By Hua Lee
For complicated working modalities and dimensionalities, the layout and improvement of high-performance sensing and imaging structures signify the main direct and critical advances within the box of process research and sign processing. during this box, the middle parts are actual modeling, mathematical research, formula of photo reconstruction algorithms, functionality assessment, and procedure optimization.
Acoustical Sensing and Imaging covers the complete scope of those parts, with an emphasis at the functions of procedure research and sign processing in acoustical sensing and imaging.
Providing a unified theoretical framework, this book:
Focuses at the solution research within the actual modeling of the platforms, engaging in the research in the course of the quantitative review of the spatial-frequency spectral insurance Addresses the foremost components of sign processing, resembling the layout of the probing waveforms, snapshot reconstruction algorithms, blunders relief and removing, and photo enhancement Formulates the picture reconstruction algorithms in line with the concept that of coherent backward propagation, within the kind of multi-frequency tomography Explains the best way to increase approach functionality, together with the correction of quadrature part error sooner than snapshot reconstruction and enhancement with coherent wavefield records through the superposition of sub-images offers numerous purposes as examples of varied working modalities, illustrating the technical and academic value of the field
Acoustical Sensing and Imaging guarantees a wide appreciation of the layout options, research, and improvement of high-performance sensing and imaging platforms.
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Extra info for Acoustical Sensing and Imaging
Subsequently, we can generalize this concept based on the linearity and space invariance. s( x , y , z) = δ( x − x0 , y − y0 , z − z0 ) The wavefield produced by this point source is in the form of a spatiallyshifted Green’s function, g(x , y , z) = δ(x − x0 , y − y0 , z − z0 ) * h(x , y , z) = h(x − x0 , y − y0 , z − z0 ) 1 j 2πr exp = λ jλr where r = (( x − x0 )2 + ( y − y0 )2 + ( z − z0 )2 )1/2 In this case, the backward-propagation image formation is in the form of s′(x , y , z) = g(x , y , z) * h* (x , y , z) = 1 j2πr −1 − j 2πr ′ exp dx′dy ′dz′ λ λ jλrr ′ ∫∫∫ jλr exp R 38 Acoustical Sensing and Imaging where r = (( x′ − x0 )2 + ( y ′ − y0 )2 + ( z′ − z0 )2 )1/2 and r ′ = (( x − x′ )2 + ( y − y ′ )2 + ( z − z′ )2 )1/2 Then, after reorganizing the terms inside the integral, it becomes s′(x , y , z) = g(x , y , z) * h* (x , y , z) = j 2π(r − r ′ ) dx′dy ′dz′ λ 1 ∫∫∫ λ rr′ exp 2 R = ∫∫∫ A(r , r′)exp( jθ(r , r′)) dx′dy′dz′ R In simple words, it can be seen that the image is formed out of an integral of a collection of vectors.
It contains two key elements. One is that the norm of the frequency vector of a plane wave is governed by the wavelength. The other one is that the incident angle of the plane wave is defined by the components of the frequency vector. 3 Impulse Responses of Wave Propagation The wavefield produced by a point source has been well established through physics experiments. For three-dimensional cases, the complex phasor version is in the form of 1 j 2πr h( x , y , z) = exp λ jλr where r = [x2 + y2 + z2]1/2, is the distance from the location of the point source to the receiver position In two dimensions, it becomes 1 h( x , y ) = jλr 1/2 j 2πr exp λ where r = [x2 + y2]1/2.
If we attach the minus sign to the propagation distance z, the filter process associated with image reconstruction is like propagating the received wavefield in the opposite direction. It is like treating the received wavefield as a source distribution and propagating it backward in the –z direction. Thus, this technique is commonly known as backward propagation. 1/2 1 H * ( f x, f y ; z) = exp − j2π 2 − ( f x2 + f y2 ) z λ 1/2 1 = H ( f x, f y ; −z) = exp j 2π 2 − ( f x2 + f y2 ) (−z) λ Using the conjugate-symmetry property of the Fourier transform, we can formulate the impulse responses of the backward-propagation algorithm in various dimensions as −1 − j 2πr h* ( x, y, z) = exp λ jλr −1 h ( x, y ) = jλr * 1/2 − j 2πr exp λ − j 2πx h* ( x) = exp λ 34 Acoustical Sensing and Imaging This shows the computation structure involved in backward propagation is simplified that both the transfer function and impulse response are the conjugate versions of that of the forward wave propagation process.
Acoustical Sensing and Imaging by Hua Lee