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errors in setting up equipment, pointing at the images, etc. Ultimately, these local 
variations set a limit to the accuracy which can be obtained from the negative if a 
mean distortion curve is used in correction. With a réseau camera it is possible to find 
a distortion value for each réseau cross, and if these values are used in correcting 
by numerical methods, then many of the local variations can be taken out. 
Very little numerical information has been published about these residual 
distortions. Refined techniques both in measurement and analysis are needed to 
detect and assign values to them. Moreover, they would normally require a much 
larger number of calibration points to be used than are commonly quoted on calibra 
tion certificates. The only results known to the present author are those reported by 
Hallert. [7] He found residual distortions of standard errors as high as 10 ¡1 in the 
outer regions of the format, with an average of 4-5 ¡jl. More information on these 
residuals and their cause is obviously desirable. 
7. Numerical Methods in Calibration 
Distortion is a complex thing, and the outcome of a laboratory calibration is in 
the first place a set of numbers, from which the principal distance, radial and tangential 
distortions, and so on, have to be extracted. There have been many attempts to put 
this process on to a rational basis. Hallert [7 > 8 > 9> 10> 221 has written a number of papers 
on this subject, including his communication to our 1960 London Congress. The 
earliest papers derive criteria for obtaining optimum values of the geometric constants 
by the method of least mean squares. His latest paper [7] contains a number of ex 
amples of calibrations treated in this way. These examples show not only the 
elegance of the method but also how it is capable of revealing unsuspected relation 
ships, otherwise hidden within the apparently random numbers. The residual 
distortions, after taking out the radial distortion, film distortion, etc., are shown to 
vary with the distance from the principal point and to have some correlation with 
the resolution. Again, this systematic analysis shows that both film and plates appear 
to have much the same residual errors—and presumably can therefore give the same 
ultimate accuracy. 
This method of analysis has so many advantages that I would like to see it 
applied as standard practice to all published camera calibration results, so that the 
reader can be sure that any conclusions have a sound statistical basis. 
8. Visual and Photographic Calibration 
So far, it has tacitly been assumed that photographic film has not been used 
on the calibration process. The I.S.P. Standard recognises both visual and photo 
graphic methods, although it expresses a preference for the photographic method. 
It is, I think, generally recognised that both can give the same results providing 
suitable precautions are taken. Some of the photographic methods use specially 
selected glass plates, rigidly mounted in the focal plane; others use the normal aero 
film either in special holders or in the actual camera magazine. However, the use of 
norma! film in the camera magazine does introduce two unknowns into the calibra 
tion process and indeed into the survey photography. The first of these is the 
flatness of the emulsion surface at the moment of exposure; the second the effect of 
subsequent processing and observational conditions. 
9. Film Flatness 
Film flatness has in the past been a convenient tag with which to label all 
residual errors, largely because it is very difficult to measure it at the actual moment