Benthowave Instrument Inc.

BENTHOWAVE INSTRUMENT INC. Acoustic Transducer & System 

Array & Aperture Design - Spatial Filtering

Benthowave's transducers and hydrophones can be used as array elements, which, depending on the operating frequency, can be simplified as Point, Line or Rectangle Aperture elements in Linear, Planar, Curved, and Conformal Array. Different mounting options are available from BII: Thru-hole/Hull, Bolt-fastening, End-face mounting, Free Hanging, Flush Mounting and Flange Mounting. With the signals of array elements, tracking of sound source, beam-steering and amplitude shading can be done in signal processing. Standard dry and underwater mateable connectors are supported for quick interfacing among data acquisition devices.

Bolt-fastening Mount is designed to be installed on portable-mounting apparatus for easy deployment, and also make configuration of the array pattern be easy, flexible and simple. Different array pattern can be set up quickly and easily in the field.
Thru-hole Mount is designed to be installed on the wall/hull of underwater submersibles, pipes, tanks and vessels to detect or produce acoustic signals outside a submersible or inside a pipe, tank or vessel. Hull mounted array (such as linear, planar and cylindrical array) can be configured.

How to use BII transducer/Hydrophone as discrete array elements?
To achieve narrow beam width at a specific frequency and steer the beam to the direction of interest, multiple BII transducers or hydrophones shall be used to set up line array or planar array. For example, to detect 1kHz signals underwater with line array, seven BII-7010 series hydrophones are used in 0.75m spacing to achieve beam width of 15°. Preamplifiers can also be integrated to drive long cable and weight the signal level of each channel for side lobe suppression.

Array Patterns:

Receiving ArrayLine ArrayT ArrayCross Line ArrayPlane ArrayCircular ArraySector ArrayArray & Aperture DesignArray & Aperture DesignArray & Aperture Design

Directivity of Array:

Array & Aperture Design  Array & Aperture Design

Array & Aperture Design                    

Technical Notes

Array Geometry Array Properties
Linear Array:
N point element, equal response, in phase, uniformly spaced
D(θ) = sin(πdN*sinθ/λ)/(N*sin(πd*sinθ/λ))
SNR gain = 10*logN
-3dB Beamwidth of Main Lobe = 2*arcsin(1.4*λ/(πdN))
First Sidelobe: θ = ±arcsin(1.5λ/(dN))
First Sidelobe: -13.4 dB
Sidelobe Fall-off: -6dB/octave
d - Spacing; λ - Wavelength; N - Element Quantity
θ - Angle to normal on the array
Linear Array:
N point element, triangular weighting, in phase, uniformly spaced
D(θ) = [sin(πdN*sinθ/λ)/(N*sin(πd*sinθ/λ))]²
SNR gain = 10*logN
-3dB Beamwidth of Main Lobe = 2*arcsin(6.35*λ/(dN))
First Sidelobe: θ = ±arcsin(3λ/(dN))
First Sidelobe: -26.8 dB
Sidelobe Fall-off: -12dB/octave
d - Spacing; λ - Wavelength; N - Element Quantity
θ - Angle to normal on the array
Dolph-Chebyshev Array Chebyshev Polynomial:
Tm(x) = cos(m/cos(x));         -1 < x < 1
         = cosh(m/cosh(x));     |x| ≥ 1
T0(x) = 1;
T1(x) = x;
T2(x) = 2x² -1;
T3(x) = 4x³ - 3x;
...
Tm+1(x) = 2xTm(x) - Tm-1(x);
...
Planar/Conformal Array: Identical Elements g(u)=∑(i(n)*exp(jkndu))
g(u)=f(u)*e(u);   u = m*λ/d; Pattern Multiplication
g(u)-Radiation/Receiving Pattern of the Array
f(u)-Array Pattern or Array Factor
e(u)-Element Pattern or Element Factor
d-interelement distance; λ-Wavelength; m = ...,-2,-1,0,1,2,...
i(n)-Element n; k-wave number; u=sinθ

The performance of an array is determined by the performance of the elements, quantity of elements, spacing among elements and array pattern.
Using an array of elements instead of single element underwater, the high array gain can be achieved or the signal-to-noise ratio (SNR) can be improved.
With space-time signal processing, the -3dB beam width of the main lobe of the array can be controlled with weighting/shading techniques, and the beam of the main lobe can be steered to a specific direction with time-delay techniques.
2D or 3D images underwater can be captured with the arrays and the echo signal processing.

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