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Albert J. Shih

Zhenhua Huang

Department of Mechanical Engineering,University of Michigan,

Ann Arbor, MI 48109-2125

Three-Dimensional OpticalMeasurements of Porous FoamsThe optical, noncontact stereovision system and data analysis procedure are developedfor the measurement of porous foams. The stereovision measurement system has demon-strated the capability to capture both the micro-scale features and the macro-scale shapeof both the open-cell and closed-cell porous foams. A computational procedure, denotedas the grid method, is developed to identify representative planes on the porous foamsurface using the stereovision measured data points. The relative positions betweenplanes can be used to calculate the angles and distances between porous foam surfaces.A SiC open-cell and an aluminum closed-cell foams are used as examples to validate thegrid method and demonstrate its computational efficiency. This research enables the formmeasurements and geometrical dimensioning and tolerancing of porous foams for qualitycontrol and assembly and contact analysis. �DOI: 10.1115/1.2194556�

IntroductionNovel metal, ceramic, carbon, and polymer porous foams are

ew classes of materials with unique mechanical, thermal, andlectrical properties. New foam materials have enabled a wideange of applications. In automotive, porous foams have beensed for lightweight bumpers, exhaust after-treatment filters, andound-proof and vibration isolation layers. Porous foams are theiffusion media for anode and cathode in fuel cell stack and theeat exchanger and catalyst carrier in fuel processors. Other no-able applications of porous foams include the bio-compatiblecaffold for human implants, structural fluid storage device forerospace applications, armor for military, and porous incubators,ioreactors, and enzyme carriers for pharmaceutical equipment.

Foam materials can be categorized as either open-cell orlosed-cell foams. Based on the cell topography, the open-celloam has the cell edges connected and leaves open the cell faces.n example of the SiC open-cell foam is shown in Fig. 1�a�. The

ize of SiC foam used in this study is about 75�50�20 mm, ashown in Fig. 1�b�. This foam, used as the filter for molten alu-inum in casting, is open to fluid flow and has relatively weakechanical strength. Closed-cell foams have solid faces and each

ell is sealed off from neighboring cells. Structures made oflosed-cell foams have high strength-to-weight ratio and are idealor impact energy absorption �1�. Measurements of both the open-ell and closed-cell foams are investigated in this study.

As foam materials embark to new precision and high-volumepplications that require the quality control and/or assembly andontact with other parts, the need for dimensional and geometricalorm measurements is generated. The dimensional and geometri-al form measurements can provide the basic understanding of theize and shape of a porous foam component and are necessary tostablish the tolerance specifications.

In the past, the research for measurement of porous foams fo-used mainly on characterization of cell size and topography. Dif-erent methods, such as light transmission �2�, optical microscopy3�, photography �4�, scanning electron microscopy �SEM� �5�,-ray tomography �6�, and magnetic resonance imaging �MRI�7�, have all been investigated. The survey shows that effectiveethods for the precision dimensional and geometrical form mea-

urements of porous foams with complicated shape are not avail-ble. This study applies the stereovision, an optical measurement

Contributed by the Manufacturing Engineering Division of ASME for publicationn the JOURNAL OF MANUFACTURING SCIENCE AND ENGINEERING. Manuscript receivedctober 17, 2004; final manuscript received February 26, 2006. Review conducted

y C. J. Li.

ournal of Manufacturing Science and EngineeringCopyright © 20

method, to acquire the data points on the porous foam surface anda mathematical procedure to identify planes representing the po-rous foam component.

The commonly used mechanical contact measurement methodsfor porous foam components are limited to simple shapes. At-tempts to apply the coordinate measurement machine �CMM�with a contact-based probe to scan the full surface and determinehigh peak points have been tested but failed to yield accurateresults. The optical-based full surface stereovision system is there-fore adopted to measure the porous foams.

In this paper, the three-dimensional �3D� stereovision opticalmeasurement method is introduced in Sec. 2. Detailed surfacefeatures on the porous foam surface, as measured using the ste-reovision system, are classified and analyzed in Sec. 3. An ap-proach to identify a representative surface plane from the mea-sured data points is discussed in Sec. 4. Two examples, one open-cell foam and the other closed-cell foam, are presented in Sec. 5.

2 Three-Dimensional Optical Measurement of PorousFoams

A wide variety of 3D noncontact optical measurement systemshave been developed and applied for industrial use. Compared tothe traditional contact-based CMM measurement, optical mea-surement systems have the advantages of flexibility, rapid dataacquisition, and full surface sampling capability. Based on theirbasic principles of data acquisition, the 3D optical measurementsystems can be classified as: laser triangulation, pattern projectionor structured lighting, stereovision, Moiré fringe, interferometry,focus detection, time-of-flight, echography, nuclear magneticresonance, and tomography �8�. The stereovision system is se-lected because it can create cloud of points representing micro-scale features, such as ligaments and thin wall surfaces of porousfoams, as well as cover a relative large area by combining, orso-called stitching or registration, images. The stereovision mea-surement experiment setup and measurement data processing arepresented in the following two sections.

2.1 Stereovision Measurement Experiment Setup. TheCogniTens Optigo 200 is the stereovision system used in the mea-surement experiment. This optical measurement system is basedon the photogrammetry with tri-linear tensor 3D reconstruction�9�. The image acquisition uses three two-dimensional imageswith 1.4 mega-pixels to generate a stereo representation of a por-tion of the porous foam surface. For each image acquisition, thetime is in the sub-ms level and the field of view is 140�180�60 mm. Several stereo images captured at different view angles

are combined into one set of cloud of points �10,11�. This feature

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s important to generate accurate cloud of points representation ofhe random porous foam surfaces. The pixel spacing in each stereomage is about 0.3 mm. By combining stereo images together, aombined cloud of points with significantly enhanced density,bout 0.06 mm pixel spacing at the top of the porous foam sur-ace, is obtained.

Targets were placed surrounding the porous foam during thetereo image capturing. In the study, the target is a 10 mm

10 mm black square with a 6 mm diameter shiny circle in theenter. The software recognizes the location of targets and useshe information to register the stereo images together. In the mea-urement of the SiC foam shown in Fig. 1�a�, more than 10 targetsre used. Figure 2 shows the cloud of points representation of the

ig. 1 Isometric overview of the SiC open-cell foam: „a… pho-ograph and „b… dimensions and surface designation of theoam

ig. 2 The SiC foam represented by points measured using

he stereovision system

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SiC open-cell foam in Fig. 1�a�. The combination of 52 stereoimages taken at different view angles around the porous foam isused to create this digital representation of the porous foamsurface.

The measurement accuracy and gauge repeatability and repro-ducibility �R&R� of stereovision system were evaluated as 30 and48 �m, respectively, by comparing with the CMM measurementsof an automotive body part �12�.

2.2 Measurement Data Processing. A mathematical proce-dure is required to find a plane to represent the measured porousfoam surface. In computational geometry, the convex hull, whichis defined as the combination of three points constructing thesmallest convex polyhedron enclosing all data points �13–16�, iscommonly used to represent the surface from measured cloud ofpoints data. However, the convex hull is not suitable for porousfoam. This study develops a computationally effective method tofind the representative plane of a porous foam surface.

3 Surface Features of the Open-Cell Porous FoamsThe SiC ceramic foam used in this study was produced using

the open-cell polyurethane foam as the template �17�. The ceramicslurry was coated onto the polyurethane foam and fired in a kiln.The polyurethane foam was burned out during the firing, leaving atriangular-shaped hollow hole inside each ligament. As shown inthe close-up view of the foam in Fig. 3, the open-cell foam struc-ture consists of ligaments creating a network of inter-connected,dodecahedral-shaped cells. The cells are randomly oriented andmostly uniform in size and shape.

Two types of surface are generated. The original surface afterfiring is illustrated in Fig. 3�a�. It is the close-up view of R1 inFig. 1�a�. In Fig. 3�a�, two features on the top surface of the foamsurface can be identified. One is the single, stand-alone ligament,as denoted by “A” in Fig. 3�a�. This is designated as the stemligament. An example of the stem ligament with rounded tip isillustrated in Fig. 4�a�. The corresponding stereovision measuredpoints is illustrated alongside the photograph in Fig. 4�a�. Thepeak point at the tip of ligament to determine a representativeplane of the porous foam surface is indicated by an arrow. Thestereovision system has demonstrated its capability to acquire de-tailed features of the mm-scale ligaments. The edge of the liga-ment of the dodecahedral-shaped cell can also be observed on thesurface. This is called the edge ligament, indicated as the regionR3 in Fig. 3�a�. The close-up view of the edge ligament in regionR3 and the stereovision measured data points representation areshown in Fig. 4�b�. The peak point is also denoted by the arrow.

The other type of surface on the porous foam, as shown in Fig.3�b�, is the machined surface. Close-up view of region R2 in Fig.1�a� is illustrated in Fig. 3�b�. This region was cut by a diamondwire �18�. A machined porous foam surface has different surfacetopography with the flat regions. As shown in R4 in Fig. 3�b� andits close-up view in Fig. 5�a�, the diamond wire can cut throughthe ligament close to the radial direction. This type of cut willreveal the triangular-shaped cavity inside the ligament. As shownin region R5 in Fig. 3�b�, the diamond wire can also cut throughthe ligament along the axial direction. A large flat surface area iscreated, as shown in the close-up view of R5 in Fig. 5�b�. Thestereovision measured data points in the close-up view of regionsR4 and R5 are also illustrated in Fig. 5. Due to the overlap ofpoints from the background surfaces, a clean point representationof the flat surface is difficult.

Figure 6 shows the distributions of depth of measured pointsbelow the representative top plane for surfaces F1 and F3 in Fig.1�b�. Two sample areas, 20 mm�20 mm in surface F1 and10 mm�10 mm in surface F3, are selected for analysis. Themethod to calculate the representative top plane is discussed laterin Sec. 4. As shown in Fig. 6�a�, for the original, as-fired surfaceF1 in Figs. 1 and 3�a�, only 2% of measured points are 0.5 mm

below its top plane. A large portion �24%� of the measured data

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oints is concentrated 1.5–2.0 mm below the top plane. This ismaller than the 5 mm average cell size of the porous foam. Theenetration of stereovision measurement into surface F1 is.5 mm, about one cell size. For the machined surface F3, ashown in Fig. 1�b�, the majority �about 51%� of measured pointsas the depth shallower than 0.5 mm from the top plane. This cane explained by the relatively large machined flat areas, such ashe surface shown in Fig. 3�b�. On surface F3, the percentage ofeasured points drops rapidly as the depth increases. The penetra-

ion of measured points into F3 is about 3 mm, smaller than the.5 mm in F1. The large machined surface close to the top planeeduces the viewing area to see inside the cell and decreases theenetration depth. For example, deep features of the cell can bebserved more clearly in F1 �Fig. 3�a�� but not in F4 �Fig. 3�b��.he setup in experiment can also contribute to the variation inenetration depth. The part was positioned as in Fig. 1�a� duringhe measurement. Surface F1, which is on the top, can be viewed

ig. 3 Surface features on the open-cell SiC foam: „a… original,s-fired surface „close-up view of region R1 on surface F1 inig. 1… and „b… machined surface „close-up view of region R2 ofurface F4 in Fig. 1…

rom a wider range of direction than side surfaces F2, F3, and F4.

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This example shows the complexity of the open-cell porousfoam surface and the capabilities and limits of the stereovisionmeasurement system. Examples of the closed-cell foam and itsmeasurement are presented in Sec. 5.2.

Fig. 4 Close-up view „photos and data points… of ligaments onthe original, as-fired surface F1 of SiC foam: „a… stem and „b…edge of a ligament

Fig. 5 Close-up view „photos and data points… of the ma-chined surface of the SiC foam: „a… machined surface of liga-ments cut axially „close-up view of region R4 in Fig. 3„b…… and„b… large machined surface ligament cut radially „close-up view

of region R5 in Fig. 3„b……

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Computational Procedure to Identify the Top Planen Porous Foam SurfacesThis section presents steps to extract the useful plane represen-

ation of the porous foam surface from measured data points. It isssumed that the measured data points have been filtered to elimi-ate outliers. Constructing a surface representation, such as thelane, cylinder, and sphere, is a necessary step for the dimensionalnd geometrical form measurements. In this study, as the first stepn geometrical measurement of porous foam, only the plane fea-ure is investigated. Based on planes representing surfaces F1, F2,nd F3 in Fig. 1�b�, the angles and distances between planes cane obtained. Although plane is a simple geometry, the approachresented in this section can be expanded to other more compli-ated geometrical shapes, such as the spherical surface determinedy four points not on the same plane.

Three points not in the same line determine a plane. The toplane representing the porous foam surface is defined as a set ofhe three points �not in the same line� among stereovision mea-ured points that all other points are on one side of this plane. Thislane is one of the facets of the convex hull representing the dataoints �13�.

Figure 7 is used as a simplified example. The isometric and topiews of the points are shown in Figs. 7�a� and 7�b�, respectively.1A2A3 is the top plane among this set of data points. Figure 7�c�hows the side view of the plane A1A2A3, which appears as a line.ll the other points are located on one side of the line. This

ndicates that A1A2A3 is a top plane.The top plane is not unique. For example, another top plane

2A3A4 exists for the set of points in Fig. 7. This study establishesselection criterion using the triangular area of the three points on

ig. 6 Distributions of point depth from the top plane: „a… F1 inig. 1„b… with the original, as-fired surface and „b… F3 in Fig. 1„b…ith the machined surface

he top plane. Among all possible top planes, the one with the

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largest triangular area of the three points determining the topplane is designated as the plane representing the porous foamsurface. A larger triangular area of the three points is theoreticallymore stable and easier to engage in contact with a rigid, perfectlyflat surface. For example, in Fig. 7, the triangular area of A1A2A3is larger than A2A3A4. Therefore, A1A2A3 is selected as the planeto represent the measured data points. Other criteria besides usingthe triangular area are possible but require more research.

A large number of points are required to accurately representthe random, intricate porous foam surfaces. As shown in Figs. 4and 5, the ligaments and machined surface features are in the 1 to2 mm size range and require dense collections of points to repre-sent these fine features. The 75 mm�50 mm surface F1 in Figs.1�a� and 2 has approximately 185,000 points. To find the top planeof F1, a direct method, which finds all possible combinations ofany three points and checks if it is a top plane, can be used. Afteridentifying all top planes, the triangular areas of the three pointsrepresenting the top planes are compared to find the plane repre-senting surface F1. This direct method is computationally inten-sive. For example, there are 1.05�1015 potential top planes to beevaluated for the 185,000 points on surface F1. For each potentialtop plane, it is necessary to check if all points are on the same sideof the plane. A more computationally efficient approach called thegrid method is developed in this study.

The grid method divides points representing the porous foamsurface into small, equally spaced grid regions. A simplified ex-ample is illustrated in Fig. 7. Measured points are represented by

Fig. 7 Example of the grid method to determine the grid peak,local peak, and top plane of a set of points for porous foam: „a…isometric view, „b… top view, and „c… side view of plane A1A2A3

spheres of three different sizes. The grid peak is defined as the

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eak point which has higher value in the Z direction than all thether points in the same grid region. The Z axis is defined asointed in the direction toward outside of the porous foam sur-ace. Examples of the grid peaks are represented by the medium-ize sphere in Fig. 7�b�. Every grid peak is compared to the grideaks in adjacent grids. The local peak is defined as the grid peakhich is higher or with larger Z value than all adjacent grid peaks.he example in Fig. 7 shows four local peaks, A1, A2, A3, and A4,sing the largest sphere. Four local peaks determine four potentialop planes: A1A2A3, A1A2A4, A2A3A4, and A1A3A4. The A1A2A3nd A1A2A4 are the top planes with all other measured points onne side of the plane. Since A1A2A3 has a larger triangular area, its designated as the top plane to represent the porous foam sur-ace.

The grid method can substantially reduce the number of pointso search for the top plane. To implement this concept in practicalomputation, more refined procedures are required. The proce-ures of the grid method are shown in the flowchart in Fig. 8 andiscussed as follows.

Step 1: Prepare the data points: The grid regions are created onn XY plane, as shown in Fig. 7. The XY plane needs to be ap-roximately parallel to the porous foam surface plane. The origi-al data points provided by stereovision measurement system areased on an arbitrary X�Y�Z� coordinate system. This set of dataoints needs to be transformed to a new XYZ coordinate systemith the Z axis in the direction toward the outside of the porous

oam surface. The Z value of each point is used as the height todentify the local and grid peaks. As a start, three points are manu-lly picked as the initial guess of the top plane.

Step 2: Define the Coordinate System and Transform the Points:his is the start of iteration to evaluate if this set of selected threeoints is the top plane with the largest triangular area. The threeelected points define a plane and the initial Z direction. All pointsith the Z value greater than −D are picked and a least-squares-lane, which is the new XY plane, is fit to the selected points. D isthreshold value to determine a layer of surface data points to

etermine the new XY plane. A new Z direction is normal to theY plane. All points are transformed to the new XYZ coordinate

ig. 8 Flowchart of the procedures to identify a representativelane for the porous foam surface

ystem.

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Step 3: Create the Grid Pattern: Among all points, find thelowest X and Y values. For example, as shown in Fig. 7�b�, pointA1 has the lowest X value and point A5 has the lowest Y value.Starting at a virtual point with the combination of the lowest Xand Y values, represented by A6 in Fig. 7�b�, a set of grid can becreated. In this study, the grid size G is the same in the X and Ydirections.

Step 4: Find the Grid and Local Peaks: In each grid, a gridpeak is identified. By comparing heights of grid peaks in adjacentgrids, local peaks are recognized.

Step 5: Find the Top Plane with the Largest Triangular Area:For all possible combinations of any three local peaks, find the topplanes. Among all top planes, find the top plane with the largesttriangular area of the three local peaks.

Step 6: Check the Grid Size: If no top plane can be found,reduce the grid size G and return to Step 3. If at least one topplane can be found, go to Step 7.

Step 7: Compare with the Three Local Peaks from the PreviousIteration. If this is the first iteration, use the three local peaks asthe new initial points and return to Step 2. If the three local peaksmatch the results in the previous iteration, it indicates that the topplane representing the porous foam surface has been found. If thethree local peaks do not match results obtained in the previousiteration, check if the number of iteration exceeds the limit. If itdoes, reduce the grid size G, reset the iteration number, and returnto Step 2. Otherwise, return the three local peaks as the new initialpoints to Step 2.

This procedure is programmed in MatLab and applied to pro-cess the data points of porous foams measured using the stereovi-sion system.

5 Examples of MeasurementThe SiC open-cell foam shown in Fig. 1 and an aluminum

closed-cell foam are used as examples to demonstrate the gridmethod to identify surface planes, angle between planes, and dis-tance between planes on porous foams.

5.1 Open-Cell Foam. The original, as-fired surface F1 andmachined surfaces F2 and F3 on the SiC open-cell porous foam inFig. 1 are studied and the results are presented in the followingsections.

5.1.1 Surface F1-Original, As-Fired Surface. The top view ofthe original, as-fired surface F1 of the SiC foam is shown in Fig.9�a�. The 729,000 points measured by the stereovision system,viewed from the same angle as in Fig. 9�a�, are presented in Fig.9�b�. Following the procedures in the previous section with D=0.5 mm, G=0.3 mm, and three arbitrary picked initial points,the XYZ coordinate system is established as per Step 2 and thegrid pattern is defined as per Step 3. Among the 43,719 grids, 521local peaks are obtained in Step 4. This can substantially reducethe computational time searching for the top plane. In the firstiteration, 26 top planes are obtained in Step 5. The three localpeaks of the top plane with the largest triangular area are used asthe initial guess for the second iteration. In the second iteration,283 local peaks and 31 top planes are obtained. In Step 7, thesame three local peaks as in the first iteration are obtained. Thisindicates the convergence of iterations and concludes the searchfor the top plane for F1.

To verify the result and to demonstrate the savings in compu-tational time, the direct method, which searches all possible com-binations of three points among all the data points, is applied tofind the representative plane for F1. The same results as the gridmethod are obtained. This validates the grid method. The compu-tational time is 50 h for the direct method versus 15 min for thegrid method on a PC workstation running MatLab.

The three local peaks of the top plane representing surface F1

are marked as points P11, P12, and P13, as shown in Fig. 9.

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lose-up views of three regions around P11, P12, and P13, includ-ng both the microscopic pictures and corresponding cloud ofoints measurements, are shown in Fig. 10.

Figure 10�a� shows the local peak P11, which is marked by anrrow, and the cell structure around P11. The cell size is aboutmm and the ligament size is about 1 mm. Ligaments surround-

ng the cells can be recognized in both the photograph and pointsepresentation. The closely matched shape of cells and ligamentsemonstrates that the stereovision measured points provide a goodepresentation of the porous foam surface. The detailed view ofhe ligament with point P11 is presented in Fig. 4�b�. The point

11, marked by an arrow in Fig. 4�b�, is viewed from the side toemonstrate that it is indeed a high point on the porous foamurface.

The second local peak P12 and its surrounding region are shownn Fig. 10�b�. The match of cell shape can be recognized bylosely examining the photograph picture and points representa-ion of ligaments at different depth levels. The capability of ste-eovision system to capture features under the top plane is appar-nt. Detailed view of P12 has been shown in Fig. 4�a�. This viewf P12 from the side confirms that it is the peak of a standing stemigament, as discussed in Sec. 3.

The third local peak P13 and its surrounding region are shownn Fig. 10�c�. Like P12, P13 is also a peak on a standing stemigament. As shown in Fig. 9, P13 is close to the boundary of theorous foam. This can be recognized on both the photo and pointepresentation of ligaments around P13.

A test is conducted to evaluate the effect of grid size G. As Gncreased from 0.3 to 0.6 mm, the same three local peaks �P11,

12, and P13� representing the top plane for F1 are obtained. A

ig. 9 Top view of surface F1 and local peaks P11, P12, and P13n the open-cell SiC foam: „a… photograph and „b… measuredoints

arger G shortens the computational time. However, when G is too

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large, in this case when it reaches 0.7 mm, no top plane can befound. This demonstrates the need to balance the computationefficiency and accuracy in the grid method.

5.1.2 Surface F2-Machined Surface. The top view of surfaceF2 is shown by the photo picture of the foam in Fig. 11�a� and by

Fig. 10 Close-up view „photos and data points… of the threelocal peaks on surface F1 in Fig. 9: „a… P11, „b… P12, and „c… P13

Fig. 11 Top view of surface F2 in the open-cell SiC foam andlocal peaks P21, P22, and P23: „a… photograph and „b… measured

points

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he measured cloud of points in Fig. 11�b�. About 24,000 mea-ured points are used to represent F2. A white band can be recog-ized on the top of surface F2. This is a concentration of points ofurface F1. As discussed in Sec. 3 and Fig. 6, the stereovisioneasurement system has a deeper penetration on surface F1.Using D=0.5 mm, G=0.3 mm, and three arbitrary selected

tarting points on the surface, 15,164 grids, 262 local peaks, and4 top planes are obtained in the first iteration. The three localeaks that form the top plane with the largest triangular area aresed as the initial guess for the second iteration. The same threeocal peaks, marked as P21, P22, and P23 in Fig. 11, are obtained inoth iterations.

A test was conducted to evaluate the selection of three initialoints in Step 1. These three points can be close to and far awayrom each other. If the three initial points are close to each other,he iterations to search for local peaks may be constrained within

small region. In this case, a locally representative top plane isound. The three initial points should be selected as far away atpposite ends of the surface as possible.

The three local peaks representing surface F2 are marked asoints P21, P22, and P23 and denoted by the arrows in Figs. 11 and2. Close-up views of the regions around P21, P22, and P23, in-luding both the microscopic pictures and the corresponding col-ection of measured points, are shown in Fig. 12. On the machinedurface, a majority of the measured points are concentrated nearhe top plane, as shown in Fig. 6�b�. In Figs. 11�b� and 12, con-entrated bands of points mimic the area of machined surface inorresponding photo pictures of the foam.

Figure 12�a� shows the location of point P21, represented by therrow symbol. P21 is located on the flat machined surface. Suchachined surface areas in the picture can be traced by the band of

ense points in the point representation. Compared to Fig. 10surface F1�, the density of points for the machined surface F2 isower. Most of the ligaments under the machined surface cannote recognized in the cloud of points representation. The limited

ig. 12 Close-up view „photos and data points… of the threeocal peaks on surface F2 in Fig. 11: „a… P21, „b… P22, and „c… P23

iew direction for side faces, as described in Sec. 3, is the likely

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cause for poor resolution and depth of penetration.The local peaks P22 and P23 for surface F2 are shown by the

arrow in Figs. 12�b� and 12�c�, respectively. Both peaks P22 andP23 are also located on the flat, machined surface.

5.1.3 Plane Angles and Distances. Based on the top planesrepresenting porous foam surfaces, the angles and distances be-tween planes can be calculated and used to specify the geometri-cal and dimensional tolerances of a porous foam component. Theangle between two planes and the distance between two parallelplanes are investigated in this study.

Each surface of the SiC foam sample in Fig. 1 can be repre-sented by a plane. The angle between two planes is used to rep-resent the orientation between two porous foam surfaces. For ex-ample, the perpendicularity between surfaces F1 and F2 of the SiCopen-cell foam shown in Fig. 1�b� is evaluated by the angle be-tween the representative top planes of F1 and F2. Based on thedata in Secs. 5.1.1 and 5.1.2, the angle between F1 and F2 is 89.8°.

The plane distance is defined between two parallel planes. First,a porous foam surface, such as F2 in Fig. 1, is identified as thedatum plane. On the other surface, such as F3 in Fig. 1, the dis-tance of all points to the datum plane is calculated. The farthestdistance is marked as the distance between two planes. Physically,the datum plane is like a porous foam surface contacting a per-fectly flat and rigid surface of a gage block. By moving anotherperfectly flat surface parallel to the datum surface, it will contactthe porous foam surface on the point with farthest distance to thedatum surface. This distance is defined as the plane distance. Byapplying this procedure to the SiC foam in Fig. 1, the plane dis-tance between surface F2 �datum� and F3 is 49.2 mm.

5.2 Closed-Cell Foam. An aluminum closed-cell porousfoam, as shown in Fig. 13�a�, is studied. This foam was producedby the melt gas injection method �17�. The 264,000 stereovisionmeasured points representing the porous foam is shown in Fig.13�b�. The 102 mm�49 mm surface F5 is investigated to find therepresentative plane.

The top view of closed-cell foam is shown in Fig. 14. Distinctdifferent features can be observed on the surface. Around pointsP31 and P33 are large flat surface areas created by machining thesection of aluminum foam. Cavities, such as the one marked by C,can be recognized. Some cavities can be measured by the stereo-vision system. A unique feature of the closed-cell foam is the edgeof thin-wall cell surface. The cell wall after machining is a curvedline, as marked by W, on the surface. The cell size of this closed-cell foam is not consistent, ranging from 4 to 12 mm, across thesurface F5 in Fig. 13�a�.

The procedures described in Sec. 4 with D=0.5 mm, G=0.3 mm is used to analyze measured data points of surface F5. Inthe first iteration, the analysis generates 27,000 grids and 194local peaks in Step 4 and 12 top planes in Step 5. The seconditeration reaches the same three local peaks as in the first iteration.This concludes the search for the top planes with the largest tri-angular area.

The three local peaks of surface F5 are denoted as P31, P32, andP33 and shown in Fig. 14. A close-up view of the regions nearthese three points and the data points representing these regionsare illustrated in Fig. 15.

The local peak P31 is located on a machined flat surface, asshown in Fig. 15�a�. The stereovision system successfully cap-tures the flat surface. Part of the cavity, marked as C in Fig. 15�a�,was also recorded by the measurement system.

Local peaks P32 and P33, as shown in Figs. 15�b� and 15�c�,respectively, are also located on machined flat surfaces. The thincell wall may be deformed, deflected, or buckled during the ma-chining and subsequent material handling process and does notextend out as high points to represent the plane surface for closed-

cell foam.

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Concluding RemarksThis study utilized the stereovision measurement system for

apid, noncontact measurements of the SiC open-cell and alumi-um closed-cell foams. Detailed surface features, such as the stemnd edge ligaments, machined surface flats, and thin-wall edges,an be captured by this optical measurement system. A computa-ionally efficient grid method was developed to identify the gridnd local peaks and to search for representative top planes of aorous foam surface. A criterion based on the triangular area ofhe three local peaks was proposed for the selection of the toplane. Effects of grid size and initial guess points selection weretudied. The depth distributions of measured points below the rep-esentative top planes were analyzed. Based on the geometricalelationships between representative surface planes, the angle andistance between porous foam surfaces were calculated.

This is an exploratory study of the dimensional and geometricalorm measurement of porous foams. Many research investigationsan follow. For example, the current stereovision measurementechnology has demonstrated to perform well for the porous foamith relatively large pore size of 2 mm or bigger. For finer pore

ize, other optical measurement systems need to be investigated.ther research needs to further advance the knowledge and appli-

ations of porous foam materials include: �1� the geometrical di-

ig. 13 Isometric overview of the surface F5 in the aluminumlosed-cell foam: „a… photograph and „b… measured points rep-esenting the foam

ensioning and tolerancing of porous foams, �2� methods to iden-

58 / Vol. 128, NOVEMBER 2006

tify more complicated shape, such as cylinder and sphere, frommeasured data points, and �3� contact stress analysis based on themeasurement data.

Fig. 14 Top view of surface F5 in the aluminum closed-cellfoam and local peaks P31, P32, and P33: „a… photograph and „b…measured points

Fig. 15 Close-up view „photos and data points… of the threelocal peak points of the closed-cell aluminum foam surface: „a…

P31, „b… P32, and „c… P33

Transactions of the ASME

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cknowledgmentThis research is sponsored by the National Science Foundation

ngineering Research Center for Reconfigurable Manufacturingystems at University of Michigan under Award Number EEC-529125. The authors would like to thank Porvair Fuel Cell Tech-ology and Cymat for supplying the foam materials. The measure-ent assistances from Eyal Mizrahi, Guy Blumberg, and Rickanden Boom of CogniTens are gratefully acknowledged.

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