Exploring the Unknown - NASA's History Office

ified. It is obvious that if, for various combinations of cloud-ground and cloud-cloud,
albedo differences are such that their contrast values fall below the limiting contrast, these
combinations cannot be observed by high-altitude weather reconnaissance.
Hewson, in an article in a meteorological journal 11 and in his book (written in collaboration
with Longley) on theoretical and applied meteorology, 12 calculated and tabulated
diffuse-reflection coefficients for clouds of various thicknesses. In doing so, as a result of
the extensive variation of cloud liquid-water densities and cloud droplet radii, he was
forced to choose one set of values for these two parameters. Those on which his figures
are based are a density of 1.0 gm of liquid water per cubic meter of cloud and a droplet
radius of 5 X 10-4 cm. Owing to the fact that these values probably apply to a large percentage
of the usable clouds observable from extreme altitudes, they may be reasonably
[10] employed in making estimates for this study. These values are plotted in Fig. 2, the
ordinate and abscissa being contrast and background albedo, respectively. Each curve represents
a particular albedo applicable to a particular cloud thickness. According to the
definition of contrast,
C= P b - P d
P b
where Pb = brightness (albedo) of the brightest thing viewed (either object or background)
Pd = brightness of darkest object viewed (albedo)
C = contrast between the two.
From the above definition, each curve may be represented by the following relation:
{1 - A b , for A b < A t
A t
C { = 0, for A b = A t
{1 - A t , for A b > A t
A b
where C = contrast between object and background
A b = albedo of background
A t = albedo of clouds of various thicknesses.
EXPLORING THE UNKNOWN 193
It is therefore seen that, except for the small range of albedo combinations around
the point of discontinuity on the curves, a large majority of possible cloud-background
albedo combinations fall within the range of at least 10 per cent contrast. As can be seen
from Table 1, assuming at least a 2.0-in. aperture and sunlight illumination, an f/10 camera
will permit at least 10 per cent contrast for approximately 500-ft resolutions. 13 Table 5
11. E. W. Hewson, Quart. J. Roy. Met Soc., Vol. 69 (1943), p. 47.
12. E. W. Hewson and R. W. Longley, Meteorology, Theoretical and Applied, John Wiley & Sons, Inc., New
York, 1944, pp. 73–75.
13. Using the equation (for altitude of 350 mi)
C = 1600
where C = contrast
a = aperture
ga t
t = exposure time (or time of one frame)
g = minimum resolvable surface dimension,
it is possible to calculate the contrast (minimum) needed to obtain at least 500 ft resolution under the conditions
given in the example of ground coverage which assumed full daylight illumination. This value turns out to
be 3.56 per cent. Owing to the unrealistic power requirements necessary to transmit 3.56 per cent contrast, this
value has been raised to 10 per cent.