68 METEOROLOGICAL OPTICS 
the ground such a parcel must have an extremely small 
diameter to cause scintillation. 
The mechanism of intensity fluctuations was ex- 
plained by K. Exner [c. 42] as follows: In Fig. 8, density 
schlieren around S are embedded at certain intervals 
in an otherwise more or less homogeneous field of density 
and cause concavities (or convexities) in an originally 
plane wave-front of light and, thus, divergence of the 
rays at A and A’ and convergence at B and B’. If the 
system of schlieren moves horizontally, an observer— 
say at B—uwill perceive alternate increases in flux dens- 
ity where the rays converge, and decreases where they 
diverge. He will also see the light come from slightly 
varying directions, that is, apparent vibratory motions 
of the star. It is easily envisioned that the same varia- 
tions occur if the schlieren system moves vertically. 
K. Exner measured the radius of curvature 7 of the 
wave-front deformation to be roughly between 2 and 
20 km. In addition to discrete schlieren, we may also 
consider the wavy structure of surfaces of temperature 
or wind discontinuity as a cause of variations in flux 
density. 
we celeem RAYS 
wave-/ © S 
a | | 
B A B! 
Fie. 8.—Scintillation resulting from density schlieren 
(after K. Exner). 
The short-term fluctuations of images received from 
terrestrial light sources or objects, or terrestrial scin- 
tillation, is of great practical importance; in particular, 
strong scintillation may interfere with blinker signaling. 
Scintillation also limits the precision of telescope point- 
ing and the useful magnification of telescopic devices 
[46]. Siedentopf and Wisshak‘ recently investigated the 
case of collimated light sources over a range 1 km long 
and 1 m above the ground, employing an objective 
receiver. With strong scintillation, the frequency of 
apparent intensity fluctuations was most often observed 
between 5 and 9 sec, with lesser scintillation between 
1 and 3 sec. The whole range covered the frequencies 
between 1 and 50 sec}. The relative variability of the 
apparent intensity ranged between 0 and 100 per cent 
and did not materially increase with lengthening of the 
ray path® beyond 1 km. The mean frequency of intens- 
ity fluctuation was found to be independent of the path 
length. Shadow bands of from 5 to 10 em width and 
several seconds duration were also observed moving 
horizontally with the wind across a screen several 
hundred meters from the searchlight. 
The fact that an air column of 1 km length produces 
almost the entire effect of scintillation shows that the 
4. R. Meyer [36] cites their paper as unpublished and gives 
a concise summary of their results. 
5. According to K. Exner’s results, the minimum source 
distance that chromatic terrestrial scintillation is observable 
is about 10 km [e. 42]. 
density discontinuities near the receiver are optically 
the most effective. Brocks [2] similarly found that the 
atmospheric conditions in the first tenth of a horizontal 
ray path (counting from the observer) are nineteen 
times as effectual in producing scintillation as the same 
conditions in the last tenth of the path. This seems to 
be the reason why various meteorological elements, 
observed near the receiver, correlate so well with the 
degree of terrestrial (and to a certain extent, astronomi- 
eal) scintillation that predictions of atmospheric optical 
conditions are possible [4, 24, 42, 55]. Such predictions 
may not hold where, for example, thermal turbulence 
is present near the light source but not near the receiver. 
In this case, scintillation presumably could still occur, 
if, at the receiver, the angular subtense of the responsible 
air parcels were large as compared to that of the light 
source. Also, in cases in which the central portion of very 
long rays grazes the earth’s surface, this portion is 
particularly exposed to density discontinuities that may 
not exist at the elevated end points of the rays. 
The optical distortions by the atmosphere of non- 
luminescent, diffusely reflecting sources are generally 
referred to as shimmer, or atmospheric boil. Riggs and 
others [46] measured photographically the apparent 
lateral displacement of vertical linear targets and the 
distortion of rectangular grids at several hundred meters 
distance. They found angular deviations from the mean 
position of line elements of the order of 1” to 5”. For 
targets separated by more than 3’ to 5’, there was no 
appreciable coherence of the observed deviations, that 
is, the horizontal dimensions of the schlieren subtended, 
at the camera, angles of less than 3’ to 5’. Unfortunately, 
no exact linear dimensions of the experimental arrange- 
ment are given, so that only the minimum size of the 
air parcels can be estimated (roughly 10 cm). In general, 
the characteristics of terrestrial scintillation appear to 
be very similar to those of astronomical scintillation; 
this fact indicates that the cause of the latter must he 
predominantly in the lower layers of the atmosphere. 
Nevertheless, the extent to which the upper atmosphere 
contributes to astronomical scintillation must still be 
considered an open question, whose answer must come 
from direct exploration of the properties of the upper 
air. 
The theories of scintillation by Montigny, K. Exner, 
and others [c. 42] explain qualitatively the observed 
phenomena. However, an exact mathematical expres- 
sion of the relationship between the frequency and 
amplitude of apparent object motion, apparent intensity 
fluctuations, and chromatic effects on the one hand, and 
periodic time-space variations of meteorological factors 
on the other, remains undeveloped. There are also 
experimental problems as follows: The scintillatory be- 
havior of uncollimated and diffuse light sources needs 
further investigation, although it is to be expected that 
diffuse sources will show a much lesser degree of scintil- 
lation than do collimated sources. Of particular interest 
would be an investigation into the size, shape, spacing, 
and transport velocity of schlieren in relation to the 
size, distance, and optical characteristics of the light 
source for various degrees of scintillation. Such studies 
