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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

, O. Paul

, and W. Osten

Institut f¨ur Technische Optik, Universit¨at Stuttgart, Pfaﬀenwaldring 9, 70569 Stuttgart, Germany

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

, and

observed along the direction

, the phase changes of the

two scattered wavefronts are

∆φ

2π

(

−

)

d, (1a)

1671-7694/2009/121109-04

° 2009 Chinese Optics Letters

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