- Email: [email protected]
Acoustic source identification using a scanning laser Doppler vibrometer
ARTICLE IN PRESS
Optics and Lasers in Engineering 45 (2007) 742–749
Acoustic source identification using a scanning laser Doppler vibrometer Joris Vanherzeele, Steve Vanlanduit, Patrick Guillaume Vrije Universiteit Brussel (VUB), Acoustics & Vibration Research Group (AVRG), Department of Mechanical Engineering (MECH), Pleinlaan 2, B-1050 Brussel, Belgium Received 18 August 2006; accepted 17 October 2006 Available online 8 December 2006
Abstract This paper shows how a scanning laser Doppler vibrometer (LDV), an instrument designed to measure vibrations of structures or objects, can be used in a non-traditional fashion to identify acoustical sources. This is achieved by measuring the changes in the optical path induced by local fluctuation of the air refraction index to which the LDV is sensitive. The acoustical signal used is sinusoidal and may be recovered by scanning at a uniform rate over a subject area (continuous scan) parallel to the source axis and demodulating this signal. Due to the fact that the measured scan area is in fact a line integral over a measurement volume between the laser head and a rigid object needed to reflect the laser beam, multiple view planes around the axis of the acoustic source are usually measured. These are then passed through a tomographic algorithm, thereby reconstructing the full sound field. In this article however, only one view plane is measured, but the acoustic source is placed on a rotating surface with fixed rotational frequency, thereby imposing a modulation on the measured spectrum. Demodulation will allow reconstruction of the three-dimensional sound field. r 2006 Elsevier Ltd. All rights reserved. Keywords: Scanning laser Doppler vibrometer; Rotating acoustic source identification; Tomographic reconstruction
1. Introduction Measuring physical phenomena in most cases means perturbing that exact phenomenon. Measurement techniques are ever evolving minimizing the interaction between measurement equipment and the physical event itself [1,2]. In the acoustic world this was and basically still is done by using microphones to measure the sound pressure level (SPL). This techniques however suffers a major disadvantage mostly due to its intrusive nature and also obtaining a complete image of the acoustic field is a tedious procedure. More recently a technique is used called acoustic holography, which still requires the use of microphones, however without the need to move them from point to point. Using a laser Doppler vibrometer (LDV) it is possible to visualize flows and acoustic fields without any intrusion Corresponding author. Tel.: +32 2 629 28 07; fax: +32 2 629 28 65.
E-mail address: [email protected] (J. Vanherzeele). 0143-8166/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.optlaseng.2006.10.008
whatsoever [3–5]. A LDV, which is traditionally used to measure vibrations, is also sensitive to changes in refractive index of the medium, in case of density variations of the measurement volume along the line of sight. Therefore it is possible to measure e.g. flows or even acoustic phenomena. Moreover it is possible to retrieve this spectral information simultaneously, without hampering measurement time or needing a different test set-up. Now, it is well-known that the signals acquired by interferometric techniques are line integrals over the laser beam optical path, so therefore images are often taken at different angles to derive local density distribution, which in turn implies needing tomographic reconstruction algorithms [6]. In this paper acquiring these views at sequential angles is done in a continuous fashion. By scanning across a retroreflective rigid object through the sound field produced by e.g. a loudspeaker it is possible to obtain a twodimensional visualization of the acoustic field. Now, by simply mounting this acoustic source on a turn table and rotating it at a certain speed, it is possible to obtain
ARTICLE IN PRESS J. Vanherzeele et al. / Optics and Lasers in Engineering 45 (2007) 742–749
the three-dimensional acoustic field by measuring a complete rotational cycle for each scan point. The measurement for each scan point then contains the (continuous) angle information necessary for the tomographic algorithms. 2. Theoretical principle The LDV is based on a modified Mach–Zender interferometer and measures a pseudo velocity depending on the variation of the optical path and the refraction index, n, of the medium within the measuring volume illustrated in Fig. 1. The classical use of the LDV is to measure the velocity or displacement of moving objects on which the laser beam impacts. The physical principle governing the measurement system is the Doppler effect that occurs when the laser light is scattered by a moving target: if the laser light has a frequency u, after being reflected from the object moving at velocity v, its frequency undergoes a shift Du given by 2v cos y , (1) l where l is the laser wavelength and v cos y is the target velocity component along the laser line-of-sight. The system output is therefore the velocity v or the displacement s recovered from the frequency shift Du; in our specific case it is the velocity. In this simplified theoretical discussion, it has to be pointed out that the measured displacement s not only depends on the optical path z of the laser beam, but also on the refraction index n of the medium through which the beam passes. Therefore the velocity obtained from the interferometer is Du ¼
vðx; y; tÞ ¼
the air pressure, and consequently of the density, within the measuring volume. In reality the turbulence not only produces a flow velocity oscillation linked to turbulent effects occurring within the measuring volume but also a sound field fluctuation due to generated acoustic waves. This is the main advantage of this measuring technique because it allows broadband measurements up to very high frequencies which can normally not be detected with other apparatus. However, a major drawback of the technique is, that it only provides a visual representation of the flow and provides no immediate quantitative information, besides the frequencies of the phenomena themselves.
3. Experimental set-up The test consists of two parts, both done in a semi anechoic chamber. In the first part of the test the acoustic source which was a simple loudspeaker (; 8 cm) was kept still to obtain a simple two-dimensional view of the field, hence measuring across the optical beam path. Using a Polytec PSV300 scanning LDV 650 scan points were measured on the rigid plate for a single sine excitation frequency at 10 kHz. The rigid plate was 45 cm wide and 40 cm high and was covered in retro reflective tape to enhance signal quality. The loudspeaker was placed in the middle between the steady plate and the laser head. The basic set-up can be seen in Fig. 2. For the second part of the test, the acoustic source was placed on a Bruel & Kjaer type 3923 microphone boom and rotated at its highest velocity of 16 s/rev (Fig. 3).
dsðx; y; tÞ d½nðx; y; tÞz dnðx; y; tÞ dz ¼ ¼z þ nðx; y; tÞ . dt dt dt dt
(2) When only the movement of an object is measured, the variation of the refraction index of the surrounding medium is zero and only the second term appears in Eq. (2), i.e. the velocity is given by the variation of the optical path. Vice versa, if one wants to measure turbulent fields the reflecting target is kept steady as is shown in Fig. 1. The only variable is the refraction index because the turbulence produces a temporal and spatial fluctuation of
Fig. 1. Measuring principle.
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Fig. 2. Test set-up, acoustic source at stand still.
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Fig. 4. Schematic of the peak detector.
course be T¼
Fig. 3. Test set-up, acoustic source rotating.
Different sized scan grids were used for each measurement. For each scan point one entire revolution of the acoustic source is measured in order to have a full 360 view. The measurement is triggered by means of an Eddy current probe attached to the microphone boom. The rigid reflector was placed on a separate table in order to avoid vibrations invoked by the rotating microphone boom. The microphone boom was placed half way between the steady plate and the laser head. The obtained signal for each scan point is of course the 10 kHz sine wave but modulated at the rotational frequency of the microphone boom. There are two ways to perform the measurement. The first is to measure each scan point broadband, acquiring a massive amount of data in the process, because of the necessary high sampling frequency and demodulating the signal afterwards. This cannot be done in the commercial Polytec software. On top of that Polytec does not output the time signals which are necessary for demodulation, and the output spectra no longer contain the DC frequency line. Therefore, other selfdeveloped codes must be used. However, while using these codes another problem arose, due to the fact that storing this massive amount of data lead to buffering issues with the measurement channels. Therefore, another approach had to be implemented. Because the measured signal is basically an amplitude modulated waveform, in case the acoustic source wave modulated at the rotation frequency of the microphone boom, it is possible to demodulate this signal electronically. For this purpose a simple peak detector [7] was developed and mounted in between the in- and output channel of the vibrometer. The schematic is shown in Fig. 4. The time constant of this circuit is t ¼ RC.
(3)
When the acoustic source has a carrier frequency f c the time between successive peaks of the carrier will of
1 . fc
(4)
Each peak charges the capacitor to a certain voltage proportional to the modulated amplitude of the AM wave. However, when the amplitude of the modulating wave changes dramatically the capacitor charge will not be recharged over its existing level by the following amplitude peaks during a certain amount of cycles of the carrier frequency. This implies that the output signal from the detector is rounded off somewhat. To avoid this so-called negative peak clipping, the detector’s time constant t must be chosen as follows: t51=f m where f m is the highest modulation frequency used in the experiment. This implies that to avoid peak clipping t should be small. On the other hand, to avoid ripple (i.e. when the detector output starts to follow the carrier frequency) t should be chosen as large as possible. This gives a range to which the time constant of the detector is bound: 1 1 btb . fm fc
(5)
In this experiment the carrier frequency is 10 kHz and the 1 Hz. To satisfy Eq. (5) the modulating frequency is 16 components of the detector were chosen as follows: R ¼ 49 kO and C ¼ 1 mF. To be sure no frequencies are present above the carrier frequency of the acoustic source, a filter with cut-off frequency 10 kHz was placed before the peak detector. This ensures that the peak detector will work properly. 4. Experimental results In the first part of the experiment the acoustic wave was measured with the SLDV while the loudspeaker was at stand still. This measurement was performed in the normal mode without the peak detector or cut-off filter. The result is of course two-dimensional, as only one image plane is measured. The result is shown in Fig. 5. This figure clearly shows the different wave fronts of the sound wave, but there is something remarkable about the result. The amplitude on the left side of the sound field is clearly higher than on the right. This is unexpected because the loudspeaker should emit the same amount of energy in all directions. To validate this result, 2 SPL measurements were done with a microphone on both sides of the test
ARTICLE IN PRESS J. Vanherzeele et al. / Optics and Lasers in Engineering 45 (2007) 742–749
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Fig. 5. Measured acoustic field with loudspeaker at stand still; one image plane: a 3D view.
Fig. 6. Schematic view of the test set-up.
set-up. This measurement revealed that the SPL was 4 dB lower on one side. This confirms the LDV measurements. This lower level is most likely due to the sound wave reflecting off the table as the loudspeaker was not positioned in the center of the table. For the second part of the experiment the loudspeaker was placed on the rotating microphone boom and rotated at 16 s/rev. Two measurements were done with the loudspeaker placed at different positions: 0.5 and 5 cm away from the axis of the microphone boom. The scan grid contained 625 spatial points (25 25) for both measurements. The grid covered an area on the steady plate of
36 36 cm. Knowing that the microphone boom is exactly in between the LDV and the flat plate, it is easy to determine that the projected measurement grid above the loudspeaker is half the size at 18 18 cm. The measurements were performed with a sample frequency of only 256 Hz, which is possible because of the peak detector, using 2048 spectral lines. This corresponds with a measurement time of exactly 16 s, which is one complete rotational period of the microphone boom. For the next scan point, the following rotation period is discarded and the next period is awaited for a new measurement.
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Fig. 7. Polar plot of the measured density variation for three scan points for a ¼ 0:5 cm: (a) top left; (b) top right; (c) top middle.
Fig. 6 shows a schematic view of the test set-up, where a indicates the distance between loudspeaker and microphone boom axis, and therefore is a measure for the modulation amplitude. The measurement for three scan points chosen on the top left, top right and top middle of the scanned grid can be seen in Fig. 7. Normally the SPL at a certain distance from the loudspeaker is the same on all sides. Therefore the measured modulated sound wave should be symmetric. When looking at Figs. 7(a) and (b), this theory is respected
quite well, with some minor deviations. However, in the first part of the measurements it was shown that the SPL level is not the same on both sides of the source. This can again be seen in these figures. Moreover, the radial plot for the measurement on the right is mirrored exactly on the left. The measurement on a point in the middle of the scan grid should portray almost no modulations for this particular measurement because the loudspeaker is almost in the center. Therefore, measuring through the center should give the same result on all sides, hence depicting a circle. This is in fact what can be seen in
ARTICLE IN PRESS J. Vanherzeele et al. / Optics and Lasers in Engineering 45 (2007) 742–749
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Fig. 8. Polar plot of the measured density variation for three scan points for a ¼ 5 cm: (a) top left; (b) top right; (c) top middle.
Fig. 7(c). There are some minor variations but this is again mostly due to the difference in SPL level on opposite sides of the loudspeaker. The same conclusions are valid when placing the loudspeaker 5 cm out of axis except for the scan points in the middle of the grid. In this particular case there will also be modulations visible when scanning across the centerline of rotation. This is clearly visible in Fig. 8(c). To reconstruct the full three-dimensional acoustic field, a tomographic algorithm from the Matlab R12 toolbox was used. Each scan point contains the angle information in the
time signal. This means that for these particular experiments where 2048 DFT lines were used the same number of angles is measured. Combining this angle information from the measured time signal in each scan point together with the spatial information from the scanned grid gives 2048 projections of the acoustic field. This boils down to an angular resolution of 0:176 , which if done manually, is a very tedious job. In Fig. 9 the sound field is shown along a cross-section in the Y-direction for the loudspeaker placed 0.5 cm out of axis of rotation (a ¼ 0:5 cm).
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Fig. 9. Acoustic field along a constant Y coordinate: a ¼ 0:5 cm: (a) slice directly above source and (b) slice far away from source.
Fig. 10. Acoustic field along a constant Y coordinate: a ¼ 5 cm: (a) slice directly above source and (b) slice far away from source.
In Fig. 9(a) a slice of the field is shown directly above the loudspeaker. This image depicts a vague ring shape, which is most probably due to reflections off the table and the varying SPL level between left and right. The amplitude is quite low, because there are hardly any modulations because the source is nearly in the rotational center. Higher up in the flow (Fig. 9(b)) a single peak can be distinguished, located almost exactly in the center as is to be expected because the loudspeaker is only 0.5 cm out of axis of rotation. In Fig. 10 the sound field is shown along a cross section in the Y-direction for the loudspeaker placed 5 cm out of axis of rotation (a ¼ 5 cm). In Fig. 10(a) a slice is shown directly above the acoustic source. Again this is quite hard to interpret, because of the same reasons as in the previous case. Fig. 10(b) shows a slice along the top of the acoustic field. One can distinguish a large peak out of axis and a ring where the level is lower. This distinct peak is shifted about 5 pixels out of the center where the rotation axis of
the microphone boom is. As was stated at the beginning of this section the measurement grid projected in the loudspeaker plane is 18 18 cm. Because the image size itself is 16 pixels square, this means that the loudspeaker is measured to be 5.62 cm out of axis which is in quite good agreement with the geometrically determined 5 cm.
5. Conclusions In this article acoustic fields were visualized using a laser Doppler vibrometer (LDV). A loudspeaker sound field at 10 kHz was measured in three dimensions by rotating the source. Measuring each scan point thereby gives a continuous representation of the rotational dimension. This was then run through a tomographic algorithm to reconstruct the three-dimensional field. A peak detector was attached to the LDV output channel to immediately demodulate the modulation due to the rotation.
ARTICLE IN PRESS J. Vanherzeele et al. / Optics and Lasers in Engineering 45 (2007) 742–749
The loudspeaker was placed in different positions, i.e. 0.5 and 5 cm of axis of rotation. From the measurements it proved possible to locate the position of the acoustical source. The technique is able to measure the sound field quasi automatically without having to change the set-up for each angle, with a measurement time of approximately 7 h for a spatial resolution of 25 25 and a rotation velocity limited to 16 s/rev. Acknowledgments This research has been sponsored the Fund for Scientific Research—Flanders (FWO) Belgium. The authors also acknowledge the Flemish government (GOA-Optimech) and the research council of the Vrije Universiteit Brussel (OZR) for their funding.
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References [1] Ambrosini D, Rastogi PK. Optical methods in heat transfer and fluid flow. Opt Lasers Eng 2006;44(3–4):155–8. [2] Prenel J, Bailly Y. Recent evolutions in fluid mechanics: from standard tomographic visualization to 3D volumic velocimetry. Opt Lasers Eng 2006;44(3–4):321–34. [3] Castellini P, Martarelli M. Aeroacoustic characterisation of turbulent free jets using scanning laser Doppler vibrometry. Sixth international conference on vibration measurements by laser techniques, SPIE, 2004. [4] Mayrhofer N, Woisetsclager J. Frequency analysis of turbulent compressible flows by laser vibrometry. Exp in Fluids 2001;31: 153–63. [5] Zipser L, Franke H. Laser-scanning vibrometry for the investigation of sound generation and propagation. Sixth international conference on vibration measurements by laser techniques, SPIE, 2004. [6] Dove EL. Notes on Computerized Tomography, Bioimaging Fundamentals. [7] Lesurf J. The Envelope Detector, www.st-andrews.ac.uk.
Optics and Lasers in Engineering 45 (2007) 742–749
Acoustic source identification using a scanning laser Doppler vibrometer Joris Vanherzeele, Steve Vanlanduit, Patrick Guillaume Vrije Universiteit Brussel (VUB), Acoustics & Vibration Research Group (AVRG), Department of Mechanical Engineering (MECH), Pleinlaan 2, B-1050 Brussel, Belgium Received 18 August 2006; accepted 17 October 2006 Available online 8 December 2006
Abstract This paper shows how a scanning laser Doppler vibrometer (LDV), an instrument designed to measure vibrations of structures or objects, can be used in a non-traditional fashion to identify acoustical sources. This is achieved by measuring the changes in the optical path induced by local fluctuation of the air refraction index to which the LDV is sensitive. The acoustical signal used is sinusoidal and may be recovered by scanning at a uniform rate over a subject area (continuous scan) parallel to the source axis and demodulating this signal. Due to the fact that the measured scan area is in fact a line integral over a measurement volume between the laser head and a rigid object needed to reflect the laser beam, multiple view planes around the axis of the acoustic source are usually measured. These are then passed through a tomographic algorithm, thereby reconstructing the full sound field. In this article however, only one view plane is measured, but the acoustic source is placed on a rotating surface with fixed rotational frequency, thereby imposing a modulation on the measured spectrum. Demodulation will allow reconstruction of the three-dimensional sound field. r 2006 Elsevier Ltd. All rights reserved. Keywords: Scanning laser Doppler vibrometer; Rotating acoustic source identification; Tomographic reconstruction
1. Introduction Measuring physical phenomena in most cases means perturbing that exact phenomenon. Measurement techniques are ever evolving minimizing the interaction between measurement equipment and the physical event itself [1,2]. In the acoustic world this was and basically still is done by using microphones to measure the sound pressure level (SPL). This techniques however suffers a major disadvantage mostly due to its intrusive nature and also obtaining a complete image of the acoustic field is a tedious procedure. More recently a technique is used called acoustic holography, which still requires the use of microphones, however without the need to move them from point to point. Using a laser Doppler vibrometer (LDV) it is possible to visualize flows and acoustic fields without any intrusion Corresponding author. Tel.: +32 2 629 28 07; fax: +32 2 629 28 65.
E-mail address: [email protected] (J. Vanherzeele). 0143-8166/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.optlaseng.2006.10.008
whatsoever [3–5]. A LDV, which is traditionally used to measure vibrations, is also sensitive to changes in refractive index of the medium, in case of density variations of the measurement volume along the line of sight. Therefore it is possible to measure e.g. flows or even acoustic phenomena. Moreover it is possible to retrieve this spectral information simultaneously, without hampering measurement time or needing a different test set-up. Now, it is well-known that the signals acquired by interferometric techniques are line integrals over the laser beam optical path, so therefore images are often taken at different angles to derive local density distribution, which in turn implies needing tomographic reconstruction algorithms [6]. In this paper acquiring these views at sequential angles is done in a continuous fashion. By scanning across a retroreflective rigid object through the sound field produced by e.g. a loudspeaker it is possible to obtain a twodimensional visualization of the acoustic field. Now, by simply mounting this acoustic source on a turn table and rotating it at a certain speed, it is possible to obtain
ARTICLE IN PRESS J. Vanherzeele et al. / Optics and Lasers in Engineering 45 (2007) 742–749
the three-dimensional acoustic field by measuring a complete rotational cycle for each scan point. The measurement for each scan point then contains the (continuous) angle information necessary for the tomographic algorithms. 2. Theoretical principle The LDV is based on a modified Mach–Zender interferometer and measures a pseudo velocity depending on the variation of the optical path and the refraction index, n, of the medium within the measuring volume illustrated in Fig. 1. The classical use of the LDV is to measure the velocity or displacement of moving objects on which the laser beam impacts. The physical principle governing the measurement system is the Doppler effect that occurs when the laser light is scattered by a moving target: if the laser light has a frequency u, after being reflected from the object moving at velocity v, its frequency undergoes a shift Du given by 2v cos y , (1) l where l is the laser wavelength and v cos y is the target velocity component along the laser line-of-sight. The system output is therefore the velocity v or the displacement s recovered from the frequency shift Du; in our specific case it is the velocity. In this simplified theoretical discussion, it has to be pointed out that the measured displacement s not only depends on the optical path z of the laser beam, but also on the refraction index n of the medium through which the beam passes. Therefore the velocity obtained from the interferometer is Du ¼
vðx; y; tÞ ¼
the air pressure, and consequently of the density, within the measuring volume. In reality the turbulence not only produces a flow velocity oscillation linked to turbulent effects occurring within the measuring volume but also a sound field fluctuation due to generated acoustic waves. This is the main advantage of this measuring technique because it allows broadband measurements up to very high frequencies which can normally not be detected with other apparatus. However, a major drawback of the technique is, that it only provides a visual representation of the flow and provides no immediate quantitative information, besides the frequencies of the phenomena themselves.
3. Experimental set-up The test consists of two parts, both done in a semi anechoic chamber. In the first part of the test the acoustic source which was a simple loudspeaker (; 8 cm) was kept still to obtain a simple two-dimensional view of the field, hence measuring across the optical beam path. Using a Polytec PSV300 scanning LDV 650 scan points were measured on the rigid plate for a single sine excitation frequency at 10 kHz. The rigid plate was 45 cm wide and 40 cm high and was covered in retro reflective tape to enhance signal quality. The loudspeaker was placed in the middle between the steady plate and the laser head. The basic set-up can be seen in Fig. 2. For the second part of the test, the acoustic source was placed on a Bruel & Kjaer type 3923 microphone boom and rotated at its highest velocity of 16 s/rev (Fig. 3).
dsðx; y; tÞ d½nðx; y; tÞz dnðx; y; tÞ dz ¼ ¼z þ nðx; y; tÞ . dt dt dt dt
(2) When only the movement of an object is measured, the variation of the refraction index of the surrounding medium is zero and only the second term appears in Eq. (2), i.e. the velocity is given by the variation of the optical path. Vice versa, if one wants to measure turbulent fields the reflecting target is kept steady as is shown in Fig. 1. The only variable is the refraction index because the turbulence produces a temporal and spatial fluctuation of
Fig. 1. Measuring principle.
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Fig. 2. Test set-up, acoustic source at stand still.
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Fig. 4. Schematic of the peak detector.
course be T¼
Fig. 3. Test set-up, acoustic source rotating.
Different sized scan grids were used for each measurement. For each scan point one entire revolution of the acoustic source is measured in order to have a full 360 view. The measurement is triggered by means of an Eddy current probe attached to the microphone boom. The rigid reflector was placed on a separate table in order to avoid vibrations invoked by the rotating microphone boom. The microphone boom was placed half way between the steady plate and the laser head. The obtained signal for each scan point is of course the 10 kHz sine wave but modulated at the rotational frequency of the microphone boom. There are two ways to perform the measurement. The first is to measure each scan point broadband, acquiring a massive amount of data in the process, because of the necessary high sampling frequency and demodulating the signal afterwards. This cannot be done in the commercial Polytec software. On top of that Polytec does not output the time signals which are necessary for demodulation, and the output spectra no longer contain the DC frequency line. Therefore, other selfdeveloped codes must be used. However, while using these codes another problem arose, due to the fact that storing this massive amount of data lead to buffering issues with the measurement channels. Therefore, another approach had to be implemented. Because the measured signal is basically an amplitude modulated waveform, in case the acoustic source wave modulated at the rotation frequency of the microphone boom, it is possible to demodulate this signal electronically. For this purpose a simple peak detector [7] was developed and mounted in between the in- and output channel of the vibrometer. The schematic is shown in Fig. 4. The time constant of this circuit is t ¼ RC.
(3)
When the acoustic source has a carrier frequency f c the time between successive peaks of the carrier will of
1 . fc
(4)
Each peak charges the capacitor to a certain voltage proportional to the modulated amplitude of the AM wave. However, when the amplitude of the modulating wave changes dramatically the capacitor charge will not be recharged over its existing level by the following amplitude peaks during a certain amount of cycles of the carrier frequency. This implies that the output signal from the detector is rounded off somewhat. To avoid this so-called negative peak clipping, the detector’s time constant t must be chosen as follows: t51=f m where f m is the highest modulation frequency used in the experiment. This implies that to avoid peak clipping t should be small. On the other hand, to avoid ripple (i.e. when the detector output starts to follow the carrier frequency) t should be chosen as large as possible. This gives a range to which the time constant of the detector is bound: 1 1 btb . fm fc
(5)
In this experiment the carrier frequency is 10 kHz and the 1 Hz. To satisfy Eq. (5) the modulating frequency is 16 components of the detector were chosen as follows: R ¼ 49 kO and C ¼ 1 mF. To be sure no frequencies are present above the carrier frequency of the acoustic source, a filter with cut-off frequency 10 kHz was placed before the peak detector. This ensures that the peak detector will work properly. 4. Experimental results In the first part of the experiment the acoustic wave was measured with the SLDV while the loudspeaker was at stand still. This measurement was performed in the normal mode without the peak detector or cut-off filter. The result is of course two-dimensional, as only one image plane is measured. The result is shown in Fig. 5. This figure clearly shows the different wave fronts of the sound wave, but there is something remarkable about the result. The amplitude on the left side of the sound field is clearly higher than on the right. This is unexpected because the loudspeaker should emit the same amount of energy in all directions. To validate this result, 2 SPL measurements were done with a microphone on both sides of the test
ARTICLE IN PRESS J. Vanherzeele et al. / Optics and Lasers in Engineering 45 (2007) 742–749
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Fig. 5. Measured acoustic field with loudspeaker at stand still; one image plane: a 3D view.
Fig. 6. Schematic view of the test set-up.
set-up. This measurement revealed that the SPL was 4 dB lower on one side. This confirms the LDV measurements. This lower level is most likely due to the sound wave reflecting off the table as the loudspeaker was not positioned in the center of the table. For the second part of the experiment the loudspeaker was placed on the rotating microphone boom and rotated at 16 s/rev. Two measurements were done with the loudspeaker placed at different positions: 0.5 and 5 cm away from the axis of the microphone boom. The scan grid contained 625 spatial points (25 25) for both measurements. The grid covered an area on the steady plate of
36 36 cm. Knowing that the microphone boom is exactly in between the LDV and the flat plate, it is easy to determine that the projected measurement grid above the loudspeaker is half the size at 18 18 cm. The measurements were performed with a sample frequency of only 256 Hz, which is possible because of the peak detector, using 2048 spectral lines. This corresponds with a measurement time of exactly 16 s, which is one complete rotational period of the microphone boom. For the next scan point, the following rotation period is discarded and the next period is awaited for a new measurement.
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Fig. 7. Polar plot of the measured density variation for three scan points for a ¼ 0:5 cm: (a) top left; (b) top right; (c) top middle.
Fig. 6 shows a schematic view of the test set-up, where a indicates the distance between loudspeaker and microphone boom axis, and therefore is a measure for the modulation amplitude. The measurement for three scan points chosen on the top left, top right and top middle of the scanned grid can be seen in Fig. 7. Normally the SPL at a certain distance from the loudspeaker is the same on all sides. Therefore the measured modulated sound wave should be symmetric. When looking at Figs. 7(a) and (b), this theory is respected
quite well, with some minor deviations. However, in the first part of the measurements it was shown that the SPL level is not the same on both sides of the source. This can again be seen in these figures. Moreover, the radial plot for the measurement on the right is mirrored exactly on the left. The measurement on a point in the middle of the scan grid should portray almost no modulations for this particular measurement because the loudspeaker is almost in the center. Therefore, measuring through the center should give the same result on all sides, hence depicting a circle. This is in fact what can be seen in
ARTICLE IN PRESS J. Vanherzeele et al. / Optics and Lasers in Engineering 45 (2007) 742–749
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Fig. 8. Polar plot of the measured density variation for three scan points for a ¼ 5 cm: (a) top left; (b) top right; (c) top middle.
Fig. 7(c). There are some minor variations but this is again mostly due to the difference in SPL level on opposite sides of the loudspeaker. The same conclusions are valid when placing the loudspeaker 5 cm out of axis except for the scan points in the middle of the grid. In this particular case there will also be modulations visible when scanning across the centerline of rotation. This is clearly visible in Fig. 8(c). To reconstruct the full three-dimensional acoustic field, a tomographic algorithm from the Matlab R12 toolbox was used. Each scan point contains the angle information in the
time signal. This means that for these particular experiments where 2048 DFT lines were used the same number of angles is measured. Combining this angle information from the measured time signal in each scan point together with the spatial information from the scanned grid gives 2048 projections of the acoustic field. This boils down to an angular resolution of 0:176 , which if done manually, is a very tedious job. In Fig. 9 the sound field is shown along a cross-section in the Y-direction for the loudspeaker placed 0.5 cm out of axis of rotation (a ¼ 0:5 cm).
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Fig. 9. Acoustic field along a constant Y coordinate: a ¼ 0:5 cm: (a) slice directly above source and (b) slice far away from source.
Fig. 10. Acoustic field along a constant Y coordinate: a ¼ 5 cm: (a) slice directly above source and (b) slice far away from source.
In Fig. 9(a) a slice of the field is shown directly above the loudspeaker. This image depicts a vague ring shape, which is most probably due to reflections off the table and the varying SPL level between left and right. The amplitude is quite low, because there are hardly any modulations because the source is nearly in the rotational center. Higher up in the flow (Fig. 9(b)) a single peak can be distinguished, located almost exactly in the center as is to be expected because the loudspeaker is only 0.5 cm out of axis of rotation. In Fig. 10 the sound field is shown along a cross section in the Y-direction for the loudspeaker placed 5 cm out of axis of rotation (a ¼ 5 cm). In Fig. 10(a) a slice is shown directly above the acoustic source. Again this is quite hard to interpret, because of the same reasons as in the previous case. Fig. 10(b) shows a slice along the top of the acoustic field. One can distinguish a large peak out of axis and a ring where the level is lower. This distinct peak is shifted about 5 pixels out of the center where the rotation axis of
the microphone boom is. As was stated at the beginning of this section the measurement grid projected in the loudspeaker plane is 18 18 cm. Because the image size itself is 16 pixels square, this means that the loudspeaker is measured to be 5.62 cm out of axis which is in quite good agreement with the geometrically determined 5 cm.
5. Conclusions In this article acoustic fields were visualized using a laser Doppler vibrometer (LDV). A loudspeaker sound field at 10 kHz was measured in three dimensions by rotating the source. Measuring each scan point thereby gives a continuous representation of the rotational dimension. This was then run through a tomographic algorithm to reconstruct the three-dimensional field. A peak detector was attached to the LDV output channel to immediately demodulate the modulation due to the rotation.
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The loudspeaker was placed in different positions, i.e. 0.5 and 5 cm of axis of rotation. From the measurements it proved possible to locate the position of the acoustical source. The technique is able to measure the sound field quasi automatically without having to change the set-up for each angle, with a measurement time of approximately 7 h for a spatial resolution of 25 25 and a rotation velocity limited to 16 s/rev. Acknowledgments This research has been sponsored the Fund for Scientific Research—Flanders (FWO) Belgium. The authors also acknowledge the Flemish government (GOA-Optimech) and the research council of the Vrije Universiteit Brussel (OZR) for their funding.
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References [1] Ambrosini D, Rastogi PK. Optical methods in heat transfer and fluid flow. Opt Lasers Eng 2006;44(3–4):155–8. [2] Prenel J, Bailly Y. Recent evolutions in fluid mechanics: from standard tomographic visualization to 3D volumic velocimetry. Opt Lasers Eng 2006;44(3–4):321–34. [3] Castellini P, Martarelli M. Aeroacoustic characterisation of turbulent free jets using scanning laser Doppler vibrometry. Sixth international conference on vibration measurements by laser techniques, SPIE, 2004. [4] Mayrhofer N, Woisetsclager J. Frequency analysis of turbulent compressible flows by laser vibrometry. Exp in Fluids 2001;31: 153–63. [5] Zipser L, Franke H. Laser-scanning vibrometry for the investigation of sound generation and propagation. Sixth international conference on vibration measurements by laser techniques, SPIE, 2004. [6] Dove EL. Notes on Computerized Tomography, Bioimaging Fundamentals. [7] Lesurf J. The Envelope Detector, www.st-andrews.ac.uk.