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Zhenhua Huang

Albert J. Shih

Jun Ni

Department of Mechanical Engineering,University of Michigan,

Ann Arbor, MI 48109

Laser Interferometry HologramRegistration for Three-Dimensional PrecisionMeasurementsA hologram registration method is developed for the laser holographic interferometrymeasurement of the 3D surface profile of objects which are larger than the field of view(FOV). The theory of laser holographic interferometry, including the phase-shifting andmultiwavelength tuning, is described. The hologram registration without using targets iselaborated. The cross-correlation analysis is used to find the translation and overlappedregions, which determine the tilt and shift correction for data registration. The proposedmethod is validated using two examples with different approaches. The first example, awheel hub, is smaller than the FOV and demonstrates only 0.1 �m discrepancy of thesurface flatness between the registered and standard measurements. The second example,an engine combustion deck surface, is larger than the FOV. The registered surface mea-surements are compared to that of coordinate measurement machine (CMM) with only2.5% discrepancy of the peak-to-valley flatness. This data registration method enables thesub-�m precision and large depth of field (several centimeters) measurement of large sizeobjects. �DOI: 10.1115/1.2335856�

IntroductionLaser holographic interferometry applies coherent light to ex-

ract the 3D surface profile of objects for sub-�m level precisioneasurement. This method, originally invented by Leith and Up-

tnieks �1–3� and Stetson and Powell �4�, has been developed foruality control and process diagnosis of shape and dimension andor strain and deformation analysis �5,6�. The object is illuminatednd viewed from the same direction. Therefore, it does not havehe shadowing �the object cannot be illuminated but is visible tohe sensor� or occlusion �object is illuminated but invisible to theensor� problems as in the triangulation-based optical measure-ents. The most significant advantage of the laser holographic

nterferometry method is the combination of sub-�m accuracynd large depth of field. A state-of-the-art laser holographic inter-erometry measurement machine, Coherix Model Shapix 1000,as a depth of field over several centimeters and sub-�m accuracyor a 300 mm�300 mm FOV �7�.

For precision measurement of large size objects, such as thenternal combustion engine head combustion deck surfaces andhe automatic transmission valve bodies, the limited size of theOV is a constraint in the current laser holographic measurementachine. Increasing the dimensions of optical mirrors in the ma-

hine to enlarge the measurement FOV is possible but cost pro-ibited. The goal of this research is to develop a hologram regis-ration method as a more practical alternative to enable the laserolographic interferometry measurement of objects larger than theOV.Several 3D image registration methods have been developed.

anderLugt �8� and Kim et al. �9,10� applied the 3D pattern rec-gnition, Dias et al. �11� fused the range and intensity data of themage, and Hsu et al. �12,13� extracted and matched the edge andurface features for image registration. However, the hologramegistration method is still lacking.

Contributed by the Manufacturing Engineering Division of ASME for publicationn the JOURNAL OF MANUFACTURING SCIENCE AND ENGINEERING. Manuscript receivedecember 27, 2005; final manuscript received March 7, 2006. Review conducted by

. N. Melkote.

006 / Vol. 128, NOVEMBER 2006 Copyright ©

This study develops a hologram registration method to enablelaser holographic interferometry for the precision measurement oflarge size objects without using externally placed targets. In Sec.2, the principle of laser holographic interferometry is described.The mathematical procedures for hologram registration are dis-cussed in Sec. 3. In Sec. 4, the accuracy of hologram registrationis evaluated using two examples and this method is validated.

2 Laser Holographic InterferometryCoherent light is generated in the laser holographic interferom-

etry to create the hologram of a measurement object. The heightof the measurement object is extracted by the phase-shifting andmultiwavelength tuning techniques.

The setup of a laser holographic measurement system is shownin Fig. 1�a�. The optical measurement unit generates the laserbeam for measurement and acquires the hologram for computa-tion. The optical measurement unit and object are both placed ona granite plate to ensure the thermal and mechanical stability. Anoff-axis parabolic mirror is located on the top of the machine toenlarge the measurement area. The mirror collimates the carrierbeam �c from the optical measurement unit to the object. Thelaser beam reflected from the object carries the surface heightinformation and reflects by the parabolic mirror back to the opticalmeasurement unit for processing.

The setup of the Twyman-Green interferometer �14� inside theoptical measurement unit is shown in Fig. 1�b�. The laser beamfrom a tunable laser source is split by the beamsplitter into twocoherent laser beams: the reference beam �r and carrier beam �c.The reference beam �r is reflected by a reference mirror, which ismoved to apply the phase-shifting for measurement. The carrierbeam �c, redirected by a mirror, is enlarged by a beam expanderand directed to the parabolic mirror and object.

In this research, the carrier beam after collimation by the para-bolic mirror is 300 mm�300 mm in size, which is the FOV ofthe measurement system.

Two reflected beams, �r reflected from the reference mirror and�c reflected from the object, interfere with each other after trav-

eling through the beam splitter again and generate the hologram in

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he charged-coupled device �CCD� camera. The Fourier transformethod �14,15� is applied to analyze the hologram to extract the

D surface profile of the object.The reference and carrier laser beams are both light waves,

hich are functions of the 3D spatial coordinates x, y, and z andhe time t. The reference beam �r is expressed as

�r�x,y,z,t� = Ur cos��r − 2��t� �1�

here Ur is the amplitude, �r is the phase, � is the frequency, andis time.The reference beam �r is a plane wave, i.e., phase �r is a

onstant across any plane perpendicular to the wave propagationirection. The carrier beam �c reflected from the object surfaceas the phase �c modulated by the height of the object. The modu-ated carrier beam is expressed by

�c�x,y,z,t� = Uc cos��c − 2��t� �2�

here Uc is the amplitude of the carrier beam �c.Two techniques, phase-shifting and multi-wavelength tuning,

re applied to measure the height of an object surface.

2.1 Phase-Shifting. The CCD camera can only measure thentensity of the light beam. The phase-shifting technology is ap-lied to convert the intensity on each pixel into the height of theorresponding point on the object surface. The light intensity I is

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ig. 1 Diagram of the laser holographic interferometer: „a…onfiguration of the machine and „b… scheme of the opticaleasurement unit in „a…

efined as the squared amplitude of the light wave, i.e., I=U . The

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light intensities of reference beam �r and carrier beam �c are Ir

�=Ur2� and Ic �=Uc

2�, respectively. The light intensity I generatedby the two interfering beams �r and �c is �14�

I = Ir + Ic + 2�IrIc� cos �� �3�

where � is a measure of the ability of two waves to interfere �14�,0�1, and ��=�r−�c is the phase difference.

The phase difference �� ranges from −� to � and can belinearly mapped to the height measurement ranging from −1/4wavelength to 1/4 wavelength. To solve ��, the phase-shiftingtechnique �16� is applied by moving the reference mirror �shownin Fig. 1�b�� with small incremental steps. Moving the referencemirror introduces a phase shift and Eq. �3� can be rearranged as

I = m + n cos��� + � �4�

where m= Ir+ Ic, n=2�IrIc�, and is the given phase shift.When the phase of the reference beam is shifted by three given

values 1, 2, and 3, three light intensities Ik=m+n cos���+k� �k=1, 2, and 3� can be measured. The phase difference ��,which corresponds to height, on each pixel is �14�

�� = tan−1 �I2 − I3�cos 1 − �I1 − I3�cos 2 + �I1 − I2�cos 3

�I2 − I3�sin 1 − �I1 − I3�sin 2 + �I1 − I2�sin 3

�5�In practice, more than three phase shifts, which introduce a set

of overdetermined equations, are applied to obtain a more numeri-cally stable solution. The least square method �14� has been de-rived to solve �� of a set of overdetermined equations. In thisresearch, four or five 100 nm incremental movements are utilizedto generate the phase shift.

2.2 Multiwavelength Tuning. To increase the range of heightmeasurement, the multiwavelength laser source, so called tunablelaser, is applied. If the single wavelength laser source is used, theoverall height range of all the pixels in the CCD camera must besmaller than 1/2 of the laser wavelength. This limits the range ofheight measurements. The use of multiwavelength tuning canovercome this obstacle.

The multiwavelength laser can be generated using a laser-cavitydesign �17�. The laser beam in the cavity strikes a diffractiongrating at near grazing incidence, i.e., an incidence angle near90 deg. The laser diffracts off the grating at different diffractionangles with different wavelengths. Each diffraction angle corre-sponds to a specific wavelength. In this study, a tunable diodelaser is used to generate infrared wavelengths ranging over abouta 20 nm interval. During measurement, the laser is tuned to aseries of equal wavelength steps.

In holographic interferometry, the concept of reference point isapplied to improve the measurement accuracy and reduce the ad-verse effect caused by mechanical vibration from the surroundingenvironment. A reference point is arbitrarily selected in the mea-surement region. The phase of the reference point is designated as0 by shifting the phase of all measurement points by a constantvalue. The height h and phase difference �� of all other points arecalculated relative to the reference point.

The height h is extracted by tuning the wavelength of the lasersource and calculating the change of the phase difference �� foreach point �18�. If the wavelength �1 is used, the phase differenceis ��1, then ��1=4�h /�1. If the wavelength is changed to �2, thephase difference is ��2=4�h /�2. The height h can be solved bycombining the two relations as below:

h =���1 − ��2��1�2

4���2 − �1��6�

Equation �6� shows that the height measurement range depends onthe wavelength tuning step ��2−�1�. A smaller wavelength tuningstep generates a larger height measurement range.

In practical holographic measurement, more than two wave-

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engths are used to achieve a more robust solution. In this study,6 wavelengths, marked as �1 to �16 were applied. During theime interval, 4 or more phase shifts are conducted to calculate ��or each wavelength. The change of wavelengths occurs at a con-tant rate with period �t and a constant tuning step �� ���=�2�1=�3−�2= ¯ =�16−�15�. At each wavelength, only the calcu-

ated phase difference �� was selected as the angle of a complexumber with unit magnitude. As the wavelength changes, theomplex number rotates around the origin of the complex plane athe frequency fs �19�. The Fourier transform analysis of the 16omplex values at 16 wavelengths generates a peak at fs in therequency domain. The height h can be expressed as �19�

h = fs�12/� �7�

here � is a constant which determines the wavelength tuningpeed, i.e., �� �=��t�. The wavelength �1 and the constant � arenown parameters. The height h on each point can be solved usingq. �7� with the identified fs.The 3D surface profile is extracted from the measured holo-

ram using the method described above. The height measurementalibration and the median filtering �20� are applied to reduce theoise.

Hologram RegistrationThe hologram registration method is developed to enable the

aser holographic interferometry for measuring objects larger thanhe FOV. Traditionally, targets have been used for image registra-ion in 3D optical measurement �21,22�. The approach proposed inhis study eliminates the use of targets and simplifies the measure-

ent procedure for image registration.The procedures to register two holographic measurements are

hown in Fig. 2. The FOV contains W rows and W columns ofeasurement points, which correspond to pixels in the CCD cam-

ra. The distance between adjacent rows or columns of points inOV is p. The size of the FOV is pW� pW, as illustrated in Fig.�a�. Mathematically, the measured data in FOV is represented byW�W matrix. Each element in the matrix is a complex number.he magnitude and angle of the complex number represent the

ight intensity I and the phase difference ��, respectively, of a

Fig. 2 Measurement regions and varimeasurement A and „b… measurement BpW=300 mm.

easurement point in the FOV.

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The length of the measurement object is larger than the widthpW of the FOV, as shown in Fig. 2. Two measurements, marked asmeasurement A in Fig. 2�a� and measurement B in Fig. 2�b�, areconducted. An overlapped region exists between the measure-ments A and B.

A procedure called masking is applied to extract the region ofthe measurement object in FOV for data analysis. The measure-ment object in Fig. 2 is a rectangle with three holes. The maskingprocedure eliminates the data points outside the measurement ob-ject area. The region after masking, called the unmasked region, ismarked by hatched lines in Fig. 2. The unmasked region can havean arbitrary shape. A rectangle shape to enclose the whole un-masked region, called the rectangle unmasked region, is selectedfor mathematical representation and processing of the region bymatrices. For example, as shown in Fig. 2�a� for measurement A,the dimension of the rectangle unmasked region is pNA� pMA.Two matrices associated with the rectangle unmasked region arethe intensity matrix IA and phase matrix ��A, which represent thearray of measured intensities and calculated phase differences,respectively. Both matrices have the dimension NA�MA. Thesetwo matrices are extracted from the measurement data in the FOV.Similarly, measurement B after masking has the rectangle un-masked region, as illustrated by the hatched region as shown inFig. 2�b�, with physical dimension of pNB� pMB. The intensitymatrix IB and phase matrix ��B, both with the dimension ofNB�MB, are extracted to represent the measurement.

The correlation analysis, to be discussed in Sec. 3.1, is used tocalculate the translation to match the two measurements and findthe overlapped region.

3.1 Translation. Translation is the lateral movement in the xand y directions between the two measurements of the same mea-surement object. The lateral translation is determined by the loca-tion of the correlation peak in the cross-correlation matrix C oftwo intensity matrices IA and IB.

The direct normalized method �23� is utilized to calculate thecross-correlation matrix C, which has the dimension of �NA+NB−1�� �MA+MB−1�,

C = IA � IB �8�where � is the cross-correlation operator.

es used for hologram registration: „a…this research, W=1024, p=0.293 mm,

Each element of the matrix C is expressed by

C�u,v� =�i,j

�IA�i − �u − NA�, j − �v − MA�� − IA��IB�i, j� − IB�

��i,j�IA�i − �u − NA�, j − �v − MA�� − IA�2 · �i,j

�IB�i, j� − IB�2�9�

abl. In

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here u and v are the lateral shift coordinates, ranging from 1 toA+NB−1 and from 1 to MA+MB−1, respectively, i and j are the

ntegers indicating location �i , j� of each element in the matrix,

nd IA and IB are the means of IA and IB, respectively.The correlation peak is the maximum value in the cross-

orrelation matrix C. If the correlation peak is located at �Np ,Mp�,he lateral translation in pixels of measurement A relative to mea-urement B is �Np−NA,Mp−MA�.

The lateral translation identified from the procedures describedbove has the resolution of pixel spacing. Subpixel spacing reso-ution is possible by using interpolated pixel data. The interpola-ion does enlarge the dimensions of the cross-correlation matrixnd increase the computation time.

A rectangular overlapped region exists between measurementsand B. This is illustrated by the overlapped regions A� and B�

n measurements A and B, as shown by the bold dashed line inigs. 2�a� and 2�b�, respectively. Overlapped regions A� and B�ave identical shape and size. The location and size of the over-apped regions can be calculated from the translation between

easurements A and B. The phase matrices of overlapped regions� and B� are denoted as ��A� and ��B� and have the dimensionf NA��MA� and NB��MB�, respectively, where NA�=NB� and

A�=MB�. The relative tilt and phase shift between Measure-ents A and B are calculated by processing ��A� and ��B�. This

s elaborated in Sec. 3.2.

3.2 Tilt and Shift Correction. Tilting and shifting are adjust-ents used to make two planes match in the 3D space. Tilt are

epresented by two angles, relative to the x and y axes, of theifference between the normal vectors of the two planes. Tilt onelane relative to the other and the two planes can be made paral-el. Shift is the translation along the z axis after the tilt correctiono make two parallel planes match in space.

The measured data points on the overlapped regions do notecessarily form a plane in practical applications. However, be-ause the overlapped regions are the same portion of the objecturface in two separate measurements, the difference betweenhases of measured data points on two overlapped regions shouldollow the trend of a plane. By least square fitting this plane, theilt and shift corrections can be calculated.

The ��A��i , j� and ��B��i , j� are the phases of the pixel in�A� and ��B� with the lateral location �i , j� in the overlapped

egions A� and B�, respectively. Define ��D�i , j� as the unmaskedverlapped phase difference which equals ��B��i , j�−��A��i , j�,here �i , j�= �i1 , j1�, �i2 , j2� , . . . , �in , jn�, and n is the total numberf unmasked pixels in the overlapped region.

Collect all the unmasked pixels in ��D�i , j� and construct aatrix L,

L = �i1 j1 1

i2 j2 1

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in jn 1� �10�

Record all the phases of the corresponding unmasked pixelsnd construct a vector P,

P = ��D�i1, j1���D�i2, j2�

��D�in, jn�

� �11�

Least square fit a plane to ��D, defined by ��D�i , j�=ai+bjc. The coefficients a, b, and c are determined by

a

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c

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The coefficients a and b relate to the tilt about y and x axes,respectively, of measurement B relative to measurement A. Thecoefficient c determines the relative shift of measurement B rela-tive to measurement A in the z axis.

Once the coefficients, a, b, and c are obtained, the phase��B�i , j� of the whole measurement region in measurement B iscorrected by

��c �i, j� = ��B�i, j� − �ai + bj + c� �13�

Fig. 3 Wheel hub: „a… isometric view, „b… top view, and „c…close-up view of the dent marked in the solid rectangle in „b…

B

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here ��Bc �i , j� is the tilt-corrected phase of ��B�i , j�.

In summary, to register two holograms shown in Fig. 2, thenmasked measurements A and B are first identified. Using theross-correlation analysis, the translation is calculated and theectangular overlapped regions A� and B� are marked. The phaseatrices of two overlapped regions are used to find the tilt and

hift between measurements A and B and complete the data reg-stration.

Accuracy Evaluation of Hologram RegistrationTwo examples using different approaches are applied to evalu-

te the accuracy of proposed hologram registration method. Therst approach uses a measurement object which is small and fits in

he FOV. The object can be accurately measured to create a stan-ard height measurement hs�i , j�. The same object is then mea-ured twice on two sides with an overlapped region in between.he proposed method is applied to calculate the registered heighteasurement hm�i , j�. The accuracy of registration method is

uantified by comparing hs�i , j� to hm�i , j�. A wheel hub is used ashe example I.

The other approach uses a measurement object larger than theOV. The CMM measurement of the whole measurement object issed as the standard measurement hs�i , j�. It is compared to theegistered measurement hm�i , j�. An engine combustion deck sur-ace is used as the example II.

4.1 Accuracy Evaluation Procedures. Two parameters, theoot mean squared �RMS� error erms of the difference between the

Fig. 4 Measured holograms of the wheel huA and B

s�i , j� and hm�i , j� and the surface flatness, are used to evaluate

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the accuracy of the hologram registration method.To compare hs�i , j� and hm�i , j�, a linear transformation is re-

quired to tilt and shift the hm�i , j� relative to hs�i , j� before calcu-lating erms. Since the measurement system in this study only de-livers the relative height measurement, this linear transformationis required. Let Fs�i , j�=asi+bsj+cs and Fm�i , j�=ami+bmj+cm bethe least square fitted planes of hs�i , j� and hm�i , j�, respectively.The linear transformation of hm�i , j� can be expressed as

hmT �i, j� = hm�i, j� − ��am − as�i + �bm − bs�j + �cm − cs�� �14�

The RMS error erms is

erms =1

d� �

�i,j�=�i1,j1�

�id,jd�

�hs�i, j� − hmT �i, j��2 �15�

where d is the total number of all unmasked pixels.The surface flatness is also used as an index to evaluate the

accuracy. Two flatness definitions are used in this study. One is 6 flatness, which is equal to six times the standard deviation ofmeasured points from the least square fitted plane �24�. This defi-nition suppresses the spike noise contribution to the flatness. Theother is the maximum peak to valley from the least square fittedplane. This is called the peak-to-valley flatness.

4.2 Example I: Wheel Hub. As shown in Fig. 3, a wheelhub, which is small to fit the FOV, is used as a measurementobject to evaluate the accuracy of the hologram registrationmethod. Five bolts were assembled to the wheel hub to transmitpower to the wheel. These bolts after being assembled may alter

a… intensity and „b… phase of measurements

b: „

the original hub surface flatness and need to be inspected. The

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aser holographic interferometry is a unique method to measurehe surface flatness of the hub with the assembled bolts. The di-meter of the hub, as shown in Fig. 3�b�, is about 150 mm.

The intensities and phases for each measurement are shown inig. 4. The solid black regions in Figs. 4�a� and 4�b� are maskednd excluded for height measurement. The intensity matrices IAnd IB have the dimension of 649�964 and 615�964 pixels,espectively.

The cross-correlation matrix C of IA and IB is represented inig. 5. The dimension of C is 1297�1927 pixels. The location of

he correlation peak is identified at �301, 964�. This indicates thathe measurement matrix A should translate 301−649=348 pixels in the +x direction and 964−964=0 pixels in the +yirection to make the strongest match with the measurement ma-rix B. With this translational movement, the overlapped regions� and B� can be chosen from measurements A and B,

ig. 5 Correlation matrix C of measurements A and B of theheel hub

ig. 6 Registered hologram of the wheel hub: „a… phase and

b… intensity

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respectively.The hologram phase ��A� and ��B� of the overlapped regions

A� and B�, respectively, are shown in Fig. 4�b� in dashed rect-angles. The reference point is marked with a plus sign. The di-mension NA��MA� of the overlapped regions is 300�964 pixels. The relative tilt and shift parameters �a ,b ,c�, de-fined in Eq. �12�, are �−1.0�10−4 rad/pixel, 1.2�10−5 rad/pixel, 1.23�10−2 rad�. Correct the relative tilt usingEq. �13� and register two holograms. The phase and intensity ofthe registered hologram are shown in Fig. 6. A clear separationlines between two measurements can be observed in the registeredintensity, as shown in Fig. 6�b�. This is because the intensity of themeasurements A and B are connected without any correction. Thisdoes not affect the height measurement, which is calculated fromthe registered phase, as shown in Fig. 6�a�.

There is a dent on the hub surface, which is marked in Fig. 3�b�and shown in close-up view in Fig. 3�c�. Because this dent is morethan 9 pixels in the image, this cannot be eliminated by 9 pointmedian filtering. The 6 surface flatness definition is applied tosuppress the effect of this dent on the surface flatness measure-ment results.

Interpolation is applied to achieve subpixel resolution for thehologram registration. First, the lateral cross-correlation process,defined in Eq. �9�, is interpolated. For example, one point linearinterpolation is utilized in the 300�964 pixels overlapped region.The lateral translation is the same after processing. For highersubpixel resolution, two or more points can be linear interpolated.

The registered height measurement hm�i , j� is shown in Fig.7�a�. The standard measurement hs�i , j�, as shown in Fig. 7�b�, isobtained in a single holographic interferometry measurement ofthe wheel hub, which is small to fit in the FOV. The 6 flatness ofhs�i , j� and hm�i , j� is 25.3 and 25.2 �m. The gauge repeatability

Fig. 7 3D profile measurement of the wheel hub: „a… registeredmeasurement hm„i , j… and „b… standard measurement hs„i , j…

�1 � of the system is evaluated as 0.3 �m. Compared to this

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alue, the 0.1 �m or 0.4% flatness difference is not significant. Itndicates that the hologram registration does not make significantontribution to the measurement error.

The difference between hs�i , j� and hm�i , j� is presented in Fig.. The RMS value erms is 0.4 �m. This further proves the accu-acy of proposed hologram registration method.

The effect of the area of the overlapped region was also evalu-ted. As shown in Fig. 9, hologram registration with 10%, 25%,nd 40% of the overlapped versus total measurement area wereonducted with the corresponding erms of 0.9, 0.5, and 0.4 �m,espectively. As the area of the overlapped region increases, therror introduced by the registration method decreases. The in-rease of overlapped region from 10 to 25% reduces the erms by.4 �m. The same 15% increase of overlapped region from 25 to0% only reduces the erms by 0.1 �m. Also, when the area of theverlapped region is larger than 40%, the error erms is approachinghe 0.3 �m system error. It is expected that increasing the over-apped region beyond 40% will not reduce erms significantly.

4.3 Example II: Engine Head Combustion Deck Surface.s shown in Fig. 10, an engine head combustion deck surface haslarge, 420�180 mm, measurement area. Two measurements,arked as measurements A and B in Fig. 10, were conducted. The

ranslation of the measurement object was achieved by moving itith the side datum surface of the measurement object in contactith a straight reference bar in the machine. The intensity matri-

es IA and IB have dimensions of 948�584 and 889599 pixels, respectively. Following the cross-correlation proce-

ure, the overlapped region with the size of 598�458 pixels isdentified. The relative tilt and phase shift parameters �a ,b ,c�,

ig. 8 Difference between hs„i , j… and hm„i , j… of the wheel hub

ig. 9 Effect of the area of the overlapped region on the error

rms

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defined in Eq. �12�, are �4.5�10−4 rad/pixel, 3.1�10−3 rad/pixel, −0.5 rad�. The tilt and phase shift are correctedusing Eq. �13� and the two measurements are registered as a1378�599 matrix.

The 3D profile of the registered surface is shown in Fig. 11�a�.In comparison, the same surface was measured by a Zeiss ModelUPMC 850 CMM with a scanning probe. The CMM measure-ment, which covers only a small portion of the surface, is shownin Fig. 11�b�.

The peak-to-valley flatness definition is applied for evaluationbecause the surface area measured by CMM and laser holographicinterferometry is significantly different. Under such condition, thestandard deviation does not provide a comparable representationof measurement results. The peak-to-valley flatness of the CMMand registered laser holographic measurement are 149.7 and153.5 �m, respectively. This close comparison, 2.5% discrepancy,

Fig. 10 Overview of a V6 engine head combustion decksurface

Fig. 11 3D profile of the engine head combustion deck sur-

face: „a… registered measurement and „b… CMM measurement

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urther verifies that the developed hologram registration method iseasible for the precision measurement of large components.

Concluding RemarksThis research developed a hologram registration method for the

aser holographic interferometry to measure the 3D profile of ob-ects larger than the FOV. Two examples were used to validate theegistration method using two different approaches. The first ex-mple, a wheel hub, was smaller than the FOV and enabled these of holographic interferometry to create the standard measure-ent for the accuracy evaluation of hologram registration. The

econd example, an engine head combustion deck surface, wasarger than the FOV and a CMM was used to create the standard

easurement. The erms was 0.4 �m for the wheel hub �example I�nd peak-to-valley flatness difference was about 4 �m for thengine head combustion deck surface �example II�. The feasibilityf the proposed hologram registration method was demonstrated.

The unique feature of proposed registration method is the elimi-ation of using target for data registration. This could simplify theeasurement procedure and reduce the time. Several research in-

estigations can follow this study. The robustness of the proposedegistration method with more complex surface geometric shapeshan examples of the wheel hub and engine combustion deck sur-aces is a good future research topic. The limit of the tilt and shiftnd optimal percentage of the area of the overlapped region canlso be investigated as a series of follow-up research for practicalpplication of proposed hologram registration method. The mea-urement object was assumed to have the translational movementithout rotation. A model to compensate for the object rotational

rror can be developed. Only two measurements are used for theologram registration examples in this study. A more comprehen-ive program to register multiple holograms can be developed andhe error propagation analysis can be conducted to further advancehe capability of hologram registration for precision measure-

ents.

cknowledgmentThis work was supported by the Engineering Research Center

or Reconfigurable Manufacturing Systems of the National Sci-nce Foundation under Award No. EEC-9529125. The technical,quipment, and financial support from Dwight Carlson, Ronwonger, Jon Nisper, Mike Mater, and Alex Klooster of Coherixre gratefully appreciated.

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