Acoustic scattering
In many fields of acoustics as ultrasound imaging, NDT or submarine acoustics, the knowledge of the reflected field of even simple scatterers are needed to understand the information of the reflections of these bodies. Thus, here we show a simple scattering example by a rigid cylinder. The following images shows the incident, total and reflected field of the scatterer. The complex reflected field can be calculated simply as:
\[\hat{P_r}=\hat{P_t}-\hat{P_i}\]
where \(\hat{P_r}\) is the reflected field, \(\hat{P_i}\) is incident and \(\hat{P_t}\) is the total measured acoustic field for a cylinder of radius \(R\) and a incident field of wavelength \(\lambda\).
Scattering by a cylinder of \(R /\lambda=0.35\)
These three images are the modulus of the complex value of the pressure (i.e. the envelope the measured time domain field) for a rigid cylinder of \(R /\lambda=0.35\) for the incident pressure field \(\hat{P_i}\), the total field \(\hat{P_t}\) and finally the computed reflected field \(\hat{P_r}\).
![doppler effect simulation video](media/scattering/acoustic scattering - abs pi field for lambda_over_R_0.35.gif)
![doppler effect simulation video](media/scattering/acoustic scattering - abs pt field for lambda_over_R_0.35.gif)
![doppler effect simulation video](media/scattering/acoustic scattering - abs pr field for lambda_over_R_0.35.gif)
The below three images are the distribution of the real part of the pressure (i.e. physical pressure you have for a fixed time) for the incident pressure field \(\hat{P_i}\), the total field \(\hat{P_t}\) and finally the computed reflected field \(\hat{P_r}\).
![doppler effect simulation video](media/scattering/acoustic scattering - real pi field for lambda_over_R_0.35.gif)
![doppler effect simulation video](media/scattering/acoustic scattering - real pt field for lambda_over_R_0.35.gif)
![doppler effect simulation video](media/scattering/acoustic scattering - real pr field for lambda_over_R_0.35.gif)
Scattering by a cylinder of \(R /\lambda=1\)
These three images are the modulus of the complex value of the pressure (i.e. the envelope the measured time domain field) for a rigid cylinder of \(R /\lambda=1\) for the incident pressure field \(\hat{P_i}\), the total field \(\hat{P_t}\) and finally the computed reflected field \(\hat{P_r}\).
![doppler effect simulation video](media/scattering/acoustic scattering - abs pi field for lambda_over_R_1.00.gif)
![doppler effect simulation video](media/scattering/acoustic scattering - abs pt field for lambda_over_R_1.00.gif)
![doppler effect simulation video](media/scattering/acoustic scattering - abs pr field for lambda_over_R_1.00.gif)
The below three images are the distribution of the real part of the pressure (i.e. physical pressure you have for a fixed time) for the incident pressure field \(\hat{P_i}\), the total field \(\hat{P_t}\) and finally the computed reflected field \(\hat{P_r}\).
![doppler effect simulation video](media/scattering/acoustic scattering - real pi field for lambda_over_R_1.00.gif)
![doppler effect simulation video](media/scattering/acoustic scattering - real pt field for lambda_over_R_1.00.gif)
![doppler effect simulation video](media/scattering/acoustic scattering - real pr field for lambda_over_R_1.00.gif)
Scattering by a cylinder of \(R /\lambda=2\)
These three images are the modulus of the complex value of the pressure (i.e. the envelope the measured time domain field) for a rigid cylinder of \(R /\lambda=2\) for the incident pressure field \(\hat{P_i}\), the total field \(\hat{P_t}\) and finally the computed reflected field \(\hat{P_r}\).
![doppler effect simulation video](media/scattering/acoustic scattering - abs pi field for lambda_over_R_2.00.gif)
![doppler effect simulation video](media/scattering/acoustic scattering - abs pt field for lambda_over_R_2.00.gif)
![doppler effect simulation video](media/scattering/acoustic scattering - abs pr field for lambda_over_R_2.00.gif)
The below three images are the distribution of the real part of the pressure (i.e. physical pressure you have for a fixed time) for the incident pressure field \(\hat{P_i}\), the total field \(\hat{P_t}\) and finally the computed reflected field \(\hat{P_r}\).
![doppler effect simulation video](media/scattering/acoustic scattering - real pi field for lambda_over_R_2.00.gif)
![doppler effect simulation video](media/scattering/acoustic scattering - real pt field for lambda_over_R_2.00.gif)
![doppler effect simulation video](media/scattering/acoustic scattering - real pr field for lambda_over_R_2.00.gif)