Bridge Maintenance, Safety, Management, Resilience and Sustainability – Biondini & Frangopol (Eds)© 2012 Taylor & Francis Group, London, ISBN 978-0-415-62124-3

Strain visualization sticker using moiré fringe for remote sensing
T. Takaki, K. Fujii, and I. Ishii

Hiroshima University, Hiroshima, Japan

S. Umemoto, H. Ohata, N. Miyamoto and T. Okamto
Keisoku Research Consultant Co. Ltd., Hiroshima, Japan

ABSTRACT: Evaluation of the strain on a bridge’s members is required to maintain its safety. To meetthis requirement, we propose a strain visualization sticker that can display numeric characters and fringes corresponding to the magnitude of strain without the use of electronic elements such as amplifiers, strain gaugesand wires. We focus on the slight displacement produced by the strain, and visually magnify and display its
displacement with a moiré fringe pattern. The sticker is simply attached to the bridge’s members, and it provides strain information by displaying characters that can be read with the naked eye. An accurate numericalvalue of the strain can be obtained from an image of the sticker through image processing. The structure ofthe sticker is simple, and its fabrication is inexpensive. We assume that a slight displacement is generated by
the strain, and results show that the sticker provides displacement information in the form of readable characters, giving accurate numerical value of displacement of less than 1 m using image processing.
members, and it provides strain information by displaying characters which can be seen with the nakedeye. An accurate numerical value of the strain can beobtained from the image of the sticker through image processing. When using a telescopic lens, thisvalue can be remotely measured. The structure of thesticker is simple, and its fabrication is inexpensive;
therefore, our proposed measurement method using
the sticker can be employed for multipoint measurement.

1 INSTRUCTIONS
Evaluation of the strain on a bridge’s members is
required to maintain its safety (Chang, S.J. et al.
2010) (Ni, Y. Q. et al. 2010) (Uchino, M. et al.
2010), and a large amount of research has been carried out by measuring such strain using electricalsensors, such as strain gauges. When such sensors
are attached to measurement points, it is necessary tosupply electrical power to these points. This implies
that external power must be supplied via wiring orthat an internal electrical power source must be fitted into the sensor. Furthermore, wired or wirelessmethods are needed to transmit the measurement data from the sensor. This tends to make the overallsystems larger and more expensive.
To solve this problem, measurement techniquesthat do not require electrical power to be supplied tomeasurement points have been developed, utilizing
optical elements or ultrasound, for example. In anearlier paper, we proposed a mechanism that utilizes
moiré fringe patterns to visualize a physical force
without the need for an electrical power supply at
the measurement point (Takaki, T. et al. 2008,2010).
In this study, we propose a strain visualization
sticker that can display characters and fringe patterns
that correspond to the magnitude of strain without
the use of electronic elements, such as amplifiers,strain gauges and wires. We focus on the slight displacement produced by the strain and visually magnify and display its displacement with a moiréfringe. Figure 1 shows the concept of how to use thesticker. The sticker is simply attached to the bridge’s

Figure 1. Concept of a proposed strain visualization sticker

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This paper is organized as follows. Section 2 presents the principle of the strain visualization sticker.
Section 3 describes a moiré fringe pattern thatachieves both high magnification and clarity, without using expensive printing technology. Section 4
describes the method for acquiring strain data using
a captured image of the sticker, and Section 5 describes the developed strain visualization sticker. InSection 6, we assume that a slight displacement isgenerated by the strain, and we experimentally verify that characters corresponding to the magnitude ofthe displacement are accurately displayed. We verify
that the developed sticker can measure even a slight
displacement of less than 1 m using the captured
image of the sticker. Section 7 concludes the paper.

firmed visually.
is the distance from the bonded
positions of the upper film to the bonded positions of
the lower film. The relationship between a slight
displacement
and stain ε is given byε.

2 STRAIN VISUALIZATION STICKER
2.1 Moiré fringe
Let us first explain moiré fringes (Kobayashi, A. S.
1987). As shown in Fig. 2 (i), by superimposing linegrating 1 of pitch
on line grating 2 with pitch∆( ∆ ≪ ), a fringe known as a moiré
fringe appears with pitch. Pitchis larger
than the pitch of line gratings 1 and 2. Their relationship is given byp ∆pp.
∆pFigure 2. Example of a Moiré fringe.

1As shown in Fig. 2 (ii), when line grating 1 at pitch
is moved in direction (A), the moiré fringe atpitch
moves in direction (A). Therefore, the displacement
can be displayed visually at a magnificationof∆ /∆ . When the relative displacement of the line gratings is , the displacementof the moiré fringe
can be described by the following equation:.

2

2.2 Structure of the strain visualization sticker
Figure 3 shows the structure of a proposed strain
visualization sticker. The sticker is composed of two
transparent films. The line grating is printed on theback of the upper film and on the front of the lower
film. To obtain a clear moiré fringe, the back of thelower film is painted with white color. To preventthe two films from separating, the region between
the two films is filled with oil. When the ends of thefilms are bonded to an object as shown in Fig. 3, theslight displacement
produced by the strain ε onan object is displayed by the moiré fringe at a magnification of M. Therefore, the strain ε can be con-Figure 3. Structure of the strain visualization sticker.

22133Figure 4. A moiré fringe with characters.

Figure 5. Moiré fringe and magnification.

tern that produces a clear moiré fringe, using inexpensive printing technology.

3 IMPROVING VISIBILITY OF THE MOIRÉFRINGE

3.2.1 Printing technology and magnification

3.1 Displaying characters with the moiré fringe

Assuming that the fabrication of a fringe involves
the use of a printer, we discuss the resolution of theprinter at magnification . For example, if a printerhas a resolution of 600 dpi, the finest lines that canbe printed are 1/600 th of an inch. The unit of widthcorresponding to finest lines that can be printed isdefined as . From Eq. (1), to obtain a high magnification , the ∆ should be small. However, considering that printing technology is used, the minimum ∆ is . Thus, henceforth, ∆ is defined as. For example, to obtain a magnificationof 10,
the pitchesand∆ must be 9 and 10 ,respectively, for line gratings 1 and 2 according toEq. (1). Similarly, to obtain a magnificationof28, they need to be 27 and 28 , respectively.
These moiré fringes are shown in Figs. 5 (i) and (ii).

The moiré fringe shown in Fig. 2 is a simple fringe
pattern, and its visibility is not necessarily adequate.
To improve the visibility, in this section, a method isproposed to display characters with the moiré fringe.
The movement of the moiré fringe is shown on theleft in Fig. 4. Similar to Fig. 2, if line gratings 1 and2 are superimposed and line grating 1 is moved indirection (A), the moiré fringe moves, as in Fig. 4(i)-(iii).
We propose a method to display characters with amoiré fringe, as shown on the right in Fig. 4. In
place of line grating 1, we propose the use of gratings in the shape of characters, which we refer to ascharacter gratings. If this character grating and line
grating 2 are superimposed and the character grating
is moved in direction (A), characters are displayed in
the order shown in Fig. 4 (i')-(iii').

3.2.2 Clarity of moiré fringes
The moiré fringes produced with this sticker
should be clear. When the grating lines are too fine
to see, the moiré fringe can be clearly observed.
Conversely, when the grating lines are thick, thegrating is visually more discernible than the moiréfringe, and the fringe cannot be clearly observed.
Thus, the moiré fringe in Fig. 5 (i) is clear because
the line grating is fine, and the moiré fringe in Fig. 5(ii) is less clear, because the grating is thicker.

3.2 Highly magnified, legible moiré fringe andprinting technology
The moiré fringe in the sticker should have highmagnification and be sufficiently legible. Moreover,for this method to be practically feasible, fabrication
should be possible with inexpensive printing technology. In this section, a method is presented toshow a highly magnified, clear moiré fringe, evenwith a grating fabricated using inexpensive printing
technology. First, we describe the printing technology and magnification, and then, the clarity of themoiré fringe pattern. Next, we propose a grating pat-2214

clearer than that in Fig. 5 (ii). If line gratings areconfigured in this way, an expensive printing technology that can print small , is not necessary; aclear moiré fringe with high magnification
canbe obtained with inexpensive printing technology.

Figure 6. Moiré fringe and magnificationHere, we explain why pitchof the moiré
fringe differs although the magnification is the same(28) in Figs. 5 (ii) and (iii). The relationship between the pitchof line grating 1, pitchof themoiré fringe, and the magnification
is obtained
asfrom Eqs. (1) and (4). Therefore,
even with the same magnification , when the pitchof line grating 1 differs, pitchof the moiré
fringe also differs correspondingly. In the cases ofFig. 5 (ii) and (iii), the values of the pitch p of linegrating 1 are 27 and 9 , respectively; therefore,
the values of the pitchof the moiré fringe are
756 and 252 .

.

3.2.3 Magnification and clarity

4 METHOD OF EXTRACTING STRAIN VALUEBY IMAGE PROCESSING

The magnificationof the moiré fringe in Fig.
5 (i), which is clear, is small at
10.
in Fig. 5(ii), which is not clear, is large at
28. Thus,
there is a tradeoff between clarity and magnificationin moiré fringes. In this grating pattern, to achieveboth high magnificationand clarity,
must besmall. However, to makesmall, a more expensive printing technology that can print very fine lines
is necessary, which is undesirable because it leads tohigher costs.

4.1 Fitted sine curve
The image of a moiré fringe is trimmed from an
original image taken by a camera, and the x- and yaxes are defined as shown in Fig. 7 (i). The size ofthe trimmed image is, , and the brightness value of the pixel at ,is defined as, .
is the average of the brightness value along the yaxis.
can be written as

3.2.4 Proposed grating pattern∑
Y

To obtain clear and highly magnified moiré fringes without the use of expensive printing technology,
we propose a line grating pattern. Figure 6 (i) showsa magnified figure of one pitch of the moiré fringe inFig. 5 (i). The dark areas where the lines of gratings
1 and 2 are superimposed are defined, in order, as(a), (b), (c), and (d). We propose a configuration ofline grating 2 in which the dark areas are repeated as(a)(a)(a)..., (b)(b)(b)..., (c)(c)(c)..., and (d)(d)(d)..., asshown in Fig. 6 (ii). In this pattern, the fringe ofpitch
repeatedtimes (in the figure,3) isplaced every∆ . Pitchof the moiré
fringe in Fig. 6 (ii) isnp ∆pp,∆p,.

5

x is a sine curve fitted to x . In the image,when a unit length corresponds to pixels,
can be written as follows:
sin2.

6Figure 7 (ii) shows the difference between
andin an example case. , , andare theamplitude of the brightness value, offset of thebrightness value, and phase of the moiré fringe inthe trimmed image, respectively. , , andcanbe obtained using the least squares method.

4and the magnification
is np ∆p /∆p . Themoiré fringe, when p 9u and n 3, is shown inFig. 5 (iii). From Eq. (2), its magnification
is 28
and the magnificationin Fig. 5 (ii) is also 28.
However, the pitch of the line grating is finer in Fig.
5 (iii). Therefore the moiré fringe in Fig. 5 (iii) is2215

Figure 7. Intensity of a moiré fringe and corresponding fittedcurve.

Figure 9. The developed strain visualization

Figure 8. Phase of a moiré fringe.

Figure 10. The developed strain visualization sticker under arange of displacement.

sticker.

4.2 Phase of fitted sine curve and displacement ofmoiré fringe

From Eqs. (3) and (8), the stain ε is given byFigure 8 (i) shows the image of a moiré fringe
when the measured object has no strain. The brightness value of this moiré fringe is fitted to, andthe phase in this state is assumed to be , as indicated by (a) in Fig. 8 (iii). When a strain ε occurs
on the object, a displacement ofoccurs, and themoiré fringe moves by, which can be calculated
from Eq. (2). In the image, when the moiré fringe
moves by, as shown in Fig. 8 (ii), the phaseshifts by ∆ , as indicated by (b) in Fig. 8 (iii). The
relationship between these two terms is given byε2

∆ .

2

∆ .

∆ .

95 THE DEVELOPED STRAIN VISUALIZATIONSTICKER
Figure 9 shows the developed strain visualization
sticker. The length, width, and thickness of thesticker are 57 mm, 10 mm, and 0.44 mm, respectively. The material of the film is polyester. The line
gratings are printed on the film using a photomask
technique. The finest line produced with this technique is 0.01 mm. The left side of the sticker displays a simple moirés fringe pattern for image processing; the right side displays characters using
moiré fringes to allow reading of the measured strain
with the naked eye. The magnificationof thesimple moiré fringe is 121, and its pitch , ∆ andthe pitch repetition number
are 0.1 mm, 0.01 mm
and 12, respectively. The magnificationof thecharacter fringe is 501, and its , ∆ , andare0.1 mm, 0.01 and 50, respectively.

7

From Eqs. (2) and (7), the displacement
given by2is82216

6 EXPRIMENT
6.1 Measurement by naked eye
Figure 10 shows photographs of the sticker for 15
m increments of the displacement. As shown, thedeveloped sticker can display the character corresponding to the displacement.
6.2 Measurement using image processing

Figure 12. Experimental result.

We assume that a slight displacement is generated
by the strain and experimentally verify that the proposed sticker and algorithm can detect less than 1
m displacement. Figure 11 shows the experimental
setup. We use a micro-translation stage to generate amicron-scale displacement, and this displacement isvisualized by the proposed sticker. An image of thesticker is taken with a CMOS camera (Micro VisionCo., Ltd. VC-4302) from a distance of 420 mm. The
size and frame rate of the image are 640 480 pixels
and 8.2 fps, respectively. The focal length of the lens
is 35 mm. For comparison, we also measure the displacement using a laser displacement sensor. The
sampling time of the laser displacement sensor is 20
ns, and a moving average of 10000 points is used asa filter to eliminate noise.
Figure 12 shows the experimentally measured
displacements where the translation stage generates
displacement steps of less than 1 m. The displacements are measured by the proposed method and thelaser displacement sensor. These two values are very
consistent. When the two films of the sticker are
bonded to an object to be measured and the distance
between the bonded points is50 mm, a displacement of 1 m corresponds to a strain of 20
10-6. In this case, our proposed sticker can measurea strain of less than 20 10-6.

7 CONCLUSION
A method was proposed to display fringes or numeric characters that correspond to a measured
strain without the use of electronic elements by anovel application of moiré fringe patterns. We assume that a slight displacement is generated by thestrain, and we have confirmed experimentally that
numbers corresponding to this displacement can bevisually represented. Using captured images of thesticker, we have verified that the developed sticker
can provide measurements of slight displacements ofless than 1 m.
8 REFERENCES
Chang, S.J., Kim, N.S. & Kim, H.K. 2010. Prediction of displacement response of a suspension bridge using FBG
strain sensors, Proceedings of the Bridge Maintenance,Safety, Management and Life-cycle Optimization, pp. 139144, 2010.
Ni, Y. Q., Xia, H. W., Ko, J.M. & Wong, K.Y. 2010. Conditionassessment of bridge deck truss using in-service monitoringdata of strain, Proceedings of the Bridge Maintenance,
Safety, Management and Life-cycle Optimization, pp. 799805, 2010.
Uchino, M., Okamoto, T., Hida, K., Ito, Y., Sumitoro, P. &Matsuda, H. 2010. Strain analysis method using multirosette analysis by digital image correlation method, Proceedings of the Bridge Maintenance, Safety, Managementand Life-cycle Optimization, pp. 2557-2562, 2010.
Takaki, T. Omasa, Y. & Ishii, I. 2008. Force Visualization
Mechanism using moiré Fringe for Robot Grippers, Proceedings of the 28th Annual Conference of the Robotics Society of Japan, 1K3-07, 2008. (in Japanese)
Takaki, T. Omasa, Y. Ishii, I. Kawahara, T. & Okajima, M.
2010. Force Visualization Mechanism Using a moiré Fringe
Applied to Endoscopic Surgical Instruments, Proceedings ofthe 2010 IEEE International Conference on Robotics andAutomation, pp. 3648-3653, 2010.
Kobayashi, A. S. 1987. Handbook on Experimental mechanics,Prentech-hall.

Figure 11. Experimental setup.

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