As
can be seen in the graph, the average brightness never returns to the
level it had in the frames prior to the pre-flash. This was somewhat puzzling.
Since the sunlight reaching the camera was slowly increasing in intensity
as the shuttle moved through space, some suggestion of an upward slope
to the brightness curve would be expected. But the curve is essentially
flat on both sides of the series of flashes and higher by 2 DN after the
flashes than before. The graph would seem to suggest that the brightness
increased in a discrete step at some point during the series of flashes.
However, a graph of brightness versus time plotted over a much longer
time period indicated that this was probably not the case.

The graph for
the longer time period showed the average frame brightness curving upward
with time but accompanied by small periodic fluctuations. This graph is
shown in Figure 6.

The fluctuations
in brightness may represent fluctuations in the camera’s sensitivity,
although they might also represent some variation in the amount of sunlight
reaching the camera. Whatever their cause, it appears that these periodic
fluctuations occasionally cancel out the continuously increasing brightness
due to the change in the sun’s position, resulting in short periods
of time over which the image brightness remains relatively constant.


As would be expected, attempts to fit the measured brightness values to
a hand-drawn curve always resulted in the measured values around the 2.2-second
time span of the flash series falling noticeably farther from the curve
than the values for other points in time. What was surprising was that
the time span over which the points failed to fit any continuously rising
curve was considerably longer than 2.2 seconds – perhaps as long
as 12 seconds. It did not appear that this could be accounted for by the
small periodic brightness variations. To confirm this impression, I performed
a curvilinear regression for all the data points, excluding those in this
12-second interval, to produce the red curve also shown in Figure 6. This
is a graph for the curve:

DN
= b0 + b1T + b2T2


Where DN is the digital brightness, T
is time, and b0, b1,
and b2 are the constants computed by the
regression procedure.

Such
a regression equation has no basis in physical theory, but it provides
a meaningful description of a population if the points in the population
conform to it reasonably well. As can be seen in the graph, the curve
fits all of the data outside of the excluded time period quite well, with
a standard deviation of 0.21 DN for the sample of 96 points.