ge when 
ation of 
jyllowing 
SPATIAL RESOLUTION (L/MM) 
8 8 8 8 8 3 
o 
  
  
  
0 10 20 30 40 50 60 
RADIUS (MM) 
LOCATION OF TARGETS AS A FUNCTION OF IMAGE RADIUS. SPATIAL RESOLUTION VALUES ARE HYPOTHETICAL 
AND FOR EXAMPLE. OVERLAP 80%. 
€ tangential 
Oradial 
70 80 90 100 110 120 
  
Figure 3. The location of targets as a function of the image radius when two targets and 80% forward overlap is used. 
The areas A; are determined on the basis of the available spatial 
resolution measurements. The image is divided into six zones, 
which have radius r values between 0-23, 23-46, 46-69, 69-92, 
92-115 and >115 mm. If the measurements presented in Figure 
3 are used, spatial resolution are calculated for r = 16, 36, 59, 
81, 104 and 127 mm, which are centres of gravity in each of the 
23 mm wide circular zones. 
2.3 Method of analysis 
2.3.1 Mathematical method 
The photographs were measured using a J-L Automation Ltd 
Microdensitometer 3CS. Let the dimensions of the measurement 
slit be Ax (width) and Ay (length) when the slit is moved in the 
direction x. AX is the width of one test bar. The narrowest bar of 
the target AX, defines the width of the measuring slit so that 
Ax«0.5- AX min- 
The 1:3 000 scale photographs were digitized with a slit size of 
Ax=5um and Ay=100um. Altogether seven profiles were 
scanned over each test target. The 1:60 000 scale photographs 
were digitized with a slit size of Ax=5um and Ay=20jum. The 
number p of scanned profiles over the test targets varied. 
To determine the spatial resolution the following calculations 
were made 
mean of bar maxima Finanz AV 44) 
mean of background bar minima famin(X,Y) = 1/MEf;min(XY), (3) 
standard deviation of bar maxima 
  
1 
= (Fw na (x, y) - f, tax (x, »» , (4) 
  
Svmax = 
m-1 
standard deviation of background bar minima 
  
1 
Stmin = — AE gis G6) 7 pin CD , (5) 
m -— 
where m=number of bars or background bars in the group. 
Each measured profile and bar group is analysed separately. The 
bar group is accepted as resolved if the condition 
Éormex CY) fummis X, Y)2 a S (6) 
holds when a=2. The constant a was determined by comparing 
the calculated results with visual observations. 
The common standard deviation of the bars and the background 
bars is determined by 
  
VO =D Ly Hm =D Shi) Om +m, —2) (T) 
where m,=number of bars in the group, 
m,=number of background bars in the group. 
The majority of the determined p spatial resolutions gives the 
final resolution of the image. 
2.3.2 Visual method 
The spatial resolution in all images was also analysed by visual 
inspection. No extrapolation was made and thus the results 
correspond with the spatial resolution of the smallest detectable 
bar width. 
3. RESULTS 
3.1 Spatial resolution as a function of image radius 
Figures 4-7 show the spatial resolution as a function of the 
image radius when permanent and transportable targets and two 
types of exposures are used. 
  
101 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B1. Vienna 1996