National Physical Laboratory

Underwater acoustics near field techniques

For transducers and arrays that are many acoustic wavelengths in dimension, it is not always possible to make the desired measurements in the acoustic far-field within a laboratory tank of finite size. To provide a method of addressing this problem, NPL is currently working on the development of techniques to predict the far-field response from measurements made in the acoustic near-field. The near-field measurements are undertaken by scanning a hydrophone over a measurement surface in the acoustic near-field and measuring the amplitude and phase of the signal at discrete points. The scans are performed in an automated manner using the precision positioning systems on the NPL Open Tank Facilities which enable high resolution measurements to be made with high stability. After the measurement data has been acquired, appropriate propagation methods are then used to predict the far-field response. Two different approaches have been investigated so far:

Plane-wave angular spectrum approach

The plane-wave angular spectrum approach is a method of decomposing an acoustic wave into plane-wave components each travelling at different angles. This is done using a spatial Fourier approach with the measurements made by undertaking a planar scan at a fixed distance from the source and two-dimensional Fourier transforms applied to the data. The far-field response may then be calculated, or the field may be propagated to another separation distance and then reconstructed (by use of inverse Fourier transforms). It is also possible to propagate the field backwards toward the source and reconstruct what the source distribution must have been (this technique is sometimes referred to as Nearfield Acoustic Holography). This can be used to show up any defects in the transducer or "dead" elements in an array.

Boundary element approach

The propagation of acoustic waves of constant frequency in homogeneous media may be described using the Helmholtz equation, which can be reformulated as an integral equation over a closed surface. This means that if the acoustic pressure distribution over a closed surface is known, the pressure value anywhere else in the medium can be calculated. Boundary element methods provide a numerical technique for solving the Helmholtz integral equation and, in collaboration with NPL's Centre for Mathematical and Scientific Computing, an investigation of such methods is being carried out. An initial investigation identified two techniques that were suitable for this problem, and initial work concentrated on the validation and comparison of these two methods. The method has so far been confined to scans on cylindrical surfaces.

Example results

The following are examples of some results of measurement scans in the acoustic near-field.

Figure 1 Measured planar scan data at a separation distance of 200 mm for large area parametric array transducer operating at a frequency of 320 kHz 

Transverse scan for circular transducer at 200mm: Pressure amplitude in dB

Transverse scan for circular transducer at 200mm: Phase

 

Figure 2 Comparison of acoustic field forward propagated from 200 mm (data from Figure 1) to a separation distance of 4 m with actual measured field at a distance of 4 m

Amplitude of forward propageted beam at z = 4000 mm for Circular transducer

Transverse scan for circular transducer at 4m: Pressure amplitude in dB

 

Figure 3 Result of back propagation to 10 mm using 200 mm data of Figure 1. Note the three circular "defects" visible. For comparison, also shown is the data actually measured on the 10 mm plane.

Amplitude (in dB) of back propagated beam at z = 10 mm for circular transducer

Transverse scan for circular transducer at 10 mm: Pressure amplitude in dB

 

Figure 4 Agreement between the directional response predicted from the near-field data using the plane-wave angular spectrum approach and the actual reponse measured in the far-field for a small array operating at 100 kHz. 

Far-field directivity (x-y plane)

 

Figure 5 Example of a cylindrical nearfield scan at a radius of 400 mm of a source transducer consisting of two coaxial cylinders operating at 27.5 kHz

Cylindrical scan for Dual transducer at 27.5 kHz and 0.4 m: amplitude in dB

Work continues to assess the uncertainties and limitations of the methods.

Last Updated: 25 Mar 2010
Created: 6 Jun 2007

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