International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B2. Istanbul 2004 
  
     
  
  
  
  
  
  
35 1 1 1 1 1 E 120 
Resolution E 110 
$rednia z 5 odczytów 
3.04 
aproksymowana E 100 
—— charact. curve [90 
28-7 local gradient d 
8 F 80 
© 
9 
D F70 = 
3 $ 
= 
2 F60 5 
2 © 
© Lsp OX 
= 
2 
© E40 
a - 
F 30 
F 20 
F 10 
0.0 HH T T -T7——--0 
-3.0 -2,5 -2.0 -1,5 -10 -0,5 0.0 
logH 
Fig. 8. Graphs of relations R=f (log H) and gmax=f(logH) for the 
USAF 1951 test exposure of 0,78 contrast and Kodak 3412 film 
processed in Versamat 1140 processor, AGFA 74, v=10 ft/min, 
T=30°C 
Substituting the relation D=f/log H/ for a polynomial enables 
additionally easy determination of local gradient (Fig. 5b and 
Fig. 8). Using the local gradient, the maximum gradient for the 
characteristic curve and exposure logarithm at the maximum 
gradient was determined. 
Determination of luminance conditions for optimum resolving 
power by means of application of the characteristic curve and 
Modulation Transfer Function (MTF) is much simpler. 
Determination of the MTF is presented in [1, 2]. Distribution of 
the local gradient of the characteristic curve presented in Fig. 7 
is obtained by means of differentiating the characteristic curve. 
Multiplying the specific values of the local gradient of the 
characteristic curve by the MTF, the Contrast Transfer Function 
(CTF) for the specific spatial frequencies is obtained. It is 
expressed as the number of pairs of lines per millimeter (Fig. 
10). 
CTF = MTF - g 
  
  
  
  
  
where: 
CTE Contrast Transfer Function, 
MTF Modulation Transfer Function, 
g local gradient of the characteristic curve. 
30 T I T T T T T 30 
| —-gmax(LogH) | 
254 D n m E + - 25 
263. ——— = > d 
| | 
[SN | 
D 1.5 X T F159 
/ \ | 
/ N 
1.0 -] x -1,0 
/ N | 
/ . 
/ YX T N 
/ | — 1 
0.54 j : —Fos 
0.0 T T T T T T = 0,0 
3,0 2:5 2.0 15 10 0,5 0.0 0,5 1,0 
LogH 
Fig. 9. Distribution of the local gradient g =f(Lo,gH) for Agfa 
Pan 80 film 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
ERE T 
ezestotliwosé 
| [Ip/mm] 
j—25 
1,5 4— —— 4.0 
| 6.4 
| — 10 
| 18 
[——25 
CTF 1,044 40 A 
|—— 64 
| —— 100 
L 
0,5 + — 
0.0 + 
-3,0 -2,5 1,0 
  
Fig. 10. Contrast Transfer Function graph for spatial 
frequencies ranging from 2.5 Ip/mm to 100 Ip/mm determined 
for the Agfa Pan 80 material 
The maximum of the CTF obtained in this way for the specific 
spatial frequencies determines the value of the exposure 
logarithm at the maximum resolving power which coincides 
with the maximum of local gradient of the characteristic curve. 
On the other hand, CTF value is defined as the difference 
between the optical densities that the human eye can distinguish 
as separate details: 
CTF = Dmax - Dmin 
where: 
Dmax — optical density of the image, 
Dmin — optical density of the background, 
lalues of the Dmax and Dmin are obtained for the luminance 
values equal LogHmax and LogHmin. It is obvious that during 
exposing a resolvogram for a test of a given contrast, increasing 
luminance (e.g. by increasing the exposure time) causes 
increase of LogHmax and LogHmin values but the difference 
between them is still constant (LogHmax - LogHmin = const.). 
Therefore, knowing the course of the characteristic curve for a 
material and using the above mentioned relation it is possible to 
determine the dependence of the CTF on exposure logarithm for 
specific contrasts of the test. Such relations determined for a 
few contrasts of the test are presented in Fig. 11. 
  
ee 
| LogH  -LogH 
—0.15 | 
20-1 —— 0.30 m 
0.45 ie N 
1|—— 0.60 | 
0.75 
—— 0.90 
1.05 
—— 1.20 
CTF 1211 ——135 -óL— 
Te L NN. - 
1 1.65 d LN Pa 
  
  
  
   
  
1.50 \ 
08-1 —— 1.80 / MS 
EN 
| 19 7 NN m 
e 
7 | 
pee ——— d 
a | 
0, = 
0 
  
  
  
  
  
“ 
  
  
  
-0,5 0,0 0,5 1,0 
  
  
  
  
  
  
  
  
  
  
0,0 d r T 
-3,0 -2.5 -20 -1,5 -1 
LogH 
Fig. 11. Courses of Contrast Transfer Function for various 
values of contrasts of the test ranging from 0.15 to 1.65 
determined for Agfa Pan 80 material. 
Maxima of the specific curves occur for various values of the 
exposure logarithm. Optimum contrasts of the photographed 
objects are determined by the curves whose maxima occur close 
to the exposure logarithm value for which the maximum 
resolving power was previously determined. 
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