Contrast Transfer Functions in Aerial Photography 
by E Welander 
  
Contrast transfer functions — or sine-wave responses — were introduced in optics about 15 years ago. 
A further development was carried out in television technique. The application of the response function has 
provided important new means for practical measurements of the quality of the optical image. In the last 
few years methods for an experimental determination of the sine -wave response of photographic emulsions 
have also been described. Thus the transfer function has been very useful in studying the photographic sys- 
tem, and now it is about time to put these methods into practice for aerial photography. 
Each one of the components affecting the quality of an aerial photograph may be expressed as a contrast trans- 
fer function. Then the individual contributions of each component may be multiplied. The resultant function 
gives the performance of the aerial photographic system. 
It shall here be attempted to present certain relations and methods, which can help the photogrammetrist in 
practical work to understand the capacity of the aerial photograph to resolve details on the ground, as these 
details vary in size and contrast. The preliminary investigations reported in this paper are a stage in the 
work of air-camera calibrating at the Geographical Survey Office in Sweden. 
Basic methods 
Contrast transfer functions for some air-camera lenses have been measured. Similar functions have been 
obtained from the manufacturer of some common aerial film emulsions. Then the effect of image movement, 
vibrations and aerial haze has been determined as transfer functions for different kinds of aerial photography. 
The most common spatial frequencies in aerial photography were measured. In doing this the resolving limit 
of the negative was investigated under various conditions from the air by photographing test targets of diffe- 
rent contrasts on the ground. Propeller-aircraft as well as jet-aircraft have been used from different altitu- 
des. 
By multiplying the transfer function for each of the different components the predicted performance of the 
aerial photographic system has been determined. The lenses were compared for different conditions at the 
most important frequencies. Also a transfer function from the air was directly measured by photographing 
a light ramp in the night. The resulting performance was compared with the predicted one. 
The lens function 
Contrast transfer functions for two modern aerial camera lenses (I and II) and an older one (III) have been 
measured by the Institute of Optical Research in Stockholm. The test method and some results from previous 
investigations of lenses for different purposes have been reported by Ingelstam (1). Fig 1 shows the first func- 
tions for photogrammetric lenses measured in Sweden. Up to now only the aerial image in the photograph cen- 
tre has been determined. The next stage is measurement along the whole diagonals.Lens I produces the highest 
values of response in the centre, specially at the common frequencies from the air between 5 and 40 lines/mm. 
Fig 2 shows the shift of focus for different wave lengths. Here the focus for maximum contrast transmission 
at the frequency 40 1/mm was estimated. For 5 000 - 7 000 A (Angstrom units) the focus changes only 0.2 mm 
for lens I, which is superior in this respect. 
Fig 3 shows CT-curves for small shifts of focus at 40 1/mm. A filter with a transmission above 5 300 A was 
used, Here also lens I is superior. 
Emulsions 
In Sweden measurements of transfer functions for emulsions were performed at the Institute of Optical Rese- 
arch by Djurle 1955 (2), by Ingelstam, Djurle, Sjógren 1956 (3) and by Hendeberg 1960 (4). 
For some air film emulsions used in Sweden, Tri X, Super XX, Plus X, Panatomic X and Infrared, sine-wave 
response curves were received from Eastman Kodak Company. The curves appear from fig 4. The exposure 
index in ASA is for Tri X 200, Super XX 100, Plus X 80, Pan X 30 and Infrared 100. 
Image movement 
The shutter speeds of the three cameras were calibrated in the laboratory by means of chronotron and oscillo- 
graph measurements. The graph in fig 5 shows response curves for different altitudes and velocities, The shut- 
ter speeds are 1/250 and 1/750 sec. The shutter efficiency is here disregarded. 
Vibrations 
In the case of vibration the phase is essential. The linear image motion may be enlarged as well as reduced ac- 
cording to the direction of the vibration motion. In the moment when the motion direction is reversed, the in- 
fluence of vibration is a minimum, 
In the investigation here reported the vibrations in propeller air-craft were measured at night photography with 
open shutter. The response curves, determined according to Scott (5), for two vibration frequencies at 1/250 
and 1/750 sec are to be found in fig 6. They show the maximum influence of vibration for 6" focal length. 
Haze 
The contrast reduction for the aerial haze may also be determined. The remission value for the haze in aerial 
photography from 4 000 - 5 000 m altitude is often about 5 % of the value of an entirely white surface. But 10 % 
as well as 20 % haze does also occur. The effect of contrast reduction owing to the haze is dependent on the lu- 
minance values of the ground, as is clear from fig 7. An investigation of more typical atmospheric conditions 
(6) indicates that a good average value for the transfer function might be about 0.25. Turbulence and density va- 
riations in the air are here disregarded. Further the contrast reduction was presumed being independent of the 
detail size.