Decemb er 10, 2009 / Vol. 7, No. 12 / CHINESE OPTICS LETTERS 1109
Measurement of in-plane deformations of microsystems by
digital holography and speckle interferometry
Invited Paper
G. Pedrini
1∗
, J. Gaspar
2
, O. Paul
2
, and W. Osten
1
1
Institut f¨ur Technische Optik, Universit¨at Stuttgart, Pfaffenwaldring 9, 70569 Stuttgart, Germany
2
Department of Microsystems Engineering−IMTEK, Universit¨at Freiburg,
Georges-Ko ehler-Allee 103, 79110 Freiburg, Germany
∗
E-mail: p edrini@ito.uni-stuttgart.de
Received September 7, 2009
The reliability of microsystem is an important issue and for their quality inspection, it is necessary to
know the displacements or deformations due to the applied mechanical, thermal, or electrostatic loads. We
show interferometrical techniques like digital holography and speckle interferometry can be used for the
measurement of in plane deformations of microsystems with nanometric accuracy and we give a description
of the measurement uncertainties.
OCIS codes: 120.2880, 120.3940.
doi: 10.3788/COL20090712.1109.
The increasing trends towards miniaturization in many
different application fields, from optical communications
to medicine, have produced in the past few years a
dramatic progress in the development of micro-electro-
mechanical systems (MEMS) and micro-opto-electro-
mechanical systems (MOEMS)
[1]
. Miniature robots, mi-
cro mirrors, micro actuators, optical scanners are some
examples of MEMS devices. New applications are emerg-
ing as the existing technology is applied to the miniatur-
ization and integration of conventional devices.
The reliability of such systems is an important issue
that still requires advanced research. For the quality in-
spection, it is necessary to know not only their geometry
but also the displacements or deformations due to the me-
chanical, thermal, or electrostatic loads. The measure-
ment of the deformation of micromechanical systems may
be used for the calculation of strain and, along with the
evaluation of applied forces, allows for obtaining stresses
and consequently extraction of material parameters
[2−5]
.
This information may in turn be used for the validation of
finite element method (FEM) models and eventually de-
tect defects in microsystems. Since the structures them-
selves exhibit typical dimensions of the order of some
micrometers, it is necessary to measure the deformation
with accuracies in the nanometer range.
Digital holography
[6−9]
and speckle techniques
[10−12]
are well suited for the measurement of deformations or
vibrations and have been extensively used for the investi-
gation of both large and microscopic objects. Since these
are interferometric techniques and use coherent light,
there is the appearance of speckles that from one side
are carrier of information but from the other side, due to
their statistical nature produce noise and thus inaccura-
cies in the measurements. It is thus necessary to know
if the setups can guarantee precision in the nanometer
range. Preliminary results where optical techniques have
been used for the measurement of in-plane displacements
of microsystems have been presented in Refs. [13,14].
The goal of this work is to estimate the errors when
in-plane deformations of microsystems are measured. At
first, the reference test objects, from which we know ex-
actly how they deform when submitted to loading, have
been developed. The reference is then measured by us-
ing interferometric systems and the uncertainty of the
measurement is determined according to internationally
recognized guidelines.
Figure 1(a) shows an arrangement based on digital
holography usually used for the measurement of deforma-
tions. The interference between the wavefront reflected
by an object and a reference wave is recorded by an elec-
tronic device (usually charge-coupled device (CCD) or
complementary metal-oxide semiconductor (CMOS) de-
tectors). Notice that in the figure there is a lens to im-
age the object on the sensor but in principle the lens can
be omitted in order to get a lensless holographic setup.
When a lensless setup is used, we need to propagate the
reconstructed wavefront in order to get an image of the
object. The sensitivity of the arrangement with respect
to object deformations is given by its geometry. For
the determination of the three-dimensional (3D) defor-
mation, we need at least three sensitivity vectors which
can be produced by illuminating the object from three
different directions. The acquisition of the deformation
along the different sensitivity vectors can be done se-
quentially (this needs more time) or in parallel
[9]
. In this
letter, we are interested only in the in-plane deforma-
tions along one direction and thus an arrangement which
uses two illumination sources shown in Fig. 1(a) is used.
Consider a deformation described by the vector
~
d. When
the object is illuminated along the directions
~
k
1
,
~
k
2
, and
observed along the direction
~
k
0
, the phase changes of the
two scattered wavefronts are
∆φ
1
=
2π
λ
(
~
k
0
−
~
k
1
)
~
d, (1a)
1671-7694/2009/121109-04
c
° 2009 Chinese Optics Letters
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