three-illumination-beam phase-shifted holographic interferometry study of thermally induced...

Three-illumination-beam phase-shifted holographicinterferometry study of thermally induceddisplacements on a printed wiring board

David W. Watt, Todd S. Gross, and S. D. Hening

Spatially resolved measurement of thermally induced surface displacements of printed wiring boards usingphase-shifted holographic interferometry is discussed. Three separate holograms with three linearly inde-pendent illumination beams were recorded. The interferograms were viewed in real time from a fixeddetector location, and phase maps corresponding to each illumination direction were generated with thephase-shifting interferometer. The phase maps are then used to compute the displacements on a point bypoint basis. The measurement accuracy is estimated to be +0.004 ,um out-of-plane and +0.02 ,um in-planeover a temperature range of 40 C. The system was tested on a through hole in a printed wiring board; the re-sults of this test are discussed. Phase computation and unwrapping, data reduction, experimental geometry,surface preparation, and displacement computation are discussed.

1. IntroductionInterferometric measurement of thermally induced

displacements on electronic packages is useful inquantifying stresses and strains for reliability analysis.In most cases the studies are primarily concerned without-of-plane displacements or qualitative assessmentsof stress concentration. In some cases, however, it isdesirable to make very accurate high resolution mea-surements of the three components of surface displace-ment. These measurements can be used to verifyanalytical or numerical predictions of mechanical be-havior and may help identify mechanisms of mechani-cal failure.

The methodology for making 3-D measurements byholographic interferometry has been long established(see Ref. 1) and is based on using three or more inde-pendent combinations of illumination and viewing di-rections. By using multiple illumination-viewingcombinations, three independent interferometricphase measurements can be obtained for each surfacelocation. These measurements are then used to com-

The authors are with University of New Hampshire, Departmentof Mechanical Engineering, Durham, New Hampshire 03824-3591.

Received 14 March 1990.0003-6935/91/131617-07$05.00/0.© 1991 Optical Society of America.

pute the three components of displacement. Multi-component techniques have not been widely appliedbecause of (1) the need for multiple views (requiringgeometric image correction) or multiple holograms (re-quiring real time interferometry or precise experimen-tal repetition), (2) the need for high resolution dataacquisition using fringe interpretation, and (3) the factthat errors in fringe interpretation lead to rather largeuncertainties in the measured displacements.

Recent innovations in digital augmentation of theinterferometric process (by phase shifting) have in-creased both the accuracy and spatial resolution ofinterferometric phase measurements. Heterodyneand phase-shifting techniques (see, e.g., Refs. 2-4)have improved the accuracy from -X/10 for visualinterpretation to a reported -X/100 for phase shifting(in the case of experiments using diffuse objects).Moreover, the use of digital image storage devices fa-cilitates high spatial resolution of measurements with-in the area of interest. The problems associated withspatial transformations needed for multiple viewingdirections may be avoided by using a single viewingdirection and three separate illumination directions.This approach requires recording a separate hologramfor each illumination direction and that the resultinginterferograms be viewed in real time.

This paper describes a system for making three com-ponent surface displacement measurements of a heat-ed constrained coefficient of expansion printed wiringboards. The system (see Fig. 1) is based on recording aseparate hologram for each of three collimated waves

1 May 1991 / Vol. 30, No. 13 / APPLIED OPTICS 1617

BEAM PATH LEGEND-~ HOR I ZONTAL

. ....... ELEVATED HORIZONTAL- -DOWNWARD--- UPWARD

Fig. 1. Schematic of the three-illumination-beam optical setup.Note that the dashed lines indicate upward, downward, and elevated

beams as indicated in the legend.

illuminating a common surface area. The hologramsare mounted in an adjustable kinematic plate holderwhich allows for simple hologram replacement andrigid body motion compensation. The holograms areilluminated with a phase-shifting reference wave andviewed from a fixed location with a charge-coupleddevice (CCD) camera. The three holograms are re-corded with the object at some reference temperature,the object is heated or cooled, and interferometricphase maps from each hologram are generated. Thedata from the phase maps are processed to remove theeffects of rigid body displacements and gross thermalexpansion. The processed phase data are then used tocompute the local relative displacements, which can beused to visualize the local strains.

Several experimental studies have utilized shearinginterferometry5 and holographic interferometry 6 tomeasure thermally induced displacements on circuitcards during thermal cycling, soldering, and operation.This study was performed to develop phase-shiftedholographic interferometry (PSHI) techniques tomeasure the 3-D displacement field around platedholes during thermal cycling. The displacement sen-sitivity of PHSI (0.02 m in-plane and ±0.004 mout-of-plane) is greater than that reported in the holo-graphic interferometry study of Ref. 6 (0.16 m out-

of-plane). Furthermore, the experimental setup de-scribed herein is sensitive to both lateral and normaldisplacements compared with only normal displace-ments in Refs. 5 and 6.

11. Phase-Shifted Holographic InterferometryReal time PSHI is a hybrid optical-digital technique

which allows direct measurement of the interferomet-ric phase of a holographic interferogram.1-4 The in-terferogram is formed by the coherent superposition ofa holographic image of an object in its original stateand the image of the distorted object itself. This isaccomplished by viewing the illuminated objectthrough the reconstructed reference hologram. Theinterferogram irradiance I(x,y) at the detector (i.e.,camera) is modulated by an optical phase differenceq(x,y), which characterizes the object distortion, and isgiven by

I(x,y) = I0(xy){1 + m(x,y) cos[0(xy) + 'P, (1)

where Io is the maximum intensity, ' is a uniformbackground phase shift, and m is the fringe modula-tion amplitude. For a single interferometric image,the interferometric phase 0 is encoded in the cosineterm, meaning that its values can only be determinedby visual interpretation of the interference patternand that its sign is ambiguous.

To overcome the obvious data reduction, accuracy,and sign ambiguity problems associated with fringeinterpretation, intentional spatially uniform phaseshifts t' are introduced into the interferogram, and theconsequent changes in the irradiance I(xy) are ana-lyzed. This is typically done by adjusting the pathlength of the holographic reference beam with a mirrormounted on a piezoelectric crystal, although othermethods are possible. By recording the irradiancedistribution for several known values of the phase shiftV/, the interferometric phase can be calculated. Al-though several algorithms for phase computationshave been demonstrated (see Refs. 1-4), the presentstudy used an algorithm due to Juptner et al.

7 in whichfour irradiance distributions are recorded for multi-ples of an arbitrary phase shift it. The irradiance ofthe four exposures is given by

I,(x,y) = 0(xy)J1 + m(xy) cos[0(xy)]},

I2 (x,y) = I(x1y)11 + m(x,y) cos[P(xy) + 0]j,

I3 (x,y) = I0 (x,y){1 + m(x,y) cos['P(x,y) + 2,1],(2)

14(x,y) = Io(xy)1 + m(x,y) cos[O(xy) + 3V,]}.

The four exposures are required to resolve the fourunknowns Io, m, , and . Since the phase shiftsintroduced by the piezoelectric crystal are not exactlyreproducible, 4t (which varied by approximately ±30)was determined using the following method proposedin Ref. 5:

1 I2 + I3 142(I2-13) (3)

1618 APPLIED OPTICS / Vol. 30, No. 13 / 1 May 1991

Then the sign and magnitude of the phase (modulo 27r)can be determined from

0 = arctaI- 2I2 + I3 + (I, - 3) cosi' + 2(I2 - I) COS21

(1 - cos2 )112(- 13) + 2(I2 - I) cosP

It should be noted that if the phase shift is affected byshortening the reference path, the phase shift is nega-tive and the value of 0 determined from Eq. (4) shouldbe multiplied by -1.

The computations in Eqs. (3) and (4) are performedon a point-by-point basis to create a modulo 2 r phasemap and then are stored as an eight-bit value between0 and 254. The fringe modulation at any point is givenby m(x,y)Io(xy) and can be determined by taking thesquare root of the sum of the squares of the numeratorand denominator of Eq. (4). This operation facilitatesdetection of image points where phase computationerrors due to low fringe contrast are likely. Thesepoints are assigned a phase of 255. Low fringe con-trast points have a number of causes including thepresence of shadows and holes, the variation of surfacereflectance, and the addition of incoherent lightsources to the image. By assigning these points asignal value, they can be avoided in the processing ofthe phase map. The uncertainty in the phase mea-surements was assessed by examining the phase fluc-tuation linear phase gradient, induced by a rigid bodytilt of a target object, and was found to have a standarddeviation of 7°.

The resulting phase map is processed to account forthe 27r phase jumps by scanning the phase map from areflerence point and assigning a fringe order numberbased on the number of positive or negative phasejumps. A rectangular area of the phase map is select-ed, and the phase is measured relative to the upper leftcorner. The perimeter of the target area is scanned,and fringe order numbers are assigned. The targetarea is then scanned from its boundaries in a column orrowwise manner. These individual column or rowscans are terminated whenever a low contrast point isencountered. By scanning from four separate direc-tions, fringe order numbers can be accurately assignedto the wake of low contrast points and objects contain-ing large areas of low contrast.

Finally, the total phase map is corrected for tiltmisalignment of the hologram and large scale thermalexpansion by subtracting a linear surface generated bya least-squares fit of the data on the perimeter of thetarget area. This flattening operation provides a localphase map relative to the upper left corner of the targetregion and is essential in the present system because ofthe slightly differing alignment of the three individualholograms.

Ill. Displacement MeasurementThe optical phase is related to the local displace-

ments L(xy,z) through the following relation:

O(x,y) = K * L(x,y), (5)

where K is the sensitivity vector, which characterizesthe illumination-viewing geometry of the optical set-

up. For the circuit board, the x- and y-directions weredefined to be in the plane of the board and the z-direction was normal to the plane of the board asshown in Fig. 1. The sensitivity vector K is deter-mined from the vector subtraction of observation wavevector k2 from the illumination wave vector kl:

K = (k, - k2 ). (6)

Since X is a scalar quantity, one must record p for atleast three noncoplanar K vectors to determine unam-biguously all three components of L. The followingset of simultaneous equations must be solved:

X = (K1.I + Klj + K1,k) * (LI + Lj + Lzh),

(7)02 = (K2x1 + K2 + K2 fi) (LJ' + Lj + Lzk),

03 = (K3x) + K3) 5+ K3zh) (L,[+ L,, j+ Lzk).

Although three K vectors can be obtained by viewinga single hologram (with one illumination beam) fromthree different directions, i.e., three k2 terms, this re-quires that the digitized phase images of off-axis viewsbe geometrically transformed to correct for foreshort-ening and spatial variation of magnification. Also,since the aforementioned simultaneous equations aresolved at each point of the digitized phase images, thethree views must be fitted so that the phase data can beconverted to displacement on a point-by-point basis.

The problems inherent in the three-view approachwere circumvented by recording three separate holo-grams with three different illumination wave vectorsk1. The observation vector was parallel to the objectnormal for all three cases. Thus the coordinate systemof the phase images was coincident for each K.

IV. Experimental MethodsAn SEM-E constrained coefficient of the expansion

circuit card was mounted on one fixed support pointnear the area of interest and two floating supportpoints as indicated in Fig. 2. This support arrange-ment was implemented to minimize the rigid bodymotion due to gross thermal expansion, which causesfringe delocalization. This allows thermally induceddisplacement gradients near the plated holes of inter-est to be studied over a wide temperature range using asingle set of three holograms. Two cartridge heatersmounted in aluminum blocks were attached to themetal core of the circuit card. This facilitated circuitcard temperature control with a proportional control-ler using a chromel-alumel thermocouple mounted ata symmetrical point near the area of interest as thetarget temperature (see Fig. 2).

The circuit card was illuminated with three sepa-rate, equal intensity, collimated beams, each of whichformed a 450 angle with its surface normal. The beamseparation was 1200 in the plane of the circuit card.The phase shift was adjusted by displacing a mirror inthe reference beam with a piezoelectric crystal excitedby an amplified digitally controlled voltage. A 25-mWSiemens He-Ne laser was used to provide illumina-tion. The interferograms were viewed with a Cohu

1 May 1991 / Vol. 30, No. 13 / APPLIED OPTICS 1619

interferogram, the displacement vector was calculatedon a point-by-point basis according to the followingformula:

L = K-'(1,02,03), (8)

where Xl, 02, and 03 correspond to the phase calculatedfrom each interferogram and K-1 is the inverse sensi-tivity matrix for the three illumination beams. Thesensitivity vectors used in this study are

K1 = (-7.021 im-')J- (16.950 um-1)h,

K2 = (6.080Oum- 1)1 + (3.511,um)f - (16.050,um-1)h,

Fig. 2. SEM-E circuit board. The painted area in the lower leftcorner was examined in this study.

4800 CCD array camera, the image acquisition boardwas an Imaging Technology FG-100, and the host com-puter was a 12-MHz 80286 based PC/AT. The setuprequired the use of a number of optical stacks to equal-ize the various optical path lengths and provide therequire illumination directions. The use of concavemirrors rather than spatial filters reduced the lengthand complexity of the optical paths with no apparentdegradation in quality of the holographic image or theinterferometer performance.

The bare circuit card had two inherent illuminationdifficulties. First, the difference between the reflect-ed intensity from the epoxy laminate and that from thesolder bumps near the holes on the bare circuit cardexceeded the dynamic range of the CCD camera. Sec-ond, the FR-4 epoxy laminate was semitransparentand rotated the polarization during heating. Thesedifficulties were overcome by painting the circuit cardwith a thin 0.0254-mm (<0.001-in.) coating of low gloss(60), heat curing, white epoxy paint, creating a diffuse-ly reflecting surface. Several thermoplastic paint res-ins and Newport Diffuse Coating proved to be unsatis-factory because their reflection surface were unstable,they rotated the polarization, and they off-gassed invacuum (which will be required in high temperaturestudies).

Single exposure holograms were recorded on 10- X12.7-cm (4- X 5-in.) by 1.524-mm (0.06-in.) thick 8E75holographic plates at room temperature for all threeillumination beams. Phase-shifted interferogramsfrom all three holograms were sequentially recorded atstable temperatures of 5.5,11, 16.5, and 220 C above thereference temperature of 230C. After each hologramwas replaced, the micropositionable holder was adjust-ed manually to optimize fringe localization and con-trast. Although this procedure introduced biasfringes into the interferometric image, the aforemen-tioned flattening procedure removes the effect of thebias fringes on the phase maps.

Since the coordinate system was coincident for each

(9)

K3 = (-6.080 pm-1 )- (3.511 Am')j- (16.050um'1)i.

These vectors were formed from an observation wavevector normal to the plane of the circuit card and threeillumination wave vectors at 450 to the circuit cardnormal and 1200 apart projected in the x-y plane.Although the x and y displacement sensitivity in-creases as the angle between the specimen normal andthe illumination wave vector increases, the low intensi-ty of the diffuse reflections and problems caused byshadows limits this angle. The sensitivity to z dis-placements is about twice that for x and y displace-ments.

The accuracy of displacement measurement hasbeen reviewed by Vest.1 One of the primary sources oferror was ascribed to separation and geometric correla-tion of the three different observation wave vectors.Since this problem has been circumvented by the useof a common observation wave vector, a simple esti-mate of the displacement accuracy based on phasedetermination accuracy can be obtained from the fol-lowing expression:

- 3 [ 1/2

ALi = I (K,-j ) Ao,j=l

(10)

where AO5 is the rms uncertainty in the phase measure-ment and ALi is the rms uncertainty in the ith compo-nent of the displacement vector. The uncertainty of xand y was estimated to be +0.002 gim/deg, and theuncertainty of z was estimated to be +0.0006 m/deg.The measured phase noise of 7' corresponds to±0.014-Atm accuracy for in-plane displacements and±0.0042-ALm accuracy for out-of-plane displacements.

V. Experimental StudyConstrained coefficient of expansion (CCOE) circuit

cards have a low expansion coefficient core (5 ppm/K)that restricts lateral thermal expansion (and contrac-tion) of the multilayer glass-reinforced epoxy laminate(FR-4 CTE = 16 ppm/K) to prevent damage to surfacemount solder connections to low expansion coefficientcomponents. The multilayer printed wiring boardsunder investigation utilize copper plated throughholes (Fig. 3) to connect the various layers of circuitry.The difference in the out-of-plane thermal expansioncoefficient between the glass-reinforced epoxy lami-nate (72 ppm/K) and the copper plating (17 ppm/K)causes axial cyclic stresses in the plating during -55-

1620 APPLIED OPTICS / Vol. 30, No. 13 / 1 May 1991

Deformed state

Original stateFig. 3. Schematic of the cross section of the plated through holeindicating the relative position of the copper plating, constrainingcore, and FR-4 glass-reinforced epoxy matrix. The thick black linesindicate the proposed distortion of the board surface that would

occur for a temperature rise.

AT = 110C

0.1

0.2

1' 0.10. qj

N =0. 1

=0.2-0. 4

'Zop

Negative A

1250C thermal cycling typically required of militaryelectronic packages. The lateral constraint from thecore should increase the epoxy laminate's thermal ex-pansion normal to the circuit card, thereby increasingthe magnitude of the cyclic stresses in the copper plat-ing. This study was initiated to measure the magni-tude of the thermally induced surface displacementsaround plated holes to estimate the magnitude of thecyclic thermal stresses and strains in the copper plat-ing of the holes. Several models have been developedthat estimate the magnitude of the thermal stressesand the number of cycles to failure for a plated holeundergoing thermal cycling.89 The surface displace-ment data obtained with this method will be used toassess the accuracy of these models in future papers.

Surface and topographic contour plots of the out-of-plane surface displacements for an 110C temperaturerise are shown in Fig. 4 where the hole has been plottedas having zero displacement. The surface plots aresplit to show the displacements near the hole edge, and

AT = 110C

z Positive Az

-1000 -500 01000 El----iiiin----

500

Fig. 4. Surface and topographiccontour plots for the z (normal)displacements for a temperaturerise of 11°C. The surface plotsare split, and the topographicplots are for positive and negativedisplacements both for improvedclarity. The hole is plotted as

having zero displacement.

0

-500

-1000 rtY-1000 -500 0 500

x (,m)

500 1000 -10007n~rTTPn13 1000 1000 Em=

500 500

-500

0

-500

1M -1000-1000 I'll01000 -1000

-500 0

-500 0 500

x (,um)

500 1000FNiCFeTfT 1000

500

0

-500

-10001000

1 May 1991 / Vol. 30, No. 13 / APPLIED OPTICS 1621

~- 0.30

00.20

C

E-~ 0.00

~4 -0.10

Pq~ -0.20CF

-0.c ~_

z displacement - constant y----z displacement - constant x

00 -500POSITION

0 500 1 000(micrometers)

Fig. 5. Constantx and constanty slice plots through the hole centerof the z displacements for a temperature rise of 110C. The hole is

plotted as having zero displacement.

AT =I 10C

0. :~_-

-11 0.02 .

0. I .i

-0. 2

c 0.

Negative Ar

the topographic contour plots are arranged to show thenegative and positive displacement contours. As ex-pected, the surface puckers inward on the periphery ofthe hole due to the copper plating restricting the out-of-plane expansion of the FR-4 epoxy matrix. Theslice plots through the center of the hole in Fig. 5 showthat the constraint at constant x is greater than theconstraint at constant y, although the displacementsare symmetric about the center for a given slice. Thisdifference in constraint is visible as a cusp in the sur-face plot (Fig. 4). Note that Figs. 4-7 contain rawunsmoothed data for a spatial resolution (pixel size) of31.2 ym.

The x and y displacements were converted to radialdisplacements using the hole center as r = 0. Thesurface and topographic plots of the radial displace-ments are shown in Fig. 6. It is interesting to observethat the displacements near the hole are negative,meaning that the radius of the hole decreases withincreasing temperature. This can be understoodwhen one considers that the low expansion coefficientcore is restricting the lateral thermal expansion of theFR-4 matrix except in the vicinity of a free surface, e.g.,

AT = 1 10C

Positive Ar

-500 0 500 1000 -1000T1T1Tl~1 000 1 000 m.~m

0 500

X (G.m)

500 500I-5:�.I I

-500

0

-500

-500 0

1000 -1000 -500 0

(M)

500 1000F7FiMffiW 1 000

'7� 5001. , '. 0

;J "i .1

' 't , -500" C ., I

-1000500 1000

Fig. 6. Surface and topographic contour plots for the radial (in-plane) displacements for a temperature rise of 110C.

1622 APPLIED OPTICS / Vol. 30, No. 13 I 1 May 1991

-10001000 GU~

500

0

-500

- 1000 -C

� '_ '_ '_ � , � � , I. . . . . . . . - 1- 1 I I- I

- I

I- - '.�IS' %9.

11___�'_

_t1Z.

U

0.2

C)

0

C)-_

H O.Cz

V-0.1

V24(1

0

00

0

Radial displacement - constant y------ Radial displacement - constant x

l . . . . . I . . . . . . . . . I l l l . . . . . . I . . .

-500POSITION

0 500 1000(micrometers)

Fig.7. Constantx and constanty slice plots through the hole centerof the radial displacements for a temperature rise of 110 C.

the hole. This is schematically illustrated in Fig. 3.The slice plots in Fig. 7 illustrate that the noise in thein-plane displacement data is significantly greaterthan that for the out-of-plane data as predicted by Eq.(10). They also illustrate that the displacements arenot symmetric about the center.

VI. SummaryThe thermally induced displacements around a cop-

per plated through hole on a multilayer constrainedcoefficient of expansion printed wiring board weremeasured using three-illumination-beam phase-shift-ed holographic interferometry. The displacementresolution was estimated to be +0.014 Am in-plane and+0.004 Am out-of-plane for a spatial resolution of -30,m. It was demonstrated that the copper plating onthe plated hole restricts the out-of-plane expansion of

the FR-4 epoxy laminate. It was also shown that theradius of the hole decreases with increasing tempera-ture due to the combination of the constraining effectof the core and that the hole is an unconstrained freesurface.

This work was jointly supported by Lockheed-Sand-ers Associates, Nashua, NH and by the University ofNew Hampshire. The programming assistance fromThomas McCallion is greatly appreciated. The dis-cussions with L. L. Lustig and Dan Holland of Lock-heed-Sanders were extremely useful both in definingthe problem and in identifying the appropriate paintfor high quality holograms.

References1. C. M. Vest, Holographic Interferometry (Wiley, New York,

1979).2. R. Dandliker, R. Thalmann, and J. F. Willemin, "Fringe Interpo-

lation by Two Reference Beam Holographic Interferometry,"Opt. Commun. 42, 301-306 (1982).

3. R. Thalmann and R. Dandliker, "High Resolution Video Process-ing for Holographic Interferometry Applied to Contouring andMeasuring Deformations," Proc. Soc. Photo-Opt. Instrum. Eng.492, 299-306 (1984).

4. P. Hariharan, "Quasi-Heterodyne Holographic Interferometry,"Opt. Eng. 24, 632-638 (1985).

5. D. A. Tossell and K. H. G. Ashbee, "High Resolution OpticalInterference Investigation of Deformation due to Thermal Ex-pansion Mismatch Around Plated Through Holes in MultilayerCircuit Boards," J. Electron. Mater. 18, 275-286 (1989).

6. T. D. Dudderar, P. M. Hall, and J. A. Gilbert, "Holo-Interfero-metric Measurement of the Thermal Deformation Response toPower Dissipation in Multilayered Printed Wiring Boards," Exp.Mech. 25, 95-104 (1985).

7. W. Juptner, T. M. Kreis, and H. Kreitlow, "Automatic Evalua-tion of Holographic Interferograms by Reference Beam PhaseShifting," Proc. Soc. Photo-Opt. Instrum. Eng. 398,22-29 (1983).

8. B. A. Mirman, "Mathematical Model of a Plated-Through HoleUnder a Load Induced by Thermal Mismatch," IEEE Trans.Components Hybrids Manuf. Technol. CHMT-11, 506-511(1988).

9. L. A. Torres, "Thermally Induced Strain in Plated ThroughHoles," International Packaging Council Technical Paper IPC-TP-510 (1984).

1 May 1991 / Vol. 30, No. 13 / APPLIED OPTICS 1623

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