TIME-VARIED-GAIN CORRECTION FOR DIGITAL ECHOSOUNDERS.

Transcription

1 TIME-VARIED-GAIN CORRECTION FOR DIGITAL ECHOSOUNDERS. PACS REFERENCE:.6.Qv,..Gv MOSZYNSKI Marek, STEPNOWSKI Andrzej Gdansk University of Technoloy ul. Narutowicza / Gdansk Poland Tel: Fax: marmo@p.da.pl ABSTRACT Time-varied-ain (TVG) is indispensable feature in sonars used in fisheries research in order to compensate for transmission loss and make the echo level independent of a taret rane. In diital processin of data acquired from modern diital echosounders, the sample by sample compensation is applied, assumin that each echo envelope sample was received from the rane determined by its time delay with reference to the soundin pulse. However, as the soundin pulse used for eneration of acoustic wave lasts for a certain period of time, the compensation should be made rather on echo waveform basis than on sample basis. In the paper the new alorithm for diital TVG correction was introduced, which allows for more accurate echo level adjustment than conventional lor or lor formulae. The developed alorithm was investiated experimentally on sonar echoes obtained from the standard sphere tarets. The results may explain the possible source of errors encountered in the field studies, especially in a shallow water. INTRODUCTION The time-varied-ain feature of a sonar removes the rane dependence of echo level. Two kinds of TVG are commonly used, viz.: so called lor function, which applies for sinle tarets and lor which applies for distributed or multiple tarets like fish schools or seabed. Both functions provide exact compensation only for the case of infinitely short soundin pulse or at infinite rane. These terms express the spherical spreadin loss in loarithmic scale for twoway transmission to rane R and are additionally extended for compensation of absorption losses αr where α is an absorption coefficient expressed in decibels per meter. For sinle tarets "lor" rane dependent function G(R) expressed in decibels and (R) in linear scale as []: G ( R) = lo R / R + αr () αr ( R) = ( R / R ) e where R reference distance (typically m) and α absorption coefficient expressed in nepers per meter.

2 Typical approach of expressin TVG function as a function of time uses simple substitution R=ct/, what leads to (omittin R =m): αct / ( t ) = ( ct / ) e () where c is speed of sound. Fi. shows transmission loss alon time-varied-ain function as a function of time as iven by Eq.. In diital echosounders not like in its analo counterparts (where TVG function was implemented in hardware) there is no restriction on dynamic rane of these functions and their rane. However, Eq. describin ain function as a function of rane is inconsistent with Eq. as a function of time due to the echo formation process []. time-varied-ain (TVG) - - transmission loss (TL) - - t[ms] Fi.. Transmission loss and classical time-varied-ain function. TIME-VARIED-GAIN FUNCTION THEORY More accurate approach distinuishes between the rane and time dependent TVG functions. Accordin to MacLennan s definition [], the rane dependent TVG function R (R) is expressed as a weihted averae of time dependent TVG function t (t): R ( R ) = V ( R,t ) V ( R,t ) ( t ) Exact rane dependant TVG functions for a sinle taret echo can be expressed as R (R)=R exp(αr) and the echo voltae after TVG correction is: α R e Vo( R,t ) = t ( t ) V( t τ ) () R where V(t) is a normalized echo waveform observed at the receiver output (before correction) and τ = R/c is a propaation delay of an echo. Exact time dependant TVG function must fulfill the interal relationship, which uarantees obtainin the same value at the echo interator output (enery) for the same taret at different ranes: t + t ( t' + τ ) V( t' ) ' αcτ () = kc τ e + where k is an arbitrary constant. V( t' ) ' () The solution of Eq. is iven as αct / lo R ( t) = ( ct) e + a + a + a( T / t) + a (6)

3 where T is soundin pulse lenth and coefficients a i can be expressed usin moments I m (normalized to pulse lenth T) of the sinal V(t) : I m = T m t e m α ct e α ct V ( t) V ( t) respectively a =-I, a =-6I +I, a =-I +I I -I, a =-I +8I I +6I - 6I I +I. The same approach for distributed or multiple tarets (e.. fish schools or sea bottom) ives: αct / lo R ( t) = ( ct) e + bt / t + b (8) with b =-I, b =I -I. Eq. 8 can be approximated by delayed TVG function: αct / a ( t) = c( t T ) e (9) with T =T +R /c-{(r /) -T } /, where T =I T and T =T(I -I ) /, which shows that not exact approach may be partly corrected introducin a delay T in TVG function which always lies between T and T +T. As T and T still depends on acquired echo envelope some echosounder manufacturers uses another approximation assumin flat frequency response of the taret in flat receiver frequency bandwih and an ideal rectanular pulse delayed by echosounder hardware (t ) for which T =t +T/ and T =T/. More adequate approach incorporates bandpass approximation of receiver bandwih. In this case normalized moments of the echo sinal (and consequently T and T ), depend on the product BT of bandwih B and pulse lenth T. Fi. shows that lor TVG function introduces decreasin error until m rane, ivin over.db error at m rane for BT=. Approximation of exact TVG function (see Fi.) can be used for ranes reater than m. This approach, however, still can not take into account taret frequency response, which depends on taret properties. (7) [db] - lor Exact TVG - - Fi.. Theoretical lor TVG function compared with exact lor (t) TVG function for receiver bandwih B=kHz and pulse lenth T=.[ms]. SAMPLE DATA ANALYSIS In this paper another approach is proposed for calculation of an exact TVG function, which uses shape of the echo envelope. As modern echosounders instead of usin analo TVG ramp, use software correction of diitized echo, it is convenient to extend calculation of values of echo samples. The calculation can include time-varied-correction derived from the echo waveform moments exactly as proposed by Eq. (6) or Eq. (8). This procedure requires taret detection alorithm to precede the TVG correction phase and involves addition computational cost. All sample echos presented in the paper were acquired with BioSonics DT series diital echosounder operated at the frequency of khz

4 [db] - lor Approx.TVG Exact TVG Fi.. Exact TVG function lor (t), its delayed approximation a (t) alon with lor function (receiver bandwih B=kHz and pulse lenth T=.8[ms]) in a short rane. Fi. shows the echo pulse modeled as the echo from the taret with flat frequency response acquired by receiver with simple LCR bandpass filter: πbt e, t < T V ( t) = () πbt πbt ( e ) e, t >= T where B is the receiver bandwih and T is transmittin pulse lenth. It is compared with actual normalized echo reflected from standard taret ball. In Table the normalized moments used for calculation of exact TVG function are presented t[ms] Fi.. Model of the echo pulse from the taret with flat frequency response acquired with a simple LCR bandpass filter compared with actual normalized echo reflected from a standard taret sphere. Tab.. Normalized moments I m used for calculation of exact TVG function for ideal wideband pulse, system modelled with bandpass receiver and for actual shape of echo from standard taret. normalized moments I I I I ideal wideband pulse and.... ideal receiver system modelled with bandpass receiver (Eq.7) actual shape from standard taret ball The results obtained for three different locations of standard taret positioned on a beam axis of transducer are illustrated in Fi., whereas their correspondin echo level calculation are

5 presented in the Table. It is evident that when the shape of the echo should be preserved, continuous time varied function can not be used in the ranes below m, as the end of echo is artificially amplified. When the peak value of the echo envelope is used echo level calculation it leads to another source of error in taret strenth estimation. It is easily seen that for actual case all the moments are reater than modeled. Hence for simple delayed approximation (Eq. 6) the delay T =.T (half of the pulse lenth) should be increased up to T =.7T for this case. In Fi. 6 and in Fi. 7 the echo envelopes acquired at the very short distances (.7m and m) from standard taret located on-axis of the system for three different values of pulse lenth T (.ms,.ms,.ms) are presented. The y-axis in these fiures is scaled in -bit analo-todiital converter values as acquired by diital echosounder. By comparison of its peak value it is evident that they does not fulfills /R (lor) law as for.7m rane the amplitude should be around two times (/.7 ) larer than for m rane. This error may be explained also by operation in the distance, which is close to theoretical near field rane defined by Rayleih distance r =ka /, where k is the wave number and a transducer radius. Also in the interal sense (echo enery) the TVG function differs from delay approximation what arees with theoretical curves shown in Fi.. 6 x 6 x 6 x... Fi.. Sample echoes acquired from standard taret located on axis at.m, m and m, alon with classical "lor" correction and correction clamped at taret rane (linear scale x-axis in meters, y-axis in AD converter samples). Tab.. Echo level EL of standard taret located on beam axis in loarithmic scale. rane R [m].[m] [m] [m] mean(el) std(el) classical lor correction [db] correction fixed at taret rane [db] CONCLUSION In the paper some problems of time-varied-ain correction are presented in the context of its application in the diital echosounder. Theoretical calculations show that classical lor and lor functions introduce error, which is reater in short distances and monotonically decreases up to around m rane. It is shown that in shallow water applications exact TVG function or its delayed approximation should be used rather than classical function calculated by R=ct/ substitution.

6 For some application includin taret reconition or bottom classification where the shape of the echo envelope need to be preserved it is very important to introduce nonlinear time-varied-ain function fixed at taret rane for a time interval equal to the of pulse lenth. For a narrow band systems, this allows to calculate taret strenth or scatterin strenth usin peak value of the echo. The sample number of the peak value is shifted in relation to taret rane due to bandpass properties of echosounder hardware. It explains the approximation of exact TVG function by delayed TVG function. x Fi.. Echoes acquired from standard taret located.7m from transducer for three different values of pulse lenth (T=.[ms],.[ms],.[ms]). x Fi.6. Echoes acquired from standard taret located.m from transducer for different values of pulse lenth (T=.[ms],.[ms],.[ms]). For short pulses due to bandpass properties of the transducer the transmitted pulse does not reach its maximum value measured durin calibration stae with loner pulses so additional correction is required. For a very short distances (i.e. fish trackin applications) the echo strenth calculated for different taret ranes does not fulfill exactly the spherical spreadin rule, so althouh it is beyond theoretical near field Rayleih distance additional corrections are also required. REFERENCES [] A. Stepnowski, R.S. Mitchell, "ECOLOG II: a real-time acoustic sinal processin system for fish stock assessment", Ultrasonics 99, Vol.8, [] D.N. MacLennan, Time varied ain functions for pulsed sonars, Journal of Sound and Vibration (986) (), -.