e receiver. Nev. 
he center of well 
plying a median 
| centered at the 
  
n target. 
m. Fig. 10 shows 
1e Patterson tar- 
ference between 
rder of 10 to 15 
? variation of the 
wn in Fig. 11. A 
to the data. Be- 
target can often 
e is corrected by 
series. 
  
  
ZI 
= 
  
  
  
  
—A 
  
  
  
  
—8— @ 450 pm 
—9— 6 350 um 
—A— 0 270 um 
—V— 9 225 um 
——] —$— 9180 um 
—4— Ó 144 um 
———] —3K— 9 108 um 
—X—9 724m 
6 8 
  
  
  
| bubbles with the 
cate the maximum 
CENTRATION 
ume 
creasing distance 
1e the measuring 
; with mean gray 
nt for the calcu- 
ir dependence of 
(11) 
t the focal plane. 
parameter gmin- 
  
05 0 450 um 
0 360 pm 
9 270 im 
04 9 225 um 
© 180 im 
%# 0144um 
normalized mean gray value 
normalized mean gray value 
   
03 LA LL 
-80 -60 -40 -200 0 20 4 60 80 
normalized distance from focal plane z/R 
02 
90084 12:520... 2^ 40 0 (8 
distance z from focal plane [mm] 
  
  
Figure 11: left: mean gray value calculated for different Pat- 
terson globes; right: mean gray value versus normalized distance 
z/R. This validates the fact that gm Only depends on z/R. 
It is important to note that the volume depends on particle 
size and increases with larger particles, because a large parti- 
cle becomes less blurred compared to a smaller particle if its 
image is convolved with the same PSF. 
6.2 Calculation of true particle size 
As mentioned above with a telecentric path of rays the true 
particle size can be easily obtained from the segmentation 
of the images. Due to the symmetry between particles lo- 
cated at the same distance, but in front or behind the focal 
plane, the intrinsic ambivalence does not cause an ambiva- 
lence in the depth or size measurement and can be ignored 
completely. The situation is different with standard optics 
where the aperture stop is not located at the back focal plane 
of the lens system. Then V4 depends on z and the segmented 
size does not necessarily meet the true size. The fact that 
there is a unique relation for the true radius r and the depth 
z of an object to the two measurable parameters, g», and 
the segmented radius 7, can be used to solve the problem 
[GeiBler and Jáhne,95a]. The relation between the four pa- 
rameters are obtained from the calibration depth series. The 
values of the output parameters (r, z) are mapped on a reg- 
ular grid in the input parameter set (rq, gm) and used as a 
fast look-up table to perform the calculation. 
6.3 Size distributions 
Segmentation and depth-from-focus result in the knowledge 
of position and size of the particles observed in an image. 
The data from a suitable long image sequence is needed to 
calculate size distributions. The result of the segmentation 
of an image sequence is shown in Fig.12. Due to the fast 
segmentation and depth-from-focus, evaluation of an image 
  
  
  
  
Figure 12: Result of the segmentation of an image sequence. 
The dark gray lines indicate the boundary lines of the bubbles. 
199 
  
  
  
  
  
   
  
  
  
  
  
  
  
Eje 7 eoo 3 
- wind speed 7 
—lü— 13.7 m/s À 
= s 9 12.5 m/s d 
ted 11.5 m/s 3 
«WE P» 10.0 m/s 
BE —P$— 9.0 m/s 7 
gr “ie 7.5 m/s E 
S pres i 
mt 3 
- 
=F 
= 
D 
= -1e2 E 
= 3 
= d 
2 3 
= 
2 
E-10 be 
j^ v i 
1 : à ta ui id A aay 
10 100 radius [uim] 1000 
Figure 13: Fresh water bubble size spectra measured at different 
wind speeds in the large wind/wave flume of Delft Hydraulics. 
can be done in less than one second on a 40 MHz i860 RISC 
processor system. 
Bubble size distributions were calculated from the number 
N(r, dr) of bubbles found in the radius interval [r, r + dr] by 
N(r, dr) 
v(r,dr) — NidrV(r) 
where NN; is the total number of images. As an exam- 
ple, Fig. 13 shows some fresh water bubble size distributions 
measured in the large wind/wave flume of Delft Hydraulics. 
These measurements have been described in greater detail in 
[GeiBler and Jähne,95b]. 
(12) 
REFERENCES 
[Ens and Lawrence,93] Ens, J., Lawrence, P.: 1993, ‘An in- 
vestigation of methods for determining depth-from-focus' 
, IEEE Trans. PAMI, 15, 97-108 
[Lai et al.,92] Lai, S. H., Fu , C. W., Chang, S. Y.: 1992, 
'A generalized Depth Estimation Algorithm', /EEE Trans. 
PAMI, 14, 405-411 
[Merlivat,83] Merlivat, L., Memery, L. , 'Gas Exchange 
Across an Air-Water Interface: Experimental Results and 
Modeling of Bubble Contribution to Transfer', Jour. of 
Geophysical Res. Vol.88, pp.707 - 724, 1983 
[Geißler and Jähne,95a] Geißler, P., Jähne, B.: 'One-Image 
Depth from Focus for Concentration Measurements', Proc. 
of ISPRS Intercommission Workshop 'From Pixels to Se- 
quences’, Zurich, March 22 - 24. In Int'l Arch. of Photog. 
and Rem. Sens., Vol 30, Part 5W1, 1995 
[GeiBler and Jähne,95b] GeiBler, P., Jähne, P.: 'Measure- 
ments of bubble distributions with an optical technique 
based on depth from focus', Air-Water Gas Transfer - Se- 
lected Papers from the Third International Symposium of 
Air-Water Gas Transfer, Heidelberg, ed. by B. Jähne and 
E. Monahan, Aeon Hanau, ISBN 3-9804429-0-X, 1995 
[Hering et. al,95] Hering, F., Wierzimok, D., Jähne, B.: 
‘Particle Tracking in Space Time Sequences’, Proc. of the 
6th Int'| Conference on Computer Analysis of Images and 
Patterns, Prague, 294 — 301 in Lecture Notes in Computer 
Sciences 970, Springer, 1995 
[Pentland,87] Pentland, A. P.: 'A new sense for depth of 
field’, IEEE Trans. PAMI, 9, 523-531 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B5. Vienna 1996