SPINDEL: PHASE FLUCTUATIONS, COHERENCE AND INTERNAL WAVES 



equivalent to a path length variation of A/2 meters. The beamwidth of 

 the array at this limit is A/2L radians. Fluctuations in phase re- 

 sulting from the ocean environment must therefore be less than 1/2 

 cycle or A/2 meters for the array to achieve its diffraction limit. 

 If the phase fluctuations are greater than 1/2 cycle, the resolving 

 power of the array is said to be environmentally limited. 



The acoustic-internal wave theory outlined above predicts an 



rms path length change that is proportional to f and to the number of 



times the ray crosses the internal wave layer, i.e., distance. It 



predicts that rms phase fluctuations will reach a limit at some 



separation of sensors, and that the magnitude of fluctuation at this 



separation is proportional to distance. It is interesting to note that 



the performance of an environmentally limited array continues to 



increase linearly with array length since R = P/L, and P becomes 



e 



constant. 



Figure 13 shows phase fluctuation data at 406 Hz and two ranges, 

 200 and 1200 km, as a function of array length. Both curves rise to 

 a plateau, about 13 meters of equivalent rms path length change at 

 200 km and 40 meters at 1200 km. Theory predicts values of about 

 15 and 45 meters, respectively. The environmental limit at 200 km 

 would thus be avoided for all A/2 > 13 m, or f < 50 Hz. At 1200 km, 

 f < 20 Hz ensures diffraction rather than environmental limited per- 

 formance. These curves were computed from data gathered during 

 synthetic aperture formation and therefore represent a limit imposed 

 by temporal as well as spatial variations. In that sense, they can 

 serve as an upper bound on coherent array performance. It is expected 

 that actual performance of a fixed spatial array will be somewhat 

 better. 



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