ELECTRO-OPTICAL METHOD AND SYSTEM FOR DETERMINING THE DIRECTION OF MOTION IN DOUBLE-EXPOSURE VELOCIMETRY BY SHIFTING AN OPTICAL IMAGE FIELD

Abstract: The present invention is an improvement on a system for double-pulsed particle velocimetry in which small scattering particles (20) are illuminated by two short pulses of laser light and then images are recorded photographically (18) to produce a record from which the particle velocity can be determined by measuring the displacement of the particle images. The known system involves a method and apparatus for resolving the ambiguity which exists with respect to the direction of displacement of particle images so recorded by multiple exposures on film or videographic media. The directional ambiguity is resolved by means of shifting the image field between exposures by an amount (XS) that is greater than any negative displacement occuring in the image field. In this way, all recorded displacement are positive, and negative displacements are obtained from the measurements. The present improvement incorporates an electro-optical device (34) that performs the desired image shifting function, without mechanical motion, in place of the shifting produced by rotating mirrors and the like.

Description: ELECTRO-OPTICAL METHOD AND SYSTEM FOR DETERMINI'IC THE DIRECTION OF MOTION IN D0U3 LE--EXP0SURE VELOCIMETRY BY SHI?'.. KG AN OPTICAL IMAGE FIELD The invention herein resulted from work which -is supported by TSI Inc. and the National Science Foundation ^ under NSF ATM 36-00509. BACKGROUND OF THE INVENTION -. .; ' - . - . The present invention is an improvement on that previously described in co-pe.nding application 023,773, " of which the present applicatio is a cαntinuation-in-part. The benefit of the filing date of that co-pending application with respect to comπon su&ject matter is herewith claimed. The present invention pertains -to. ' the measurement .of the velocity of -fluid flows, and, " more particularly, to _systerαs in which the fluid flow rate is inferred - from measurements made in the context of dou ble--pulsεd particle . image velocimetry, in which saall scattering particles are illuminated by two short pulses of laser light or. other light, and their images are recorded pho togra ' phicaΪLy. to produce a .record SUBSTITUTE SHEET from which the particle velocity can be determined by measuring the displacement of the particle images. For "specif ic " background material,, reference may be made to U.S. patent 4, 729 , 109,. assigned to the assignee" of the present invention; also to •".co-pending application serial number 023,773, also assigned ' to. the assignee of the present invention. As will be appreciated by the ' references cited above, particle image vεlocimetrv fPIV) is a ell-established technique in experi ental photo-mechanics .for quanti atively measuring velocity data at a given instajit of time over an extended flow field. A variety of other references which were- " cited- in co-pending "'.. application 02;3 , 773- may ' be con-suited for the details of -the " technique involved. Generally speaking, in the PIV technique the flow is seeded with small particles, "typically ten micrometers or less in size, and illuminated by a thin sheεt of pulsed laser light, typically coded with a .double pulse. Particles moving wi thin the l ight sheet are recorded SUBSTITUTE SHEET - photographically as pairs of particle images. The local fluid velocity is found on a grid of small "interrogation spots" on the photograph by sequentially measuring the displacement - jlx of ' 5 the images within each spot. Interrogation is accomplished by a variety of methods including the ' Young's fringe method, direct measurement of image-to- image displacement, and spatial correlation analysis. By successively analyzing 0 the photograph at many adjacent interrogation regions, local velocity may be inferred in a large number of points ι._ _ιiε flow field. Given identical conditions in viewing each of the t o exposures on a double-pulsed P I V 5 photograph, there exist no characteristics on the _.- " photograph to distinguish first images from -sεcond i agεs. As a rεsult, measurement .of the particle image separation cannot determine the polarity of the fluid velocity and the velocity "0 "vector is " ambiguous in sign: ± ^ Clearly, it is necessary to determine the order of the two exposures on . the photograph to eliminate directional ambiguity. SUBSTITUTE SHEET - In ' accordance with the invention described in co-pending application 023,773, a technique known as "image shifting" has been shown .to "be "' effective ' in resolving " directional " ambiguity. This method displaces the photographic image . field by an appropriate uniform, known distance bεtweεn the " first and second pulses. As a result, the second image of εach .particle image pair is shifted by a displacement ' such that the most negative fluid velocity still produces a positive displacement o.f the second particle image with respect to the first. Alter " the interrogation, the artificial shift X s * is subtracted mathematically to -obtain the actu-al fluid velocity. Several methods have been 'implemented- to produce the- mage shifting during the recording procedure, in particle iaa ' ge " vεlociaetry . Image shifting has been accomplished by placing a " rotating, π-irror- ,.i.h front of the photographic, lens, and by translating the ca ar ' a apparatus between exposures. . Other methods have- also been proposed, including moving tihe-film within the ca ' εra - and translating the camera lens with a SUBSTITUTE SHEET piezoelectric device. The drawback with each of the abovε-noted raεthods is thε mechanical motion involved in part of the recording apparatus between the first and second light ' pu.lses. Consequεntly, they are subject to limitations on speed due to the dynamics of moving components, and limitations on accuracy and consistency. Accordingly, it is a primary object of thε present invention to overco ε thε limitations on opεrations at high and low speeds in connection with image shifting in pulsed velociraetry systems, and to carry out the operations with a high degrεe of accuracy. Another obje ' ct is to ' permit image shifting in periods . of time lass than one microsecond. A-f ' urther' ob ect is to provide precise •repro-ducible shifts without the nee-d for moving parts to accomplish them. SUMMARY OF THE INVENTION The above and other objects are fulfilled in accordance ' with the present invention by ε primary fεatu ε involving an electro-optic image shifting arrangement • including a birefringεnt , SHEET sυr ~ uniaxial crystal plate; and a camera lεns intεrposed between said crystal platε ' ■ and ' thε image plane, the crystal plate being cut. with its "surface normal'.' aligned parallel, to t.h e 5 crystal's optic axis, such that a given light ray from any source ' in the object plane ' is refracted into two parallel light rays having mutually orthogonal statεs of linear polarization. Accordingly, for a. given scattering particle in 10 .the object plane, two images of thε particle are formed> at the film plane of the camera, separated by x s , which is thε amount of image -shifting introduced by the present invention. However, it will be understood that when the moving particle 15. or the image thereof is recorded by means of two illuminating pulses, four images are thereby formed " . . . ' ' •- " In accordance with a more specific featurε of the present invention, means are providεd for 20 controlling thε polarization of thε " light scattεrεd from thε seeding particles so that the first illuminating pulse from the source scatters light which is linearly polarizεd and parallεl to thε principal pl3ne of the birefringent crystal, iUBSTITUTE SHEET and the second pulse scatters light which is linearly- polarized _at 90 degrees, with respect to the light from the first pulse, whereby only two particle images will be -formed for a single . 5 moving particle ' . Other and further obj-ects, advantages and features of. th ' e^ present invention will bε understood by reference to- the - folio i ng specification in conjunction with the annexed JLO drawing , ' . wherein like parts have been given like, numbers . SUBSTITUTE SHEET 3RIEF DESCRIPTION OF DRAWING * . - . Fig. 1 -is a schematic diagram of the electro- optic image shifting system of thε - - present invention. F.ig. 2 i lrl u s t r.a t-εs ' the polarization of linεarly-polarizεd light at 90 dεgrεεs by a spherical particle. ' " "Figs. 3A and 3B ' illustrate the light scattering response of plastic particles in ' watgr (n/n o =1.20) for linearly-polarized illumination (? = 694.3nm), at 90 degreεs side-scatter, using a finite light gathering <-nne- Numerical calculations incorporate Mie scattεri ' ng thεory and assumε a lεns aperture of fl6. The .two horizontal bars .in each graph bound the approximate range of scattering response suitable for Kodak Technical Pan 2415 film. . . . F.igs. 4A, 4B, and 4 " C„illustrate imagε shift rεsponse using a calcitε crystal (n 0 = 1.65259, n e =l.43382), having an optic axis anglε ~- a = 53.53 . Opεn circles indicate observed measurements. Fig. 4A shows principal image shift vs. the tangent of the principal angular derivation from thε photographic axis; FigT ' 43 is SUBSTITUTE SHEET the same as Fig. 4A but reduced . scalε ; Fig. 4C shows transverse image shift vs. the tangent of the transverse angular, deviation from thε photographic axis. X so is the on-axis image- shift, and s^ is the image distance. . Figs. 5A and 5B illustrate PIV velocity vector ' maps of a. uniformly-displaced water flow field ' Slaving a small transient flow velocity, • using electr.o -optic image shifting. Fig. " 5 A shows ' stationary referencε framε. # Fig. 5B shows rεferencε framε moving at the uniform translation ' velocity. DESCRIPTION OF PREFERRED EM30DIMENT Refεrring now to the figures of the drawing and, in particular, Fig. 1, therε is illustrated in .this figure an embodimen "of the electro-optic image shifting system of the presεnt invention. As will bε sεε thεrεin, a bire ringent, uniaxial crystal plate 10 (for "example, calcite) is - positioned, in .front of a camera lens 12.. The plate is cut with its "surface normal" aligned -parallel to thε crystal's principal plane and ' at an obliq e angle υ a to the crystal's optic axis, SUBSTITUTE SHEET such that- a given light. ray from any source in the object plane 14 is rεfractεd into two parallεl light rays 16A and 16 B , commonly referred to as an b-ray and an -e-ray, having 5. utually orthogonal states of linear polajization. Consequently, thε s-eparation of the * two rays is nearly uniform for a wide range of incident angles and scaled to the desirεd imagε shift X s seen on the ' imagε plane 13 for the 10 chosen camera magnification. For^ a given scattering particle 20 in thε •.> n ect. plane 14 within the flow field, two ima es of that particlε are formed at thε film or imagε pla ε- IS of thε canεra, separated by X s . The 15 intensitiεs of thε two images are equal to the intensitiεs of thε two orthogonal compqnεnts of polarization, with respect to the crystal's principal, planε, of thε light incidεnt ' on thε plate 10. Accordingly, when a moving particle is • "20 re'cordεd vrith two illuminating pulsεs, four i agεs are for εd, arrangεd in ' a parallεlogram ha.ving two sides equal in length to the imagε displacement and two sides equal . SUBSTITUTE SHEE- If thε - polarization of the light scatterεd from thε seeding particles is controlled ' so that the first illuminating pulse scatters light which is linearly ' polarized and parallel to the 5 principal plane of the birefringent crystal plate 10, and thε second pulse gathers light which is linεarly polarized- at -90 degrees with respect to thε light from thε first pulse, thεn only two particle images will be formed for a single 10 particle, displaced by the vector sun of Ax and , x s . This is the desired result for any image shifting technique. In the system shown in Fig. 1 , the polarization of the scattered light is controlled 15 by switching the polarization • ■ of the laser beam • 30 at the ' exit of the ' cavity ' of double-pulsed" . laser 32. A Pockels cεll 34, well-known per sε, is usεd with the doublε-pulsε lasεr to switch the -linear polarization, bεtweεn pulses, from a ' 20 vertical state to a horizontal state (or vice - versa). The output of Pockels cell 34 is transmitted to sheet forming optics means 36, also well-known, thus producing thε light sheet 38. An alternate "s ste ' to that of Fig. 1 SUBSTITUTE SHEE " . incorporates thε output from . two orthogonally- polarizεd single-pulsed lasers, fired in sequencε, which are combined using a polarizing beam-splitting cube. 5 ' .In the system of Fig. l; the extinction by;' the uniaxial plate 10 of the shifted image of thε first εxposure and the- unshifted imagε of the " second εxposure depends upon creating linear, orthogonal states of polarization ovεr thε solid 10 angle ldεfined by the photographic aperturε. In gεneral, f or spherical particles , the whεrε A and 3 arε co plεx functions of J and all 15 other quantities are de iπεd --in Fig. 2. When . side- scattering occurs over -an infinitεsimal solid angle, perpendicular to thε direction of illumination .g . centered on the photographic axis z,. the pc-lariz-ation "of thε 20 scattered light .wave is linear. If the illuminating beam is polarized vertically. (En^), then the side-scattered light is also vertically . " polarized: If -the -illuminat :im; g SHEET wave is polarized horizontally, then the side- scattered wave is also polarized horizontally: _ * " - Ϋ> (*"._*) " " * n t h e i d e a l l i m i t o f inf initεsimal solid angle, the first and second exposures of a particle centered in the camera's " field of view would be polarized, respεctivεl , in thε X and Y dirεctions -of thε camera coordinatεs . (Fig . • 1) , as dεsirεd. • Practical applications of this approach require . orthogonal pola-rizatioή of the two scattered light waves v ea the photographic field of view is finite and the solid angle of the lεns is finite. Thε lattεr. εffεct has been evaluated by calculating the -scattering " characteristics of typical PIV seeding particles, using Miε scattering theory. ■- ' " " - ■ - .- • Figure 3 .shows the results of calculations of the scattering efficiency (defined as the . ratio of the- particle imagε intensity t.o thε illumination -i.n ensity) performed for a polystyrene particle in water, in which the particle diameter is varied up to 10 a and a lens aperturε of flδ ' is used. In ' Fig. 3A, " tvo curves are shown corresponding to the X and Y SUBSTITUTE SHEET -components of the scattered light, for a y - polarizεd light source. Thε polarization • component is over four orders of magnitude larger than the X component for the entire range of 5 particle diameters. In Fig. 33, the source is switched ' -to z-polarization , and the X and _ respo ' nses likewise switch. The X-component ' dominates by o'vεr four .orders of agnitudε. -. Calculations using a variεty of othεr particle 10 sizes and compositions (including hollow spheres and metallic-coated spherεs) show similar tendencies for the scattered light waves to retain linear, orthogonal polarization when the scattering occurs over finite solid angles normal 15 to the illuminating light. The effect of finite field- o ' f .view is - to include' scattεring from off-axis particles whose mean scattering anglεs arε not pεrpεndicular to thε light -shεεt -(ε.g. * τj J= 90° ). In gεnεral, thε 20. polarizations at the.se angles neεd not bε linear or orthogonal. However, experimental -examination of the ratio of the horizontally 'and vertically polarizεd waves indicatεs that the " extinction o - ratio is large over. " a i.20 f ield-of-view for 15 SUBSTITUTE SHEET micron polystyrene particles in water and 4 micron silver-coated glass spheres in water. The use of a finite field of view is thus not a limiting factor in thesε cases. The design of the uniaxial crystal platε 10 (Fig. 1) -involves appropriate selection of the angle betwεεn the- optic axis τj_ .-and thε normal to thε transmitting surfaces, " and the. "plate thickness T. " y a is chosen so that the image shift X s (X, Y) is nearly uniform across the photograph, and T selεctεd so that thε shift is scalεd -to the desired- constant value X 3 for the user-chosen camera magnification. The opti al value of. \j a has beεn de ermined computationally by modeling the propagation of light through -uniaxial calcite πatεrial using Huygens's vavefront ' construction in .three dimensions. " A ' value Y a = 53.58 degrees results in a shift magnitude X s along the principal plane of " the " cr stal " which is. very un'ifor . The calculations in Fig. A indicate -a maximum variation of the shift in the X-direction that is less than 0.15 per cent. -The computations indicate thε presence of a no n-n eg 1 i gi b 1 ε SUBSTITUTE. SHEET transvεrsε component Y S (X,Y), perpεndicular to thε .principal planε, which is shown in Fig. 4C. Thε imagε shift vεctor X s is thus ' somewhat non- uniform, but the non-uniformity is known a priori and thus may be correctεd computationally during thε interrogation procedurε_ EXPERIMENTAL RESULTS -. . . .; • . - An εlεctro-optic image shifting system using • the" Pockεls cell system of Fig. 1 has-been constructed. The rεsponse time of thε Pockεls cεll is approximatεly 10 ns, which is comparable to the pulse width of -the double pulsed lasεrs used for ' PIV, and therεforε c ' apablε of image shifting the fastest flo fields that are currently, contemplated. Currently -there- are three calcite plates- in use .having thicknesses of 2 mm, ' 6 -mm, and 10 mm,, which may be " mounted separately -or combined in front of the. camera -.lens' to • provide- -image shifts. magnitudes of 0.2 m<X s <1.8 mm. . Two " experiments were pεrfor εd to evaluate ' the image-shifting technique .. " In the first, the accuracy of image-shifted measurements was SUBSTITUTE SHEET evaluatεd across a PIY photograph. For this- εxpεri ent, single-pulse illumination was used to rεcord a stationary flow fiεld " illu inatεd by a circularly polarized beam. The Pockels cell was "not activated in this experiment. As a result, thε PIV photographic field contained two images of each particle, separatεd- by the local value of X s for -that- imagε pair. Ovεr three hundred particle image displacεaεnts. were measured across t h e . p h o to g r a p h . -A selection of. thesε measurements , collapsed along the X- and Y directions, are plotted ' in Figs. 4B and 4C. The measurements agree ell . with thε numerical predictions The RMS error of the measurements is approximately 0.8% full-scalε, most ' of which may be attributed to the -accuracy limitations of . the PIV interrogation sys em " used . to- -extract information from the photograph. -- In thε sεcond experiment, the entire image .shifting system was evaluated using PIV photos of. nearly-quiescent water contained in a test - section which was horizontally displaced with a uni -orm ..velocity U. A small transient -velocity • u t (x,y,z) was present in the " flow .during-the UBSTITUTE SH> ,_.-=. " uniform translation, whεre |u^ _ιa < 0.15 U. Thε calcite plate was oriented to provide a vertical image shift. The photographs were takεn over an extended field of view (£15 ) using, a finite 5 camera aperture (fδ). Each interrogation of a PIV photograph of the flow generally produced a highly detachable measurement of the particlε - image displacement, consisting of the vector sum .of the image • shift C S (X,Y) , the displacε εnt 10 M_\tU, and a .small component which is attributed to the transient displacement Mutu (M is thε mag-.ification ' of the camera). Thε vector ι_ap of the interrogatεd PIV photograph (Fig. 5A) shows a - highly resolved- velocity field U + _u ( x » v ) ' When 15 the translation velocity U is subtracted from the vector field, -the resulting map (F.ig. 53) clearly - _ reveals the transient structure., . SUMMARY AΪD CONCLUSIONS . . ■- . ' In summary, imagε shifting basεd on εlectro- 20 optic " hardware is an εffεctivε approach in PIV that offers several advantages ov-er mechanical shifting techniques; T o systems ' for implementing this approach, one incorporating a SUBSTITUTE SHEET Pockels cell to modulate the output from a single laser and the other incorporating the output from two orthogonally polarized lasers have been describεd.- -The use of a properly designed calcite element results in an image shift which is nearly uniform ovεr a widε light-gathεring conε. Thε εthod is accuratε, rεliablε and fast εnough to a c c ora ra ' o d a t . ε thε highεst - fluid velocities likely to bε studied with particle image velocimεtry, and it is equally applicable to laser specklε velocimetry. It is undεrstood that thε ef f εctivenεss of εithεr of the two systems described above depends upon retaining" light pol a"r ization af ter sidescattεr. Consεquεntly they- ay be limited to -certain ranges of particle types ,- particle .sizεs , "angular fields of view and camera apertures-. Further investigation is required to determinε these limitations. An alternative electro- .optical systε , which incorpor3tεs a wide-angle Pockels cell in front of the uniaxial platε for directly modulating the particle-scattered light, is anticipated. to expand the εffεctiveness of BSTITUTE SHEET electro-optic" image shifting, and is currently • being ' investigated. While there has been shown and describεd what is considered at present to bε thε prεfεrrεd. εmbodimεnt of thε prεsεnt invεntion, it -will be appreciated by those skilled in the art that "modifications of such- embodiment may be made. It is thereforε desired that the invεntion not bε limited to this embodiment, and it is intended to cover in the appendεd claims all such modifications as fall within thε true spirit and scope of the invention. ITUTE SHEET

Claims: CLAIMS .1. In a particle -image velocimetry system, in which images are created by accurately timed puls"es "of .light from -a " light source, and successive particle ' images, resulting from " seeding _ particles being displaced by the motion ' of a fluid, are .recorded, .such that the fluid- velocity is in ' f erred from. the. tiisplacεmεnt of the image field -between exposures,- the improvεmεnt which comprises: means for determining unambiguously the direction of displacement and hence the sign of the velocity vector, said means including means for shifting the succεssivε particle imagεs with " ,", r w eεfpe.ct " o the .. first image so that all image . displacements are positive ' even though physical displacements " of the seeding particles may be- negative,- said means for shifting bεin ' g " an ' electro-optic imagε shifting arrangement, including -a biref ri-ngent -, uniaxial .crystal plate; - and a camεra lεns . interposed betwεεn said platε and the image plane; SUBSTITUTE SHEET 2. The system as definεd in claim 1, in which said crystal platε is cut with- its surface normal aligned parallel to thε crystal's principal plane" and at an oblique angle "rj . to the crystal's optic axis, such that a given light ra * from . any source in t he optic planε is rεf ractεd into two parallel light rays haying mutually ' orthogonal state. s of..'linear polarization. . - In a system as dεfinεd in claim 1 in which thε light sourcε is a doublε-pulsεd -lasεr n ,s ' .-.^,'-j < tt • I ■ and furthεr comprising a Pockεls cεll7 shεεt- /. forming optics' and a light shεεt producεd by said sheet-forming optics. 4. In a system as defined .in claim __ , the improvement further comprising means for controlling thε polarization -of thε light scattered ' from the ' sεεding -particlεs so that -the first illuminating pulse scatters light which-is linearly polarized and parallel to the principal plane "o the birefringent crystal p.late, the second pulse ' scattεrs light which is linearly ' SUBSTITUTE SH polarized at 90 degreεs with rεspect to light from the first pulse, whereby only two particle ■images are formed ' for a single particlε, displacεd by the v ' εctor sum of x and x s , whεrε Ax is the displacement between successivε .images and ± and g is thε imagε shift for εach of thε imagεs. "" ' 5. In a system as dεfined in-claitn 4, in ' . which said means for controlling the polarization of the scattered light includes means for - switching the polarization of the laser, hea at the exit of the laser cavity. - 6. . In a system as definεd in claim 5, in " which said mεans for switching co p isεs _a_ -'- ' - "' Pockεls ' cell ' ' for switching the linear - . polarization, between pulses, from a vertical state, to a. horizontal state. SUBSTITUTE SHEET

Inventors: ADRIAN RONALD J, LANDRETH CHRISTOPHER C, ADRIAN, RONALD, J., LANDRETH, CHRISTOPHER, C.
Applicants: UNIV ILLINOIS, THE BOARD OF TRUSTEES OF THE UNIVERSITY OF ILLINOI
Application year: 1990
Main classification: G01P3
IPC codes: G01P5, G01P13