A long-range and variable focus phase ... - Semantic Scholar

A long-range and variable focus phase-conjugation experiment in shallow water W. S. Hodgkiss, H. C. Song, and W. A. Kuperman Marine Physical Laboratory, Scripps Institution of Oceanography, University of California, San Diego, La Jolla, California 92093-0701

T. Akal and C. Ferla SACLANT Undersea Research Center, La Spezia, Italy

D. R. Jackson Applied Physics Laboratory, University of Washington, Seattle, Washington 98105

~Received 10 April 1998; accepted for publication 17 November 1998! A second phase-conjugation experiment was conducted in the Mediterranean Sea in May 1997 extending the results of the earlier time-reversal mirror experiment @Kuperman et al., J. Acoust. Soc. Am. 103, 25–40 ~1998!#. New results reported here include ~1! extending the range of focus from the earlier result of 6 km out to 30 km, ~2! verifying a new technique to refocus at ranges other than that of the probe source @Song et al., J. Acoust. Soc. Am. 103, 3234–3240 ~1998!#, and ~3! demonstrating that probe-source pulses up to 1 week old can be refocused successfully. © 1999 Acoustical Society of America. @S0001-4966~99!02603-X# PACS numbers: 43.30.Vh, 43.60.Gk, 43.30.Bp, 43.30.Hw @DLB#

INTRODUCTION

A recent experiment1 first demonstrated an acoustic time-reversal mirror ~TRM! in the ocean. A TRM2,3 also referred to as the process of phase conjugation in the frequency domain,4–8 focuses sound from a source–receive array ~SRA! back to the probe source ~PS! which ensonified the SRA. The SRA receives the probe-source field, time reverses it ~phase conjugation in the frequency domain!, and then uses the time-reversed data as the excitation for an array of sources which are collocated with the receiving hydrophones. If the ocean environment does not change significantly during the two-way travel time, the phase-conjugate field will refocus, regardless of the complexity of the medium, with the caveat that excessive loss in the system degrades the process. The focus is both spatial and temporal, recombining the multipaths from the first part of the transmission.9 Since this process offers an approach to com-

pensate for multipath interference and other distortion through a complex medium, it may be applicable to various adaptive sonar and communication concepts. This paper describes a second phase-conjugation experiment conducted in May 1997. The new results reported in this paper include: ~1! extending the range of focus from the earlier result of 6 km out to 30 km, ~2! validating a new technique to refocus at ranges other than that of the probe source, and ~3! demonstrating that probe-source pulses 1 day, 2 days, and as much as 1 week old can be successfully refocused. I. EXPERIMENTAL GEOMETRY

The second TRM experiment was performed off the west coast of Italy in May 1997 at the same location as the previous experiment.1 Figure 1 is a schematic of the experiment, and indicates

FIG. 1. Experimental setup for the May 1997 phaseconjugation experiment.

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FIG. 2. Sound-speed profiles derived from CTDs for the period 11–24 May 1997.

the types of environmental measurements that were made. The TRM was implemented by a 77-m source–receive array ~SRA!, in 123-m-deep water, which was hardwired to the Isola di Formica di Grosseto. The SRA consisted of 23 hydrophones with 23 collocated slotted cylinder sources with a nominal resonance frequency of 445 Hz. The sources were operated at a nominal source level of 160 dB. The received signals were digitized, time reversed, and after being converted back to analog form, retransmitted. A flextensional probe source ~PS! was deployed from the NATO research vessel ALLIANCE. The probe source, together with a receiving hydrophone, also was used as a transponder in some parts of the experiment. The ALLIANCE also deployed a 48element vertical receive array ~VRA! spanning 90 m which, for most of the experiment, was located 14.8 km from the SRA. The VRA radio telemetered all individual element data back to the ALLIANCE. For the runs in which we simultaneously varied the range of the PS and the VRA, the VRA was suspended from the ALLIANCE to ensure its being very close to the probe source ~within 60 m!. Additional hardware details can be found in Appendix B of Ref. 1. Figure 2 shows a collection of sound-speed profiles obtained from a conductivity–temperature–depth ~CTD! probe, which provides an indication of the sound-speed variability over the duration of the experiment. Note the increase in sound speed of the surface layer due to surface warming. The range-dependent bathymetry obtained from an echo sounder and the bottom sound-speed structure determined from earlier experiments1,10 are shown in Fig. 3, along with the mean sound-speed profile over the period 12–14 May 1997. Note that the sound speed in the sediment layer ~the thickness of which varies with range from the SRA! is smaller than the sound speed in the water column. II. LONG-RANGE SHALLOW-WATER PHASE CONJUGATION

The previous experiment1 contained TRM results at only 6.3 km. Here, we present results out to 30 km. For these runs, the VRA and the PS were both suspended from the ALLIANCE. Just from the size of the ship, the difference between their ranges to the SRA was within 60 m. Figure 4 1598

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FIG. 3. The range-dependent bathymetry obtained from an echo sounder and the bottom sound-speed structure determined from earlier experiments are shown along with a sound-speed profile averaged over the period 12–14 May 1997. The range is relative to the SRA. The sound speed in the sediment layer is smaller than in the water column, such that the top and bottom sound speeds are assumed to be 1460 and 1490 m/s, respectively. The depths of the SRA elements are also included.

shows the results for PS at an 81-m depth for five different ranges from the SRA: 4.5, 7.7, 15, 20, and 30 km. As expected, the temporal focus remains compact while the spatial focus broadens with range due to mode stripping. The latter can be seen more quantitatively in Fig. 5~a!. Note, however, that there is a significant sidelobe around a 40-m depth at a 15-km range, as shown in Fig. 4~c!. Also, in Fig. 4~a! the focus appears to occur at 85 m, which is below the PS depth. The depth axes in Fig. 4 are based upon the assumed arrayelement depths for a perfectly vertical receive array, although the VRA was suspended from the freely drifting ALLIANCE @except in the case of Fig. 4~f!#. In fact, the ALLIANCE was drifting at approximately 1/2 kt during the period of Fig. 4~a!, 1/3 kt during the period of Fig. 4~b!, and there was almost no drifting of the ship during the periods of Fig. 4~c!–~e!. Incorporating a nonvertical shape of the array resulting from the ship drifting could bring the focus of Fig. 4~a! back to the PS depth. We also note that the mainlobes of the focus have longer tails towards the bottom for ranges greater than R515 km. This is due to the contribution of lower-order modes excited for a deep PS source ~81-m depth! in a strongly downward-refracting environment. Simulations using the environment of Fig. 3 as an input confirm that the focal structure is consistent with theory.1 The broader mainlobes around the PS depth in Fig. 5~a! when R520 and R530 km are due to backpropagated noise components in the vicinity of 460 Hz ~close to the carrier frequency of 445 Hz!, which are embedded in the data received by the SRA. The simulations also predict the sidelobe around the 40-m depth at the 15-km range. As described below, this sidelobe is due to the nonoptimum spatial coverage of the source–receive array ~SRA! in this particular environment. There are two issues in spatial sampling: array aperture and element spacing. We used a 23-element SRA spaced 3.33 m, i.e., approximately l at the frequency 445 Hz. The uppermost element is at a 25-m depth and the SRA spans 77 Hodgkiss et al.: Long range and variable focus experiment

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m of a 123-m water depth. Here, l spacing is sufficient for a vertical array due to the waveguide nature of the channel.11 Figure 6 shows simulation results for various SRA configurations, clearly demonstrating that the sidelobe can be removed by lowering the SRA 10 m towards the bottom. As can be seen, element spacing is not the issue. The results indicate that in a strongly downward-refracting environment, it is better to sample the field in the lower part of the water column. For a different sound-speed profile, however, the sidelobe disappears as shown in Fig. 4~f! ~also at 15-km range!, which was obtained 10 days later than Fig. 4~c!. Figures 7 and 8 show the experimental results for the PS at a 47-m depth at various ranges. We note from Fig. 2 that this depth undergoes considerably more sound-speed structure variability than the deep probe-source position. An attempt to simulate the double peaks at the 30-km range using

a simple time-invariant environment as above had little success. In addition, the structure of the double peaks changes significantly over the 15-min period ~the duration of this portion of the experiment!. The spatial and temporal variability of the sound-speed structure at this time is under investigation. Figure 7~a! also suggests that the array shape was not vertical due to drifting of the ship, as pointed out in Fig. 4~a!. To summarize, the TRM is still quite effective at 30 km—particularly for the deeper probe source, which is in the more stable part of the water column. This focal property of the waveguide TRM is quite impressive. The focal region has a vertical extent of about 25 m ~3 dB down from peak! at a range of 30 km, which corresponds to 20% of the waveguide depth at a range of about 250 waveguide depths. Although we did not map out the radial extent of the focus, Fig. 9 is a simulation using the environmental parameters which

FIG. 4. Experimental results for 50-ms, 445-Hz center frequency probe-source ~PS! pings at 81-m depth and various ranges, R, between the PS and the source–receive array ~SRA!. ~a! R54.5, ~b! R57.7 km, ~c! R515 km. ~d! R520 km. ~e! R530 km. ~f! R515 km. The vertical receive array ~VRA! is within 60 m of the PS. Both the VRA and PS were suspended from the ALLIANCE except in ~f!, which was from another run where the rf-telemetered VRA was at 15-km range. Note the different depth coverage of the VRA in ~f! in comparison with ~a!–~e!. 1599

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FIG. 5. The energy over a 0.3-s time window of the pulse received on the VRA as a function of depth for various ranges. The depth of the PS was 81 m. ~a! Experimental results. ~b! Simulation results using the environment shown in Fig. 3. Note the sidelobe at around 40-m depth and 15-km range in both cases.

have successfully described this process, indicating that the radial size of the focal region ~depth of field! is on the order of 800 m ~3 dB down from the peak! at a 30-km range and 300 m at a 5-km range. III. TRM WITH VARIABLE-RANGE FOCUSING

Here, we present results which experimentally confirm a technique to change the range focus of a TRM12 based on the frequency-range invariant of the interference pattern in a waveguide. The technique involves retransmitting the data at a shifted frequency according to the desired change in focal range. The expression which governs this shift is ~ D v / v ! 5 b ~ DR/R ! ,

~1!

FIG. 6. Energy over 0.3-s time window of the simulated data at 15-km range as a function of depth for various SRA configurations. The original SRA spans 77 m of a 123-m water depth with the top element at 25-m depth and the element spacing of 3.3 m ~L577 m, d53.3 m! as shown with solid circles. The line with squares is obtained with the same aperture but more dense sampling (d52 m). The result from extending the aperture towards the bottom (L587 m) is displayed with open circles. Last, the line with solid triangles shows the result with the original aperture (L577 m) but shifted down 10 m ~i.e., the top element at 35-m depth!. 1600

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where R is the horizontal distance of the SRA from the PS. The invariant b is determined by the properties of the medium, and is approximately equal to 1 in a shallow-water acoustic waveguide. In a mildly range-dependent waveguide, the value of b varies with range R. During the experiment, the frequency shift was implemented in near real-time by a simple fast Fourier transform ~FFT! bin shift of the probe-source data received by the SRA prior to retransmission. In the following results, the nominal PS range is 15 km. Figure 10~a! shows the focusing for the PS at a depth of 47 m when the VRA was 500-m inbound of the probe source; Fig. 10~b! shows the focusing using a theoretically predicted 215-Hz shift to refocus the pulse at the SRA ~b51!. The results for the PS at a depth of 82 m are shown in Fig. 11 when the VRA was 700-m outbound of the PS. A 130-Hz frequency shift brought the focus back, as shown in Fig. 11~b!. In Fig. 12~a!, the VRA was 600-m inbound of the probe source, which resulted in considerable defocusing. Figure 12~b!–~d! show frequency shifts of 20, 25, and 32 Hz with the best focus resulting from the 32-Hz shift. It is interesting to note that this latter result corresponds to b51.4, and in essence, this procedure is a way of determining b. To summarize, it is possible to shift the focal range on the order of 10% of the nominal range of the probe source. The theory on which this shift is dependent is valid only over a frequency range in which the mode shapes do not change significantly. Frequency shifts of greater than about 10% violate this condition. A practical limitation also comes from the transducer characteristics of the SRA, the resonance of which is around 445 Hz with a 3-dB bandwidth of approximately 35 Hz, as shown in Fig. B1 in Ref. 1. Therefore, it is difficult to excite the pulse at a carrier frequency more than 10% offset from the original resonance frequency. From the results presented above, temporal compression appears to be a robust property of the TRM focus since it occurs even when spatial focusing is absent. In this particular environment, our narrow-band 50-ms pulse ~22 cycles at 445 Hz! is dispersed to about 75 ms one-way duration for the PS Hodgkiss et al.: Long range and variable focus experiment

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FIG. 7. Experimental results for 50-ms, 445-Hz center frequency probe-source ~PS! pings at 47-m depth and various ranges, R, between the PS and the source–receive array ~SRA!. ~a! R53.7 km. ~b! R57.8 km. ~c! R515 km. ~d! R530 km. The vertical receive array ~VRA! is within 60 m of the PS. Both the VRA and PS were suspended from the ALLIANCE. Note the double peaks at the 30-km range.

at a 15-km range from the SRA @see Fig. 13~a!#. The VRA results show that the retransmissions have been compressed roughly to the original pulse duration. A shorter-duration pulse, however, would have displayed more significant spreading when not in focus than in the immediate vicinity of the focal spot. Note also that the out-of-focus ranges considered here are within 10% of the nominal focal range. IV. TRM WITH LONG-TIME MEMORY

Clearly, for a time-independent medium, one can use stored probe pulses to focus on specific locations.3 However,

FIG. 8. The energy over a 0.3-s time window of the pulse received on the VRA as a function of depth for various ranges. The depth of the PS was 47 m. Note the double peaks at the 30-km range. 1601

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the temporal variability of the ocean is expected to limit such a procedure. In the previous experiment,1 we found that a single probe-source pulse received at the SRA could be used to provide a stable focus for up to 3 h ~the total duration of that portion of the experiment!. In the May 1997 experiment, we found that probe pulses up to 1 week old still produced a significant focus at the original probe-source location. Figure 13~a! shows the original probe-source pulse as received by the SRA ~on Julian day 132 at 17:42:05 Z! for the PS at a depth of 81 m, and Fig. 13~b! shows the time-

FIG. 9. Simulated results of the energy over 0.3-s time window of the pulse received on the VRA as a function of range with respect to the focal range for various source ranges: 5, 10, 15, and 30 km. Hodgkiss et al.: Long range and variable focus experiment

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FIG. 10. Experimental results for the PS at a depth of 47 m. ~a! Out-of-focus results on the VRA when the VRA is 500-m inbound of the PS. ~b! Same as ~a! except a 215-Hz frequency shift has been applied to the data at the SRA prior to retransmission. Note that the focus is improved significantly.

FIG. 11. Experimental results for the PS at a depth of 82 m. ~a! Out-of-focus results on the VRA when the VRA is 700-m outbound of the PS. ~b! Same as ~a! except a 130-Hz frequency shift has been applied to the data at the SRA prior to retransmission. Note that the focus is brought back onto the VRA.

FIG. 12. Experimental results for the PS at a depth of 68 m. ~a! Out-of-focus results on the VRA when the VRA is 600-m inbound of the PS. ~b! 220-Hz frequency shift. ~c! 225-Hz frequency shift. ~d! 232-Hz frequency shift. The 232-Hz shift in ~d! shows the best focus, which corresponds to b 51.4. 1602

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FIG. 13. Experimental results using an old ping which was received by the SRA on JD 132 at 17:42:05 Z. ~a! The pulse data received on the SRA for the PS at depth of 81 m. ~b! The original data received on the VRA from the time-reversed transmission of the pulse shown in ~a! when the PS and VRA were at the same range of 15.2 km. ~c! The results on the VRA from the retransmission of ~a! 1 day later. The VRA was 400-m inbound of the PS. ~d! The results on the VRA from the retransmission of ~a! with a 216-Hz frequency shift 1 week later. The VRA was 300-m inbound of the PS. ~e! The results on the VRA from the retransmission of ~a! 10 days later. The VRA was 300-m inbound of the PS. Note the different depth coverage of ~b! from ~c!–~e! because the VRA was suspended from the ALLIANCE at that time.

FIG. 14. Experimental results using an old ping which was received by the SRA on JD 138 at 21:48 Z. ~a! The original data received on the VRA when the VRA was 600-m inbound of the PS. ~b! The data on the VRA 1 day later from the same ping used for ~a!. In both cases, a 232-Hz frequency shift was applied to the ping received by the SRA prior to retransmission. 1603

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reversed pulse received on the VRA just a short time later ~16 min!. Figure 13~c!–~e! show the results on the VRA for the Fig. 13~a! pulse retransmitted 1 day, 1 week, and 10 days later. Note the different depth coverage of Fig. 13~b! from the others because the VRA was suspended from the ALLIANCE at that time, not moored as in the other cases. The biggest environmental change that occurred during this experiment was a gradual warming of the surface layer, resulting in an increase in sound speed near the surface as indicated in Fig. 2. Therefore, the results from a deep probe source will be less sensitive to these environmental variations over the period than will be the case for a shallow source. It is surprising that a 1-day-old ping apparently shows better focusing, as seen in Fig. 13~c!. Although the focus is significantly degraded after a week along with the appearance of a side-lobe in the upper water column, the TRM clearly retains a memory. Furthermore, it might be possible to enhance the focus with techniques related to that of the last section. In Fig. 13~d!, a 216-Hz frequency shift was applied prior to retransmission of the pulse in Fig. 13~a! where the VRA was 300-m inbound of the PS. In fact, the mismatch in environmental parameters such as sound speed and water depth can be compensated by shifting the frequency.13 Figure 14 shows the results for the PS at a depth of 68 m using a day-old ping which was received by the SRA on JD 138 at 21:48 Z along with the original result from the same ping ~15 min later!. The results in this section suggest that the repetition rate required to keep a stable focus may be less than originally suspected. V. SUMMARY AND CONCLUSIONS

We have demonstrated that a time-reversal mirror can produce significant focusing out to long ranges in a shallowwater environment—30 km in water depths on the order of 125 m. Furthermore, we have confirmed experimentally that

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the range of focus can be varied up to about 10% around the nominal focal range. Finally, we have demonstrated that a time-reversal mirror can have substantial memory. In this experiment, probe-source pulses up to 1 week old were successfully refocused. ACKNOWLEDGMENTS

This research was supported by the Office of Naval Research Code 321 US, Contract N00014-97-D-0003. 1

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