MEASUREMENT OF OBJECT SPATIAL DISPLACEMENT BY ULTRASONIC SPECKLE CORRELATION METHOD

Transcription

1 MEAUREMEN OF OBJEC PAIA DIPACEMEN BY URAONIC PECKE CORREAION MEHOD (No.56 H. Zhu W. Zheng and Z Huang Det. of Mechancs Huazhong Unversty of cence and echnology Wuhan P. R. Chna Abstract: When an obect oves ultrasonc secles bac-scattered fro ts surface wll follow the obect to ove. Fro the Krchhoff dffracton theory and the correlaton rncles of rando sgnals the necessary condton for eeng the correlatvty between the secle felds before and after the obectve dslaceent was deduced. Based on ths condton the forulas for the relatonsh between the secle dslaceent and the obectve dslaceent were obtaned. Practcal easureent was erfored. Correlaton ethod was used to easure the nlane dslaceent and out-of-lane dslaceent of an obect. he dslaceent of the obectve surface were obtaned after the dslaceent of the secles were easured. hs ethod can be also used to easure the dslaceent of an nner obectve surface. A ountan-clbng search ethod was roosed whch enabled us to fnd the axu correlaton coeffcent n the correlaton oeraton qucly and effcently. he exerental results showed good agreeent wth the theoretcal redctons. Introducton: When a rough obectve surface s nsonfed by ultrasound ultrasonc secles are fored n the bac-scatterng sace []. Ultrasonc secles have any useful features e.g. ultrasonc secles can exst wthn a sold obect and they are not easly affected by bad envronent such as dust frost etc.. Esecally as the obect oves the ultrasonc secles wll follow the obect to ove. Accordng to ths feature the dslaceent of an obect can be fgured out by easurng the dslaceent of the secles n the sace. In order to acheve ths goal the forulas for the relatonsh between the secle dslaceent and the obect dslaceent were deduced. hen accordng to these forulas ractcal easureents were ade by usng correlaton ethod. In the exerent a ountan-clbng search ethod was eloyed to fnd the axu correlaton coeffcent. Results: In order to fnd the relatonsh between the dslaceent of secles bac-scattered n the sace and the dslaceent of an obectve surface the ordnate O XYZ n the sace and the ordnate O X Y Z on the obectve surface are establshed resectvely as shown n Fg.. Fg. et-u dagra of the ordnates on the obectve surface and n the sace Before the obectve dslaceent these two ordnates concde wth each other. he sound source E s located n the (Y-Z-lane wth = EOZ beng the ncdent angle. he ordnate O ξης s establshed n the observng sace where the ( ξ -lane s located n the focus η

2 lane of a focus robe R for recevng the secles. he focus length of robe R s F and the daeter of ts head face sφ. O s located n the (Y-Z-lane. O ξ s arallel to OX and OO and O ς are n the sae drecton. θ = O OZ s the observng angle and both the θ and are sall quantty. Accordng to the Krchhoff dffracton theory [] the colex altude of the secle at q n the observng sace s: ex( ( q = P( r ( r dxdy where = π λ λ s the ultrasonc wavelength r = x + y P( r the aerture functon of the area on the obectve surface nsonfed by the ncdent ultrasound s: r nsde of Σ P( r = 0 r outsde of Σ and A & (r s the sound colex altude on the obectve surface: cos D( r ex( ( r = λ where D( r s a crcular syetrc colex Gaussan rando varable whch s deendant on the scatterng features of the obectve surface. θ and are noted as n Fg. and θ θ. et the oston of a ont whch s fxed on the obectve surface n the sace ordnate O XYZ be r = ( x y0 where (... eans the transosed atrx. As the obectve surface has sall translatons u v w n the drectons of X Y Z and sall rotaton anglesα β γ about the axes of XYZ resectvely the oston of ths ont n the surface ordnate O X Y Z changes to be r = ( x 0. We have the followng relatonsh between r and r : r = [ M ] r [ M ][ ] cos β cosγ where [ M ] = snα sn β cosγ sn γ sn β cosγ + snα sn γ cosγ snα sn β sn γ sn β sn γ snα cosγ sn β snα cos β cos β and [ ] = ( u v w. After the obectve dslaceent the ultrasonc colex altude A & ( q at q n the observng sace ordnate O ξηζ s : ex[ ( ( + A & = ] cos cos ( ( + θ q Pr D r d d 5 λ cos β sn γ where r = + and θ and are noted as n Fg. and θ θ. hus the correlaton functon of the scatterng sound feld n the observng sace before and after the obectve dslaceent can be wrtten as: R[ ( q ( q ] = P( r P( r >< ( ( < D r D r > λ 6 ex{ [( + ( + ]} (cos dxdyd d where denotes the conuncton oeraton and < Λ > eans the asseble average. If the obect has a strongly rough surface we have: < D( r D r >= Cδ[ r ([ M ] r [ M ][ ]] 7 (

3 where C s a ostve real constant andδ(. s a two densonal Drac functon. Eq.(7 eans: C r = r = [ M ] r [ M ][ ] < D( r D ( r >= 0 r r = [ M ] r [ M ][ ] ubsttutng Eq.(7 nto Eq.(6 we have:. 8 C R[ ( q ( q ] = ( ([ ] [ ][ ] < P r P M r M > λ ex{ [( + ( + ]} (cos dxdy. 9 When the ntegral functon n Eq.(9 s a real one.e. ( + ( + = 0 0 R [ A ( q ( q ] the two secle felds roduced resectvely by the surface before and after ts oton. Usng the ethod roosed by Wu [] we fnd the rules of the ultrasonc secle oveent n the sace whch are slar to that of the laser secle oveent to be: U = (cos β + (sn snθ γ + u( + cos cos sn cos V = ( + α + v(cosθ + + w( snθ cosθ cosθ cosθ W = v(snθ sn + w(cosθ + cos where U V W are the translatons of the secles n the ξ η ς drectons resectvely and and are noted as n Fg.. Dscusson: It ust be onted out that the translatons u v w and the rotaton anglesα β γ of the obect can not be drectly fgured out fro the dslaceent U V W of the secles n the bac-scatterng sace accordng to Eq.(. However we can see that f θ and are set to be zero Eq.( s slfed to be U = u V = v and W = w. hus the dslaceent of the obectve surface can be drectly fgured out accordng to the dslaceent of the secles on the obectve surface. o deterne the secle dslaceent the dgtal correlaton ethod [] was used. uose that before the obectve dslaceent the altude dstrbuton of the secles n a sall sub-feld n the sace ordnate O XYZ s f ( x y z. After the obectve dslaceent the altude dstrbuton of the secles n the sae sub-feld n the sace ordnate s f x y z whch can be exressed as g(x z n the surface ordnate O X Y Z. he ( dslaceent of all the onts n ths sall sub-feld can be treated to be unfor. he correlaton coeffcent of f x y z and g z s defned as: where ( ( [ f ( x y z f ] [ g( x y z g] C( uvw α β γ = = = = y z f ] [ g( z g] [ f ( x f = = = = = = f( x y z = C( uvw α β γ = 0 = = = = = = g = g( z and f ( x y z and g( z beng correlated f ( x y z and g( z beng not correlated.(

4 If the obect has only an n-lane dslaceent of translatons u and v n the X and Y drectons and a rotaton angleγ about the Z axs Eq.( becoes to be [ f ( x ][ ( y f g x y g] = = C ( uv γ = ( = = [ f ( x y f ] = = [ g( g] where = ( x ucosγ + ( y vsnγ. (5 = ( x usnγ + ( y vcosγ In order to reduce the search te for fndng the axu correlaton coeffcent and rase the easureent accuracy a ountan-clbng search ethod s roosed. he dea s as follows. C(u vγ s a trnary functon wth a ea value. If u and v or v and γ orγand u rean to be constant C (γ or C(u or C(v becoes to be an one densonal Gaussan functon. Moreover f f (x and g x are correlated C (γ or C(u or C(v s at the ea ont of y ( the curve of the one densonal Gaussan functon resectvely. By usng ths search ethod exerent was erfored to easure the n-lane dslaceent of the secles on an obectve surface. he easureent syste s shown n Fg.. Probe Rφ 0 f.5mhz F0was erendcularly laced and focused on the ont O on the obectve surface n water. R was connected to a three densonal translaton stage whch was drven by the steng otors controlled by a PC. hus R could ove n X Y and Z drectons sultaneously wth a ste length of 0. whch equaled to a half of the average lateral sze of the secles [5]. R scanned n a sall square area n the (O-XY-lane wth ont O beng ts center and R receved the sgnals one by one. he sgnals were then alfed dgtzed rocessed and nut to a PC. A total of secle sgnals were easured and they conssted of a secle altude dstrbuton functon f ( ( = after a lnear nterolaton x y was oerated. After the obect had sall translatons u v n XY drectons and a rotaton angleγ Fg. Measureent syste by Z axs the easureents were reeated n the sae way n the sae area and functon g x ( = was obtaned. hen the correlaton calculatons were ( o oerated as follows. Frstly u and v were reaned to be zero but γ was changed fro to o wth an ncreent of 0. o. After the correlaton calculaton based on Eq.( was done a ea value of C ( γ and the corresondent angle γ were obtaned. Next γ was reaned to be γ and u was reaned to be zero but v was changed fro. to. wth an ncreent of 0.. v could be obtaned accordng to the ea value C(v after the correlaton oeraton. Fnally γ and v were reaned to beγ and v resectvely but v was changed fro. to

5 . wth an ncreent of 0... u was obtaned accordng to the ea value C (u after the correlaton oeraton. As a result u and were the dslaceent of the secle on the easurng ont O whch equaled to the n-lane dslaceent of the ont O on the obectve surface to be exaned. he out of lane dslaceent of an obect can also be easured by usng ths ethod. In ths case R whch was focused on the ont O at frst scanned n the Z drecton. Before and after the out of lane dslaceent of the obect the secle altude dstrbuton functon f ( z ( = and g z ( = were obtaned. After the correlaton oeraton could be ( obtaned accordng to the ea value C( w. w was the out-of-lane dslaceent of the ont O. v In the easureents the errors between the easurng dslaceent and the calbratng dslaceent were 8.7% 6.% and 6.9% for u v and w resectvely. Conclusons: he relatonsh between the dslaceent of an obectve surface and the dslaceent of the secles bac-scattered fro the surface was deduced based on the Krchhoff dffracton theory and the correlaton rncles of rando sgnals. When a robe whch wored n a self transttng and recevng ode was erendcularly laced and focused on the obectve surface the dslaceent of the secle easured by the robe was drectly equal to the dslaceent of the easurng ont on the obectve surface. Moreover the dslaceents of the secles can be easured by usng the correlaton ethod. o verfy the theoretcal results a secal exerental set-u was bult. In the easureent the ountan-clbng search ethod whch was eloyed n the correlaton oeraton enable us to fnd the correlaton coeffcent ea value qucly and effcently. he exerental results rove that the theoretcal results are correct. nce the ultrasonc secles can exst wthn a sold obect the ethod roosed n ths aer can be also used to easure the dslaceent of the nsde surface of an obect. References:. Abbott J G hurstone F. Acoustc secle: theory and exerent analyss. Ultrason. Iag. 979; :0-. Goodan J W. 985 tatstcal Otcs. (New Yor: John Wley and ons. Wu X P He P and Z C. Moveent of the secles n the sace. Acta. Phys. n. 980; 9-50 ( n Chnese. Peters W H. Alcatons of dgtal correlaton ethods to dgtal body echancs. Ot. Eng. 98; : Zhu H M and Q H Qn. tatstcs of ultrasonc secles reflected fro a rough surface. Archve of Aled Mechancs 00; 7:89-98 w