parametric study of a laser-generated thermoacoustic signal

Parametric study of a laser-generated thermoacoustic signal Luis J. Gonzalez and Ilene J. Busch-Vishniac

•4œœlied Research Laboratory, The University of Texas, •4ustin, Texas 78713-8029

(Received 9 February 1988; accepted for publication 11 May 1988 )

A parametric study of the generation of a sound-pressure signal generated underwater by a moving thermoacoustic source has been conducted. Numerical results indicate that the source speed and the azimuthal angle between the source initial location and the receiver are the parameters that most affect the pressure signal. Nine signal properties were examined: six time- dependent properties and three pressure-dependent properties. Of these, the ratio of the peak to rms pressure is the most sensitive to source variations, and the duration time of the signal is least sensitive.

PACS numbers: 43.88.Ar, 43.35.Ud, 43.30.Yj, 42.60. Lh

INTRODUCTION

In the last 15 years, there has been a substantial amount of work reported on the generation of sound by a moving, laser-driven, thermoacoustic source. This work was re- viewed by Lyamshev and Sedov • in 1981 and more recently by Pierce and Hsieh. 2 Much of the work on moving thermoacoustic sources has concentrated on the efficiency and di- rectivity of the sound generated in this process. Although important, these measures obscure the fact that the sound signal generated by a moving source varies in form as the source-receiver geometry changes. In the research reported here, we study the acoustic signal generated by the moving laser in detail. Properties of the signal are identified and the manner in which these properties change with respect to source and receiver parameters is quantified. This information identifies those aspects of the sound signal that are most and least susceptible to change. If the thermoacoustic source is to be used for underwater communication in the future, the statistics complied here will be quite useful.

In the work described here, a computer program called MTS, written by Berthelot, 3 is used to numerically predict the received acoustic signal for the system shown in Fig. 1. Note that this system has a horizontal air-water interface at z = 0. The computer program is based on the time domain approach discussed by Berthelot and Busch-Vishniac. 4 In this approach, the fluid that is irradiated by the laser is divided into many segments, each of which corresponds to a precise excitation time and a precise distance to the receiver. The sound signal received is found by applying the appropriate delay and spreading loss to the signal generated at each fluid segment, and adding the pressure signals received at the same instant. Note that this analysis includes only losses due to spreading. Although spreading will generally be the domi- nant loss mechanism, we will present some results for long- range (up to 2 km) propagation of high-frequency sound in fresh water. The effect of absorption losses in these situations is not negligible, and will be discussed qualitatively.

In this work, various properties of the received acoustic signal, such as the signal duration, are examined as a function of the source parameters, such as velocity and source- receiver range and angle. This enables us to determine quan-

titatively which signal properties are most and least sensitive to variations.

The laser assumed to be generating the sound is a neody- mium-glass laser identical to that used by Berthelot and Busch-Vishniac. 4 This laser has a wavelength of 1.06 pm, and corresponding optical coefficient of absorption a of 13.7 Np/m in fresh water, where the speed of sound c is 1486 m/s. The laser pulse duration is 0.8 ms, and the laser beam radius is 0.005 m. A Gaussian intensity distribution across the laser

,.

beam is assumed. The laser intensity is modulated at fre- quencyf within an exponential envelope as shown in Fig. 2.

The parameters of the system that we vary may be classed in two categories: those associated with the source and those associated with the source-receiver geometry. The parameters of the source that are varied are the modulation frequency of the laser intensity and the velocity v or Mach number M -- v/c of the laser beam on the surface of the wa-

ter. The parameters associated with the source-receiver geometry that are varied are the initial distance between the source and the receiver ro, the initial horizontal angle •bo, and the depth of the receiver h. Table I shows the values of the parameters that were used in the study. All possible combinations of these values were used, resulting in a total of 675 cases. The values were carefully chosen to cover the whole range of physically realizable situations.

FIG. 1. System geometry for laser generation of sound.

1587 J. Acoust. Soc. Am. 84 (5), November 1988 0001-4966/88/111587-11500.80 ¸ 1988 Acoustical Society of America 1587

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FIG. 2. Modulated laser intensity.

The examined properties of the received acoustic signal may be placed into two categories: time-related properties and pressure-related properties. The time-related properties of the acoustic signal that we numerically investigated are as follows: the duration of the received signal Ta, with the beginning and end defined by the times at which the signal is 40 dB below the peak pressure level; the time at which the absolute peak pressure occurs Tpk, with zero time defined as the time at which the received signal begins; the maximum period in the signal Tma x found from zero crossings of the signal; the minimum period Tmin; the average of all periods of the signal, Tave; and the ratio of the time at which the peak pressure occurs to the duration time Tp•,/Ta. Because of the noise inherent in a real signal, it would be difficult to com- pute the time from the signal beginning to the first zero crossing and the time from the last zero crossing to the signal end. Therefore, these time intervals were not considered in Tmax, Tmin, and Tave unless the signal contained only two zero crossings, an event that only occurs when the Mach number as seen by the receiver RM is approximately equal to 1. The Mach number observed by the hydrophone is defined by RM = M sin 0o cos •bo, where 0o = arccos (h/ro), and Fig. 1 shows how 0o and •bo are defined. Note that R• only equals the Mach number of the laser beam when the source is moved in a straight line directly toward the hydrophone.

The pressure-related properties of the sound signal that we examined are the absolute peak pressure Pv•, the root- mean-square pressure of the acoustic signal Prms, and the pressure ratio Pv•,/Prms'

In order to obtain the pressure and time properties just described, MTS was modified and run on a Cyber 830 Con- trol Data Corporation computer system using time steps of 0.671/•s. The choice of size for the time step was determined by running simulations with progressively smaller time steps

TABLE I. Parameter values.

ro (m) 100,750,2000 h (m) 5,15,40 •o (deg) 0,45,90,135,180 M 0,0.5,1.0,1.5,2.0 f(kHz) 5,30,60

until halving the time interval produced negligible changes. As one would expect, the simulations most sensitive to the size of the time step are those involving the source moving with R• near Mach 1. In addition, one should be cautioned to read the results corresponding to source speeds with R• near Mach 1 with some skepticism since experimental results obtained by Berthelot and Busch-Vishniac 4 at this source speed are not in good agreement with predicted results.

I. RESULTS•TIME-RELATED PROPERTIES

In this section of the article, we present the numerically obtained results for the variation of the time-related signal properties as the source and geometric properties of the laser sound system are varied. Each signal parameter is discussed independently in terms of its sensitivity to changes in the system characteristics.

A. Duration time, Ta

The numerical results obtained for Ta are shown in Fig. 3. Figure 3 is typical of the figures that will be shown in this article. A total of seven graphs are presented, each display- ing Ta vs •bo. In each graph there are five curves corresponding to five different source velocities.

Figure 3 (a)-(g) shows that Ta is quite sensitive to changes in the initial horizontal angle •bo, and the Mach number M, of the laser beam on the surface of the .water. Both of these variables affect the apparent Mach number of the source as observed by the hydrophone, so the sensitivity of Ta to them comes as no surprise. However, note that Ta is not sensitive to changes in the angle •bo when M = 0 since the stationary source radiates sound omnidirectionally. Gener- ally, Ta becomes more sensitive to changes in •bo as M increases from 0 to 2 since the source tends to become more

directive as the source speed increases. We also note that Ta is least sensitive to changes in M

when •3o = 90 ø, i.e., when the laser beam moves in a path normal to the line connecting the hydrophone and the start- ing point of the laser. The apparent Mach number Ru, under these conditions, begins at zero and slowly increases as •b changes. From the data for the cases with •bo = 90 ø, we see that Ta does increase slightly as M increases from 0 to 2, since the range of angles of •b increases, but the difference between Ta for M = 0 and M = 2 is only on the order of 2%. Notice that Ta generally becomes more sensitive to changes in M as •bo decreases from 90 ø to 0 ø, and increases from 90 ø to 180 ø. Restated, Ta is most sensitive to changes in Mwhen the laser is moving directly towards the receiver, or directly away from the receiver.

Viewing Fig. 3, we conclude that the duration of the signal increases monotonically as the laser moves away from the receiver, that is, when •b is in the range of 90 ø- 180 ø, and that the maximum duration of the received signal occurs when M = 2 and. •bo = 180 ø. This result can be explained by the fact that if the source is moving away from the hydrophone, then the distance that the last wavelet must travel from the source to the receive? increases as the velocity of the

1588 J. Acoust. Soc. Am., Vol. 84, No. 5, November 1988 L. J. Gonzalez and I. J. Busch-Vishniac: Laser-thermoac. sig. ,

1588


2.5

ro= 750 m 2.0 h=5m

/=6o•k

0.5 • O.Oo • •o ' •;• ' •o

•o- deg (d)

• M=O

-o- M-- 0.5

-4- M=I.O

-o- M=l.5

-•- M=2.0

2'•l ro=1OOm 'Slro='OOm 2.0•' h=5m f•,t•l 2.0• h=5m •• 2.0[ h=5m 1.5 1.5

•1.0 , 1.01 • I 1.0}

i I 0.0 0 45 • ' 1•5 ' 180 0.06 45 • ' 1•5 ' 1• 0.06 45 • 135

•o-• •o-• •o-• (e) (0

FIG. 3. Duration of the received signal.

source increases, and is greatest when the laser is moving directly away from the receiver.

Finally, an explanation can be given of the manner in which Td varies as the laser moves towards the receiver, that is, when •bo is in the range of 00-90 ø. In this region, the received signal becomes more compressed in time as R M increases from 0 to 1, and will then become less compressed as R M increases further. The shortest duration of the signal should occur near Ru = 1, since, for this case, the whole signal arrives at the receiver more or less at the same time. The duration of the signal increases as R u becomes greater than one, because the distance that the last wavelet must travel to reach the receiver decreases as the velocity of the source increases. Therefore, the last wavelet emitted by the source arrives at the receiver increasingly earlier than the first wavelet emitted by the source as the velocity of the source increases. The result is that the signal duration increases with the source velocity. Proof of this is shown in Fig. 4, which displays Ta vs Ru for one set of system parmeters.

Figure 3 (a)-(c) represents identical cases except for the depth of the receiver. From these three graphs, ones sees that Ta is very insensitive to changes in the depth h of the receiver. The data for these cases reveal that Ta increases slightly as h increases. The increase between the cases for which h -- 5 m and h = 40 m is on the order of 0.3%.

The cases used to generate Fig. 3 (e)-(g) are identical except for the modulation frequency of the laserf From this figure we conclude that Ta is very insensitive to changes in the modulation frequency. The data for these cases show

that the duration of the received signal increases slightly as the modulation frequency increases. The increase between the cases for which f--- 5 kHz and f= 60 kHz is on the order of 0.6%. This slight increase in Ta as fincreases can be explained as follows: Berthelot and Busch-Vishniac 4 have shown that the pressure amplitude of the received signal increases as f increases (as will also be shown later by the pressure-related properties). Therefore, the beginning and end of the received signal are detected earlier and later, respectively, by the receiver, causing an increase in Td.

Figure 3 (a), (d), and (e) was generated from identical

0.80

0.60

0.40

0.20

0.00 0.00

ro= 100 m, h = 5 m, f = 5 kHz, •0 = 45ø

ß I ß I ß I ß I ß

0.28 0.56 0.85 1.13 1.41

FIG. 4. Pulse duration versus Mach number for a specific case.

1589 J. Acoust. Soc. Am., Vol. 84, No. 5, November 1988 L.J. Gonzalez and I. J. Busch-Vishniac: Laser-thermoac. sig. 1589


r 0 = 2000 m r 0 = 2000 m 0.81- h=5m I 0.8 h=15m

0.6 0.6

0.4• 0.4 0.2 0.2

0.0• 45 90 135 180 0.0 45 90 135 180 •o-d• •o-d•

(a)

1.0 '

0.8 h=40m /

0.4

o., 0.0 0 45 90 135

•0 - deg (c)

180

1.0

0.8

0.6

0.4 0.2

0.0

r0= 750 m h=5m

f=60kHz

0 45 9'0 1•5 150 •0 - deg

(d)

-- M=0

--o- M=0.5

• M=I.0

-o- M=l.5

• M=2.0

1.0[ tO= lOOm 0.8 t h=Sm

•f=60 kHz

02

0'0 • . . . ' 0 45 90 135 180

½0 - deg

.0

r0= 100 m .8 h=5m

f= 30kHz .6

.4

.2

.0 0 45 90 135 •0 - deg

(o

180

1.0

0.8

0.6

0.4

0.2

0.0

ro= 100 m h=5m

0 45 90 135 180

•0- deg (•)

FIG. 5. Time of peak pressure.

situations except for the source-to-receiver initial range. They show that Ta is also very insensitive to changes in the initial distance between the source and receiver to. The re- suits for these cases show that the duration of the received

signal decreases slightly as ro increases. The difference between the cases for which ro = 100 m and ro = 2000 m is generally on the order of 3 %. This result can be explained by the fact that spherical spreading will decrease the pressure amplitude of the received signal, and that spherical spreading increases as ro increases. Therefore, the beginning and end of the received signal, as defined by a -- 40-dB thresh- old, are detected later and earlier, respectively, by the receiver, thus decreasing Ta. One should note that according to Fisher and Simmons, s the attenuation due to absorption of sound in fresh water is roughly 8 X 103 dB/m at 60 kHz, and varies as the inverse of the frequency squared. For the long- range source-receiver distances, absorption thus will cause a significant decrease in amplitude and a corresponding decrease in Ta in excess of the 3 % changes shown in Fig. 3.

From these results, we conclude that the duration of the sound signal generated by the thermoacoustic source is insensitive to changes in to, f, and h, but is dependent on the apparent speed of the source as seen by the receiver. In terms of geometrical parameters, this means that the duration of the signal is highly dependent on •bo, M, and 0o.

B. Time of peak pressure, Tpk

Figure 5 shows the results for Tpk , the time at which the peak pressure is observed, where the zero of the time axis is

defined as the time of arrival of the first wavelet. Like the

time property Ta, Tpk is quite sensitive to changes in •bo and M. For a stationary source, the graphs in Fig. 5 show that Tpk, like Ta, is not a function of •bo since the same signal would be observed at all angles. However, unlike Ta, Tpk does not increase monotonically as the laser .moves away from the receiver, although there is a pattern in the way Tpk varies with M when •bo = 0. Figure 6, which displays Tpk vs M for a specific case, more clearly reveals this pattern. It is important to note that, for this specific case, RM is approximately equal to M, so the apparent and actual speeds of the source are about the same. Figure 6 shows that Tpk decreases as M goes from 0 to 1, and increases as M goes from 1 to 2.

1.0

r0= 2000 m, h = 5 m, f = 60kHz, ½0=0 ø 0.8

• 0.6 !

• 0.4

0.2

0.0 0.0 1.0 2.0

M

FIG. 6. Time of peak pressure versus Mach number for a specific case.



This is a result of the signal being compressed in time (Doppler shifted) when M = 1 is approached from below or above. This time straining would lead one to expect Fig. 6 to be roughly symmetric about M = 1. However, a second effect resulting from inversion of the signal when M > 1 skews the curve. In our simulated signals from a stationary source, the peak pressure occurs relatively early. If the source is moved rapidly, so that the entire source line appears to the receiver to be moving with M> 1, then the signal is inverted. This has the effect of delaying the time after signal onset at which the peak pressure is observed. From Fig. 6, we conclude that the time inversion which occurs above Mach 1 is

more important than the compression or expansion of time intervals.

The cases used to generate Fig. 5 (a)-(c) are identical except for the depth of the receiver. On comparing these figures, it can be concluded that Tvk is sensitive to changes in h, and more so when the velocity of the laser on the surface of the water v is greater than the speed of sound in water c. However, note that Tvk is not sensitive to changes in h when 3//--0.

Figure 5 (a), (d), and (e) was generated from identical situations except for the source-to-receiver range. Except when M = 0, Tvk is sensitive to changes in ro, and more so when v > c. Note that varying either ro or h has the effect of changing the apparent source speed. Hence, it is not surpris- ing that the pattern of signal variations is similar in the two cases. Note also that since the entire signal will suffer absorp-

tion losses, Tvk is unlikely to be changed significantly by including absorption.

Figure 5(e)-(g) represents identical cases except for the modulation frequency of the laser. They show that Tvk is sensitive to changes in f, even when M = 0. The fact that the frequency of modulation affects Tv even for a stationary source is primhrily due to the fact the modulation may serve to shift the observed peak of the intensity envelope. At very high modulation frequencies, one would expect that the laser intensity envelope peak would determine the sound peak time regardless of the modulation.

From these results, we conclude that the time of the peak pressure is sensitive to changes in •o, M, h, f, and ro.

C. Time inversion property, T.•,/Td As described above, motion of the laser source has two

effects that operate on the time at which the pressure signal peaks: time dilation, which affects the signal duration, and time inversion (if RM > 1 ), which affects the location of the peak relative to the signal beginning. For our laser system, the ratio Tvk/Ta can be used as a measure of the degree of time inversion of the received acoustic signal. Since time inversion of the signal can only occur if the source is moving, no time inversion takes place if M = 0. Therefore, the ratio of Tvk/Ta for M = 0 can be used as a reference for the level of time inversion of the received signal. Figure 7 shows the results for Tvk/Ta.

1.0

0.8

0.6

[•0.4 0.2•

0.0 0 ;5

r0 = 2000 m h=5m

' ' 9;) ' ,•5 •0 - deg

1.0

• ro = 2000 m 0.8 h=15m

f=60kHz 0.6

0.4

0.:2 --- - •

•o-•g (b)

180

1.0 ] _ r o = 2000 m

0.8• h=40m I 0.6

0.4

0.2

0.0 0 45 90 135 180 •0 - deg

(c)

1.0

0.8

0.2 •

0.0

• r 0 = 750 m hz5m

! i ! - -

•b 0 - deg (a)

-- M=0

-o- M=0.5

-•- M=I.0

• M=l.5

-•- M=2.0

FIG. 7. Time inversion property.

1.0

0.$1

0.6 •

[•0.4 0.2 (

0.0 0 415

r0=100 m h=5m

0 ' 1;5 ' 180 •o-,•g

(e)

1.0

r0=100 m

0.8 • h=5 m

0.4

0.:2

•b 0 - deg (o

1;5 ' 180

1.0 • ro= 100 m 0.8 •.•,•q• n=Sm

0.4 0.2

o.o o - - •0 - deg

(g)

180



By comparing Fig. 7(a)-(g) one sees that Tpk/T,• is generally not sensitive to changes in •o when v < c, but is quite sensitive to changes in •o when v•>c and the laser is moving towards the receiver. Also, note that Tpk/Td is generally not sensitive to changes in M when the laser is moving away from the receiver, but is sensitive to changes in M when the laser is moving towards the receiver, especially as M goes from 0.5 to 1.5. In other words, the received signal is heavily time inverted when the laser velocity is greater than the sound speed and is moving towards the receiver. Further- more, the level of time inversion is highly dependent on 4o and M since these greatly affect R•n.

Figure 7 (a)-(c) was generated from identical cases except for the depth of the receiver. They show that Tpk/Td is fairly insensitive to changes in h as these changes only affect R•n in a minor way.

The cases used to generate Fig. 7 ( e)-( g ) are exactly the same except for the modulation frequency of the laser. These figures show that Tpk/T,• is fairly insensitive to changes inf. As in the case of Tpk, any variation in Tpk/Ta would be expected to be a low-frequency effect associated with delays in the peak of the laser intensity due to modulation.

Figure 7 (a), (d), and (e) was generated from identical situations except for the source-to-receiver range. They show that Tpk/T,• is also fairly insensitive to changes in ro. Were one to include absorption losses, the values of Tpk/Ta would vary even more than shown in Fig. 7.

From these results, we conclude that the time property

Tpk/Td is primarily sensitive to changes in 4o and M, so long as M> 1. Therefore, the level of time inversion of the signal is very sensitive to changes in •o and M.

D. Minimum period, rmi n

Figure 8 shows the results for Train, the minimum period in the received signal. Figure 8 (a)-(g) shows that Tmin is quite sensitive to changes in 4o and M. However, notice that Tmi , is not sensitive to changes in •o when the laser is stationary. Also, notice that when •o- 90ø, Train is the same regardless of the velocity of the laser. The latter result stems from the fact that when •o -- 90ø, R•n is nearly zero for the entire laser path. Therefore, the signal almost appears to be generated by a gtationary source. Nevertheless, one would expect Train to increase slightly as M increases from 0 to 2 at •o---- 90ø, since the signal will be slightly stretched in time when the laser is moving away from the receiver; the data in which results were printed up to the fourth significant digit do not show this. It is most likely that the difference was simply too small to detect.

Figure 8(a)-(g) shows that Train is particularly sensitive to changes in the velocity of the laser when it is moving directly towards and away from the receiver, that is, when •o equals 0 ø and 180 ø, respectively. These figures also show that Tmin increases monotonically (with respect to M) when the laser is moving away from the receiver. The largest value of Tmi n in all cases occurs when •bo = 180 ø and M = 2. As dis-

0.40 r0= 100 m 0.40 [ r0= 100 m ] 0.40• r0=100 m ] 0.32 h = 5 m 0.32 t h = 15 m I 0.32 •\ h = 40 m I /=60k•z • V =6ø k•z I

' 0 45 90 13.5 180 ' 0 45 90 135 180 ' 0 45 90 135 180 *o-des *o-des *o-des

(a) Co) (½)

0.40 f r0 = 750 m 0.32 h=5m f=60kHz 0.24

0.16

0.08

0.00 0 45 90 135 180

'0 - deg

• M=0

-o- M=0.5

--e- M=I.0

-o- M=l.5

• M=2.0

FIG. 8. Minimum period.

0.40 0.45[ ro=2000rn •! 3.0[ r o = 2000 m r o = 2000 rn •,• 0.32 h = .5 rn 0.36 t h = 5 rn •,,•

0.24 f=60kHz 0'27 1 f=30kHz • /=SkHz 1.8

0.00 • 0.00 ' 1•5 ' . _ , - i , 0 as •o •, •s0 0 as •o •s0 0 as •o •a• •s0

•0-•g •0-a•g •0-a•g (e) (f) (g)



cussed earlier, this case produces the greatest stretching of the received signal, and therefore the largest Tmi,.

Figure 8 (a)-(c ) was generated from identical cases except for the depth of the receiver. They show that Tmi n is sensitive to changes in h, particularly when the source is moving towards the receiver, and M equals 1 or 1.5.

The cases used to generate Fig. 8 (e)-(f) are identical except for the modulation frequency of the laser. As would be expected, these figures show that Tmi n decreases as the frequency increases. Also, the data for these cases indicate that Tmi n acts almost as if it were inversely proportional to f, regardless of the Mach number.

Figure 8 (a), (d), and (e) represents identical situations except for the source-to-receiver range. These figures show that Tmin is not particularly sensitive to changes in ro. This result would not be affected by absorption losses.

From these results, we conclude that the time property Tmi n is sensitive to changes in h,f, M, and 4o. In addition, the manner in which Tmi n varies with respect to f, M, and 4o is quite evident.

E. Maximum period, Tm=,

Figure 9 shows the results for Tmax, the maximum period in the received signal. Figure 9 ( a)-(g) shows that Tma x is very sensitive to changes in •o and M. As for the previous properties, Tma x is not sensitive to changes in •o when the

laser is stationary. All the graphs in Fig. 9 indicate that Tma x is least sensitive to changes in M when 4o -- 90ø. Again, for this case, the Mach number as seen by the receiver is nearly equal to zero for the duration of the pulse; therefore, the sound appears to be generated by an almost stationary source. However, the data for these cases do show that Tma x generally increases slightly as the velocity of the laser increases. Like Tmin,Tma x increases monotonically (with respect to M) when the laser is moving away from the receiver. The largest value of Tma x in all cases occurs when 4o -- 180 ø and M--2, since this combination induces the greatest stretching of the received signal.

Figure 9 (a)-(c) represents identical cases except for the depth of the receiver. They show that Tma x is sensitive to changes in h, and especially when v•c.

The cases used to generate Fig. 9(e)-(f) are identical except for the modulation frequency of the laser. Like Tmin, Tma x decreases as the frequency increases, and also acts almost as if it were inversely proportional to f

Figure 9 (a), (d), and (e) was generated by identical situations except for the source-to-receiver range. These figures show that Tma x is not particularly sensitive to changes in ro; nor would the addition of absorption affect this result.

From these results we conclude that the time property Tma x is sensitive to changes in the parameters h,f, M, and 4o. Also, like Tmin, the manner in which Tma x varies with respect to f, M, and 4o is very evident.

0.10

0.10[ to= 100 m to= 100 m 0.10 4k to= 100 m 0.08• h=Sm 0.08 h=15m 0.08t• • h=40m 0.06 0.06 0.06

o.o4 L o.o• o.o• 0.02 _•.•..•_ 0.02 . _ 0.02 _

o.oo 45 90 1;5 180 0 45 90 135 180 0 45 $0- deg $0- deg $0- deg

(a) Co) (c)

0.10

0.08

0. O6

o.o4

0.02

ro= 750 m h=5m

f=60kHz

0.00 • '•••'•'• ' ' 0 45 90 1•5 180 $0-deg

(d)

• M=O

-o- M=0.5

• M=I.O

--o-- M=l.5

--1- M=2.0

FIG. 9. Maximum period.

0'10[•=2• m 0'10[•=2• m 1ø'4ø[•=2•m 0.08 t h = 5 m 0.08 • h = 5 m I 0.32 [ h = 5 m

o.o= o.o= I O'00•lllm•'•'•rll' ''1•5 45 • 1•5 000•' • • ' 1•5 ' 1•0 0 45 • 180 0'000 .... 180 ' -

•) (O (g)



F. Average period, T=vo

Figure 10 shows the results for rave, the average of all periods in the received signal. Like the two previous time properties, rave is very sensitive to changes in •o and M. Also, rave is least sensitive to changes in M when •o - 90ø, but the data for these cases indicate that rave increases slightly as M increases. Like rmi n and Truax,rave increases monotonically (with respect to M) when the laser is moving away from the receiver. In all cases, the largest value of rave occcurs when •o = 180 ø and M = 2, since this combination of parameters induces the greatest elongation of the received signal.

Figure 10(a)-(c) was generated from identical cases except for the depth of the receiver. These figures show that rave is sensitive to h, particularly when M equals 1 or 1.5, and the source is moving towards the receiver.

The cases used to generate Fig. 10(e)-(g) are identical except for the modulation frequency of the laser. Like rmi n and Tmax, rave decreases as the modulation frequency increases, and also behaves almost as if it were inversely proportional to f.

Figure 10(a), (d), and (e) represents identical situations except for the source-to-receiver range. These figures show that rave is not very sensitive to changes in ro, and again absorption would not alter this result.

From these results, we conclude that Tav e is sensitive to changes in the parameters h,f, M, and •o, and that its behav-

ior, like Tmi n and Tmax, with respect to changes in f, M, and •bo is very evident.

From the results for Tmin, Tmax, and Tav e one can determine the frequency spreading of the signal that results from motion of the laser source. The general pattern observed is that the frequency spread depends primarily on RM and, hence, on M, h, •bo, and ro. Since the laser signal generated is essentially a shaped sinusoidal pulse, the received signals corresponding to Mach 0 (i.e, •bo = 0) tend to have the smallest values for A(t)/(Dav e . The only exception to this rule occurs for an apparent source speed very close to Mach 1, in which case the frequency spread can be shortened. For all other source speeds, there is an increase in the frequency spread that accompanies the motion, often by as much as a factor of 4.

II. RESULTS•PRESSURE-RELATED PROPERTIES

A. Pressure peak, Ppk, and root-mean-square pressure, Prms

Figure 11 shows the numerical results for Ppk, the abso: lute peak pressure of the received signal. Figure 11 (a)-(g) shows that Ppk is very sensitive to changes in •o and M. However, notice that, as one would expect, Ppk is not sensitive to changes in •o when the laser is stationary. Also, Ppk is least sensitive to changes in M when •o = 90ø, since at this point the sound appears to be generated by an almost station-

0.75 r0=100 m 0.75 r0=100 m 0.75•- r0=100m ] ' 0.60 h = 5 m 0.60 h = 15 m 0.60 o.4

0.00 • 000 • 000 • 0 45 90 135 180 0 45 90 135 180 0 45 90 135 180

(a) (b) (c)

0.75

ro= 750 m

•_ 0.60 h=Sm • /=60kHz

•:• 0.45

0.30

0.15

0. ffi o 45 90 135 180

, ½o-deg (d)

• M=O

-o- M=0.5

ß 0- M=I.O

-o- M=l.5

--m- M=2.0

0.75 ro=2000 m 0.75 [ r0=2000 m ] 3.0[ r0=2000 m 0.60 h=Sm 0.60

0.15 0.15 0.6

0.00 0.00 0 0 ' ' ' 0 45 90 135 180 0 45 90 135 180 0 45 90 135 180

•o-,• •o-,• •o-d• (½) (0

FIG. 10. Average period.



0.70 [ ro= 100 m 0.70 0.56 • h = 40 m 0.56

• f- 5kUz 0.42 • 0.42

o.•n .• o.•n 0.00 • 0.•

0 45 • 135 180

(a)

r0= 100 m h=15m

0 45 90 135 180

½o- deg

1.20

0.96

0.72

0.48

0.24

0.00 0 45

•=100m h=5m

f 5kHz

90 135 180

•-&g g)

1.60

1.28

I

•:• 0.96 X 0.64

I•ø' 0.32 0.00

r0= 750 m h=40m

f =5kHz

0 45 90 135

½o- deg (d)

180

• M=0

-o- M=0.5

--e- M=I.0

• M=l.5

-•- M=2.0

0.6[ rø=2000m ] n 'ø=•øøøml ø'6[--7•••=2000m] o.5 t • h=40m I0.• /X h=40m ] 0.5•' • h=40m I

0.4 0.4 0.4

0.2 0.2 0.2 o.o - : - - o.o oo

•o-d• •o-d• •o-• (e) (• (g)

FIG. 11. Pressure peak.

ary source. Figure 11 (a)-(g) also shows that Ppk is less sensitive to changes in M when the laser is moving away from the receiver, and that generally Ppk decreases under these conditions as M increases. At least in part, the decreased amplitude of the peak for circumstances in which the source is moving away from the hydrophone is due to increased spherical spreading of the highest amplitude sound wavelet.

Figure 11 (a)-(c) represents identical cases except for the depth of the receiver. From these three graphs, one sees that Ppk generally increases as h increases when M equals 0.5 or 2, and decreases with increasing h when M equals 1 or 1.5. This behavior is consistent with the statement that the pressure peak amplitude is highest for an apparently transonic laser source, i.e., for RM near 1.

The cases used to generate Fig. 11 (e)-(g) are identical except for the modulation frequency of the laser. These figures show that Ppk generally increases as f increases. This result can be explained by the fact that the magnitude of the time derivative of the laser intensity (which drives the pressure) increases as fincreases.

Figure 11 (a), ( d ), and ( e ) was generated from identical situations except for the source-to-receiver range. These figures show that Ppk generally decreases as r o increases. This decrease is due to spherical spreading. If absorption losses were included, the decreases with increasing range would be' more pronounced.

From these results, we conclude that the absolute peak pressure is sensitive to changes in all of the parameters, and

1595 J. Acoust. Soc. Am., Vol. 84, No. 5, November 1988

is generally more sensitive to these changes than the time- related signal properties.

The results for Prms are shown in Fig. 12. The patterns of behavior, as parameters ate varied, are identical for Prms and Ppk' From these results, we conclude that Prms is sensitive to changes in all the parameters.

B. Pressure ratio, Pp•/Prms

The results for Ppk/Prms are shown in Fig. 13. Figure 13 ( a)-(g) shows that Ppk/Prms is quite sensitive to changes in •bo and M. Like all of the previous properties, Ppk/Prms is not sensitive to changes in the angle •bo when the laser is stationary. Also, notice that Pp•/Prms is sensitive to changes in M even when •bo = 90 ø. We also note that the ratio of the pressure peak to the rms pressure is not necessarily the highest when RM = 1. This is because the time dilation that produces the higher peak amplitude also causes a corresponding increase in the rms pressure.

Figure 13 (a)-(c) represents identical cases except for the depth of the receiver. From these three graphs, one sees that Pp•/Prms is very sensitive to changes in h, but that its sensitivity to changes in h decreases as h increases.

The cases used to generate Fig. 13(e)-(g) are identical except for the modulation frequency of the laser. These figures show that Pp•/Prms is quite sensitive to changes in f In particular, Pp•/Prms seems to be more sensitive to changes in fwhen the laser is moving towards the receiver.

L. J. Gonzalez and I. J. Busch-Vishniac: Laser-thermoac. sig. 1595


r0= 100 m h=lSm

f=5 kHz

90 135 180

•0 - deg

r0= 100 m h=5m

f--SkHz

45 90 135

•0 - deg (c)

180

• M=0

-o- M=0.5

+ M=I.0

-•- M=l.5

+ M=2.0

2.5

2.0

1.5

1.0

0.5

0.0 _ ! _ _

o 45 90

•0 -dcg (•)

r0 = 2000 m h=40m

f--5 kHz

135

2.0• •r• h=40m I •.0[ \ h=40m /

0.5 0.5

- 00 00 18o o 45 90 135 180 0 45 90 135 18o

•o-d•g •o-d•g (f) (g)

FIG. 12. Root-mean-square pressure.

4.20• r0=100m I 4.20 t ro=lOOm [ 4.20 r0= 100 m 3.76 h = 40 m I 3.76 • •x h = 15 m I 3.76 h = 5 m

,,.,,[1\ \

' 0 & • 1'35 180' 0 4• * 13, 180

(•) ½) (c)

4.20

r 0 = 750 m 3.76 h = 40 m

f=Sk•z

"000•' 4•' •) ' 1;5 ' 150 •0- deg

(d)

• M=0

-o- M=0.5

• M=I.0

-•- M=I.5

• M=2.0

FIG. 13. Pressure ratio.

3.80[ ro=2000m /1• 3.80[ ro=2000m • 3.80[ ro=2000m 3.38 t h=40m • /I 3.38• h=40m /I 3.38• h=40m 2.96

1.70• ;• • ' 1•5' 1• 1'700 4•0 1'700 4• • ' ' 5' 180

(e) (0 (g)



Figure 13 (a), (d), and (e) was generated from identical situations except for the source-to-receiver range. They show that Ppk/Prms is very sensitive to changes in ro. Note that unless the acoustic signal contains a very broad band of frequencies, this result for Ppk/Prms should not change significantly if absorption losses were included.

From these results we conclude that the ratio Ppk/Prms is sensitive to changes in all the parameters. It is, in fact, the most sensitive measure studied.

III. SUMMARY AND CONCLUSIONS

The acoustic signal generated by a moving laser has been studied in detail. Properties of the signal have been identified and the manner in which these properties change with respect to source and receiver parameters has been quantified. This information identifies the aspect• of the sound signal that are least and most susceptible to change.

A computer program written by Berthelot, 3 with modi- fications suitable for this project, was used to numerically predict the received acoustic signal. This computer program is based on the time domain approach discussed by Berthelot and Busch-Vishniac. 4

The parameters of the source which were varied are the modulation frequency of the laser intensity and the velocity, or Mach number, of the laser beam on the surface of the water. The source-receiver geometrical parameters that were varied are the initial distance between the source and

receiver ro, the initial horizontal angle •bo, and the depth of the receiver h. The values of the parameters were carefully chosen to cover the whole range of physically realizable situations. All possible combinations of the parameters were used, resulting in a total of 675 cases.

The properties of the received acoustic signal that were examined may be placed in two categories: time-related and pressure-related properties. The time-related properties of the acoustic signal that were numerically investigated are the duration of the received signal T a, the time at which the absolute peak pressure occurs Tpk, the maximum period in the signal Tmax, the minimum period Tmin, the average of all periods Tave, and the time inversion property Tpk/Ta. The pressure-related properties studied were the absolute peak

pressure Ppk, the root-mean-square pressure Prms, and the pressure ratio Ppk/Prms'

Of the signal properties examined, it was found that Ta is the least sensitive to the source characteristics, being dependent almost solely on the apparent Mach number of the source. The signal property most sensitive to variations in the source system properties was found to be Ppk/Prms, which responds to changes in any of the system parameters. In general, the pressure-related properties were found to be more senstive to system changes than the time-related properties.

The results show that all of the signal properties are very sensitive to changes in the initial horizontal angle •bo, and the Mach number M of the laser beam on the surface of the

water. However, the signal properties are generally not sensitive to changes in the angle •bo when the source is stationary arid are least sensitive to changes in M when •bo = 90 ø. In these cases, the apparent speed of the source is about zero. In addition, the modulation frequency is a critical parameter for all of the pressure related properties, and all of the time- related properties which are determined from zero crossings of the signal.

ACKNOWLEDGMENTS

This work was supported by the Office of Naval Re- search under Contract N00014-85-K-0819, and Applied Re- search Laboratories, The University of Texas at Austin.

IL. M. Lyamshev and L. V. Sedov, "Optical generation of sound in a liquid: thermal mechanism (review)," Sov. Phys. Acoust. 27 ( 1 ), 4-18 ( 1981 ).

2A. D. Pierce and H. Hsieh, "Radiation of sound induced by laser beams incident on water surfaces," J. Acoust. Soc. Am. Suppl. 177, S 103 (1985).

3y. H. Berthelot, "Generation of underwater sound by a moving high-pow- er laser source," Applied Research Laboratories Report No. 85-21, ARL- TR-85-21, Applied Research Laboratories, The University of Texas at Austin, 1985.

4y. H. Berthelot and I. J. Busch-Vishniac, "Thermoacoustic radiation of sound by a moving laser source," J. Acoust. Soc. Am. 81, 317-327 (1987).

-SF. H. Fisher and V. P. Simmons, "Sound absorption in sea water," J. Acoust. Soc. Am. 62, 558-564 (1977).



parametric study of a laser-generated thermoacoustic signal

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