High-speed three-dimensional shape measurements of objects with laser speckles and

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High-speed three-dimensional shapemeasurements of objects withlaser speckles and acousto-optical deflectionMartin Schaffer,*Marcus Grosse,Bastian Harendt,and Richard Kowarschik Friedrich-Schiller-University Jena,Institute of Applied Optics,Fröbelstieg1,07743Jena,Germany*Corresponding author:martin.schaffer@uni‑jena.deReceived June7,2011;revised July5,2011;accepted July12,2011;posted July12,2011(Doc.ID148885);published August8,2011Many three-dimensional(3D)shape measurement techniques in stereophotogrammetry with temporal coded struc-tured illumination are limited to static scenes because the time for measurement is too long in comparison to the object speed.The measurement of moving objects result in erroneous reconstructions.This is apparent to reduce measurement time to overcome this limitation,which is often done by increasing the projection rate for illumination while shrinking the amount of images taken for reconstruction.The projection rate limits most applications in its speed because digital light processing(DLP)projectors,which are widely used,bring a limited projection rate along.Our approach,in contrast,does not take a DLP.Instead we use laser speckles as projected patterns which are switched using an acousto-optical deflector.The projection rate is10×higher than what the fastest stripe projec-tion systems to our knowledge achieve.Hence,we present this uncommon but potential approach for high-speed(≈2503Dfps=[3D measurements per second]),dense,and accurate3D measurements of spatially separated objects and show the media that emphasizes the ability of accurate measurements while the objects under testing move.©2011Optical Society of AmericaOCIS codes:120.0120,120.3940,120.4630,150.6910,100.6890.Three-dimensional(3D)measurements of objects using stereophotogrammetric setups have been improved over the last decades.Techniques with structured illumination have been proposed and later on used in many industrial applications.They lead to accurate dense point clouds representing the surface of the object under testing. Because of higher production rates in industries,it be-comes difficult to use those methods as stated,because they assume static objects and lose accuracy when ob-jects move during measurement.Therefore,researchers try to decrease the time necessary for one3D shape mea-surement so that the measurement time is negligible in comparison to the object speed.This goal was and is usually addressed by higher projection rates and/or reduction of the amount of patterns necessary for one reconstruction[1,2].In recent years it has become difficult to differentiate fast3D shape methods because of the construability what“fast”means.We suggest not to use the term“fast,”since its meaning/predicate is relative(e.g.,to the move-ment of the objects under testing).Attributes well-known from the film-industry like“real-time,”“video-like,”or “highspeed”are preferable.Stripe projection attracts the most attentiveness by re-searchers.Stripe systems at video-like rates of253Dfps (3D measurements per second)usually omit the gray code sequence and/or disassemble color wheels of digital light processing(DLP)projectors to use a higher projec-tion rate[3].Another group of rather highspeed stripe setups(≈2503Dfps)use defocused binary stripes to cre-ate sinusoidal-like fringes and have made very fast mea-surements possible[1,4].However,those techniques lose accuracy and the ability to measure scenes with multiple objects or object discontinuities,although techniques have been proposed that increase the ambiguity interval or handle defocused gray codes[5,6].Additionally,this 3D shape measurements published recently show comparably small measurement volumes,due to bright projection for short exposure times and nonsinusoidal fringes out of focus.Several researchers also use acousto-optical or elec-tro-optical effects to create stripes for3D shape measure-ments[7–9].But again,they measure only steady objects since no gray code is applied that solves the phase ambiguity.Regarding the goal of higher projection rates,our idea in[10]and now is to replace the projection device that mainly is responsible for the limited abilities of high-speed3D shape measurements.This Letter will cover the following material:we will explain the setup and the cor-relation technique to find homologous points for3D reconstruction,explain the replaced projection device for pattern creation,and present the results with all necessary parameters to compare this setup to others.The setup consists of two highspeed cameras (f Acq¼4630Hz,720×480pixel)with a base distance of0:28m,a focal length of17mm,and a speckle projec-tion unit.During measurement,a sequence ofstatisticalFig.1.(Color online)Speckle projection setup deflecting the laser beam by an AOD.August15,2011/Vol.36,No.16/OPTICS LETTERS30970146-9592/11/163097-03$15.00/0©2011Optical Society of Americaspeckle patterns is projected onto the object surface and is acquired by the cameras(see Fig.1).After that,a gray-value vector for every pixel of each view/camera can be generated which corresponds to an object point illumi-nated with the pattern sequence.In contrast to phase calculation and matching thatstripe systems apply,a temporal correlation technique proposed in[11,12]is used to find corresponding pixels between two perspectives of an illuminated object.First, gray-value vectors yielding N gray values coming from N consecutively projected speckle patterns are generatedfor every pixel.For a pixelði;jÞin the first camera, Eq.(1)is evaluated with every pixelði0;j0Þof the second camera(Fig.2).The pixel coordinate pair that yields the highest correlation valueρMax is labeled as homologous.A subpixel accurate refinement using bicubic interpo-lated gray-value vectors follows for accurate point corre-spondences and point clouds:ρi;j;i0;j0¼PNt¼1ðg i;j;t− g i;jÞ·ðg i0;j0;t− g i0;j0ÞffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPNt¼1ðg i;j;t− g i;jÞ2q·ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPNt¼1ðg i0;j0;t− g i0;j0Þ2q:ð1ÞBecause no spatial information is correlated,a tempor-al information is used instead;this technique is calledtemporal correlation.The consecutive projected speckle patterns can be generated in two ways.In[10],a published speckle pro-jection unit used a stepwise rotating diffuser in the focalspot of a laser beam to generate the objective speckles.A projection rate of500Hz was realized,and3D measure-ment rates of12:753Dfps were achieved.The new idea,illustrated in Fig.1,is to alter the laserbeam direction and therefore change the illuminated areainstead of moving the scattering surface under focus.This is done with an acousto-optical deflector(AOD).The laser beam is diffracted at a refractive index grating induced by an acoustic wave.The crystal of an AOD isthus driven by a piezo-electric transducer that emits anacoustic wave with adjustable frequency into it.A fre-quency change in return alters the period of the refractive index grating and the angle of the first-order diffractionvaries.The diffracted first-order beam is focused onto thestatistically rough diffuser from which the statisticalspeckle pattern then propagates and illuminates the ob-ject.By carefully choosing the axial diffuser position infocus or slightly out of focus,the objective speckle size ofthe patterns can be adapted to achieve the highest accu-racy.To guarantee precise subpixel correspondences, we investigated an optimal structure size(bright to dark)of about6−10pixelsðPxÞin both camera views.At a diffraction efficiency ofη≈75%,a velocity ofsound of v¼617m=s,and a frequency range of57–107MHz,the first diffraction beam and in return the laser spot position can be varied depending on thebeam diameter(d exp¼3mm)with unprecedentedly 205;000Hz in a step and settle regime.Summarizing this, 205,000statistical independent speckle patterns per sec-ond can be generated for acquisition,correlation,and3D reconstruction.To characterize the system in means of accuracy and speed we created a object scenery consisting of moving parts as well as static ones.Furthermore,a plane stan-dard was placed in the measurement volume to validate the accuracy of3D reconstructions.The accuracy was distinguished by fitting a plane to the point cloud repre-senting the plane surface and calculating the standard deviation(σ)of points about the fitted plane.As denoted in Fig.3,3083Dfps could be acquired achieving a point localization accuracy of50μm when 15images/gray values per vector were used for correla-tion.By taking more images for one reconstruction,an even better accuracy can be reached.The relative accu-racy of this3D shape measurement approach can be calculated to1:9·10−4according to the measurement volume of20cm×15cm×10cm at3083Dfps.Respec-tively,when39images are used,nearly1203Dfps can be acquired with a relative accuracy of1:1·10−4.The amount of reconstructed points is≥95%of all visible points,so that dense measurements could be realized.A qualitative result can be seen in Figs.4and the asso-ciated media.A static scene can be acquired within a short time,and moving objects can be recorded in highspeed.The major disadvantage of this approach is that it assumes small subjective speckles on the CCD.Since subjective speckle come from the rough object surface and are perspective-dependent,they would hinder the correlation.But in our application,the aperture,focal length,and pixel size combination was advantageous so that the subjective speckle were tiny in comparison to the pixels and not resolved.We presented a new projection method for highspeed 3D shape measurements using structured illumina-tion stereophotogrammetry.This method shows high accuracy(1:5·10−4)and the ability to measure fast (≈2003Dfps)separate,arbitrary textured objects in a Fig.2.(Color online)Corresponding pixels with similar gray-value vectors using temporalcorrelation.Fig.3.σversus gray-value length N.3098OPTICS LETTERS/Vol.36,No.16/August15,2011comparably large measurement volume.Furthermore,as the speckle patterns can be generated magnitudes faster than the cameras can capture,this approach is limited in speed by the cameras and not as usual by the projection device.If cameras would be used that reach the switch-ing rates of the AOD,theoretical 85403Dfps could be acquired at the above mentioned accuracy.In the future we will work on improving reconstruction algorithms to accelerate the calculation to the level of acquisition.Additionally,we will investigate subjective speckle suppression strategies to apply this method to denser shape measurement with high resolution cameras and small pixel sizes.We expect the accuracy then to im-prove further and the lateral resolution to be in a range where objects are covered denser.References1.S.Lei and S.Zhang,Opt.Lett.34,3080(2009).2.C.Bräuer-Burchardt, 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pseudocolors (Media 1and Media 3).(b)Moving objects acquired with 1933Dfps,σ¼36μm (Media 2and Media 4).August 15,2011/Vol.36,No.16/OPTICS LETTERS 3099。