An imaging white light velocimeter consisting of 2 image superimposing Michelson interferometers in series with the target interposed is demonstrated. Interferometrically measured 2-D velocity maps can be made of moving surfaces using unlimited bandwith incoherent and extended source-area lamps. Short pulse and broadband chirped pulse lasers can be used to provide temporal resolution not previouslypossible with monochromatic illumination. A 20 m/x per fringe imaging velocimeter is demonstrated using an ordinary camera flash for illumination

Erskine, D. J.

Holmes, N. C.

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Optical Society of America Annual MeetingRochester, NYOctober 20-25, 1996 LawrenceLivermoreNationalLaboratoryUCRL-JC-125275An Imaging White Light VelocimeterD. ErskineN.C. HolmesOctober 1996This is a preprint of a paper intended for publication in a journal or proceedings.  Since changes may be made before publication, this preprint is made available with the understanding that it will not be cited or reproduced without the permission of the author.PREPRINTThis paper was prepared for submittal to theDISCLAIMERThis document was prepared as an account of work sponsored by an agency ofthe United States Government.  Neither the United States Government nor theUniversity of California nor any of their employees, makes any warranty, expressor implied, or assumes any legal liability or responsibility for the accuracy,completeness, or usefulness of any information, apparatus, product, or processdisclosed, or represents that its use would not infringe privately owned rights.Reference herein to any specific commercial product, process, or service by tradename, trademark, manufacturer, or otherwise, does not necessarily constitute orimply its endorsement, recommendation, or favoring by the United StatesGovernment or the University of California.  The views and opinions of authorsexpressed herein do not necessarily state or reflect those of the United StatesGovernment or the University of California, and shall not be used for advertisingor product endorsement purposes.1An Imaging White Light VelocimeterDavid J. Erskine and Neil C. HolmesLawrence Livermore National Laboratory, PO Box 808, Livermore CA 94550An imaging white light velocimeter consisting of two image superimposing Michelson interferometers inseries with the target interposed is demonstrated.  Interferometrically measured 2-dimensional velocitymaps can be made of moving surfaces using unlimited bandwidth incoherent and extended source-arealamps.  Short pulse and broadband chirped pulse lasers can be used to provide temporal resolution notpreviously possible with monochromatic illumination.  A ~20 m/s per fringe imaging velocimeter isdemonstrated using an ordinary camera flash for illumination.The interferometric measurement of velocitiesthrough the Doppler shift of reflected waves is animportant and widespread diagnostic tool.  Until recently,these velocimeters were restricted to the use ofmonochromatic illumination so that the Doppler shift waslarger or of the same order as the illumination bandwidth.Recently, we presented1 a method we call white lightvelocimetry that allows the use of an arbitrary source,including unlimited bandwidth incoherent illumination,and non-collimated beams (lamps having extendedemitting areas).  Short pulse and chirped pulse lasers canbe used for the first time to perform time-resolvedvelocity interferometry.Fig. 1.  Grayscale representation of multi-color fringesproduced by the white light velocimeter prior and during ashot.  The fringes were recorded on Kodak Royal 1000color film.  The illumination source was small cameraflash of 20 µs duration.  The target was a stationary pieceof paper (left side with dot) overlapping non-uniformlymoving graph paper behind it (right side with blue gridlines).  This demonstrates the imaging capability, the useof non-collimated white light, and the recording of a non-uniformly moving target.  a) The target during the shot; b)The target prior to the shot when both surfaces arestationary.  The fringes on the graphpaper side haveshifted vertically due to velocity.Fig. 2.  The red, green and blue components of the colorphotograph discussed in Fig. 1, for the shot.  The fringecomb spacing is proportional to average wavelength ofsensitivity for the given film emulsion component.  Thefringe shift at position 1 is approximately 1/2 and atposition 2 approximately unity.  Analysis shows thevelocity increasing from 3 m/s to 20 m/s from left to rightside of the image.  Uncompensated interferometerdispersion causes the center of the fringe pattern to differfor different colors.  The fringe contrast is poorer for bluebecause the spherical mirror coating is not ideallyreflective, causing the interferometer arms to haveunequal intensities for blue.2Fig. 3.  Target configuration.  Target was a ~25 mmsquare aluminum foil propelled by a spark behind itscenter toward a stationary bar.  A white piece of graphpaper with 1/4 inch (6.4 mm) blue grid was glued to foilfront.  White paper was glued to front of the bar and asmall dot indicated the approximate axis of spark.  Theviewing interferometer saw both the stationary andmoving surfaces in the image.  The moving surface wasclamped more strongly at the top edge, resulting in non-uniform motion.The use of broadband illumination allowsunambiguous determination of the zeroth fringe, so thatthe fringe phase can be tracked through discontinuousvelocity histories, such as found in the measurement ofshock waves.  It produces optimal resolution of debrishaving different velocities but overlapped in view of thedetector, such as debris from a disintegrating target orground clutter in radar.  For targets which can have anunanticipated or evolving albedo spectrum, broadbandillumination increases the likelihood of a reflected signalof significant intensity.  Femtosecond pulses can be usedto provide time resolution.  Or, the use of chirpedillumination with a diffraction grating on output creates anall-optical streak camera capable of measuring motionover a line image with picosecond resolution2.  Finally,the white light velocimeter allows the use of incoherentsources which are attractive for their convenience,compactness, cost or large total energy for illuminating awide area.Figure 1 and Fig. 2 are the grayscale and colorcomponent representations of a color photographrecording the multicolor fringes produced by the whitelight velocimeter prior and during a shot.  Figure 3 showsthe target consisting of stationary and moving sheets ofwhite paper.  Since they are recorded in the same field ofview,  as a whole this is a discontinuous non-uniformlymoving target.  In addition, the moving portion has avelocity which varies continuously, because one edge ofthe surface was more strongly clamped than the oppositeedge.   Analysis of red, green, and blue fringe shiftsindicates the velocity grows from 3 m/s to 20 m/s fromthe left to right of Fig. 2.  The illumination source was asmall camera flash.  Conventional velocimetry is withlaser illumination and is non-imaging, measuring velocityat a single point, or at most along a line.  This experimentis notable because it demonstrates the imaging capability,the use of wideband incoherent and non-collimated sourceof light, and the recording of a target whose velocitychanges across its surface.Figure 4 is a line diagram depicting the whitelight velocimeter (WLV) method.  Two nearly delay-matched image superimposing interferometers are used inseries with the target interposed.  The interferometers arelabeled "source" and "viewing", and have delays τ1 andτ2, respectively.  The superimposing condition requiresthat for a given interferometer, all images created by theinterferometer superimpose longitudinally, transverselyand in magnification, even though there is a temporaldelay between the rays.  This is produces aninterferometer delay which is independent of ray angle,for each image pixel.  The condition of imagesuperposition distinguishes our device from other two-interferometer devices3 and allows the use of non-collimated broadband sources and the imaging ability.The two interferometers can either be distinct, asin this demonstration, or can be realized by the sameoptics if the illumination retro-reflects from the target, asdemonstrated in Ref. 1.  The latter configuration is thesimplest because the delays τ1 and τ2 are automaticallymatched.  However, separate interferometers may bedesired to eliminate glare from shared optics so that weakreflectors can be observed, and so that one interferometercan be aligned differently than the other to form a finefringe comb across the target image.If the delays τ1 and τ2 approximately matchwithin the coherence length of the source, then partialfringes are formed whose phase depends on (τ1-τ2).  Letτ ≡ τ1 ≈ τ2 be the gross delay value.  The velocity perfringe sensitivity η is given approximately byη=<λ>/(2τ) (1)where <λ> is the average wavelength of the light beingdetected.  Equation (1) is used to choose the general sizefor τ , which can range from 1 mm to 10 meters forapplications ranging from plasma physics to windtunneldiagnostics.White lightsourceDelay1TargetDelay2IntensitydetectionImage superimposing interferometersSource intrf. Viewing intrf.Fig. 4.   Line diagram of a white light velocimeter.  Theparallelograms represent generic image superimposinginterferometers.  If interferometer delays τ1 and τ2 matchwithin a coherence length of the source, partial fringes areproduced at the output which vary with (τ1-τ2).  Targetvelocity scales the apparent value of τ1 due to the Dopplereffect, changing the fringe phase.The production of fringes can be explained eitherin the time domain, as in Ref. 1, or in the frequencydomain, as is done here.  Consider each interferometer tobe a comb filter with sinusoidal pass bands periodically3spaced 1/τ apart, in frequency space.  The target velocitythrough the Doppler effect causes the sourceinterferometer comb spectrum to scale by a factor(1+2v/c), where v is the target velocity for normalincidence and c is the speed of light.  As the velocitychanges, the overlap between the two slightly differentcomb filters produces fluctuations in the intensity passingthrough both interferometers, integrated over the range ofwavelengths detected.  This is analogous to moiré fringesfrom two overlaid meshes having slightly differentpitches.For Michelson superimposing interferometers,the time averaged output intensity <I> from the viewinginterferometer in the region of fringes variesapproximately sinusoidally above a constant backgroundas∆ I ∝ cos 2πλc τ1 − τ2( ) − 2πλ cτ1( )2vc + φ0 (2)where ∆<I> is the fluctuating part of the time averagedintensity, and φ0 is some phase constant.  The averagewavelength is often determined by the detector.  Forexample, in our case by the sensitivity spectra of the red-,green- or blue- emulsions in color film.A single channel wideband detector could beused to record intensity.  However, it is preferable to use amulti-channel detecting system where channels areorganized either by wavelength or delay difference (τ1-τ2).  Both methods are used in this demonstration.  Byslightly misaligning an interferometer mirror, the delaydifference is made to vary across the image.  Then targetvelocity causes the fringe comb to displace transverselyacross the image.  In addition to this, the use of color filmcreates a 3-channel recording organized by wavelength.Alternatively, a grating could be used to diffracta line or point image into a spectrum.  Equation (2)indicates that fringes will be observed versus 1/<λ>.When this configuration is used with a chirped pulse, acorrespondence is made between wavelength and time atthe target.  This forms an optical streak camera2 whichmeasures velocity history along a line across the target.The interferometers can be of a Michelson class(generating two images) or Fabry-Perot class (infiniteseries of images of decreasing intensity).  Monochromaticsuperimposing Michelson interferometers achieved by anetalon in one arm have been used in VISAR velocityinterferometers for many years4.  These satisfy thesuperimposing condition only for one wavelength due todispersion in the etalon and thus are unsuitable for aWLV.  An example of a non-superimposinginterferometer is the conventional Fabry-Perot, whichlongitudinally displaces the successive output rays for agiven input ray.  A Fabry-Perot can be madesuperimposing by adding a positive lens internal to thecavity so that there is exactly +1 magnification per roundtrip.The achromatic superimposing Michelsoninterferometer used in this demonstration uses a relay lenssystem in one arm.  This is shown in Fig. 5, except that atransmissive lens L2 represents a spherical mirror actuallyused.  The interferometer delay is given by the path lengthdifference between the two arms.  Lenses L2 and L1image the surface of a spherical reflector RM1 to a so-called apparent mirror surface.  This must superimposewith the image of M1 seen in the beamsplitter BS, andwhich is called the principal plane.  The goal of theinterferometer is to superimpose the apparent mirror andprincipal plane surfaces for a wide range of incident rayangles, positions and wavelengths.  Other lenses, notshown, relay the principal plane to the target.The interferometers of our apparatus have4 meter delays so that the velocity per fringeproportionality for white light is about 20 m/s.  Thisallows the use of low velocity targets safe for tabletopdemonstrations.L1M1PrincipalplaneApparentmirrorOverlap desiredRM1BSL2Fig. 5  A Michelson superimposing interferometer.  Inactuality, an equivalent spherical reflector is substitutedfor L2.  The principal plane is the reflection of M1 seen inthe beamsplitter BS.  The apparent mirror surface is thesurface of spherical reflector RM1 imaged by L2 and L1.To achieve full WLV capabilities, the apparent surfaceshould overlap the principal plane for as many input rayangles,  positions and wavelengths as possible.AcknowledgmentsThis research was performed under the auspicesof the U.S. Department of Energy by the LawrenceLivermore National Laboratory under contract W-7405-Eng-48.References1. D.J. Erskine and N.C. Holmes, "White-lightVelocimetry", Nature 377, 317-320 (1995); Errata:the sentence one paragraph above Eq. (2) should read"In general, there is no restriction on the design ofeither interferometer provide they individuallysuperimpose images created by each armlongitudinally, transversely and in magnification."2.  A simple argument estimates the time resolution of achirp illuminated streak system to be∆t =Tpf 2 − f1, where Tp is the pulse durationhaving a range of frequencies f1 to f2.3.  S. Gidon and G. Behar, "Multiple-line laser Dopplervelocimetry", Appl. Opt. 27, 2315-2319 (1988).4. W. Hemsing, "Velocity sensing interferometer(VISAR) modification", Rev. Sci. Instrm. 50, 73-78(1979).Technical Information Department  • Lawrence Livermore National LaboratoryUniversity of California • Livermore, California  94551

An Imaging White Light Velocimeter

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An Imaging White Light Velocimeter

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