Beamforming with a circular microphone array · 18 Acoustic Technology, Technical University of...
40
Guest lecture Antoni Torras Rosell [email protected] Salvador Barrera-Figueroa [email protected] Finn Jacobsen [email protected] CCAUV, 13th of May 2012
Transcript of Beamforming with a circular microphone array · 18 Acoustic Technology, Technical University of...
Guest lecture
Antoni Torras Rosell [email protected]
Salvador Barrera-Figueroa [email protected]
Finn Jacobsen [email protected]
CCAUV, 13th of May 2012
17/04/2008 Presentation name 2 Acoustic Technology, Technical University of Denmark
Introduction
The propagation of light
The acousto-optic effect
Application 1: Visualization of sound fields
Tomography
Acousto-optic tomography
Application 2: Beamforming
Conventional beamforming
Spatial aliasing
Acousto-optic beamformer
17/04/2008 Presentation name 3 Acoustic Technology, Technical University of Denmark
The measurement of sound with conventional techniques requires the immersion of the transducers into the sound field.
17/04/2008 Presentation name 4 Acoustic Technology, Technical University of Denmark
Electromagnetic wave equation:
: Electric field
: refractive index
: speed of light in vacuum
OBS Light travels slower in dense media
Vacuum Air Water
1 ~1.0003 ~1.3
[kg/m3] 0 ~1.2 ~1000
[%] 0 0.03 ~23
• What happens if the properties of the medium are not constant?
The refractive index changes The propagation of light is influenced
17/04/2008 Presentation name 5 Acoustic Technology, Technical University of Denmark
• What does it influence the refractive index in air? Temperature
Pressure
Humidity
…
17/04/2008 Presentation name 6 Acoustic Technology, Technical University of Denmark
Large temperature gradients above the pavement bend the light rays coming from the sky.
• What does it influence the refractive index in air? Temperature
Pressure
Humidity
… Example: Road mirages
17/04/2008 Presentation name 7 Acoustic Technology, Technical University of Denmark
Propagation of sound Pressure fluctuations
Density variations changes
Physical principle:
Refractive index
propagation of light
Influence on the
Acousto-optic effect
17/04/2008 Presentation name 8 Acoustic Technology, Technical University of Denmark
( : is the oscillation period of light)
In air and within the audible frequency range, the acousto-optic
effect changes the phase of light , but not its amplitude.
Let us assume the following solution to the electromagnetic wave equation:
Can we still use the electromagnetic wave equation?
(E.g. when light propagates along the -direction)
17/04/2008 Presentation name 9 Acoustic Technology, Technical University of Denmark
We can measure the phase of a beam of light using a laser
Doppler vibrometer (LDV)
Mechanical vibrations
17/04/2008 Presentation name 10 Acoustic Technology, Technical University of Denmark
We can measure the phase of a beam of light using a laser
Doppler vibrometer (LDV)
Mechanical vibrations
Acousto-optic effect
17/04/2008 Presentation name 11 Acoustic Technology, Technical University of Denmark
Can we use the apparent velocity measured with the LDV to visualize an acoustic field?
The sound pressure can be reconstructed using tomographic techniques
17/04/2008 Presentation name 12 Acoustic Technology, Technical University of Denmark
Tomography
Single photon emission CT (SPECT)
Gamma rays
Computerized Tomography (CT)
X-rays
Magnetic Resonance Imaging (MRI)
Radio-frequency waves
Ocean Acoustic Tomography
Sound waves
...
“Non-invasive” techniques
17/04/2008 Presentation name 13 Acoustic Technology, Technical University of Denmark
The phase of the light integrates the acoustic field:
Projection of the sound field
Radon Transform:
With a laser Doppler vibrometer:
17/04/2008 Presentation name 14 Acoustic Technology, Technical University of Denmark
The acoustic field cannot directly be
measured.
The Radon transform of the acoustic field
can be obtained with an LDV,
17/04/2008 Presentation name 15 Acoustic Technology, Technical University of Denmark
The acoustic field cannot directly be
measured.
The Radon transform of the acoustic field
can be obtained with an LDV,
A single line scan is not enough.
Complete reconstruction of an arbitrary
sound field requires:
- Parallel lines scanning over a plane.
17/04/2008 Presentation name 16 Acoustic Technology, Technical University of Denmark
The acoustic field cannot directly be
measured.
The Radon transform of the acoustic field
can be obtained with an LDV,
A single line scan is not enough.
Complete reconstruction of an arbitrary
sound field requires:
- Parallel lines scanning over a plane.
17/04/2008 Presentation name 17 Acoustic Technology, Technical University of Denmark
The acoustic field cannot directly be
measured.
The Radon transform of the acoustic field
can be obtained with an LDV,
A single line scan is not enough.
Complete reconstruction of an arbitrary
sound field requires:
- Parallel lines scanning over a plane.
17/04/2008 Presentation name 18 Acoustic Technology, Technical University of Denmark
The acoustic field cannot directly be
measured.
The Radon transform of the acoustic field
can be obtained with an LDV,
A single line scan is not enough.
Complete reconstruction of an arbitrary
sound field requires:
- Parallel lines scanning over a plane.
- Take projections in different directions.
17/04/2008 Presentation name 19 Acoustic Technology, Technical University of Denmark
The acoustic field cannot directly be
measured.
The Radon transform of the acoustic field
can be obtained with an LDV,
A single line scan is not enough.
Complete reconstruction of an arbitrary
sound field requires:
- Parallel lines scanning over a plane.
- Take projections in different directions.
17/04/2008 Presentation name 20 Acoustic Technology, Technical University of Denmark
The acoustic field cannot directly be
measured.
The Radon transform of the acoustic field
can be obtained with an LDV,
A single line scan is not enough.
Complete reconstruction of an arbitrary
sound field requires:
- Parallel lines scanning over a plane.
- Take projections in different directions.
17/04/2008 Presentation name 21 Acoustic Technology, Technical University of Denmark
Projecting the acoustic field into different
directions yields a very well defined inverse
problem,
17/04/2008 Presentation name 22 Acoustic Technology, Technical University of Denmark
Projecting the acoustic field into different
directions yields a very well defined inverse
problem,
The acoustic field is
reconstructed by computing the
inverse Radon transform.
17/04/2008 Presentation name 23 Acoustic Technology, Technical University of Denmark
Measured Radon transform
Pure tone at 2 kHz.
Measuring plane located 12 cm
above the loudspeaker.
17/04/2008 Presentation name 24 Acoustic Technology, Technical University of Denmark
Measured Radon transform
Pure tone at 2 kHz.
Measuring plane located 12 cm
above the loudspeaker.
Reconstructed sound field
17/04/2008 Presentation name 25 Acoustic Technology, Technical University of Denmark
Microphone array Tomographic reconstruction
• Spatial res.: 2 cm
• Angular res.: 10º
• Planar array of 60 microphones
• Spatial resolution: 7.5 cm
17/04/2008 Presentation name 26 Acoustic Technology, Technical University of Denmark
Microphone array Tomographic reconstruction
• Spatial res.: 2 cm
• Angular res.: 10º
• Planar array of 60 microphones
• Spatial resolution: 7.5 cm
17/04/2008 Presentation name 27 Acoustic Technology, Technical University of Denmark
Localization of sound sources
17/04/2008 Presentation name 28 Acoustic Technology, Technical University of Denmark
Beamforming techniques
Region Key feature
Farfield Phase
Nearfield Phase and amplitude
17/04/2008 Presentation name 29 Acoustic Technology, Technical University of Denmark
Beamforming techniques
Region Key feature
Farfield Phase
Nearfield Phase and amplitude
Example: Delay and Sum Beamforming (DSB)
Measured pressure
Phase shift
17/04/2008 Presentation name 30 Acoustic Technology, Technical University of Denmark
To improve the beamforming output:
Design an optimum array layout/geometry
Optimize weighting coefficients ( )
Adaptive beamforming
What do these techniques improve?
Resolution
Maximum sidelobe level (MSL)
Frequency range of analysis, etc.
Line array
17/04/2008 Presentation name 31 Acoustic Technology, Technical University of Denmark
Beamforming techniques are based on a finite number of input
signals This inevitably causes spatial aliasing!
E.g. DSB when
17/04/2008 Presentation name 32 Acoustic Technology, Technical University of Denmark
Beamforming techniques are based on a finite number of input
signals This inevitably causes spatial aliasing!
E.g. DSB when
Theoretical solution: Use an infinite number of transducers ( )
?
17/04/2008 Presentation name 33 Acoustic Technology, Technical University of Denmark
Beamforming techniques are based on a finite number of input
signals This inevitably causes spatial aliasing!
E.g. DSB when
Theoretical solution: Use an infinite number of transducers ( )
17/04/2008 Presentation name 34 Acoustic Technology, Technical University of Denmark
17/04/2008 Presentation name 35 Acoustic Technology, Technical University of Denmark
Acousto-optic beamformer
DSB – Line array
17/04/2008 Presentation name 36 Acoustic Technology, Technical University of Denmark
Acousto-optic beamformer
DSB – Line array
17/04/2008 Presentation name 37 Acoustic Technology, Technical University of Denmark
Acousto-optic beamformer
DSB – Line array Spatial aliasing!
17/04/2008 Presentation name 38 Acoustic Technology, Technical University of Denmark
Microphone LDV
(High-pass filtered signals)
LDV
Thanks for your attention!
17/04/2008 Presentation name 40 Acoustic Technology, Technical University of Denmark
Microphone LDV
(High-pass filtered signals)
