Small-size planar array three-dimensional beam forming method and device based on acoustic vector hydrophone and medium
A three-dimensional beam, plane array technology, applied in instrumentation, design optimization/simulation, radio wave measurement system, etc., to avoid vertical amplitude and phase errors
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[0114] The three-dimensional beam pattern required by the design is based on the maximum directivity factor, and the maximum spherical harmonic function order N=3 is designed, and the directivity angle is (θ d ,φ d ) of the 3D beam pattern, such as figure 2 shown as designed (θ d ,φ d ) = (45°, 45°) three-dimensional beam pattern.
[0115]
[0116] That is, after the designed three-dimensional beam pattern is expanded by spherical harmonics, the coefficient vector is composed of coefficients of spherical harmonics of each order.
[0117] According to the relationship between spherical harmonics and multipole modes, the spherical harmonics of each order are expanded into the form of multipole modes. For the spherical harmonic function Y with m≥0 n Multipole mode Ψ with m(θ,φ) and γ≤1 α,β,γ =(sinθcosφ) α (sinθsinφ) β (cosθ) γ The connection between can be expressed as:
[0118]
[0119] in, Yes constant coefficient of , represents the binomial coefficient...
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