e which is then used with the coefficients evaluated in Step 2 to evaluate 
= 2 3 4 5 
Org s! Ys, s! K, s! p^ t Ys, 8! Kos! rt... 
From this and the x,y plate coordinates of the image (referred to the principal point 
as origin), the provisional corrections 
dx 
Oy 
are evaluated. 
Step 4. Iteration. The addition of dx, dy to the image coordinates provides an 
initial correction for distortion. This permits a repetition of the analytical tri- 
angulation leading to more accurate object space coordinates. These, in turn, 
may be employed in a repetition of Steps 2 and 3 leading to refined distortion 
corrections. The iteration of this process to convergence generates the total 
correction. 
ANALYTICAL METHODS OF CALIBRATING DISTORTION 
The above section outlined the procedure for applying distortion corrections 
for close range photogrammetry when the distortion functions for two distinct object 
planes are known in advance. Now we shall address briefly the matter of how to 
perform the needed calibration for various chosen object planes. We shall confine 
our consideration to strictly analytical methods . For a description of an instrumental 
method the reader can consult Magill (1955). The methods to be reviewed may be 
classified as follows: 
1) Stellar Calibration 
2) SMAC (Simultaneous Multiframe Analytical Calibration) 
a) Stellar 
b) Aerial 
Finite Target Range Calibration 
a) Two Dimensional Range 
b) Three Dimensional Range