- 6 - 
residual image movement during the exposure time. The 
simplest case is linear movement, for which the MTF has 
the form sin X/X, the first zero of the function occurr 
ing at a frequency given by 1/d, where d is the distance 
moved by the image. (Fig. 4) MTF's for other kinds of 
image movement have also been derived. (71)» 
In high resolution aerial photography the non 
homogeneity or turbulence of the atmosphere may be a 
factor limiting definition. When the turbulent disturb 
ances are rapid compared to the exposure time, so that a 
statistical uniformity can be considered to apply, the 
turbulence may legitimately be considered to have a trans 
fer function. More generally, the turbulence can only be 
assigned an effective or apparent transfer function 
derived from its disturbance of the optical wavefront 
entering the lens and applicable only to the stated condi 
tions. Similar limitations apply to components such as 
filters and windows. So far, only limited data is available 
about the magnitude of atmospheric turbulence in transfer 
function terms. It is probably not very significant in 
photogrammetry except at the outer limits of wide-angle 
photography, when resolution is limited in any case by the 
contrast-reduction due to scattered light. Reference (71) 
may be consulted. 
Lenses used in enlarging or printing equipment or in 
projectors having essentially incoherent illumination, can 
be assigned MTF's, which in principle should be good enough 
that nothing is lost from the detail in the original negative. 
Little information has so far been published on the MTF's of 
such lenses, but it is clear from available knowledge that 
completely loss-free enlarging or projection of high quality 
negatives or transparencies is not practicable. The MTF 
will, however, enable quantitative studies to be made so 
that practically acceptable losses may be established. Sim 
ilarly, very valuable studies can be made of the imaging 
performance of stereoscopes and other viewing optical devices. 
It goes without saying that the MTF Measurements in all these 
cases should be made with due regard to the spectral sensit 
ivity of the receiver, be it printing paper or human eye. 
Image Calculations 
The availability of MTF's, high-speed computers and 
Fourier transform programs, has made it practicable to 
calculate image intensity distributions corresponding to 
given objects. Examples of such calculations are given 
in Ref. (66). Such calculations will be of value to photo 
grammetry in studying the errors of dimensional measurement 
on images. Recently it has become possible to make such 
calculations two-dimensionally. The exact application of