These signals from the same transmitters are coherent and can interfere. If the path 
difference is an odd number of half wave-length (because of phase-change of 180? at 
surface reflection) the resulting signal is reinforced, otherwise at differences of even 
numbers it is extinguished. Due to different ranges and view-angles a lot of reinforce- 
ments and extinctions are recorded and repeated transmissions give a series of fringe 
patterns in the sound image (Fig.2). 
The corresponding geometric situation of Lioyd-Mirror is shown in simplified manner in 
Fig.3. Confined to signal reinforcement - further on called interference - this geometry 
leads to expressions for the determination of water depth and horizontal distance for an 
interference point P4. Because of the physical situation range and recording direction 
can be fixed. 
c 
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virtual sensor 
* sea - surface 
=n 
I 
| 
! 
| 
| 
P 
I 
| 
| 
| 
| 
  
1 
* sea - bottom 
A 
Fig.3: The geometry of Lloyd-Mirror 
The path difference of the two signals can be expressed as 
o 
F-Rn - (2r-1h 2 - tn-5- à (1) 
Refering to Figure 3 is 
— 
P = ({Za + d)? + Yz)l72 (2) 
O 
and 
Ya = Ra - Zn - dd (3] 
The combination of (1), (2) and (3) leads to 
1 2 2 
[2n-1): A. R4 (n - 3X3 
  
a^ zd y ud is 
Yn * (RA - (Za - d)*1772 (8] 
where n = number of fringe areas 
range of m (can be taken from image refering to scale] 
i