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1 I PHOTOGRAPH THIS SHEET li LEVEL INVENTORY z Asmri ooi %he srorisr7cx DOCUMENT IDENTIFICATION <~ p-ee 199b3- L~)~,71'% DISTRIBUTION STATEMENT ACCESSION FOR INTrIS GRA&i DTIC TAB DTIC UNANNOUNCED D]TC - S oct IJST!IFICATION', 1EL ECTED BY -- - DISTRIBUTION / AVAILABILITY CODES DIST AVAIL AND/OR SPECIAL DATE ACCESSIONED -...DATE ACCESSIONED DISTRIBUTION STAMP DATE RETURNED DATE RECEIVED IN DTIC REGISTERED OR CERTIFIED NO. PHOTOGRAPH THIS SHEET AND RETURN TO DTIC-FDAC DTIC FORM 70A DOCUMENT PROCESSING SHEET PREVIOUS EDITION MAY BE USED UNTIL T R 86 OSTOCK IS EXHAUSTED. MAR 86

2 Contrct AFOSR Lf Annul Report to AFOSR Reserch on the Sttistics of Grin Lttice Echoes Gnd their use in Grin Size Estimtion nd Grin Echo Suppression I by Isrel Amir, Ph.D. Deprtment of Electricl nd Computer Engineering Drexel University nd V.L. Newhouse, Ph.D. Robert C. Disque Professor of Electricl nd Computer Engineering Drexel University December 1985 Ii b pps. he dw #md mi * b

3 !ZFC.2-R''' CASSIFiC.AT- CF THI ms PA, C REPORT DOCUMENTATION PAGE is REPOPR SEi.RT, CLASS" CA' 'CN lb RESTRICTIVE MARKINGS 2s SECR,. I CL-ASS, F ICA T!ON 3T-'- DIST RI 8UTION/AVAI LAB ILITY OF REPORT 2h DECLASSF CATION.DO~vNGRADING SCHEDULE -EFCMN ORGANIZATION REPORT NUJMBERi) 5. MONITORING ORGANIZATION REPORT NUMBER(S) 6 NAME OF PERFORMING ORGANIZATION b, OFFICE SYMBOL 7& NAME OF MONITORING ORGANIZATION 6c. ADDRESS (City. Slte nd ZIP Code) 7b. ADDRESS (City. Stte nd ZIP Code) I PHILADELPH-(Ai PA 191r14 So, NAME OF FUNDING/SPONSORING jb. OFFICE SYMBOL 9. PROCUREMENT INSTRUMENT IDENTIFICATION NUMBER ORGANIZTIONIo pplicble) Sc ADDRESS ICity. Stte nd ZIP Code) 10. SOURCE OF FUNDING NOS. BLLing Air Force Bse. D.C PROGRAM PROJECT TASK WORK UNIT ELEMENT NO. NO. NO. NO. AFOSR TITLE (intclude Security Cl..ficon, RESEARCH ON THE STATISTICS OF GRAIN LATTICE EC OES j 12. PERSONAL AUTHOR(S) LAMTR Proiect Director: V-L. ewhouse 13& TYPE OF REPORT 13b. TIME COVERED j14. DATE OF REPORT (Yr.. Mo.. Dy) 15. PAGE COUNT YerLy IRM&..4.T 5 85/12/ , SUPPLEMENTARY NOTATION 17 cosati CODES I8. SUBJECT TERMS (Continue on reverse if necessry nd identify by block numberl FIELD GROUP SUB. GR. 19 ABSTRACT 'Continue on rev'erse if necessry nd iden tfy by block nuimber) Two topics deling with the reflection of ultrsound bursts from rndom medi re discussed in this work. In chpter 2 we develop generl. formultion of the echo received from rndom sctterer ensemble illuminted by short electromgnetic or sonic signl. We show theoreticlly tht grdient in either sctterer concentrtion or in the field function of the trnsmitter/receiver will return n echo which is prtilly sptilly coherent i.e. speculr). Furthermore we show tht from the degree of coherencyf i.e. from the rtio of the rndom prt to the non-rndom prt of the reflected signl0 the sctterer concentrtion nd scttering cross-section cn be clculted. We lso show experimentlly tht scttering concentrtion grdient cretes coherent reflection from whose degree of coherency the scttering concentrtion cn be estimted. 20 DIST R-SU7ION'AVAILABI LIT Y OF ABSTRACT 21 ABSTRACT SECURITY CLASSIFICATION UNC-.SSI-9'_ UN~LIMITED 7 SAME AS RPT OTIC USERS F 2;'& 1S 4Ef OF RESPCNSIBLE INDIVIDO AL 22t) TELEPHONE NUMBER 22c OFFICE SYMBOL (include Areo Cdci DOD FORM 1473, 83 APR EDITION OF I JAN 73 is OBSOLETE. SECURITY CLASSIFICATION OF THIS PAC,

4 19. Abstrct I In chpter 3 nd 4 we del with signl processing techniques for the reduction of clutter noise creted by rndom medi composed of high concentrtion of Point sctterers. The problem is to enhnce trget embedded in rndom medium when the clutter noise vrince nd the trget echo loction nd mrlitude re unknown. In chpter 3 we nlyze theoreticlly technique tht ws first proposed by Newhouse et l (3) the so clled Minimiztion lgorithm. In this technique we split the received signl spectrum into n frequency windows. The minimum of the squred signls t ech rnge dely is then chosen. The clculted SNRE (signl-to-noise-rtio enhncement ) of this technique grees well with experiments performed by N.M.Bilguty (4). We clculte lso the-receiver Operting Chrcteristics (ROC) nd find out tht the improved SNRE of Minimiztion is negted by Loss in detection properties. In chpter 4 we describe method for clutter reduction tht lso uses the split spectrum principle. In this technique we construct the optimum receiver for ech rnge dely from the n outputs of the frequency windows. We clculte the ROC for this technique nd find it to be superior to minimiztion for most cses. We show experimentlly the effectiveness of this lgorithm in clutter reduction. In chpter 5 we summrize the results of this reserch work nd show the flexibility nd verstility of the techniques by introducing improvements nd pplictions to the described methods. I d I

5 4iii 4 TABLE OF CONTENTS CHAPTER 1: INTRODUCTION CLUTTER PROBLEMS IN IMAGING SYSTEMS... I GENERAL LITERATURE REVIEW... 2 Scttering from Rndom Medi... 2 Signl Processing Techniques for Clutter Reduction... 5 Signl Processing Techniques for Speckle Reduction in Ultrsonic Imging... 6 Frequency Compounding... 8 MOTIVATION FOR RESEARCH... 9 SYNOPSIS OF REMAINING CHAPTERS CHAPTER 2: SCATTERING FROM RANDOM MEDIA INTRODUCTION THE REGULAR LATTICE RANDOM MEDIUM WITH UNIFORM SCATTERING CONCENTRATION...16 RANDOM MEDIUM WITH NONUNIFORM SCATTERING DENSITY SNELL'S LAW FOR DENSITY GRADIENTS EXPERIMENTAL RESULTS DISCUSSION CHAPTER 3: THE MINIMIZATION ALGORITHM INTRODUCTION ANALYSIS Trget Model nd Signl to Noise Rtio Signl to Noise Rtio Enhncement for Non-Liner Averging Signl to Noise Rtio Enhncement for Liner Averging Signl to Noise Rtio Enhncement for Minimiztion of the Squred Signls

6 iv Receiver Operting Chrcteristics EXPERIMENT DISCUSSION CONCLUSIONS CHAPTER 4: OPTIMAL PROCESSING INTRODUCTION... o THEORY Detection Performnce... ; EXPERIMENTAL RESULTS RESOLUTION AND RANGE BIAS SUMMARY AND CONCLUSIONS CHAPTER 5: SUMMARY, CONCLUSIONS AND FUTURE WORK INTRODUCTION DISCUSSION PHASE REVERSALS AND OVERLAPPING FREQUENCY WINDOWS SPECKLE REDUCTION SUGGESTED FUT1URE WORK ANALYSIS OF PHASE REVERSALS AND OVERLAPPING CHANNELS AUTOMATIC FLAW DETECTION EDGE SHAiRPENING OPTIMUM DYNAMIC RANGE REFERENCES APPENDIX A APPENDIX B APPENDIX C

7 v LIST OF FIGURES Pge Figure 2.1. A regulr lttice Figure 2.2. A photogrph of the surfces of sponges A,B,C nd D. The fine honeycomb structure is visible. (The width of ech picture corresponds to 6.5 mm.) Id Figure 2.3. Sponges B nd C side by side. It is seen tht the honeycomb structure of sponge B is finer thn tht of sponge C Figure 2.4. Four different echoes from sponge B. Note tht the coherent echo component from the sponge boundry nd the * incoherent component from within the sponge Figure 2.5(A). Four trces (one on top of the other) of the reflected echo from sponge A. Note the lrge coherent component of the echo from the boundry Figure 2.5(B). Sponge B. Note tht the coherent component is not s lrge in comprison to the echo from within the sponge s in Figure 4(A) Figure 2.5(C). Sponge C. Note tht the coherent component is smller in comprison to the echo from within the sponge in Figure 4(B)... Figure 2.5(D). Sponge D. The coherent component ws found to be negligible in repetitive experiments Figure 2.6. The received echo from 2 lyer sponge complex * composed of sponges D nd B. The coherent component cn be seen on the centrl verticl line. Also note tht the power reflected from sponge D is less thn tht reflected from sponge B Figure 2.7. Angle dependence of the coherent component (sponge B). Note tht while the coherent term is highly sensitive to ngle vritions, the echo from within the sponge is ngle insensitive Figure 3.1. The split spectrum process (from 24) Figure 3.2(A). Trget echo with Gussin envelope before frequency splitting Figure 3.2(B). Trget echo fter Minimiztion, showing invrince of pek position d

8 dh vi Figure 3.3. A theoreticl comprison between different frequency splitting techniques using four independent frequency windows, of SNR enhncement for dditive Gussin noise. (SNR defined in eq. 29). Note tht only Minimiztion produces SNR enhncement Figure 3.4. Possible probbility density functions for the Minimiztion process compred to tht of n optimum receiver Pge Figure 3.5. Receiver Operting Chrcteristics for Minimiztion nd verging using two, four nd six frequency windows for vrious rtios of o, to l, (curves thinned-out in the top right-hnd corner to retin clrity). A. Two frequency windows B. Four frequency windows C. Six frequency windows Figure 3.6 (from 24) Input-Output flw-to-grin echo rtio curves nd discrete vlues for stinless steel smples of indicted S grin size. Af is the spcing between the frequency windows nd b is their bndwidth Figure 3.7(A). A signl resulting from the sum of signl from stinless steel (with n verge grin size of 75 um) nd flt surfce reflector trget Figure 3.7(B). The signl of Figure 3.6(A) squred Figure 3.7(C). Processed output for the Minimiztion Algorithm for 10 non-overlpping frequency windows Figure 4.1. The rectngulr noise spectrum in the exmple Figure 4.2. Genertion of expnsion coefficients, A. Filter opertion B. Correltion opertion Figure 4.3. Detection probbility versus signl-to-noise voltge rtio for vrious expnsion sizes n. The probbility of flse lrm is set to (tken from 36) Figure 4.4. Detection probbility versus signl-to-noise voltge rtio for optiml processing for vrious expnsion sizes n. The probbility of flse lrm is set to (tken from 36) Figure 4.5(A). Detection probbility versus signl-to-noise voltge rtio for optiml processing, the originl deconvolved signl nd the minimiztion lgorithm for co/l-1. o/l is the rtio between the stndrd devition of cell contining only clutter nd the vrince in the trget rnge cell Figure 4.5(B). The sme s 5 with o/l

9 vii Figure 4.5(C). The sme s 5 with do/1= Figure 4.5(D). The sme s 5 with o/i Pge Figure 4.6(A). Simultion of received signl from trget plus clutter Figure 4.6(B). Processed output for optiml processing of the signl of Figure 6. b-0.2 MHz nd n-10 windows Figure 4.7(A). Simultion of the echo from two trgets 1/2 wvelength prt Figure 4.7(B). Processed output for optiml processing of the signl in Figure 11(A). Note tht the trgets re resolved but tht there is bis in the distnce between them nd tht their mplitude is substntilly reduced Figure 4.7(C). Processed output for the minimiztion lgorithm of the signl in Figure 11(A). Note tht the signls re not resolved nd tht the mplitude of the processed dt is substntilly reduced Figure 4.8(A). SImultion of the echo from two trgets full wve length prt Figure 4.8(B). Processed output for optiml processing for the signl in Figure 12(A). Note tht the trgets re not resolvble but tht the mplitude is lrge Figure 4.8(C). Processed output for the minimiztion lgorithm for the signl in Figure 12(A). Note tht the trgets re not resolvble Figure 4.9(A). Trgets seprted by 3/2 wvelengths Figure 4.9(B). Processed output for the Optiml Processing. The trgets re resolvble nd there is bis in the distnce between them Figure 4.9(C). Processed output for the Minimiztion Algorithm. The signls re very noisy nd not resolvble Figure 4.10(A). Trgets seprted by 4 wvelengths Figure 4.10(B). Processed output for the Optiml Processing. The signls re fully resolvble nd the signl-to-noise rtio is high Figure 4.10(C). Processed output fnr the Minimiztion Alg-"thm. The output is noisy nd the signls re not resolvble

10 viii d Figure 4.11(A). Trgets seprted by 8 wvelength Figure 4.11(B). Processed output for the Optiml Processing. The signls re fully resolvble nd there is no bis in the distnce between the signls Figure 4.11(C). Processed output for the Minimiztion Algorithm. The signls re fully resolvble nd there is no bis in the distnce between the signls Figure 5.1(A). Processed output for the signl of Figure 4.6(A) for the Minimiztion Algorithm without phse reversl lgorithm usig 10 non-overlpping frequency windows Figure 5.1(B). Processed output for the signl of Figure 4.6(A) using the Minimiztion Algorithm with phse reversl lgorithm using 10 non-overlpping frequency windows Figure 5.2(A). Processed output for the signl of Figure 4.6(A) for the Optiml Processing without phse reversl using 10 non-overlpping frequency windows Figure 5.2(B). Processed output for the signl of Figure 4.6(A) for Optiml Processing with phse reversl lgorithm using 10 non-overlpping frequency windows Figure 5.3. A block digrm of the receiver s described in eq. (5.9) for two overlpping frequency windows Figure 5.4. Processed output for two signls seprted by 1/2 wvelength (see Fig. 4.7(A)) for Optiml Processing, with (B) nd without (A) phse reversl Figure 5.5. Processed output for two signls seprted by 1/2 wvelength (see Fig. 4.7(A)) for the Minimiztion Algorithm, with (B) nd without (A) vhse reversl Figure 5.6. Processed output for two signls seprted by full wvelength (see Fig. 4.8(A)) for Optiml Processing, with (B) nd without (A) phse reversl Figure 5.7. Processed output for two signls seprted by full wvelength (see Fig. 4.8(A)) for the Minimiztion Algorithm, with (B) nd without (A) phse reversl Figure 5.8. Processed output for two signls seprted by 3/2 wvelegths (see Fig. 4.9(A)) for Optiml Processing, with (B) nd without (A) phse reversl Figure 5.9 Processed output for two signls seprted by 3/2 wvelengths (see Fig. 4.9(A)) for the Minimiztion Algorithm, with (B) nd without (A) phse reversl Pge

11 ix Pge Figure Processed output for two signls seprted by 4 wvelengths (see Fig. 4.10(A)) for Optiml Processing, with (B) nd without (A) phse reversl Figure Processed output for two signls seprted by 4 wvelengths (see Fig. 4.10(A)) for the Minimiztion Algorithm, with (B) nd without (A) phse reversl Figure Processed output for two signls seprted by 8 wvelengths (see Fig. 4.11(A)) for Optiml Processing, with (B) nd without (A) phse reversl Figure Processed output for two signls seprted by 8 wvelengths (see Fig. 4.11(A)) for the Minimiztion Algorithm, with (B) nd without (A) phse reversl

12 x ABSTRACT Two topics deling with the reflection of ultrsound bursts from rndom medi re discussed in this work. In chpter 2 we develop generl formultion of the echo received from rndom sctterer ensemble illuminted by short electromgnetic or sonic signl. B We show theoreticlly tht grdient in either sctterer concentrtion or in the field function of the trnsmitter/receiver will return n echo which is prtilly sptilly coherent (i.e. speculr). li Furthermore we show tht from the degree of coherency, i.e. from the rtio of the rndom prt to the nonrndom prt of the reflected signl, the sctterer concentrtion nd scttering cross-section cn be clculted. We lso show experimentlly tht scttering concentrtion grdient cretes coherent reflection from whose degree of coherency the scttering concentrtion cn be estimted. In chpter 3 nd 4 we del with signl processing techniques for the reduction of clutter noise creted by rndom medi composed of high concentrtion of point sctterers. The problem is to enhnce trget embedded in rndom medium when the clutter noise vrince nd the trget echo loction nd mplitude re unknown. In chpter 3 we nlyze theoreticlly technique tht ws first proposed by Newhouse et l [3] the so clled Minimiztion lgorithm. In this technique we split the received signl spectrum into n frequency windows. The minimum of the squred signls t ech rnge dely is then chosen. The clculted SNRE (signl-to-noise-rtio enhncement) of this technique grees well with

13 xi experiments performed by N.M. Bilguly [4]. We clculte lso the Receiver Operting Chrcteristics (ROC) nd find out tht the improved SNRE of Minimiztion is negted by loss in detection properties. In chpter 4 we describe method for clutter reduction tht lso uses the split spectrum principle. In this technique we construct the optimum receiver for ech rnge dely from the n outputs of the frequency windows. We clculte the ROC for this technique nd find it to be superior to minimiztion for most cses. We show experimentlly the effectiveness of this lgorithm in clutter reduction. In chpter 5 we summrize the results of this reserch work nd show * the flexibility nd verstility of the techniques by introducing improvements nd pplictions to the described methods. d

14 CHAPTER 1 INTRODUCTION CLUTTER PROBLEMS IN IMAGING SYSTEMS One of the most importnt limittions of Ultrsonic Imging Systems j using pulse echo techniques is imposed by clutter noise t the system output. This clutter noise is usully cused by reltively smll, highly dense, rndomly positioned sctterers. In one type of clutter problem the trget to be detected cn be modelled s strong reflector. Even though the trget echo is significntly lrger thn ech of the individul smll rndom sctterers round it, the trget is sometimes difficult to detect due to the high density of the interfering sctterers. Such problems exist in lmost every field ssocited with imging. In Ultrsound Nondestructive Testing the lrge grin boundry echoes mkes it dif -ilt to detect reltively lrge flws [1,2,3,4]. In medicl imging the fine tissue microstructure echoes sometimes mkes it hrd to outline the orgn boundry [5,6], nd in Rdr Systems, rin drops, chff or se clutter [(7,8,9,10,11,12,13,14] re often strong enough to msk the trget. Time verging or correltion techniques, which reduce rndom therml noise significntly, re not suitble for reducing coherent noise resulting * from echoes due to the sttionry interfering sctterers. In nother type of clutter problem the trgets re composed of high density of point sctterers. The reflected signl is ccompnied * by speckle pttern (sptil brightness fluctutions) which is due to

15 2 the rndom interference pttern of the reflectors composing the trget. This type of problem pper often in coherent opticl imging [15] when the object (tht cn be modelled by high density of smll rndom reflectors) is imged by highly coherent illumintion. In Ultrsound Medicl Imging the echo from the tissue microstructure which cn be modelled in similr wy, is n importnt prt of the imge nd helps to diferentite nd chrcterize the different orgns (16,17,18,5,6,19-21, 22-25]. In the text we refer to the first problem in which we wish to suppress the clutter echo nd enhnce lrge trget echo s problem in "clutter reduction", nd we refer to the second problem in which we wish to reduce the speckle pttern of trgets composed of lrge sum of point reflectors s problem in "speckle reduction". Some conventionl techniques to reduce clutter nd speckle re described below. GENERAL LITERATURE REVIEW Scttering from Rndom Medi Ultrsonic signl processing techniques hve developed drmticlly in the lst decde minly due to the introduction of low cost powerful computers. But before reviewing the recent literture on modern signl processing techniques in Ultrsound we should py some ttention to the bsic understnding of the scttering from rndom medi s the modelling of rndom medi is the bsis on which most of the signl processing techniques bse their pproch. The theory covering the propgtion of wves in rndom medi is vst. In [26,27,28] one cn find the description of the bsic cousticl models for wve propgtion nd in [29,30] discussion on some of the

16 3 theories when pplied to biologicl tissues is given. The scttering from bodies with simple geometry cn be clculted by methods introduced in (26,27,31]. In the limit, for reflectors which re much smller thn the wve length the solutions re explicit. These solutions cn be extended to complex elements by ssuming combintion of severl individul centers. The scttering is described through the definition of scttering cross section. The totl cross section is defined s [26,32] =. P 1.1 I where I is the incident wve nd P is the scttered signl. Of more prcticl importnce is the definition of differentil scttering cross section which is relted to by - f 'da 1.2 4w where A is the solid ngle. In generl '-'(A). For the importnt cse of smll sphere (smller thn the wve length [261) K -K 3P-3p ' 1.[ w14 6 [-. + s cos 9]2 if X >> 9 X K 2ps+p where X= wvelength - rdius of the sctterer 8 ngle between the incident wve nd the direction of scttering. Ps = density of the sphere. p - density of the medium. K s - K - compressbility of the sphere. compressbility of the medium.

17 4 For prcticl cses isotropic scttering cn be ssumed only if either ps-p or if the rnge of ngles in eq. 3 is smll enough nd is such tht -'A o. The structure of biologicl tissue is very complex nd it exhibits nonhomogeneities in lmost ny scle. So the ssumption of discrete, wek scttering which is often used is clerly simplified ssumption s the scttering bodies rnge from much smller thn the wve length up to much lrger thn the rnge cell [32]. Theoreticl results bsed on these ssumptions should be constntly chllenged nd verified to be considered relible. The sttisticl properties of the bckscttered clutter echo ply mjor role in the optiml signl processing to be chosen for clutter or speckle reduction. It cn be shown tht if the sctterers re uniformly distributed nd the number of sctterers in the rnge cell is high enough, the bckscttered echo mplitude ssuming the plne or sphericl wve pproximtion, cn be considered Gussin with zero men [331. In [34] the verge power bckscttered from rndom medi with density profile is given for continuous wve propgtion. In this publiction Siegert nd Goldstein show tht medium which exhibits density profile gives rise to coherent term which trnsltes to n echo with non-zero men. In [35,36] Glotov clcultes the verge bckscttered power from slb filled with nonuniform size sctterers illuminted by burst. The echo gin contins coherent term which resembles speculr reflection. If the slb is much smller thn the wve length the reflection is mostly coherent nd the rndom component becomes insignificnt. In chpter 2 we will develop generl formultion for the bckscttered echo from rndom medi on which our signl processing pproches will be bsed.

18 5 Signl Processing Techniques for Clutter Reduction One of the most populr techniques used in rdr systems to overcome clutter noise is the use of frequency diversity (gility). In this technique the Rdr system possesses center frequency which is vried between pulses. This is similr to incresing the effective bndwidth of the trnsmitted signl nd thus, the clutter noise power which is inversely proportionl to the system bndwidth [7,8,14], is reduced. The other improvements obtined with the use of frequency gile Rdrs nmely, ntijmming cpbilities, rnge improvement nd trcking re not of ny importnce in biomedicl Ultrsound nd non-destructive testing. However, techniques used for processing the frequency diverse signls will be the mesure ginst which the new techniques (to be introduced in chpters 3 nd 4) will be compred. A very good review of the literture on frequency gility is given in [4]. To summrize, we only mention tht the two most populr processing schemes re composed of either direct summtion of the successive echoes before demodultion (which is equivlent to opertion with wide bndwidth or trnsmitting nd receiving with ll the frequency windows simultneously) or summing the different frequency windows fter demodultion (envelope detection). This is done when the trget echo phse is lost between pulses (due to fst fluctution of the trget position between pulses). After processing the frequency diverse signls threshold is set to enble decision whether trget exists in prespecified rnge cell. In the technique which is most often used nd clled "CELL AVERAGING" we evlute the clutter noise power [9,37,38,10,11,12,13] from some "test cells". Then ssuming tht the sme clutter noise power exists in the i ing mmifm m

19 rnge cell of interest CFAR (constnt flse lrm rte) detector cn be designed. This technique provides noise riding threshold nd only cells ssumed to contin trgets re presented. The detector design depends on the sttistics of the clutter echo. Usully the ssumption of Gussin distribution for the clutter noise mplitude is used which is true only if the number of scttering centers in the rnge cell is high enough. A good review of clutter properties (in Rdr pplictions) I is given in [39]. In 1981 "Split Spectrum Processing" ws introduced by Newhouse et l [3,4] for the improvement of flw visibility in the presence of grin noise. In this technique the received echo is split into severl frequency windows (possibly overlpping) nd the minimum of the squred Anique windowed signls t ech rnge dely is then chosen. In [3,4] the tech- is compred experimentlly with other conventionl techniques nd proved to hve n improved flw to grin noise enhncement. As the 'Optiml Processing' technique introduced in Chpter 4 in this report is prtilly bsed on elements in this lgorithm nd will be compred with it, we nlyze the minimiztion lgorithm theoreticlly in chpter 3. Signl Processing Techniques for Speckle Reduction in Ultrsonic Imging Becuse the Lser speckle phenomenon is so similr to Ultrsound speckle the Lser literture ws the min source for techniques for speckle reduction in Ultrsound. An excellent review of the opticl speckle phenomenon is given in [15]. It ws only towrds the middle of the lst decde tht techniques for Ultrsound speckle reduction were introduced nd substntil number of signl processing techniques ppered in the open literture especilly in the lst few yers [17,18,5, n

20 7 20,22-24]. One of the erliest ppers (40] uses sptil compound scnning to reduce Ultrsound speckle. In this technique the region of interest is illuminted from different directions nd the different gry levels re then compounded to crete n imge. This technique cn be successful only when Lhe interrogted medium cn be considered isotropic nd non refrctive nd the region of interest is ccessible from different directions. Orgns such s the brest re idel for such compound imging. In 1978 Burckhrdt rgued for the first time tht Ultrsound speckle should be treted in similr wy to opticl speckle. He modelled the tissue s collection of high density of point sctterers nd he evluted the signl to noise rtio s the men of the signl envelope to the envelope stndrd devition. From this definition the signl to noise rtio is He lter introduces new lgorithm "Compound scn with mximum mplitude writing". In this technique the mximum of the different echoes ssocited with certin point in spce is selected insted of the verge. He clims tht the difference between verging which is the optimum processing for this model nd "Mximiztion" is negligible. In 1919 Abott nd Thurstone [19] nlyzed the Ultrsound speckle phenomenon bsed gin on the concept of Lser speckle. The pper outlines the wys in which speckle cn be reduced i.e vritions in time, spce or frequency prmeters. The first of these, time, involves phse diffuser which is equivlent to generting rndom pttern in phse from burst to burst or imge to imge. This technique ws found to be useless in Ultrsound s it resulted in imge degrdtion due to phs ifsrwihi qiet ognrtn dmpteni deteriortion in focusing nd distortion of the trnsmitted wve front. The second of these, sptil vrition, involves either illuminting the

21 8 object from different directions or simply moving the trnsducer in dreltion to the object sufficiently to chnge the phse distribution cross the trnsducer perture. The third of these is equivlent to frequency gility concept tht ws discussed erlier in connection with trget detection nd will be discussed lter in this section in connection with speckle reduction. In 1983 Wgner et l published pir of ppers on speckle. In the first [16] they clculte the second order sttistics of Ultrsound speckle in B imges s function of trnsducer dimensions nd rnge. Their results seem to fit resonbly with experiment. In the second pper f[17] they use the results obtined in the first pper nd some known results from sttisticl decision theory to obtin decision rules for lesion detection. The results turn out to be sptil verging. Severl djcent cells re summed to crete new cell (or decision rule). Obviously resolution is scrificed in this procedure. In 1983 [5] Robinson nd Knight checked experimentlly the performnce of some sptil pulse echo compound scn techniques. The performnce of pek detected, minimum detected nd verged reconstruction of point trgets is compred. They conclude tht verging is cpble of incresed rnge resolution compred to pek detection nd tht the speckle pttern is smoother. The minimum detected signl hs n improved resolution of point trgets nd "shows promise in loction of shdowing structures". Frequency Compounding A discussion on frequency compounding in connection with Ultrsonic medicl imging is given in [22]. It is found tht the degree of speckle contrst reduction is inversely proportionl to the bndwidth of the trnsmitted coustic burst. Also, considerble increse in signl to...

22 9 noise rtio of the speckle pttern cn be chieved. In nother pper M [23] the received spectrum of the bckscttered signl is split into two overlpping frequency windows nd the respective chnnels re then summed fter envelope detection. This technique is reported to increse the signl to noise rtio of the speckle pttern with improved resolution. We will show lter in the this report tht the optimum receiver is somewht different from the one implemented in [23] nd should provide better results. MOTIVATION FOR RESEARCH The fct tht current techniques re not effective enough in the reduction of clutter nd speckle noise in Ultrsonic imging systems is the driving force for this project. Techniques such s sptil verging (or sptil compounding) re difficult to implement due to the reltively high refrction of the biologicl tissue nd mn-mde mterils, the high ccurcy required from the scnning system, nd the fct tht mny of the regions of interest re not ccessible from different directions. Frequency diversity (or frequency verging) is successful when it is esier to trnsmit nrrow frequency windows one t time insted of the entire vilble spectrum. In Ultrsound however it is possible to trnsmit extremely wide bndwidths. A Extending the frequency rnge by using severl elements with different center frequency rises more problems thn it solves. First the propgting medium is highly frequency dependent (i.e frequency ttenution dependence) nd secondly the scttering from the microstructuze rpidly increses with frequency. The bem pttern of the trnsducer is lso sensitive to frequency. Thus simple frequency compounding is not useful.

23 In this work we concentrte our effort on different type of 3Lg:i j processing. We concentrte on clutter nd speckle reductlon through post reception A scn processing only. By working on individul A scns we eliminte the mny prcticl problems ssocited with compound scnning nd mke the problem solely signl processing one. The techniques to be introduced here require tht the signls should be processed t the RF level. Techniques usully described in the literture do not del with id processing t the RF level, but s we see lter the hrdship of working t the RF level hs its rewrds. SYNOPSIS OF THE REMAINING CHAPTERS In this section we summrize the remining chpters in this report. In chpter 2 we develop generl formultion for the bckscttered echo from rndom medium tht cn be modelled s n ensemble of rndomly distributed point sctterers. To simplify the mthemtics we ssume isotropic scttering. The verge bckscttered power from the rndom ensemble is clculted s function of trnsducer prmeters nd the sptil density profile of the sctterers. It is shown tht the echo from rndom ensemble exhibiting shrp volume density grdient my resemble speculr reflection. This explins for exmple the "speculr" reflection from orgn boundries in medicl Ultrsound B scns. It is lso shown tht the rtio between the power of the "speculr" echo, i.e. the sptilly coherent portion of the echo mplitude to the echo vrince should enble us evlute the scttering density if there is either density grdient or field grdient. The results for the former cse re verified qulittively by experiment. After studying in chpter 2 the generl behvior of the bckscttered echo from n ensemble of point sctterers we investigte in chpter 3

24 11 theoreticlly n lgorithm for clutter reduction tht ws first suggested A In [3,4]. The technique is clled the "Minimiztion Algorithm" nd in fct provided the impetus for this reserch project. We clculte the improvement in signl to noise rtio of this lgorithm nd compre it with experimentl results obtined in [3,4]. The theoreticl results seem to fit well with experiment. Finlly we clculte the Receiver Operting Chrcteristic of this lgorithm. ;" In chpter 4 we pose the problem of clutter reduction under the ssumption tht the locl properties of the clutter echo re unknown, nmely the locl vrince. We describe technique to estimte the locl n properties of the signl without priori knowledge of whether trget exists in the region of interest. We use the results to develop so-clled optimum detection lgorithms for both dditive nd multiplictive noise 1 bsed on some known results in sttisticl decision theory. For the Optimum Detector lgorithm for dditive noise, we clculte the probbility of detection s function of signl to noise rtio (for the clutter reduction problem). Some experimentl results for this type of processing for the enhncement oi flw to grin echoes in metl re lso given. Resolution performnce nd rnge bis of the suggested technique * re evluted experimentlly. We lso compre the performnce of the "Minimiztion Algorithm" with the new technique on the bsis of ROC (Receiver Operting Chrcteristics), resolution, bis, nd mplitude S dynmic rnge of the processed dt. Finlly In chpter 5 we present conclusions, remrks nd some suggestions for future work.

25 12 CHAPTER 2 SCATTERING FROM RANDOM MEDIA I INTRODUCTION In this chpter we investigte the properties of the bckscttered echo from rndom medi. The results obtined here suggest new techniques for sctterer density estimtion nd lso form the bsis for the clutter reduction lgorithms to be discussed in chpter 3 nd 4. The rndom medi throughout this work re ssumed to be composed of high density (concentrtion) of point sctterers tht cn hve rndom size (strength) nd/or rndom position. For simplicity we ssume tht the verge distnce between the sctterers is much lrger thn their rdius thus llowing the ssumption tht their volume density is Poisson distributed (if their position is rndom). It is well known tht under the ssumption of plne wve pproximtion nd constnt scttering density the bckscttered echo from rndom medi cn be considered Gussin with zero men provided the sctterers concentrtion is high enough (centrl limit theorem). However, if the verge scttering concentrtion (or size) is not uniform s function of rnge dely, or the sonic field exhibits grdient the problem becomes more complex. Siegert nd Goldstein (34) clculted the bckscttered echo from continuously illuminted time vrying rndom medium, composed of identicl size sctterers under the ssumption of plne wve illumintion. They found out tht the bckscttered echo should hve non zero

26 13 men (coherent echo) which is proportionl to the grdient of the sctter- U ing density. Some yers lter Glotov (36) nlyzed the cse of short trnsmitted signl illuminting slb filled with discrete inhomogeneities for both the plne wve nd sphericl wve pproximtion nd gin showed tht the returned echo should hve non zero men. In this chpter we investigte the properties of the bckscttered echo from rndom medi for pulsed trnsmission by extending the existing theories to tke into ccount field fluctutions nd the scttering density profile. We strt by nlyzing the bckscttered echo from regulr lttice with equl spcing nd rndom scttering cross-section, lter we proceed to evlute the returned echo from rndom medi with uniform scttering density nd finlly we nlyze the bckscttered echo from rndom medium with non uniform scttering density nd rbitrry field structure. THE REGULAR LATTICE Let the echo detected by sonic receiver t time t fter trnsmission of pulse, due to single point sctterer t t be written s Es(t) - pig(ci,t) (2.1) where G(t,t) is defined s 'he impulse response of system composed of trnsmitter/receiver illuminting sctterer locted t ti nd p is proportionlity constnt tht depends on the sctterer scttering cross section. Suppose tht we illuminte regulr lttice for which the scttering cross-section of the prticles is rndom vrible (see Figure 1). The bckscttered echo from the lttice cn be written (ssuming the Born pproximtion)

27 Figure 2.1 The regulr lttice. (The scttecers within the lttice were niot drwn to retin clrity). 14

28 - 15 n E(t) - pig(fi,t) i-l (2.2) where n is the number of the sctterers in the rnge cell, defined s tht region in spce from which echoes re received t time fter trnsmission. The verge power of the bckscttered echo becomes n n P(t) - I Pi~pG(,t)G(Citt) (2.3) i=l M~ Where - mens ensemble verge (nd not time verge). In order to mesure this verge one would move the trnsducer with respect to the lttice nd verge the received power for given rnge dely t. Assuming pi to be sttisticlly independent of pj eq. (3) becomes Rewriting eq. (4) we obtin n p7 - G(i,t)i n ngit)g(tjjr) i-i i-l J- (2.4) i j n (t)- IG(ji,t) [G(ft 1,t)[G(t 1,t) + i-i + G(* 2,t) G(fn-t) - G(*,,t)] + + I (2.5) Replcing the summtions by integrls we obtin PET P2 f IG(t,t)[ 2 dv + 2 If G(tt)dv[ 2 Av v Av 2 v -2 (2.6) - f IG(t,t)I 2 dv AV- V 0 where Av is the volume of unit cell of the lttice. but 1 v. n = N (2.7) Iv v v

29 16 nd* eq. (6) becomes P(t) N - f IG(,t)1 2 dv + N 2 52 If G(t,t)12 v v i v - N- 2 f IG(t,t)1 2 dv (2.8) s we see in the next section the second term in eq. (8) very often vnishes. In this cse P- becomes P(t) - N2f IG(i,t)1 2 dv (2.9) nd the bckscttered power is directly proportionl to the vrince of the scttering cross-section of the lttice prticles,. It is obvious tht if the sctterers re uniform in size no bckscttered power is expected. RANDOM MEDIUM WITH UNIFORM SCATTERING CONCENTRATION When rndom ensemble is illuminted by trnsducer the received echo t time t fter trnsmission cn be written** n E(tln)- pig(f*it) i-i (2.10) where n is the number of the sctterers in the rnge cell. We ssume tht the rnge cell hs volume V, nd tht it contins n rndomly positioned sctterers t loctions rl,r2,r3,...,rn of strengths P102'',Pn" The instntneous power t time t is *For non cubic unit cell vvil]. be directly proportionl to n nd not equl to n s is ssumed ere for cubic unit cell. **E(tln) should be red: E t rnge dely t given tht there re exctly n sctterers in the rnge cell.

30 17 n n P(tjn) - ii 1 Pj Pj G(i~,t) G(j t) (2.11) This cn be seprted into two prts n n n P(tln) _ I IG(ei,t)12p 2 + I I G(fi't)G(fj't)PiOj i-1 i il JGl (2.12) i *j The verge power t time t fter trnsmission, for differing loctions of the sctterers in the rnge cell of volume V cn be written P(tln) - n pjig(i,t)i 2 + n(n-1) pi pj G(Lit) G(fjpt) (2.13) Note tht P(tln) is the verge over ll possible configurtions of the sctterer loction ti in the rnge cell. Assuming tht ti is uncorrelted with it for i*j, we cn rewrite eq. (2.13) s P(tjn) - n pz f IG(f,t)I 2 p(it)dv + n(n-1) 2 1 f G(t,t)p(t)dv1 2 V V (2.14) where p(t) is the probbility of finding one individul sctterer in the volume element t it, nd where the integrls re tken over the volume V of the rnge cell. We my write 1 p~t) - - (2.15) V Using these two reltions we cn write the ensemble verged power P(tln) P(tln) - n p 2 f IG(t,t)I 2 dv + n(n-1)-2 If G(f,t)dvl 2 (2.16) V V V 2 V To find the verge power P(t) we hve to evlute

31 18 U from eq. (16) nd (17) P(t) - P(tjn) p(n) (2.17) n-0 P(t) - iz f IG(I, t)12dv I np(n) + V V n-l + ;2 If G(t,t)dvi 2 7 n(n-l)p(n) (2.18) V 2 V n-l * where n is Poisson distributed with n s its verge. Replcing ) np(n) - i (2.19) n-0 * nd (s is known for the Poisson distribution), we obtin where n-o n(n-1) p(n) - if 2 (2.20) - Np(t) I G( t,t)1 2 dv + N 2-02 if G(t,t)dvI 2 (2.21) V V N - V Note gin tht P(t) is ensemble verge nd not time verge nd tht to *obtin this verge one would hve to move the trnsducer with respect to the medium (if the medium is sttionry) nd verge the received power for given t. We see tht the first term on the right hnd side of eq. * (21) is proportionl to N7 i.e. to the verge of the sum of the individul bckscttered powers. We will therefore refer to it s the incoherent power Pinc The second term is proportionl to (- 2, i.e. to B the squre of the sum of the bckscttered mplitudes. We will therefore describe it s the coherent bckscttered power, Pcoh" m mm m * i.mmm itn m m m

32 19 d We now show tht Pcoh equls the mgnitude squred of the verged echo, nd tht Pinc equls the vrince of this echo. From eq. (10), (15) nd (19) E(t) - T E(tT'n) p(n) - N- f G(tt)dv (2.22) n 0 V So tht Pcoh ' N 2.2 If G(t,t)dvl 2 (2.23) V The fct tht Pinc is the vrince of E(t) follows immeditely, since 2.i2 (2.24) Thus from eqs. (21) nd (24), 2 incg(t) 2 dv (2.25) V From eq. (21) one cn see tht the coherent term will be pprecible if either N or f G(t,t)dv re sufficiently lrge. Let us exmine the inte- V grl f G(t,t)dv for simple bem geometries. For exmple consider plne v wve trvelling long the z xis for which the field function cn be written G(f,t) - I(t - 2 Z)dz (2.26) c The coherent term of eq. (22) becomes ET) - Np f I(t - 1zJdz (2.27) c Chnging vribles t' - t-2z/c eq. (22) becomes Et7 - jn- f I(t')dt' (2.28) 2

33 20 The integrl nd with it the coherent term reduces to zero since the signl cnnot contin dc component. Likewise for point trnsmitter/ receiver E(t) - N5 f (I(t-2r/c)/r 2 )4irr 2 dr (2.29) 0 which gin reduces to zero. Thus we see tht both for the cse of plne wve pproximtion s well s for the cse of wves emitted from point trnsmitter/receiver the coherent term vnishes. However in work which is currently performed by Goyo Yu from Drexel University it is shown tht for lmost ny other geometry of trnsimitter/receiver the integrl f G(t,t)dv does not vnish. For exmple, v Mr. Yu clculted numericlly this integrl for point trnsmitter nd ring shped receiver nd showed tht the coherent integrl is different from zero in the ner field. However in the fr field the coherent integrl prcticlly vnishes. It is cler tht the integrl If G(t,t)dv1 2 is v usully much smller thn f IG(t,t)1 2 dv. However the integrl IfG(e,t)dvI 2 v v is multiplied by N 2 while the integrl f JG(1,t)j 2 dv is multiplied v only by N (in eq. 2.21) which should mke the rtio IE1 2 /02E mesurble. These results obtined by Mr. Yu give rise to the hope tht sctterer concentrtion nd scttering cross section estimtion would be possible using coherent reflection cused by field grdients. RANDOM MEDIUM WITH NONUNIFORM SCATTERING DENSITY If the sctterers exhibit certin scttering concentrtion profile N(f) the lgebr introduced erlier becomes somewht more involved. Redefining p(t) to be N(t)! the verge power t certin rnge dely t cn be shown to be, B mmm mm mm inmm lmmmm mmmu N i m m

34 21 p - pt) 7 f N(:t)IG(,t)I 2 dv +.2 If N(f) G(r,t)dvl 2 (2.30) V V with - f N(t)G(2',t)dv (2.31) V It cn be seen by inspection tht the integrl of eq. (31) will be nonzero provided N(it) hs grdient in the sme direction s tht of the function G(ft), i.e. in the direction of the sound bem. For the integrl to be lrge the grdient of N(t) should be shrp compred to the sound wvelength. The vlue of the integrl for step function in density N(f) is derived below. Eq. (31) shows tht grdient in scttering * density in the direction of propgtion of the sound bem will return sptilly coherent echo. The sme holds true for the echo from the boundry between two regions with different scttering densities. For simplicity we ssume the imginry boundry to be plnr. Replcing f by z we cn write, N~z)- N z < o Mct o N(z)-N 1 z<z - (2.32) - N 2 z ;0z o For plne wve G(z,t) - b(t-2z/c)cos[u<t-2z/c) + 8]; thus from eq. (31) the returned echo from the boundry becomes E(to) = c N 1 p 1 f b(t)cos[wt+e]dt + 2S N 2 2 b(t)cos[wt+e]dt P o 2 P2 (2.33) j nd P 2 re the verge reflection coefficients of the sctterers in region 1 nd 2 respectively. Note tht the volume integrl in eq. (30) becomes time integrl by chnge of vribles. If the rnge cell is situted such tht the boundry is t its center the vrince of E(to) cn be b lown o be,

35 22 ~2 02 _ 1[of + i] B c [NjP + N 2 P] f Ib(t)I 2 dt 4o (2.34) where ond 2 re the vrinces of the returned echo from region 1 nd region 2 respectively. For N 2 -O eqs. (33) nd (34) become E(to) - N, p 1 f b(t)cos[wt+o]dt (2.33) 20 2 = 1 2 = Npf- f Ib(t)1 2 dt 24 (2.34) Hence the rtio -_22 E fob(t)cos(wt+o)dt E (t o ) N, P (2.35) 1 f Ib(t)1 2 dt 0 Mesurement of the quntities on the left hnd side of this eqution, should llow us to estimte the quntity N32 since the integrls on the p7 right hnd side cn be computed. For uniform sctterers, 02/p-7 is unity, llowing the density N nd the scttering cross-section to be estimted independently. SNELL'S LAW FOR DENSITY GRADIENTS It is esy to show tht the scttered sound from density grdients in rndom sctterer ensemble obeys Snell's lw. Consider two plne wve trnsducers used for trnsmission nd reception respectively, oriented t + 0 nd - 0 degrees with repect to the z xis. Then the * nd components of V G(t,t) re zero where the function G(it,t) is s defined in eq. (1) but for seprte trnsmitter nd receiver. Although eq. (31) bove ws derive for the cse of single trnsducer used for both trnsmission nd reception, it is eqully vlid for

36 23 the trnsducer pir descilbed in the previous prgrph. For plne wve A trnsmission nd reception it cn be shown tht the integrl in eq. (31) is non zero provided tht the grdients of N(t) nd G(t,t) re prllel. Thus density grdient in rndom sctterer ensemble will sctter coherent incident bem in the direction given by Snell's lw, i.e. in the sme direction in which the bem would be reflected by mirror prllel to the plnr constnt density. This result is not unexpected nd is Iencountered often (without much excitement) in lmost every field of ultrsonic mesurement. * EXPERIMENTAL RESULTS According to eq. (33) we should be ble to observe coherent echo from the boundry between two different regions of differing scttering d density. One of the esiest wys to obtin shrp boundry for sctterers immersed in wter, is to use sponges. A sponge cn be cut to produce shrp boundry nd when immersed in wter the complex structure of the sponge fibers cn be considered s rndomly distributed sctterers. Furthermore, one cn clmp together two sponges with different scttering * properties nd thus compose shrp boundry between two different medi, or one cn use only one sponge, simulting two medi with N-O in region 1 nd N 2 in region 2. Figures 2(A)-2(D) show pictures of sponges used in * such experiments. One cn see tht sponge A hs the finest honeycomb structure. Sponge B hs lrger honeycomb structure, sponge C is even more dilute nd sponge D is the most dilute in comprison to sponges A,B * nd C. In Figure 3 we see sponges B nd C side by side. One cn see tht the boundry is shrp in comprison to wvelength (frequency of I

37 24 A B AnA Figure 2.2. A photogrph of the surfces of sponges A,B,C nd D. The * fine honeycomb structure is visible. (The width of ech picture corresponds to 6.5 mm.) Im~ m mmll n~m nnjmnmu ~ulm

38 25 j C B or I Figure 2.3. Sponges B nd C side by side. It is seen tht the honeycomb structure of sponge B is finer thn tht of sponge C. I.E-m. wm I--. ASW I -- I lmmmllmmmll h,%r, m. Im Figure 2.4. Four different echoes from sponge B. Note tht the coherent echo component from the sponge boundry nd the incoherent component from within the sponge.

39 * MHz). One cn lso see gin tht the honeycomb structure of sponge * B is finer thn tht of sponge C. Figure 4 shows echoes returned from sponge B. One cn see tht the echoes from the boundry re highly coherent nd exhibit negligible phse chnge in comprison to the more rndom echoes from inside the sponge. These echoes re incoherent in the sense tht for certin rnge dely the mplitude is rndom with zero men. Note tht the echoes in close vicinity to the first echo seem somewht weker thn those from deeper inside the sponge (t greter depths the echoes weken due to ttenution). The reson is probbly due to the fct tht the trnsducer surfce is not perfectly prllel to the sponge surfce nd thus it tkes more time for the incoherent term to fully develop. This slight misorienttion hs this prcticlly no effect on the coherent term mgnitude. However becuse of effect, the estimtion of the incoherent term should not be done in the immedite vicinity of the first echo. From eq. (35) we know tht the rtio between the squre of the verge boundry echo nd the verge power from inside the sponge, neglecting ttenution, is proportionl to the scttering density. Thus it should B be possible to estimte the sponge density from A-mode echoes of the types obtined. We will not ttempt here to estimte the sponge density quntittively, but will show qulittively tht the experimentl results behve ccording to the theory. Figures 5(P,(B),(C) nd (D) represent the echoes received from sponges A,B,C nd D respectively. Ech of these pictures is composed of four superimposed trces from four different loctions in the sponge, with identicl distnces between the trnsducer nd the sponge surfce. In Figure 5(A) which represents the received echo from sponge A one cn i

40 27 B A B C *mml*.p,.., D 1h1 Figure 2.5(A) Four trces (one on top of the other) of the reflected echo from sponge A. Note the lrge coherent component of the echo from the boundry. (B) Sponge B. Note tht the coherent component is not s lrge in comprison to the echo from within the sponge s in Figure 4(A) to (C) Sponge C. Note tht the coherent component is smller in comprison the echo from within the sponge in Figure 4(B) (D) Sponge D. The coherent component ws found to be negligible in repetitive experiments. 0

41 d 28 d see clerly tht the coherent echo is lrge in comprison to the echo returned from within the sponge. Figure 5(A) is similr to Figure 4 but with the trces superimposed. One cn see tht the coherent component of the echo from the boundry is not s lrge s tht of Figure 5(A) in comprison to the echo returned from within the sponge. Notice lso the gret difference in the degree of coherency for sponges B nd C. The honeycomb structures of these sponges re similr in shpe so tht we cn ssume tht 32/-p - is lso similr. The integrls in eq. (30) re lso similr for the two sponges since they involve only trnsducer nd medium prmeters which were the sme for ll experiments. Thus the rtio between the coherent term nd the incoherent term of sponge B nd C should be proportionl to the sctterer density. Evluting the I coherent term from the rtio of the verge of the first echo from the boundry to the power from inside- the sponge, (the incoherent term) we find the rtio to be bout 2.1 for sponge B nd bout 0.8 for sponge C which implies density rtio of bout 2.6. rhe ctul sctterer density tht cn roughly be estblished from the microgrphs is bout 2.2 which is in sufficiently close greement considering the fct tht only four smple points were used nd tht no specil rrngements were mde for producing extremely smooth surfces nd for keeping the sponge surfce prllel to the trnsducer surfce. Figure 5(D) corresponding to sponge D with the lrgest honeycomb structure hs prcticlly zero coherent effect. This is due to the fct tht sponge D hs much lower density thn the other sponges, too low to show coherent term from only 4 smple points. Figure 6 shows the echo from sponge D clmped to sponge B. Coherent echoes re clerly seen long the center verticl line of the picture. The ngle dependence of the reflected echo ws lso investigted,

42 dh 29 [A 'Eml ll II Figure 2.6. The received echo from 2 lyer sponge complex composed of sponges D nd B. The coherent component cn be seen on the centrl verticl line. Also note tht the power reflected from sponge D is less thn tht reflected from sponge B. Sulumi.l w Figure 2.7. Angle dependence of the coherent component (sponge B). Note tht while the coherent term is highly sensitive to ngle vritions, the echo from within the sponge is ngle insensitive. I