflect the general color of the land or seascape. Distinctly
colored images ranging from red and yellow to green and blue are
observed when unusual conditions of mirage occur near sunrise or
sunset (e.g., Red and Green Flash) or, at night, during rising or
setting of the moon or of a planet such as Venus.
In the presence of atmospheric turbulance and convection, the effects
of scintillation become superimposed on the large-scale mirage image.
When scintillation occurs, extended mirage images appear in constant
motion by changing their shape and brightness. When the image is
small and bright, as may be the case at night, large fluctuations in
brightness and under unusual conditions in color can give an illusion
of blinking, flashing, side to side oscillation, or motion toward and
away from the observer. The effects associated with scintillation can
dominate the visual appearance of any bright point-object in the area
between the horizon and approximately 14 degrees above the horizon.
The theory of ray optics adequately explains such observed
large-scale aspects of the mirage as the number of images, image
inversion, and apparent vertical stretching and shrinking. However,
if the interference and focussing of wavefronts within the refracting
layer are as fundamental
Sir C. V. Raman's application of wave-optics to mirage suggests that
under special conditions of illumination, the upper boundary of an
atmospheric temperature inversion could exhibit a large
concentration of radiant energy due to focussing of wavefronts. Also,
interference of wavefronts could produce alternating layers of high
and low brightness. Under what conditions and to what extent these
brightness effects can be observed in the atmosphere is not known.
Relevant observations have not been encountered in the literature,
although some unusual observations of the green flash made under
mirage conditions (O'Connel, 1958) could possibly have been caused by
the enhancement of brightness in an inversion. The visual effects
from focussing and interference of wavefronts must be considered as
the least explored aspect of mirage.
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(Akademische Verlagsgesellschaft, Geest & Portig K. - G., Leipsig
1957).
Eldridge, Ralph G., "Climatic Visibilities of the United States,"
J. Appl. Meteorol., Vol. 5, No. 3 (June 1966).
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1930).
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1961).
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the
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Tolansky, S., Optical Illusions (Pergamon Press, New York 1964).
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Wallot, S., "Der senkrechte Durchgang elektromagnetischer Wellen
durch eine Schicht raumlich veranderlicher Dielektrisitats
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Figure 2: Normal Summer Sunshine
Click on Thumbnail to see Full-size image.
Figure 3: Inversion Frequency
Click on Thumbnail to see Full-size image.
Figure 4: Visibility Distribution
Click on Thumbnail to see Full-size image.
4. Visual Characteristics of Light-Refraction Phenomena
in
the Cloud-Free Atmosphere
A. General
B. Characteristics of the Mirage
C. Light Scattering by Aerosol Particles
A. General
Figure 5: Astronomical refraction
Click on Thumbnail to see Full-size image.
B. Characteristics of the Mirage
Figure 6: Mirage Geometry
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Figure 7: Light Ray Parabolas
Click on thumbnail to see full-size image.
Figure 8: Image Inversion
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Figure 9: Image Elongation
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Figure 10: Double-Image Refraction
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Figure 11: Sunset/Moonset Mirages
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ABNORMAL REFRACTION
Off Coast of Portugal
Rising Sun
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Figure 12: Energy in Inversion
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Figure 13: Wavefront Diagram
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Figure 14: Refractive Color Separation
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SETTING OF THE PLANET VENUS
Indian Ocean
GREEN FLASH
South Atlantic Ocean
Red Sea
Green Flash
Click on Thumbnail to see Full-size image.
North Pacific Ocean
GREEN AND RED FLASHES
South Pacific Ocean
SETTING OF THE PLANET JUPITER
Gulf of Mannar
Figure 15: Refractive Color Separation Geometry
Click on Thumbnail to see Full-size image.
C. Light Scattering by Aerosol Particles
Figure 16: Light Scattering Geometry
Click on Thumbnail to see Full-size image.
5. Evaluation of the State-of-the-Art Knowledge
6. Conclusions
A. Meteorological Conditions
B. Geometry of Illumination and Viewing
C. Shape and Color
D. Present Uncertainties
BIBLIOGRAPHY