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Technical Note

Full-field optical deformation measurement inbiomechanics: Digital speckle pattern interferometryand 3D digital image correlation applied to bird beaks

Joris Soonsa,n, Pascal Lavab, Dimitri Debruyneb,c, Joris Dirckxa

aLaboratory of Biomedical Physics, University of Antwerp, Groenenborgerlaan 171, B2020 Antwerpen, BelgiumbDepartment of Mechanical Engineering, Catholic University College Ghent, Gebroeders Desmetstraat 1, B9000 Gent, BelgiumcDepartment MTM, Katholieke Universiteit Leuven, Kasteelpark Arenberg 44, 3001 Leuven, Belgium

a r t i c l e i n f o

Article history:

Received 15 March 2012

Received in revised form

2 May 2012

Accepted 6 May 2012

Available online 18 May 2012

Keywords:

Digital image correlation (DIC)

Digital speckle pattern

interferometry (DSPI)

Finite element modeling

Validation experiment

Beak

nt matter & 2012 Elsevie.1016/j.jmbbm.2012.05.00

hor. Tel.: þ32 32653438; fajoris.soons@ua.ac.be (J. S

a b s t r a c t

In this paper two easy-to-use optical setups for the validation of biomechanical finite

element (FE) models are presented. First, we show an easy-to-build Michelson digital

speckle pattern interferometer (DSPI) setup, yielding the out-of-plane displacement. We

also introduce three-dimensional digital image correlation (3D-DIC), a stereo photogram-

metric technique. Both techniques are non-contact and full field, but they differ in nature

and have different magnitudes of sensitivity. In this paper we successfully apply both

techniques to validate a multi-layered FE model of a small bird beak, a strong but very light

biological composite. DSPI can measure very small deformations, with potentially high

signal-to-noise ratios. Its high sensitivity, however, results in high stability requirements

and makes it hard to use it outside an optical laboratory and on living samples. In addition,

large loads have to be divided into small incremental load steps to avoid phase unwrapping

errors and speckle de-correlation. 3D-DIC needs much larger displacements, but auto-

matically yields the strains. It is more flexible, does not have stability requirements, and

can easily be used as an optical strain gage.

& 2012 Elsevier Ltd. All rights reserved.

1. Introduction

The beaks of granivorous birds have to withstand large forces

during the crushing of seeds. The large ground finch (Geospiza

magnirostris), for instance, only weighs 30 g but can generate a

50 N bite force (pers. obs.). These birds are also constrained

by their flying lifestyle. As a result, beaks are expected to be

highly optimized, making them interesting from both a

biological and a mechanical point of view. The multi-layered

beak consists of trabecular bone in the center, surrounded by

compact bone and the keratinous rhamphotheca. Previous

r Ltd. All rights reserved4

x: þ32 32653318.oons).

studies on the java finch include morphology, ontogenesis,

material characterization and finite element (FE) modeling

(Soons et al., 2010, 2012a, in press; Genbrugge et al., 2012).

Finite element modeling has proven to be an important tool in

biomechanics (Dumont et al., 2005; Degrange et al., 2010; Groning

et al., 2009; Bright and Groning, 2012; Ross et al., 2011; Kupczik

et al., 2007). It allows us to understand complex problems. An

important step in a good FE analysis is a relevant validation

measurement. Strain gauging is a well-known and straightfor-

ward validation technique (Ross et al., 2011; Kupczik et al., 2007),

but it has some major disadvantages. Strain gauges are attached

.

Fig. 1 – Experimental setup. Top left: schematic drawing of

the digital speckle pattern interferometry (DSPI) setup.

Bottom left: schematic drawing of the digital image

correlation (DIC) setup. Inset: the skull and jawbones of a

java finch are constrained in a sample holder, filled with

polyester resin. The seed reaction force is simulated by an

indentation at the tip of the upper beak.

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to the sample, which may influence the measurement. The

installation is also time-consuming and difficult, especially on

small and complex structures such as the beak of finches.

Moreover, the strains can only be obtained on a small number

of measurement locations. These issues can be overcome by

using optical techniques. In this paper, we will show two easy-

to-build full field methods: out-of-plane digital speckle pattern

interferometry (DSPI), also known as electronic speckle pattern

interferometry (ESPI), and digital image correlation (DIC). The

main goal of this paper is to test their applicability in validating

FE analysis derived results. Both techniques will be assessed by

measuring the bending of the java finch’s upper beak and by

comparing it with FE model results. The presented techniques,

however, are applicable in a wide range of biomechanical

problems.

Both techniques rely on speckles. The nature of the speck-

les is, however, completely different. In DSPI a speckled

image is obtained by diffuse reflections of coherent light

on a rough surface. The reflected light will have the same

frequency, but different phases and amplitudes caused by the

random microscopic height variations. When added together,

the resultant amplitude, and therefore intensity, will vary

randomly. As a result, a speckled pattern is observed.

DSPI is an interferometric setup. If the speckle pattern from

an object is combined with a reference beam, a complex

interference pattern is obtained. After the deformation of the

object, phase differences are introduced in this complex

interference pattern. These phase differences can be linked

to the displacement. If the displacement is measured in three

different directions, and the surface shape is known, one can

calculate the surface strains. The very high sensitivity (sub-

wave length resolution) makes it a valuable tool for non-

destructive testing. The sensitivity is independent of the pixel

size. The pixel size determines the number of phases that can

be resolved and as such the maximum permissible displace-

ment. The high sensitivity requires sub-wavelength stability

and makes it difficult to apply this technique outside the

optical lab or in vivo. Recently, DSPI has been introduced in

biomechanics. Some examples are found in literature, includ-

ing the displacement of the tympanic membrane (Del Socorro

Hernandez-Montes et al., 2009), the strains on human and

macaque tooth (Zaslansky et al., 2005, 2006; Barak et al.,

2009a, 2009b; Chattah et al., 2011) on human bones (Barak

et al., 2009a, 2009b), the mouse femur (Yang et al., 2007), the

ovine callus (Bottlang et al., 2008), the human mandible

(Groning et al., 2009) and zygomatic arch of the pig (Bright

and Groning, 2012).

DIC, on the other hand, is a photogrammetric setup. The

speckled pattern is physically applied to the object. Coordi-

nates of points, labeled by the randomly applied stochastic

(speckled) pattern are captured with a camera and identified

with a computing intensive image correlation. These points

are followed when the object is deformed and displacements

are acquired with sub-pixel resolution. Three-dimensional

surface results can be acquired using a stereo camera system.

The optical setup is straightforward and there are no inter-

ferometric stability requirements, making this technique

easy-to-use, scalable, highly usable for applications outside

the lab and for measurements in biomechanics. Increasing

computer power has made the technique more popular

(Schmidt et al., 2003) and has recently resulted in biomecha-

nical applications: including strain measurements on human

bone and tendon (Tyson et al., 2002), on mouse arteries

(Sutton et al., 2008) and on mouse bone (Sztefek et al., 2010).

2. Material and methods

2.1. Bending experiment

It is difficult to constrain the bite position and to apply the

(muscle) forces to the tiny jaw bones of the java finch’s upper

beak, especially if interferometric stability is required. Hence we

work the other way around and propose a bending experiment

to mimic tip biting on a seed (inset in Fig. 1). In this experiment

the jaw bones and the skull are constrained in a sample holder

filled with cured polyester resin (VIAPAL 223BS/65). A seed

reaction force is introduced with a stepper motor (steps of

16 nm per motor step, range 2 mm, PI M-235.2DG) at the tip of

the beak and the precise force is measured with a loadcell

(Sensotec 31, 5 N and 50 N range). Two java finches were used

for the bending experiment: one for DIC and one for DSPI.

Those beaks were approximately 15 mm in length and the

difference in length and width were smaller than 10%. Lower

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beak, feathers, muscles and brains were removed. The resin

was allowed to cure for a minimal time of 48 h. The study was

performed according to the regulations of the Ethical Commit-

tee for Animal Experiments of the University of Antwerp. More

information about this bending experiment and the sample

preparation can be found in Soons et al. (2012a, in press).

2.2. Finite element model

A third java finch was imaged at the European Synchrotron

Radiation Facility (ESRF, Grenoble) (image matrix of 2 kpx�

2 kpx with a resolution of 45 mm). Bone and keratin were

segmented semi-automatically (Amira 4.1; 64-bit version, TGS

systems) and a multi-layered volumetric grid, consisting of a

bony core surrounded by a keratin layer, was established (as

described in Soons et al., in press). This FE mesh of the beak

was subsequently scaled to the same dimension as the upper

beaks used in the bending experiments. Boundary conditions

were chosen in order to simulate the mechanical loading: a

loading force in the z-direction, depending on the measured

reaction force, was applied at the bite position, and the

embedding in polyester resin (Fig. 1) was simulated by con-

straining elements of the jaw bones and the beginning of the

skull. The Poisson’s ratio for bone and keratin was chosen to

be 0.4 (Franck et al., 2006, Wroe, 2008). The Young’s modulus

for avian bone and dry keratin are 7.3 GPa and 3.1 GPa,

respectively (Soons et al., 2012a). All FE analyses were con-

ducted in FEBio, a FE program designed for the mechanical

analysis of biological structure (Maas and Weiss, 2008).

2.3. Digital speckle pattern interferometry

A He–Ne laser (l¼632.8 nm) was expanded with a telescopic

lens with spatial filter (Fig. 1, top). Next, a Michelson setup,

placed on a vibration-isolated table, was used to illuminate

the top of the upper beak in the bending experiment and a

reference plate. Interference patterns of both were combined

and captured with a telecentric camera (AVT pike F-505,

2048�2452 pixels, resulting in a 8 mm pixelsize). A displace-

ment of 5 mm was introduced with the stepper motor. Corre-

lation between the undeformed and deformed interference

pattern gave the full field out-of-plane displacement (w).

With the beak in undeformed state, four phase-shifted inter-

ferograms were recorded by translating the reference plate in

subsequent steps of an eighth of the light wavelength. From

these four undeformed interferograms and one interfero-

gram recorded in the deformed state, the object deformation

can be calculated with high precision (720 nm). The deriva-

tive of the out-of-plane displacement (z) was calculated. For

the characterization of bending, this value seems to be more

useful than just the out-of-plane displacement. Indeed, the

derivative of a rigid body movement, which is not interesting

from a mechanical point-of-view, yields a constant and can

be easily neglected (Leendertz and Butters, 1973). The corre-

sponding FE model boundary conditions are estimated based

on photos of the experimental setup. More information about

this technique can be found in Soons and Dirckx (2010) and

Soons et al. (2012a).

The coefficient of determination (R-squared) is calculated to

compare DSPI with FE modeling results (Soons et al., 2012a, in

press). For this comparison, the derivative of the out-of-plane

displacement along the x-direction is considered for all visible

points, except for the bending area and some noisy parts. If the

experiment and model results coincide, an R-squared of 1

is obtained. R-squared values smaller than 0 indicate that

the model prediction is less accurate than the mean of the

experimental data.

2.4. Digital image correlation

A Stereo system with two cameras (AVT pike F-505, 2048�2452

pixels, Smc Pentax bellows lens 1:4 100 mm, f/32, resulting in

a 7 mm pixelsize and a field of view of 14�17 mm2) with an

opening angle of approximately 301 is used (Fig. 1, bottom).

Polarized light is used to illuminate the sample. As a conse-

quence, polarizers in front of the camera can be used to reduce

specular reflections. Automatic system calibration was con-

ducted before and after the actual measurements using various

images of a translated and rotated regular grid pattern within a

bundle adjustment technique (Triggs et al., 2000). As a result,

intrinsic (focal lengths, distortions and image plane center

location) and extrinsic (rotation and translation) camera para-

meters were obtained.

Four stereo images were taken, two before and two after the

125 mm displacement. In the first step, the initial undeformed

shape was reconstructed by finding the corresponding speckles

in the images captured by camera 1 and camera 2 and via a

triangulation method invoking the determined stereo camera

parameters (Lava et al., 2011). Next, a similar procedure was

applied to the images of the deformed state. Finally, a direct

comparison of the deformed (x,y,z) and the undeformed

(x0,y0,z0) shape yields the 3D deformation coordinates (u,v,w).

These contain all the information needed to determine the in-

plane normal and shear strain components (ex,ey,exy).

The following settings were used in the displacement deter-

mination: a subset size of 21 pixels, a step size of 10 pixels,

correlation algorithm, bicubic interpolation and affine shape

functions. Strains were calculated in the Green–Lagrange con-

vention and a strain window of 50�50 pixels2 and a bilinear

interpolation was taken. Results are transformed into the

coordinate system of camera 1 (Fig. 3), which is aligned parallel

to the direction of the punch force. Accordingly, the correspond-

ing FE model can be easily transformed to the same coordinate

system. DIC requires the presence of a random pattern on the

specimen. This is applied by air brushing on top of the upper

beak (pattern can be seen in Figs. 2 and 3). The influence of this

pattern is expected to be minimal due to the stiff keratin and

bone. All calibration and correlation are executed in the

MatchID software package (in-house developed: http://www.

matchid.org/).

3. Results

The full-field out-of-plane displacements (w) obtained with

DIC and DSPI are shown in Fig. 2 (left). The results presented in

this paper are from a single measurement. Repetition of the

experiment shows a very small variation for the displacement

measurement of both DSPI and DIC. The variation for the

derivatives (and strains) was larger due to the induced noise.

Fig. 2 – Left: out-of-plane displacement (w) for DIC (top) and DSPI (bottom). Notice the different magnitude in displacement:

80 lm for DIC (reaction force¼5.5 N) and 3 lm for DSPI (reaction force¼0.21 N). Right: derivative of the out-of-plane

displacement (w) along the x-direction (longitudinal cross-section indicated at the left), normalized to the reaction force for

DIC (top) and DSPI (bottom), compared to FE results.

Fig. 3 – Strains (ex: 1st row, ey: 2nd row, exy: 3rd row) measured with DIC (1st column) and calculated from FE model (2nd

column). Cross-sectional results are shown in the 3rd (longitudinal, dashed line in 2nd column) and 4th column (transversal,

dotted line in 2nd column). DIC results are presented with the continuous lines, FE results with the dashed lines.

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Multiple measurements will improve the signal-to-noise ratio

(Soons et al., in press). We did not combine measurements to

show the capability of both techniques. The precision and

accuracy are described by comparing the experiments with the

FE results. For DSPI, the measured displacement at the tip of

beak was approximately 3 mm and a reaction force of 0.21 N

was obtained. In contrast, for DIC a 25 times larger displace-

ment (80 mm at the tip) and reaction force (5.5 N) were

obtained. The sub-wavelength sensitivity of DSPI is approxi-

mately 20 nm, independent of the pixel size used. On the other

hand, the sensitivity for DIC is highly scalable. For our setup,

an out-of-plane displacement precision of approximately 1 mm

and an in-plane of 0.5 mm was found.

Next, the derivative of this out-of-plane displacement (w)

along the x-direction was taken. The longitudinal cross-sections

obtained with DSPI and DIC, normalized to the reaction force, are

presented in Fig. 2 (right) and compared with the corresponding

FE models. A full field R-squared of 0.89 between DSPI and FE

was calculated on the entire visible surface, except for some

noisy locations (Soons et al., in press). For DIC, the results were

noisier, so a larger window was used to calculate the derivatives

and a lower R-squared of 0.52 was obtained.

Besides the displacement in the z-direction, DIC also yields

the coordinates (x,y,z) of the surface and the displacement

(u,v,w) at every (visible) point. As a result, we can obtain the

strains (ex, ey, exy) over this surface. The full field results of the

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strain, compared with their corresponding FE results, are

presented in Fig. 3. A qualitative examination indicates a fairly

good correspondence between model and experiment, except

for a noisy part at the left side of the upper beak.

A quantitative comparison for the longitudinal and transversal

(Fig. 3) cross-sections shows a good correspondence. Maximal

strains in both experiment and model are approximately 3000

microstrain. A good correspondence is found for ex. The quite

uniformly negative values for ex indicate an almost uniform

compression at the top of the beak of approximately 1000

microstrain. For in vivo bite forces, which are expected to be

approximately 2 times larger, strains about 2000 microstrain are

expected. This compression is a result of the bending. More

towards the edge of the beak, the bending becomes smaller and

so do the ex value (Fig. 3, 1st row, 4th column). For x-values

smaller than 2, a larger deviation is observed (Fig. 3, 1st row, 3rd

column). We believe that this deviation is a local error, caused by

the modeling approach of the bending zone. The results for eyshow positive strains, thus an extension in the y-direction, on

top of the upper beak. A deviation, probably due to noise,

between experiment and model is observed for y smaller than

3 mm. The shear strain exy shows, except for the same noisy

part, good correspondence in the transversal direction (Fig. 3, 3rd

row, 4th column). The longitudinal results (Fig. 3, 3rd row, 3rd

column), however, show some offset towards the tip of the beak.

This deviation is, in our opinion, due to the use of two different

samples, resulting in a misalignment.

4. Discussion

The two optical techniques, digital speckle pattern interfero-

metry (DSPI) and digital image correlation (DIC), were achieved

with an easy experimental setup (Figs. 2 and 3). The results for

DIC, DSPI and FE were obtained on three different specimens.

As a result, intra-specific variation between the specimens is

neglected and a direct comparison is difficult. Nevertheless, a

qualitative comparison between the experimental techniques

and the modeling outcome shows good correspondence.

DIC requires the presence of a random pattern on the

specimen. This coating can influence the results on compli-

ant materials or if one is interested in dynamical behavior.

DSPI only needs a coating if the reflection is low or to avoid

specular reflections. On macroscopic irregular surfaces one

needs to avoid ‘shadow’ artifacts. For 3D-DIC, this means that

every point has to visible by both cameras. In out-of-plane

DSPI, shadow artifacts are easily avoided by the perpendicu-

lar laser illumination and viewing direction. Nevertheless, if

one wants to obtain in-plane displacements with DSPI, one

also needs to take these shadow artifacts into account.

The derivative of the out-of-plane displacement along x,

normalized to the reaction force (d(w/F)/dx) was shown to be a

good parameter to describe the bending (Leendertz and Butters,

1973). Indeed, a rigid body movement will introduce a constant

factor. This additional factor is neglected in our analysis because

an offset is expected due to an approximation near the bending

zone. The normalization to the force, allows us to compare the

two experimental techniques. The reaction force and the

induced displacement of DSPI are 25 times smaller than DIC.

This large difference is caused by the different sensitivities of

both optical techniques. Indeed, large displacements for DSPI

will cause phase unwrapping and de-correlation errors, while for

DIC, too small displacements cannot be captured on camera.

The normalization requires a linear behavior of the sample. This

assumption is reasonable, because the reaction forces of 0.21 N

for DSPI and 5.5 N for DIC are below the natural maximum bite

force of 9.0 N (Soons et al., in press). A good correspondence is

found between the FE model and the DSPI results (R2¼0.89). As a

consequence, this measurement can be used in an inverse

analysis to obtain values for the elastic modulus of bone and

keratin (Soons et al., 2012a). It should be noted that the signal-to-

noise ratio, and thus the R-squared, will drop drastically if the

interferometric stability is not met. Some important require-

ments for a good stability are the use of an optical table and

dehydrated samples. The dehydrated state is easily obtained

during the 48 h curing of the resin. After this curing period, the

deformation did not change significantly. The lower coefficient of

determination between DIC and FE modeling (R2¼0.52) is caused

by a noisier result, but, as can be seen in Fig. 2, a reasonable

correspondence was obtained. DIC does not need high stability

requirements and can be used without an optical table and on

fresh samples. In future research, we plan to use it in vivo.

Another major advantage of DIC over DSPI, besides its robust-

ness, is the possibility to acquire full 3D coordinates and

displacements in one single measurement. Hence, surface

strains (ex,ey,exy) can be calculated. It should be mentioned that

one could combine three or more DSPI measurements so one

could also obtain 3D displacements (e.g. Yang et al., 2007; Bright

and Groning, 2012). The strains, measured with DIC and calcu-

lated with FE, are shown in Fig. 3. A good qualitative agreement,

and a reasonable quantitative agreement is observed for all the

strains and DIC can be a simple alternative for strain gauges. We

plan to make a full quantitative comparison, by calculating

R-squared values between DIC and FE strains. In this way, an

inverse analysis should be possible (Soons et al., 2012a).

5. Conclusions

In this paper we presented two easy-to-use optical setups for the

validation of FE models. DSPI is a very sensitive (20 nm) inter-

ferometric setup that makes it possible to measure very small

deformations (sub-micron). As a result it can be used for non-

destructive testing. Its high sensitivity, however, makes it difficult

to use outside the lab and for in vivo experiments. DIC is less

sensitive (1/10 of the pixelsize), but much more robust, so it

allows us to do in vivo experiments and it can easily be used for

full 3D displacement measurements. In addition, the technique

is highly scalable. One just needs to apply a speckle pattern on

the surface and capture the deformation with two cameras. As a

result, we suggest that DIC is the preferred technique to measure

the deformation on bird beaks and by extension in a lot of other

biological structures. In future, we plan in vivo measurements.

Acknowledgments

Financial support to this project is given by the Research

Foundation–Flanders (FWO). We thank F. Wiese for his tech-

nical assistance and J. Peacock for English proofreading.

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