An aerial photographic system is used for stereophotography. The film negative is a square of sides, the focal length is f, the baseline is band the photographs (which are acquired with the camera pointing vertically downwards) are obtained from a height H above sea level. The stereophotographs are used to determine the height h of topographic variations above sea level. It can be assumed that f « h « H, and that the spatial resolution measurable on the negative is a.

(i) Show that the accuracy Δh with which heights can be resolved by this system is approximately H²a / bf.

(ii) Show that the widthwof the area on the ground that is imaged in both photo-graphs, measured in the direction of the baseline, is sH / f - b.

(iii) Hence show that the value of b/H that maximises the value of w/Δh is s/2f, and that the corresponding height accuracy is 2Ha/s.
(iv) Comment on the results in (iii) in the light of the commonly adopted rule that heights can be determined from stereophotographs with an accuracy of about H/1000.