823 
& - Xg) 1 is the transpose of the above vector 
Figure 3. 1960 CIE-UCS u, v target coordinates indicate color shifts associated with flight altitude 
and relative exposure. 
The spectral transmittance of the white target is so nearly the 
same as that of the "clear” film that the usual procedure of 
obtaining internal transmittance as the basis for all subsequent 
calculations could not be followed» As a result of using the 
higher transmittance distribution of air as the divisor in place 
of the lower transmittance distribution of "clear” film, the 
Table 2 and Figure 3 entries for the white target do not have 
the same reference base as the red and green targets. There 
fore, the resultant visual transmittance, Y, for the white target 
is shown as being much less than the near 100 percent that would 
result from the conventional methods of calculation. 
In Table 2, the visual transmittance, Y, and the analytical den 
sities are boxed with a dashed line to indicate that the values 
are not comparable to the values for the red or green target as 
noted previously. The 1960 CIE-UCS u,v coordinates listed for 
white are closely comparable to those listed for red and green 
targets as the color of the clear film used as the divisor to 
obtain internal transmittance for the red and green targets is 
fairly near the coordinates for standard source C light, thus 
indicating little film stain. 
STATISTICAL ANALYSIS 
2 
Mahalanobis’ D Critical Value 
The 1960 CIE-UCS u,v diagram produces two variable data from 
three variable measurements. Therefore, a multivariate form of 
the ’t’ test must be used for statistical comparisons of target 
color. 
2 
Hotelling T s T is the multivariate form of the univariate ’t’ 
test (Morrison, 1967). To maintain a distance analogy, the 
Mahalanobis* D 2 distance between multivariate images was calcu 
lated and by using the relationship between Hotelling’s T 2 
and Mahalanobis’ D 2 , critical limit values for the significance 
of a test comparison were set in terms of Mahalanobis’ D 2 . 
The Mahalanobis’ D 2 distance is given by the following formula 
where prior probabilities are equal, a pooled variance-covariance 
metric is used and equal sample sizes are employed as was done 
in the comparisons made in this study. 
D 2 = (X 1 - X 2 )' S" 1 (X x - X 2 ) 
where: (X., - X^) is the difference vector between the two 
mean vectors being compared