Precision calibration of echo sounder by integration of standard sphere echoes

J. Acoust. Soc. Jpn.(E) 14, 4 (1993) Precision calibration of echo sounder by integration of standard sphere echoes Kouichi Sawada and Masahiko Furusawa National Research Institute of Fisheries Engineering, 5-5-1 Kachidoki, Chuo-ku, Tokyo, 104 Japan (Received 16 July 1992) Precision calibration of echo sounder by integration of sphere echoes is studied. In this method, the total sensitivity of the system is easily and quickly determined by com paring the echo integrator output for standard sphere echoes with the theoretical value. A strict theoretical expression is derived considering the bandwidth of receiving system and the time varied gain (TVG) effect on the sphere echo shape. The strict expression is compared with approximate ones and with experimental values. Experimental values agree fairly well with the theoretical calculations. For precise calibration, the effective pulse width should be calculated from the actual echo shape since the bandwidth of the receiving system changes the echo shape. When a long pulse width is used, the TVG effect should not be neglected. Key words:echo sounder, Echo integrator, Standard sphere, TVG effect, Effective PACS number:43. pulse width 85. Vb 1. INTRODUCTION Quantitative echo sounders are widely used for acoustic surveys to estimate fish abundance. In order to get reliable estimates, the calibration of the sounder is fundamental. The calibration is performed for transducer sensi tivities, directivity patterns, amplifier gains, and so on. Among these, the calibration of transmitting and receiving sensitivities is most important, be cause the sensitivities sometimes vary and users of the sounder must calibrate them. A traditional method is to use a calibrated transducer which is positioned at the acoustic axis of the sounder trans ducer. However, this method is not easy to per form and has some problems in reliability. About one decade ago, a calibration method using a standard sphere (sphere calibration method) was developed by Foote 1) and other researchers. Figure 1 shows a block diagram of the quantitative echo sounder, focusing on the calibration process. In the sphere calibration, one observes the receiver output of the sphere echoes, measures the amplitude, and converts it to the combined transmitting and receiving sensitivity using the known target strength (TS) value of the sphere. This method can be extended to calibrate the total system, if the sphere echoes are integrated by an echo integrator which is the most important echo signal processor to estimate fish abundance (see Fig. 1). We call this method the "sphere echo integration method." Scrutinization and im provement of this method is the purpose of this paper. This method has been described in the papers of Knudsen, 2) Foote, 3, 4) and Foote et al. 5) The aims of the sphere echo integration suggested in these references may be classified into two types:(1) to use the integrator output as a reference value for more strict calibration by the sphere calibration method;(2) to use the integrator output directly to calibrate the total system. For the second aim,

J. Acoust. Soc. Jpn.(E) 14, 4 (1993) Fig. 2 Sphere echo and integration layers. Fig. 1 Simplified block diagram of quanti tative echo sounder. Definitions of variables are shown. strict relationship between the integrator output for the sphere echo and sounder parameters such as sensitivity must be established. This is the main subject of this paper. (The output of the echo integrator is the volume backscattering strength (SV) or the area backscattering strength (SA). The output for sphere echoes is called "sphere SV" or "sphere SA.") Knudsen 2) presented an expression of the sphere SA. His intention was to provide a calibration method for the Simrad EK500 echo sounder. This sounder digitizes echoes in the earlier stage of the receiver and has no analogue output. His expression is based on the volume scattering theory. The present authors consider that the sphere echo integration method is superior in preciseness and totality and that this method should be more widely used. The method, however, has not been suffi ciently studied, especially in theoretical considera tions. We derive a theoretical expression of sphere SV by applying the actual echo integration process to a theoretically simulated sphere echo. Some ap proximations are introduced to simplify the calcula tionand the approximation errors are examined. Experimental calibration measurements are com pared with theoretical values. We compare - our expression with Knudsen's. Some suggestions are proposed for precision calibration and future re search needs. - 2.1 General Expression 2. THEORY Figure 1 shows the echo processing in typical quantitative echo sounding systems. The preamplifier output is ER, and Er is the time varied gain (TVG) amplifier output of ER corrected for spreading and absorption losses. The echo inte grator calculates SV in a depth layer by averaging - and scaling the squared echo voltage in a given time period. Figure 2 shows schematically a sphere echo shape at the TVG output. If the echo shape function is expressed as w(t) and w(t)=1 at the maximum level, the echo voltage amplitude (ET) can be ex pressed as where P0 is the source pressure amplitude, M is the receiving sensitivity of hydrophone, GR is the preamplifier gain, GT is the TVG coefficient, D is the directivity function, rs is the sphere depth measured from the transducer, a is the absorption coefficient, Ts is the linear value of the target strength of stan dard sphere, defined as the ratio of backscattered - intensity to incident intensity, 6, 7) r=ct/2 is the range, t is the time measured from the instant of transmis sion, and c is the sound speed. Note that, -differing from ordinary approximate expression, we dis criminate the sphere range rs and the observationrange r. In this paper a decibel variable for a cor responding linear one is discriminated by making - the first two letters of linear variable upper case, for example, SV=10 log Sy. The integrator output of sphere echo, Sy, is where KM is a system scaling coefficient appropriate for multiple echo conditions, ru and r1 are the upper and lower ranges of integration layer respectively, is the width of integration layer (r1-ru), Ė is the effective pulse width and ě is the

K. SAWADA and M. FURUSAWA:PRECISION CALIBRATION BY SPHERE ECHO INTEGRATION equivalent beam angle. Eq.(2) yields Substitution of Eq.(1) into Table 1 Conditions of approximation formulas. 2.2 Approximations The integration of Eq.(4) is difficult to evaluate exactly, so some approximations are introduced. As can be seen from the dotted line in Fig. 2 or from Eq.(1), the echo amplitude of the target grad ually increases with time due to TVG charac - teristics (r2 exp (4ƒ r) where r=ct/2). This is - called "TVG effect." If this effect is slight, then it is ne - glected by putting r=rs in Eq.(4). An actual echo wave form is not rectangular but has a shape as shown in Fig. 2. This can be theoret ically simulated using the step response of -a reso nantsystem to a rectangular wave as8): shown in Table 1. In order to facilitate the com parison of approximate formulas, Eq.(4) is - sep arated into three terms:the common part is Sv - U; the first part of the integrand is related to echo shape; and the second part is related to TVG com pensation. - Then the eight approximations are derived as follows. (1) no TVG effect, rectangular, flat part: where ƒñ0 is the pulse width at the input, ƒà=ƒî f, U (t) is the unit step function. Examples of the wave form for various bandwidths are shown in Fig. 3. There are two methods to choose the integration layer as shown in Fig. 2:integration of the whole sphere echo and integration of a flat part of the sphere echo. Considering the above three factors, that is, the TVG effect, the wave form, and the integration layer, there can be 23=8 approximate expressions as (2) no TVG effect, rectangular, whole wave: where ƒñ0 is the pulse width of rectangular wave. (3) no TVG effect, w=w(t)(eq.(6)), flat part: where wave: (4) no TVG effect, w=w(t)(eq.(6)), whole where ƒñ is the effective pulse width comnuted by using the echo shape w(t) observed in the process of the sphere calibration performed in ad vance and is given as one of the parameters of -the echo integrator, and ƒñ' is the effective pulse width for the echo shape observed in the sphere echo Fig. 3 Simulated echo wave shapes as re sponsesof rectangular wave (0.6ms) to bandpass systems. integration. (5) TVG effect, rectangular, flat part:

(6) TVG effect, rectangular, whole wave: where re is the range corresponding to the end point of the sphere echo (see Fig. 2). (7) TVG effect, w=w(t)(eq. (6)), flat part: where (8) TVG effect, w=w(t)(eq.(6)), whole wave: The parameter, rp, shows the range corresponding to the peak point (see Fig. 2). Fig. 4 Errors of approximate expressions of sphere Sv as a function of bandwidth. Errors of Sv2, Sv4, and Svs with respect to SV8 are plotted for pulse width of (a) 0.6, (b) 1.2, and (c) 2.4 ms. 2.3 Calculation and Results The theoretical results shown above are examined. The more important cases of the integration of the whole echo are considered here. Since Sv8 is the most exact expression, this is selected as the reference for other cases. Therefore, the approximation error is calculated as In the calculations, we assumed ƒ =10 db/km (frequency is 38 khz) and c=1, 500 m/s, and f, To, and rs were selected to fit the actual system under typical conditions. The integration layer (r1-ru) Fig. 5 Errors of approximate expressions of sphere Sv as a function of the distance from the transducer surface to the sphere. appears only as a coefficient parameter in the case of whole wave integration, so that this parameter does not affect the errors of Sv2, Sv4, and Sv6. Figure 4 shows the error as a function of bandwidth, f, which is the parameter that determines the echo shape (Fig. 3). The pulse width, To (see Eq. (6)), is varied as 0.6, 1.2, and 2.4 ms. The sphere range rs is 20 m. As the pulse width increases, the errors of Sv2 and Sv4 are shifted in the negative direction because the TVG effect is ignored. The errors of Sv2 and Sv6 gradually approach asymptotical values, because the echo envelope shapes become rectangular with increasing f as seen in Fig. 3. The nearly

K. SAWADA and M. FURUSAWA:PRECISION CALIBRATION BY SPHERE ECHO INTEGRATION constant differences between Sv6, and Sv2, and be tween Sv8 and Sv4 are caused by the TVG effect. - Figure 5 shows the error as a function of sphere depth (rs) for a pulse width of 0.6ms, and bandwidth of 3kHz. The error of Sv4 gradually ap proaches 0 as depth increases and similarly the error - of SV2 approaches that of SV6. 3. EXPERIMENT During one of the acoustic surveys of walleye pollock (Theragra chalcogramma) in the Bering Sea, we applied the standard sphere calibration and sphere echo integration methods to our quantita tive versatile echo sounding system (VESS) - 9) in Makushin Bay, Unalaska Island, Alaska, on 5 and 6 August 1991. Figure 6 shows the system block diagram of VESS. The sounder is a dual-beam system operating at 38kHz with TS measurement and echo integration functions. A copper sphere 3) with diameter of 60.0mm was lowered to 20.5m below the surface of the water. The echo integration period (a parameter of the echo integrator) was selected to be 60s in time base and the integration layer was set from 19m to 24m to minimize noise and fish contamination. The dual-beam processor (DBP) 9) was also operated to measure the TS and position of the sphere during the sphere echo integration. The parameters set in the echo integrator and DBP were calibrated by the ordinary sphere calibration method. 5) The following parameters are used: (a) Measured target strength of standard sphere. (b) Estimated position of standard sphere. Fig. 7 Target strength (a) and position angle ƒæ (b) of 60mmƒÓ copper sphere mea Figure 7 shows (a) one of the examples of TS measured by DBP and (b) estimated sphere position in angle ƒæ off acoustic axis. The horizontal axis in both figures is ping number. A one-minute integra tion period represents 180 pings. From Fig. - 7 (a) the average TS is -33.7dB. This measured value agreed with the known TS value of -33.7dB, demonstrating that the calibration of the transmit ting and receiving system was performed correctly -. The sphere was located at 0.3 `1.1 from the acoustic axis. The average angle corresponding to each integration period is listed in Table 2. From this position angle, we can estimate the two-way directivity (D4) correction and can estimate SV values on beam axis. Table 2 shows measured sphere SV and pertinent values. The theoretical SV from Eq.(15) for narrow and wide beam are -45.35dB and -47.51 db, respectively. The directivity corrected SV values agree well with the theoretical ones, i.e. within about }0.35dB. Considering the precision of the system's digital controlled TVG amplifier Fig. 6 System block diagram of versatile echo sounding system. with 0.375dB gain step, these slight differences between theoretical and experimental values are trivial.

J. Acoust. Soc. Jpn.(E) 14, 4 (1993) Table 2 Results of sphere echo integration obtained in 1991 summer. Echo samples rep -resents approximately 180 pings. The best way is to observe an actual wave form 4. DISCUSSION and use, for example, Simpson's method to 4.1 Knudsen's Expression evaluate the integral in Eq.(4). This, however, is We compare our expression of the sphere Sv not easy and the alternative method is to use Eq. with Kundsen's expression. 2) Using Knudsen's (15). The parameter Af, which determines the formula for sphere SA and dividing it by rw yields echo shape, must be given and it can be derived by the following Sv in our terminology: fitting the actual shape and the simulated one as shown in Fig. 3. An easy method to approximate is to measure the rise time, tr, from beginning of where Ts' is energy based Ts defined as the ratio of received echo energy, normalized to the reference range from a target, to incident energy. Equation (17) is similar to Eq.(5) except for the directivity correction D. The relation between energy based TS, Ts', and intensity based TS, Ts, is position a sphere at the beam center for a long time (several integration periods). Therefore, the direc where T0 is nominal or transmitter pulse width. If tivity correction for the sphere SV is necessary - as this is substituted in Eq.(17) and T0 is changed to shown in the above example and in Foote. 4) This can easily be accomplished if the sounder has the ability to measure the position angle of the sphere and this formula (Sv4) looks like Knudsen's expres sion. As can be seen in Fig. 4, the error of - Sv4, is rather small especially for a short pulse width, but caution must be paid for large pulse widths. Equation (18) is the alternative definition or time domain definition of the operational TS suggested in Foote. 1) The two schemes can be exchangeable by this equation. 4.2 Precise Calibration Method As described above, for precision calibration the theoretical value must be calculated as exactly as possible. The method is suggested in Eqs.(4) and (15). the echo to the time when the amplitude becomes the asymptotical value and compute f by 7) Recent quantitative echo sounders utilize very narrow beams because of the need to measure TS in situ. With a narrow beam it is very difficult to as is possible with the dual-beam method or the split-beam method. 10) Figure 4 shows that when is small, the approxi mation error becomes large, so that exact -calcula tion of the effective pulse width is necessary. - When the energy based TS is used, the correction of the TS value itself may be an alternative procedure. 3) Also from Fig. 4, when pulse width is small, Sv4 is almost equal to Sv8; but when pulse width is large, we must consider TVG effect and the strict formula of Eq.(15) must be employed. It is best to choose a large sphere depth to decrease TVG effect as seen from Fig. 5, so long as restriction of anchoring vessel permits.

K. SAWADA and M. FURUSAWA:PRECISION CALIBRATION BY SPHERE ECHO INTEGRATION 4.3 Future Applications We tried to integrate sphere echoes at their flat part (Fig. 2). The method is theoretically treated in Section 2. The difficulty to set an integration layer at exactly the flat part interrupted the trial. This method, however, is attractive for the definition of intensity based TS, because it is less dependent on system bandwidth. Therefore, future investiga tion is expected. ACKNOWLEDGEMENTS The authors are in debt to Y. Takao, National Research Institute of Fisheries Engineering, for his help. They wish to thank J. J. Traynor and N. J. Williamson, Alaska Fisheries Science Center, NOAA, Seattle, USA, for discussing the present method and for reviewing the manuscript. They also thank E. Ona and H. P. Knudsen, Institute of Marine Research, Bergen, Norway, for their useful advice and discussions. REFERENCES 1 ) K. G. Foote,"Optimizing copper spheres for precision calibration of hydroacoustic equipment," J. Acoust. Soc. Am. 71, 742-747 (1982). 2 ) H. P. Knudsen,"Bergen echo integrator:an intro duction,"j. Cons. Int. Explor. Mer 47, 167-174 - (1990). 3 ) K. G. Foote,"Maintaining precision calibrations with optimal copper spheres," J. Acoust. Soc. Am. 73, 1054-1063 (1983). 4 ) K. G. Foote,"Bad-weather calibration of split beam echo sounding systems," Counc. Meet. - int. Counc. Explor. Sea. 1990/B:22, 5 pp.(mimeo). 5 ) K. G. Foote, H. P. Knudsen, G. Vestnes, D. N. MacLennan, and E. J. Simmonds,"Calibration of acoustic instruments for fish density estimation:a practical guide," Int. Counc. Explor. Sea Coop. Rep. 144 (1987). - 6 ) J. Saneyoshi, Y. Kikuchi, and O. Nomoto, Chouonpa Gijyutu Binran (Handbook of Ultrasonic Technique) (Nikkan Kogyo Shinbun-sha, Tokyo, 1966), p. 48 (in Japanese). 7 ) M. Furusawa, "Designing quantitative echo sounders," J. Acoust. Soc. Am. 90, 26-36 (1991). 8 ) M. Furusawa, K. Ishi, and Y. Maniwa,"A theo retical investigation on ultrasonic echo method - to estimate distribution density of fish," J. Acoust. Soc. Jpn. (J) 42, 2-8 (1986)(in Japanese). 9 ) M. Furusawa and Y. Takao, "Outline of a versatile echo sounding system (VESS)," Doc. Work. Group U.S.-Jpn. Jt. Surv., 1-38 (1988). 10 ) J. E. Ehrenberg,"A review of in situ target strength estimation techniques," FAO Fish. Rep. 300, 85-90 (1983). Kouichi Sawada was born in 1963. He received the B. Eng. and M. Eng. degrees in physics and applied physics from Waseda University, Tokyo, in 1986 and 1988, respectively. Since 1988 he has been working at National Research Institute of Fisheries En gineering. His research interest - is underwater acoustics, in particular fish target strength. He is a member of the Acoustical Society of Japan, the Nippon Suisan Gakkai, the Marine Acoustics Society of Japan, and the Laser Society of Japan. Masahiko Furusawa was born in 1944. He received the B. Eng. degree in electrical engineering and the Dr. Eng. degree from Tokyo Institute of Technology, Tokyo, in 1967 and 1989, respectively. Since 1968 he has been working at National Research In stitute of Fisheries Engineering. He - is a member of the Acoustical Society of Japan, the Nippon Suisan Gakkai, the Marine Acoustics Society of Japan, and Institute of Electronics, Information and Communication Engineering of Japan. 249