Lison, Portugl, -9 June, Extension of the compressed interferometric prticle sizing technique for three component velocity mesurements Disuke Sugimoto 1, Konstntinos Zrogoulidis, Ttsuy Kwguchi 3, Kzuki Mtsuur 4, Ynnis Hrdlups, Alex M.K.P. Tylor, Koichi Hishid 1 1: Dept. of System Design Engineering, Keio University, Yokohm, Jpn, sugimoto@mh.sd.keio.c.jp : Dept. of Mechnicl Engineering, Imperil College, London, UK, konstntinos.zrogoulidis@imperil.c.uk 3: Dept. of Mechnicl nd Control Engineering, Tokyo Institute of Technology, Tokyo, Jpn, kwt@mep.titech.c.jp 4: Jpnese Aerospce Explortion Agency, Tokyo, Jpn, mtsuur.kzuki@jx.jp Astrct The present contriution extends the presently plnr dvnced interferometric lser imging prticle sizing technique with compressed fringe ptterns to mesuring the third velocity component of prticles present in two phse flows. Two different methodologies re investigted to mesure the depth velocity; one employing just one cmer nd the other two cmer stereoscopic rrngement. Both employ opticl compression systems to increse prticle numer concentrtion per imge. The first method, one-cmer rrngement, clcultes the prticle depth position vi its fringe pttern length. The reltionship etween the depth position nd the fringe pttern length is constructed y trversing monodisperse droplet genertor inside the mesurement volume. The resolution long the depth direction ws found to e 14μm when one pixel chnge occurs in the fringe pttern length, which is low given the uncertinty of the fringe length estimtion. For the stereoscopic rrngement, the 3D position is determined y mtching the compressed fringe ptterns for ech prticle on oth views nd determining their depth position from the clirtion mpping informtion. To verify the ccurcy of the three component velocity, monodisperse genertor ws inclined reltive to the lser sheet plne. Regrding the size mesurement, the men droplet dimeter ws estimted with n error of.%. The results from the spry mesurement confirmed the pplicility of the proposed stereoscopic instrument. As conclusion, the stereoscopic rrngement proposed is cple instrument for ccurtely mesuring the sizes nd the three component velocity of prticles in two phse flows. 1. Introduction Mny processes in industril nd every dy life pplictions involve liquid prticles. Exmples include ut re not limited to fuel injection in comustion systems, spry inhlers in medicl pplictions nd ink jet printers. The etter understnding nd optimiztion of such processes is very importnt. A cse of specil interest is comusting sprys, where engine performnce nd emissions re directly ffected y the qulity of the spry injector tomistion. It is therefore cler tht the development of cple tools tht cn help in the design nd optimistion of such systems is necessity. To investigte liquid prticle systems, the size nd velocity distriutions of the individul prticles re required for detiled nlysis of the flow structure nd chrcteristics. Mny instruments hve een proposed for the mesurement of these prmeters. The most commonly used re point mesurement systems with the most representtive eing the Phse Doppler Anemometer (PDA). The PDA utilises the properties of the light scttered y the prticles. The prticle size nd velocity informtion is extrcted from the scttered light phse s prticles trverse the proe volume tht two intersecting ems form. The min disdvntge of the PDA is tht mny mesurements re required for nlysis of the flow dynmics in lrge mesurement volume due to its point mesurement nture. Due to this, flow visulistion is not s esy s with imging techniques tht re cple to instntly visulise reltively lrge re of the flow. Interferometric lser imging droplet sizing (ILIDS) is plnr mesurement technique tht overcomes this difficulty. ILIDS provides the instntneous sptil, size nd plnr velocity - 1 -
Lison, Portugl, -9 June, distriution of the prticles y nlysing the interference pttern creted y the reflected nd refrcted rys tht originte from the surfce of ech prticle (Glover et l. 1995). The size of the prticle is given y the ngulr frequency of its fringe pttern (Hesselcher et l. 1991) or lterntively, the numer of fringes in the pttern. In ddition, the two dimensionl velocity informtion is redily ville y estimting the individul prticle displcement etween consequent imges using trditionl Prticle Trcking Velocimetry (PTV) methodology. Trditionl ILIDS imge processing is hindered y fringe pttern overlpping in dense prticle res, mking the prticle identifiction process difficult tsk. To cter for the fringe overlpping prolem, Med et l. () introduced n opticl compression system tht reduces the circulr fringe ptterns produced y ILIDS to line fringe ptterns (Fig. 1). Appliction of this opticl compression system increses significntly the droplet numer density per imge nd therefore the instrument pplicility in dense prticle flows. Lser sheet α Droplet Cylindricl lens θ Collecting lens with msk CCD rry Fringe imge Conventionl ILIDS technique The originl receiving optics Opticl prtil compression technique Fig 1. Opticl rrngement of the dvnced interferometric imging technique As mentioned, ILIDS is cple of mesuring prticle size nd two dimensionl velocity informtion. Even though this cpility is cler dvntge over the PDA, there re prticle flows where three dimensionl motion is very importnt, such s strong swirl flows. Recently, instruments sed on the sme sizing mesurement principle to the one ILIDS hve een proposed, cple of mesuring prticle size nd three component velocity simultneously (Dmschke et l. 1, Zm et l. 4). These systems employ stereoscopic rrngements of one out of focus cmer for the sizing processing nd second in focus cmer for prticle trcking nd verifiction. This pproch hs two disdvntges. The first is tht the prticle vlidtion is chieved y estimting the right spot distnce on the surfce of the prticles nd such n estimtion crries n inherited uncertinty due to the lck of sufficient resolution in present typicl imging systems. The second is tht oth employ the trditionl uncompressed fringe ptterns, mking overlpping serious issue in dense prticle res. Due to the ove, the development of new mesurement instrument for mesuring the size nd three component velocity of prticles in dense flow is vile. In the present contriution two different methods to determine the size nd three dimensionl loction of prticles in regions with high numer density concentrtions re considered. The first method clcultes the depth position vi the prticle fringe pttern length, while the second y locting the prticle in two cmer views nd extrcting the depth velocity from the comined informtion like stereoscopic PIV. These methods re pplied for piezoelectric mono disperse genertor nd the stereoscopic rrngement pproch is in ddition pplied for typicl spry in swirling flow. The results re discussed nd evluted.. Mesurement Technique.1 Sizing nd plnr velocity mesurement y interferometric lser imging technique When light illumintes sphericl droplet, there is n ngulr region (for wter, ~8 to the - -
Lison, Portugl, -9 June, forwrdly propgting light) in which only reflected nd first order refrctive rys re emnted from the droplet surfce. Due to these two rys, in the focl imge plne two very right spots (glre points) re oserved (Vn de Hulst nd Wng 1991). Although the distnce etween the glre points is proportionl to the prticle size, evluting the size from this distnce is difficult due to the lck of the dequte resolution in conventionl imging equipment. On non focl plne, the two rys interfere with ech other nd n interferogrm cn e oserved. ILIDS mesures the dimeter of sphericl trnsprent prticle from the fringe undultion frequency or the numer of independent of the solute light intensity (Hesselcher et l. 1991, Roth et l. 1991).The reltionship etween the two is derived y the phse difference etween reflection nd first order refrction rys originting from the droplet. The reltion etween the prticle dimeter d nd the numer of fringes N is given y the eqution 1 1 λn θ θ θ d = + m m + m, (1) cos sin 1 cos α where λ is the lser light source wvelength, m is the reltive refrctive index of the liquid droplet, θ nd α re the scttering nd the collecting ngles respectively (Med et l., ). Due to their circulr shpe, fringe pttern recognition in the conventionl ILIDS technique is difficult or even impossile due to pttern overlpping in high prticle concentrtion regions. Fig. 1 illustrtes the opticl rrngement of the dvnced interferometric lser imging technique which ims t incresing the prticle numer density nd to simplify the imging processing procedure. It comprises of pir of cylindricl lenses plced etween the imging plne nd the ojective lens in order to project the horizontl out of focus imges on verticlly focused plne (Med et l.,, Kwguchi et l. ). The cylindricl lens cn e moved long the opticl xis of the receiving optics enling djustment of the horizontl defocusing degree. By using the squeezing opticl system, the degree of fringe pttern overlpping in the resulting imges hs een drsticlly reduced which in turn increses the pplicility of the instrument in rel world pplictions. In ddition to the instrument s sizing cpilities following common PTV prctice the two dimensionl velocity is mesured in consequent frmes using cross correltion. In conjunction to the cross correltion coefficient, the vlidity of the plnr displcement estimtion cn e vlidted y compring the prticle size of the prticle in the first frme to the size of the cndidte prticles inside the predefined interrogtion window. As lredy mentioned, evlution of the three component velocity is of importnce. To determine the three dimensionl droplet loction nd velocity, two methodologies cn e pplied. The first utilises one cmer, while the second utilises stereoscopic rrngement of two cmers.. Three dimensionl velocity mesurement using one cmer methodology The schemtic of the mesuring principle of this method is shown in Figure. The position of the droplet in the lser sheet cn e determined y the size of the fringe pttern in the resulting imge, since its size is dependnt on the distnce of the droplet from the imging lens nd the size of the receiving perture. The pprent simplicity of this pproch for position determintion cn still e hrd in the cse of typicl ILIDS system. It is common the re imged y ny typicl system to not eing prllel to the CCD rry s imging is required t scttering ngle θ, which is different thn 9. This results to imges tht hve longer fringe ptterns t one side of the imge nd shorter t the other. This cn e solved y pplying the Scheimpflug condition on the cmer (Prsd & Jensen 1995), illustrted in Fig. 3. The Scheimpflug condition requires the plnes of the lser sheet, the imging lens nd the imging plne to intersect t one point in spce. This llows for rottion of the field of - 3 -
Lison, Portugl, -9 June, view, mking the plne imged to e prllel to the centrl plne of the lser sheet, insted of prllel to the imging rry. This mens tht the droplets tht re physiclly on the sme plne prllel to the lser sheet plne will hve the sme fringe pttern length in the resulting ILIDS imge. This mkes the depth position determintion esier, since the only requirement is wy to correlte the length to the physicl depth position. Certinly, n lterntive pproch to pplying the Scheimpflug condition is performing fringe length interpoltion long the horizontl direction of the ILIDS imges, ut this pproch cn e hrder for depth determintion since the fringe pttern length in this cse is vrile not only in the depth direction ut lso in the horizontl. In the context of the present contriution, only the Scheimpflug rrngement is considered. Droplet (z = ) Droplet (z = ) Droplet (z = ) Compression optics CCD Arry Focus point x y z Opticl System L > L > L L Fig.. The length of the fringe pttern is defined y the distnce of the prticle from the lens L x y z Fig. 3. The Scheimpflug condition imposes sme length fringe ptterns for prticles on the sme z plne position L To clirte the one cmer Scheimpflug rrngement, n in house uilt monodisperse droplet genertor (Pergmlis, ) cple of producing constnt strem of eqully spced, one size droplets cn e trversed long the depth of the lser sheet. The length of the fringe ptterns cn then e mesured in different depth loctions long the lser sheet so tht mpping function for the fringe pttern length cn e implemented. This function ws decided to e second order polynomil dependent on the z position of the droplet genertor L = c +, () + c1z cz nd its c i coefficients re clculted y lest squres pproximtion..3 Three dimensionl velocity mesurement using two cmers methodology The second method utilises two cmer stereoscopic rrngement such s Steroscopic PIV (Prsd, ), illustrted in Figure. The 3D position is determined y mtching the imged prticles on oth views nd mesuring their depth position from trnsltion of the imge spce to physicl coordintes. Given the nture of the position determintion, the clirtion informtion gthered for such system is crucil fctor in the resulting mesurement precision. As with the previous method, pplying the Scheimpflug condition is helpful though not necessry. Imges from simple clirtion plte cn e used to mp the physicl spce to the cmer imge spce. To locte the nodes on such clirtion imges, the imges cn e cross correlted with circulr templte. The - 4 -
Lison, Portugl, -9 June, cross correltion peks provide the dot centre imge coordintes (i,j) nd since the physicl coordintes of the dots (x, y, z) re lso known, one cn mp the physicl coordintes to the imge coordintes imge (Willert & Ghri 199). In the current contriution, this mpping function ws chosen to e the following liner comintion of the dot prmeters x = y 1 1 3 3 4 4 5 5 7 7 8 8 1 i j z 9 i j. (3) 9 j z i z i j z By collecting s mny dot centre coordintes s possile, liner lest squres pproximtion is possile for estimting the twenty coefficients i nd i for ech cmer. Compred to the explicit model proposed y Willert & Ghri (199), this mpping model hs the dvntge tht the depth z loction is used implicitly. By using the ove model when the clirtion coefficients re known, the position informtion cn e extrcted nd vlidted y comining the informtion from oth cmers. The flow chrt of the imge processing nd the schemtic of the coordintes extrction re shown in Fig. 4 nd Fig. 5. The steps tken to determine the three dimensionl position re (1) Clcultion of the sizes nd plnr velocities for oth cmer frme pirs. () Since for every prticle p (i,j) re known, only z is required to determine x nd y. (3) To mtch the prticle from cmer 1, p 1, to the prticle from cmer, p, the dimeter devition must e lower tht predefined threshold d1 d d 1 d thresh (4) If step 3 holds, for the two prticles to e identicl, the quntity X ( p, p ) = x 1 ( p 1) x ( p ) hs to e equl to zero. From X ( p1, p ) =, z cnd is otined. (5) If for z=z cnd Y ( p p ) = y ( p ) y ( ) is the cndidte for which Y(p 1, p ) is closest to zero, p 1 1 then z=z cnd nd p 1 is vlidted. If not, proceed to the next prticle p in step (3). () If p 1 ws not vlidted, proceed to the next prticle from cmer 1 t step (3). - 5 -
Lison, Portugl, -9 June, Cmer 1 Cmer Determine the plnr position y Wvelet Trnsform Determine the plnr position y Wvelet Trnsform Droplet size clculted y ILIDS Droplet size clculted y ILIDS The plnr velocity clculted y PTV The plnr velocity clculted y PTV Determining the 3 dimensionl loction of droplet Droplet size nd 3 components velocity Fig. 4. Flow chrt of the extrction of the size nd three-component velocity process Cmer 1 Pir Repet for ll cmer 1 prticles By enforcing x 1 =x, z is extrcted For the found z it must e y 1 =y Size nd plnr velocity clcultion Cmer Pir Find the closest mtch y dimeter vlidtion in set correltion window If y 1 =y holds, z is correct so extrct position nd velocity informtion. Else, proceed to the next prticle cndidte or reject frme 1 prticle if no more cndidtes exist Fig. 5. Schemtic of the coordintes extrction process - -
Lison, Portugl, -9 June, 3. Mesurement system For the cse of the two cmer rrngement, the mesurement system schemtic is shown in Fig.. It consisted of two CCD cmers (Kodk Megplus ES4., 8it, 48 48), positioned on Scheimpflug mounts, ech ering n ojective lens (Nikon) with perture msk nd pir of cylindricl lenses. To get highly visile interference, the scttering ngle θ ws set to 73, where the intensity of the reflection nd refrction is equl. The collecting ngle α, which is equivlent to the ngulr inter fringe spcing multiplied y the fringe count, ws set to. The specific cmers provide field of view of pproximtely mm, which is twice the field of view of typicl ILIDS system. The light source ws dul pulsed Nd:YAG lser t wvelength of 53nm, nd its mximum output power is 1mJ/pulse. The thickness of the lser sheet ws set to 3mm. The sme system ws employed for the one cmer rrngement. For clirtion purposes, xmm clirtion plte ws mnufctured. Plte through dots were drilled on its lck surfce so tht the dot imged y ech cmer is the sme to the one imged y the other. The dots where eqully spced with ech other nd in ddition depth step ws introduced t oth surfces of the clirtion plte so tht two plnes cn e imged simultneously insted of one. The plte ws trversed y computer controlled mechnicl liner μm/step ccurte stge in three different depth positions of the lser sheet. By this procedure, the sme three plne pirs were imged y oth cmers long the lser sheet providing for consistent physicl coordintes spce mpping. Nd:YAG lser Ojective lens y x z Compression optics CCD cmer Sheimpflug condition 4. Results nd Discussion Fig.. Schemtic of the mesurement system 4.1 Verifiction of the effectiveness of Scheimpflug condition nd fringe length function To verify the effectiveness of the Scheimpflug condition nd the fringe pttern length function long the depth position, the in house monodisperse genertor ws trversed long the lser sheet. The monodisperse droplet genertor tomising wter t n injection pressure of.15mp, while the flow rte ws 4.1 1-8 m 3 /s wter. The resonnce frequency of the piezoelectric elements of the monodisperse genertor ws set to khz. Under this condition, the dimeter of the monodisperse is clculted to e pproximtely 159μm with n ccurcy of 97% (Pergmlis, ). The droplets from the monodisperse droplet genertor were imged t seven different positions long the z direction nd 5 positions long x direction. On ech loction, imges were cquired with constnt numer of droplets per one frme. The verge fringe pttern length long the x - 7 -
Lison, Portugl, -9 June, position is shown in Fig. 7 nd the verged fringe pttern length long the z position is shown in Fig. 8. Every point in Fig. 7 is the x verged fringe pttern length for the specific depth position. From Fig. 7, the pttern length uniformity due to the Scheimpflug condition is confirmed. From Fig. 8, it is oserved tht the fringe length is proportionl to the depth position, which rnges from 11 to 13 pixels within the 3mm lser sheet. Using this result, the function of the fringe pttern ws estimted y eqution () = 111.13 7.715z 111.13z. L This results to rther poor sptil resolution long the z xis with pproximtely displcement of 14μm for fringe pttern chnge of only one pixel. Displcement utomticlly trnsltes t velocity resolution of over 7m/s for typicl time difference of μs etween consecutive frmes. It is mde cler y this conclusion tht the one cmer cse hs lrge uncertinty in the position clcultion, especilly if the uncertinty in the pttern length determintion y the imge processing softwre is tken into ccount. Even so, the fringe pttern length long the depth direction is not useless informtion, s it cn e used s n extr lthough rough vlidtion criterion to the position determintion when the stereoscopic rrngement is used. Fringe length(pixels) 15 1 115 11 15 1 1-3 - -1 1 3 - -1.5-1 -.5.5 1 1.5 x(mm) Fig. 7. The vrition of the fringe pttern length long the x direction Fringe length(pixels) 15 1 115 11 15 1 z(mm) Fig. 8. The vrition of the fringe pttern length long the z direction 4. Verifiction the three components velocity y the monodisperse droplet genertor The mono disperse genertor ws lso used to verify three components velocity. The condition of the monodisperse is the sme to the forementioned experiment. For this experiment the monodisperse genertor ws inclined t 75 in respect to horizontl xis on z-y plne. As lredy mentioned, for the one cmer rrngement it is difficult to estimte the velocity due to the poor depth resolution. The verge z position ws clculted y the fringe pttern length function nd the result is shown in Figure 9. The inclintion ws estimted to e 7 thus the error is pproximtely 3.9%. In the stereoscopic rrngement, the instntneous velocity vector mp ws clculted from imges. The two dimensionl vector on the z y plne is presented in Fig. 1 while the three dimensionl vector is presented in Fig. 11. The depth velocity to xil velocity rtio ws 4.5. The inclintion in respect to the horizontl xis clculted y these rtios ws estimted to e 7 for the z y plne therefore the error is estimted t 1.5%. The droplet size ws lso mesured. The proility density function of droplet size is exhiited in Figure 1. Most droplets re mesured very closely to 15μm nd the men droplet dimeter is 13.μm so the error ws estimted t.%. Therefore the ccurcy of this method is cceptle for the mesurements of droplet size nd three components velocity. - 8 -
Lison, Portugl, -9 June, 4 y = -3.85x +.1588 R =.981 5(m/s) y(mm) 8 y(mm) 1 1 1 1 - -1.5-1 -.5.5 14 14 - z(mm) 1 1.5 Fig. 9. The verge droplet depth position s clculted from the function of their fringe pttern length 14 - z(mm) Fig. 1. The third component velocity of 75 inclined monodisperse droplet genertor of z y plne.. y(mm) 5(m/s) Proility.35.3.5..15.1 x(mm) 8 1-1.5 1.5 z(mm) 1. 14. Fig. 11. The three component velocity of 75 inclined monodisperse droplet genertor.5 1 1 14 1 18 droplet dimeter (μm) Fig. 1. Proility density distriution of the droplet dimeter for the monodisperse flow - 9 -
Lison, Portugl, -9 June, 4.3 Experiments in dense spry The stereoscopic method ws pplied on typicl spry flow creted y Delvn Type B solid cone nozzle with wter injection pressure of.8mp nd volumetric flow rte of 5.3 1-7 m 3 /s of wter. The mesurement loction is shown in Fig. 13. The verged three component velocity vectors for the spry droplets whose dimeter is lrger thn 4μm is presented in Fig. 14. The vector mp shows tht the droplets t ech loction move n lmost sme verge velocity vector, which is pproximtely 1(m/s). The proility density distriution of the droplet dimeter is shown in Fig. 15. The droplet size rnges from 5μm to 9μm. From these results, it is seen ovious tht the method with stereoscopic method cn e pplied in typicl sprys. x 85(mm) 5 ( x, y )=(, 5 ) y y Fig. 13. Snpshot of the mesured spry nd mesurement loction 1.5-1.5 z(mm) 5 54 58 y(mm) x(mm) 1 4 1(m/s) 4 Proility.1 1.88.44 4 8 1 Droplet dimeter (μm) Fig. 14. The verge three component velocity for droplets in the spry whose dimeter is more thn 4 μm, t x = mm nd y = 5mm Fig. 15. Droplet dimeter proility density distriution for the spry t loction x = mm nd y = 5mm - 1 -
Lison, Portugl, -9 June,. Conclusions The interferometric lser imging technique ws extended to mesure the three component velocity nd size of prticles in two phse flows. To chieve the third component mesurement of ech droplet, two different methods were proposed to determine the three dimensionl loctions of ech droplet; single cmer rrngement nd two cmer stereoscopic rrngement. The first method clcultes the prticle depth position from its fringe pttern length, while the second y locting the prticle in oth cmer views nd extrcting the depth velocity from the comined informtion. Both pproches were tested on piezoelectric monodisperse genertor inclined to the lser sheet plne. The stereoscopic rrngement ws lso pplied on typicl spry re. The min conclusions of the study re summrized elow. (1) To determine the three dimensionl loction y using only one cmer, the function of the fringe pttern length long the depth position is estimted. The resolution long z direction for the current system ws pproximtely 14μm/pixel of only one pixel chnge to the fringe pttern length. This pproch is not ccurte enough to e pplicle for mesuring the three component velocity of prticles, ut could e used in conjunction to the informtion from the clirtion plte s n extr vlidtion criterion for the stereoscopic rrngement. () The stereoscopic rrngement tht employs the Scheimpflug condition ws used to mesure 15 inclined monodisperse droplet genertor, to verify the droplet size nd three component velocity mesurement ccurcy. The error in the droplet sizing ws estimted to e.%. The inclintion of the monodisperse genertor ws estimted 7 y the depth to xil velocity rtio, thus the error ws 1.5%. These results indicte tht the mesurement system enles us to mesure the droplet size nd their three components velocity dequtely. (3) The method with stereoscopic rrngement ws pplied on typicl spry region. The distriution of the verge three components velocity vectors ws shown for prticles with dimeter greter thn 4 μm droplets. At ech loction the vectors re of the sme size in the re of (x, y) =(, 5), of pproximtely 1(m/s). For the droplet size mesurements, the droplet size rnged from 5μm to 9μm t (x, y) =(, 5). From these results, it is seen ovious tht the method with stereoscopic method cn e pplied for typicl spry. References Dmschke N, Noch H, Nonn TI, Semidetonv N, Trope A (1) Multi dimensionl prticle sizing techniques. Exp Fluids 39:33 35 Glover AR, Skippon SM, Boyle RD (1995) Interferometric lser imging for droplet sizing: A method for droplet size mesurement in sprse spry systems. Appl Opt 34:849 841 Hesselcher KH, Anders K, Frohn A (1991) Experimentl investigtion of Gussin em effects on the ccurcy of droplet sizing method. Appl Opt 3:493 493 Kwguchi T, Aksk Y, Med M () Size mesurements of droplets nd ules y dvnced interferometric lser imging technique. Mes Sci Technol 13:38 31-11 -
Lison, Portugl, -9 June, Med M, Kwguchi T, Hishid K () Novel interferometric mesurement of size nd velocity distriution of sphericl prticles in fluid flow. Mes Sci Technol 11:L13 L18 Med M, Aksk Y, Kwguchi T () Improvements of the interferometric technique for simultneous mesurement of droplet size nd velocity vector field nd its ppliction to trnsient spry. Exp Fluids 33:15 134 Pergmlis H () Droplet impingement onto quiescent nd moving liquid surfces. PhD Thesis, Imperil College London Prsd AK, Jensen K (1995) Scheimpflug stereocmer for prticle imge velocimetry in liquid flows. Appl Opt 34:79 799 Roth N, Anders K, Frohn A (1991) Refrctive index mesurement for the correction of prticle sizing methods. Appl Opt 3:49 495 Vn de Hulst HC, Wng RT (1991) Glre points. Appl Opt 3:4755 473 Willert CE, Ghri M (199) 3 dimensionl prticle imging with single cmer. Exp Fluids 1:353 8 Zm Y, Kwhshi M, Hirhr H (5) Simultneous mesurement method of size nd 3D velocity components of droplets in spry filed illuminted with thin lser light sheet. Mes Sci Technol 1:1977 198-1 -