"rin 
try 
r an 
n 
rm 
— 
I 
(2) 
  
À used wave length 
d = towing depth 
Zn = water depth of Py 
Y 
n = horizontal distance of Pp 
The equations (4) and 5) are the fundamental relations for the determination of discrete 
three-dimensional coordinates from a two-dimensional image if fringe order n and towing 
depth d are known. 
The missing coordinate Xg is exclusively given by the sensor position due to ship speed 
and recording time. 
2.2 Synthetic Processing of Interference Fringes 
The natural appearance of Lloyd-Mirror fringes is limited because of wind and weather 
conditions. For a convenient use of this effect for topographic mapping it has to be pro- 
cessed synthetically. Preserving the hydrodynamic properties of a towing system it is 
necessary to use two transducers which work exactly synchroneous and are transmitting 
to the same side an in the same plane. The interference geometry then is simplified be- 
cause of loss of surface reflection. This situation is shown in Fig.4 (Kolouch. 1980). 
  
| INTERFEROMETRISCHES SONAR ||| || 
J ABBILDUNGSGEOMETR IE I 
[11] 
CN ! i Ji 
SEL mn 
| Fg 
Fd jj HT FE HH gen Fa 1 HH 
fiir] He] 
FLERE EE 1 airy 5114 
2 / i4 Ahh m i 
TRI n 
hA AU 
Vy ] yl J) i / A 
HH / 
n 
   
  
  
  
   
    
   
    
   
    
mr: m 
     
    
HH 
  
  
  
P = INTERFERENZPUNKT 
MEERESBODEN 
DIURH SFE 145 HANNQUER 
  
Fig.4. Interference pattern processing using two transducers 
The water depth is now calculated from the sensor centre as zero point. There is no 
longer a phase change at reflection and therefore path difference has to be now an in- 
teger number of wave length used. The towing depth is replaced by half of sensors 
distance D. Regarding to this situation the equations (4) and (5) change to 
Ra:n-*A rn? "1? 
En: D... D 
(6)