Simultaneous 2D in-plane deformation measurement
using electronic speckle pattern interferometry with
double phase modulations
Yunlong Zhu (朱云龙)
1,
*, Julien Vaillant
1,2
, Guillaume Montay
2
, Manuel François
2
,
Yassine Hadjar
1
, and Aurélien Bruyant
1,
**
1
ICD-L2N, UMR CNRS 6281, Université de Technologie de Troyes, 10004 Troyes, France
2
ICD-LASMIS, UMR CNRS 6281, Université de Technologie de Troyes, 10004 Troyes, France
*Corresponding author: yunlong.zhu.2015@utt.fr; **corresponding author: aurelien.bruyant@utt.fr
Received March 15, 2018; accepted May 8, 2018; posted online June 28, 2018
Electronic speckle pattern interferometry (ESPI) and digital speckle pattern interferometry are well-
established non-contact measurement methods. They have been widely used to carry out precise deformation
mapping. However, the simultaneous two-dimensional (2D) or three-dimensional (3D) deformation measure-
ments using ESPI with phase shifting usually involve complicated and slow equipment. In this Letter, we solve
these i ssues by proposing a modified ESPI system based on double phase modulations with only one laser and
one camera. In-plane normal and shear strains are obtained with good quality. This system can also be de-
veloped to measure 3D deformation, and it has the potential to carry out faster measurements with a high-
speed camera.
OCIS codes: 120.6160, 120.5060, 120.5050, 070.2615.
doi: 10.3788/COL201816.071201.
In-plane deformations can be easily measured by a simple
electronic speckle pattern interferometry (ESPI) measur-
ing system
[1]
. In such a system, the temporal phase-
shifting technique is often applied for phase retrieval
to improve the performance
[2]
. However, in a standard
two-beam configuration, only one displacement compo-
nent is measured.
In order to measure the two-dimensional (2D) in-plane
displacement f ield [or the whole three-dimensional (3D)
displacement field], several solutions have been proposed.
The most direct one is to use digital speckle photography
(DSP) (or to combi ne DS P wi th ou t-of-pl ane ESPI for
the 3D measurement)
[3]
. Nevertheless, the sensitivity of
DSP is not as good as that o f ESPI. A natural solution
is then to combine ESPI measuring systems
[4,5]
.Morere-
cently, in-plane ESPI measurement systems were notably
combined with out-of-plane ESPI to perform 3D analysis
using optical switches, though with a limited time reso-
lution (for example, the acquisition time for the “Q-300
3D-ESPI System” is 3.5 s for 3D analysis), due to the iter-
ative process requirement
[6–8]
. To solve the time issue, a
spatial phase-shifting technique can be applied
[6]
;how-
ever, it often makes the system substantially more com-
plex and expensive.
In this Letter, we show the possibility of doing simulta-
neous 2D measurement using the widely recognized ESPI
technique and a single laser without switches. The optical
arrangement is shown in Fig.
1. There are three coherent
laser beams originating from a single laser: Beam 1, Beam
2, and Beam 3. The phases of Beam 1 and Beam 2 can be
modulated by the corresponding piezo-actuated mirrors.
When two temporal phase modulation functions, F
1
ðtÞ
and F
2
ðtÞ, are applied to them, respectively, the scalar
light field of the subjective speckles Eðx; yÞ can be ex-
pressed as
Eðx; yÞ¼A
1
ðx; yÞe
i½2πf
c
tþθ
1
ðx;yÞþF
1
ðtÞ
þ A
2
ðx; yÞe
i½2πf
c
tþθ
2
ðx;yÞþF
2
ðtÞ
þ A
3
ðx; yÞe
i½2πf
c
tþθ
3
ðx;yÞ
: (1)
A
m
ðx; yÞ and θ
m
ðx; yÞ are the amplitude and the initial
phase of Beam m (m ¼ 1; 2; 3) at point (x, y), respectively,
and f
c
is the optical frequency of the laser.
On the sample surface, the light intensity I ðx; yÞ can be
expressed as
I ðx; yÞ ∝ jEð x; yÞj
2
¼½A
2
1
ðx; yÞþA
2
2
ðx; yÞþA
2
3
ðx; yÞ
þ 2A
1
ðx; yÞA
2
ðx; yÞ cos½θ
1
ðx; yÞþF
1
ðtÞ
− θ
2
ðx; yÞ − F
2
ðtÞ
þ 2A
1
ðx; yÞA
3
ðx; yÞ cos½θ
1
ðx; yÞþF
1
ðtÞ
− θ
3
ðx; yÞ
þ 2A
2
ðx; yÞA
3
ðx; yÞ cos½θ
2
ðx; yÞþF
2
ðtÞ
− θ
3
ðx; yÞ: (2)
COL 16(7), 071201(2018) CHINESE OPTICS LETTERS July 10, 2018
1671-7694/2018/071201(5) 071201-1 © 2018 Chinese Optics Letters