Constant Beam Width Acoustic Transducer Design
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Solution Overview
Problem
Existing methods for designing constant beam width transducers are complex and inflexible, particularly when trying to achieve precise half-angle beam widths, as they require computing non-integer Legendre polynomials and adjusting Legendre polynomial orders, which complicates array and shading function design.
Innovation Solution
A method involving an axisymmetric transducer array configuration, where an integer order Legendre polynomial is used with a control parameter Z0 to adjust the beam width, allowing for a simpler and more flexible design by modifying the Legendre polynomial to achieve a specified beam width, and suppressing side lobes by increasing the control parameter.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If non-integer Legendre polynomials are used to achieve precise beam widths, then manufacturing precision of beam width is improved, but device complexity increases
Solution Approach 1:
The patent changes the parameter approach by using integer-order Legendre polynomials with a modified control parameter Z0 instead of non-integer orders. The shading function is defined as Sn(Z0cosθ) where Z0 is a controllable parameter that adjusts beam width while maintaining integer polynomial orders, simplifying computation and design.
Solution Approach 2:
The patent uses standard integer-order Legendre polynomials (which are well-established and easily computable) as a template or copy, then modifies them through the Z0 parameter rather than creating entirely new non-integer polynomial functions, reducing computational complexity while achieving precise beam width control.
2Adaptability or versatility
If Legendre polynomial order is adjusted to change beam width, then adaptability of beam width control is improved, but device complexity increases
Solution Approach 1:
Instead of changing the polynomial order to adjust beam width, the patent maintains fixed integer orders and introduces a control parameter Z0 that scales the cosine argument. This allows continuous adjustment of beam width while keeping the polynomial structure simple and computationally efficient.
Solution Approach 2:
The modified Legendre polynomial Sn(Z0cosθ) serves multiple functions: it maintains the orthogonal properties of Legendre polynomials for efficient computation, allows continuous beam width adjustment through Z0, and works across a broad frequency range, making it a universal solution for constant beam width transducer design.
3Length of moving object
If higher order Legendre polynomials are used to narrow beam width, then beam width is reduced, but device complexity increases
Solution Approach 1:
The patent decouples beam width control from polynomial order selection by introducing the Z0 parameter. Lower order polynomials (e.g., n=2,3,4) can be used with adjusted Z0 values to achieve narrow beam widths, avoiding the computational complexity of very high order polynomials while maintaining beam focusing capability.
Data Source
AI summary
A method for providing a broadband constant beam width acoustic array includes providing a transducer array in an axisymmetric configuration. A beam width is specified, and an integer order Legendre polynomial is determined for that beam width. A control parameter is determined that will increase the integer order Legendre polynomial to that beam width. The Legendre polynomial is used to provide a shading function for the array of transducers that will give the specified beam width.