ACTIVE INTERFEROMETRIC SYSTEM FOR MEMS/MOEMS MEASUREMENT
Jacek Kacperski, Malgorzata Kujawinska
Institute of Micromechanics and Photonics, Warsaw Univ. of Technology,
8 Sw. A. Boboli St., 02-525 Warsaw, Poland
ABSTRACT
The Twyman-Green interferometer with extended capabilities of shape and out-of-plane displacement measurement is
reported. This interferometer is adopted for investigation of active MEMS and MOEMS with reflective surfaces. The
interferometer is modified by implementation of Liquid Crystal on Silicon (LCoS) Spatial Light Modulator (SLM) as the
reference mirror. The SLM is electrically addressed, reflective and phase only device. This allows introducing an arbitrary
phase in the reference wavefront what may simplify displacement measurement, enable increase of measurement range of the
interferometer and make possible to visualize Bessel function which modulates fringe contrast in interferograms of vibrating
elements. The SLM works simultaneously as interferogram’s phase shifter and can serve as virtual gauge for quick control of
MEMS/MOEMS shape (null-fringe interferometry). The usefulness of the system is shown at the examples of active
microelements (micromembranes and microbeams with piezoelectric layer) testing in static and dynamic work modes. Errors
and measurement uncertainty of the system are analyzed.
Introduction
Micro-Electro-Mechanical Systems are nowadays frequently used in many fields of industry. The number of their applications
extends and the requirements for their performance increases. Therefore precise knowledge about their static (shape,
deformations) and dynamic (resonance frequencies, amplitude and phase of vibration) properties is necessary. Reliability,
fatigue tests or other long term examinations also become important. Knowledge about material properties (Young modulus,
internal stress) may be obtained from displacement measurement of loaded element. Due to fragility of MEMS parts and small
sizes non-contact and high sensitive measurement method is required. Two-beam laser interferometry is one of the most
popular testing methods of microelements [1, 2]. Such method implemented in Twyman-Green interferometer allows for fullfield shape determination and out-of-plane displacement measurement. However the elements under test often bring
additional challenges: their surface may have complicated shape or large shape gradients which restrict their testing by means
of interferometer with flat reference mirror (fringes in the interferogram may be to dense to be distinguished by CCD camera).
To overcome such problems and to simplify out-of-plane displacement measurement through object wavefront compensation it
is proposed to use an active reference element in an interferometer setup. “Active” means that it can modify the phase in
reference beam in order to facilitate fringe pattern analysis and allow to compensate totally or partially the phase introduced by
an object. The active reference element is electrically addressed, phase, Spatial Light Modulator (SLM), fabricated in Liquid
Crystal on Silicone (LCoS) technology [3]. Phase distribution in the reference beam may be modified on the base of
mathematically calculated data (e.g. conical or spherical shape) or data obtained from an interferogram of the object under
test.
Active wavefront correction in interferometry has been used for several years but it is still not common. Deformable mirror [4],
liquid crystal matrix [5, 6, 7] or DMD [8] are reported as the useful devices for wavefront shaping, most often for measurement
of relatively big elements (in the order of a few centimetres). The aim of this work is to show great benefits given by using
phase, LCoS spatial light modulator as a reference element in Twyman-Green interferometer used for MEMS/MOEMS
elements studies.
Measurement setup
The scheme of measurement platform is presented in Fig. 1. The main optical module consists of Twyman-Green
interferometer and long working distance microscope (LDM). The interferometer is formed with a beam-splitter cube, beam
expander and SLM as a reference element. Beam expander is used to increase dimension of the reference beam and to
image LCoS SLM surface in the object plane of the microscope. This is necessary to adjust size of the LCoS SLM active area
2
(15 x 20 mm ) and size of its pixel (19 μm) to the field of view of the microscope and to CCD camera resolution. Simply, the
size of LCoS SLM matrix is too big in comparison with the field of view of the microscope and phase modification of the
reference beam with high spatial resolution (comparable to CCD’s resolution) would not be possible without using additional
optics. The beam expander applied has 15x magnification what allows using approximately 75% of LCoS SLM active area
(Fig. 1b) when field-of-view of the microscope (LDM) equals 0.75 mm x 1 mm. The LCoS display may be easily replaced by an
ordinary, flat mirror on piezoelectric shifter to compare results obtained using SLM.
a)
b)
LCoS SLM
active area
Area used in
our system
Fig. 1. Scheme of the interferometric platform: a) overall scheme of the system, b) mutual relationship between LCoS SLM
active area and size/location of the reference beam; A, B – reference and object beams respectively
He-Ne laser (λ = 632.8 nm) is applied as a light source. Its coherence length is large (approx. 800 mm) what is necessary in
order to assure high contrast of the interference fringes when significant optical paths difference occurs, caused by the
presence of beam expander, in the interferometer.
An active microelement under test (e.g. silicon micromembrane or microbeam) may be loaded by voltage signal (optionally
amplified) supplied from the generator. The computer with special software is utilized for interferogram processing and
controlling SLM element.
Main technical parameters of the system are listed in table 1.
Table 1. Main technical parameters of the system
Feature
Field of view
Sensitivity
Value
2
0.75 x 1 mm ÷ 0.95 x 1.25 mm
316.4 nm/fringe (for λ = 632.8 nm; He-Ne laser)
Uncertainty (2·RMS)
± 35 nm
Measurement range
up to ~ 30 μm
Spatial resolution
2
2
640 x 480 pixels; 1.6 μm/pixel when field of view is 0.75 x 1 mm
LCoS SLM and its calibration
Spatial light modulator used in our system is an electrically addressed, reflective, phase modulator produced by Hana
Microdisplay Technologies Inc. [9]. It has high resolution (1024 x 768 pixels) and relatively small pixel size (19 µm), as well as
the ability to correct 1 wave magnitude with at least 8 pixels without loosing much efficiency. The control of the SLM is very
similar to an ordinary liquid crystal display; a XVGA static image or video signal is generated by computer and directly input to
the LCoS driver. 2-D phase information can be written to the phase-only device, at high accuracy with video speed. Wavefront
modifications are obtained by introducing to the LCoS driver Phase Correction Maps (PCM, 8 bit, gray-level bitmaps)
representing computer generated or experimentally determined phase distribution in the form of phase modulo (2π). The
amount of the phase shift depends on the grey level in a given pixel of such map and the light wavelength applied in the
system. Most often Phase Correction Maps are created on the basis of phase maps calculated from interferograms which are
delivered also as mod 2π maps. This allows creating PCM in very simple way without necessity to perform any time
consuming phase unwrapping procedure. Detailed metrological analysis of Twyman-Green interferometer with LCoS SLM and
process of its calibration are presented in [10].
The performance of LCoS display in an interferometric system depends on:
• the flatness of the LCoS SLM reflective surface;
• the influence of crosstalks between neighbouring pixels;
• the proper calibration.
The reflective surface of the SLM is not ideally flat. Moreover the beam expander aberrations also affect wavefront shape of
the reference beam. These two wavefront deformations add each other in the output of reference interferometric channel. This
systematic error may be, however, actively corrected through introducing by LCoS SLM the Phase Correction Map created on
the base of the measured wavefront deformation.
The other specific feature of LCoS device is that molecules of liquid crystal in neighbouring pixels cannot have drastically
different orientation what means that violent phase change between neighbouring pixels of LCoS display is impossible. There
are intermediate regions between these pixels and size of these regions depends on the value of phase difference introduced
in the neighbouring pixels [11]. The biggest intermediate region occurs on the border of phase jump 0 - 2π. The size of such
region is comparable with the size of a few pixels which can significantly disturb the interferogram and consequently the phase
values.
The use of LCoS SLM for proper phase correction of the reference beam in the interferometer is possible when we know
relation between grey level in PCM and phase retardation introduced by LCoS display. Such relation is called Electro-Optical
(E-O) characteristic. To find out such characteristic the calibration process is necessary. The process relies on measuring of
interference fringe shift while different, uniform gray level maps are sent to the SLM controller. Determined characteristic is
strongly nonlinear and range of the phase delay (for λ = 632.8 nm) equals approx. 3π. We also analysed the spatial
nonuniformity of phase shift introduced by LCoS SLM pixels and we concluded that it is neglectable.
Objects under test
The measured object was fabricated by THALES Research & Technology and Institute FEMTO-ST Université de FrancheComté within EU project OCMMM [12] and NEMO [13]. These are silicon micromembrane (450 x 450 x 17 μm, Fig. 2) and
microbeams (400 x 50 x 17 μm and 200 x 50 x 17 μm, Fig. 3) with piezoelectric layer. Technological process, which includes
introducing piezoelectric layer at top of the elements, introduces internal stress, what causes that microelements are bent. It is
seen in exemplary interferograms of these elements (Fig. 2c and 3c). These interferograms were taken when flat mirror was
used as a reference element.
a)
Top electrode
Bottom electrode
PZT TiO2
Cladding layer
b)
c)
Core layer
SOI wafer
Buffer layer
Fig. 2. The silicon micromembrane: a) cross-section through micromembrane, b) photograph and c) interferogram for U = 0 V
a)
NiCr
b)
c)
Au
Fig. 3. The silicon microbeam: a) cross-sections, b) photograph of 400 μm-long microbeam and c) interferogram of it
Description of measurement methodology
Selected examples of the application of LCoS SLM for active silicon microelements testing are presented and discussed
below. LCoS display has been fulfilling several tasks during the measurements including:
• phase shifter for Temporal Phase Shifting (TPS) interferogram analysis method;
• object’s shape compensator/corrector;
• virtual (computed) reference phase generator.
In the case when LCoS is used for phase shift of an interferogram only, the best way to introduce the phase shift is to supply a
set of uniform grey level maps (3, 4 or 5 maps depending on TPS algorithm used) corresponding to a phase change equalled
π/2 according to the LCoS device O-E characteristic. When LCoS SLM is supposed to act as a phase shifter and phase
corrector simultaneously the best way to shift the phase of an interferogram is to mathematically shift the mod(2π) phase map
used for wavefront shaping. This approach does not require LCoS SLM phase range bigger than this necessary for PCM i.e.
2π, independently of the number of phase shifts. Therefore the 5-frame TPS method can be used and some errors caused by
phase shift inaccuracy are corrected. However the shift of phase fringes means that crosstalk regions are shifted also and it
introduces additional errors into the interferograms and fringe pattern processing.
Besides performing interferogram phase shift, linear spatial carrier frequency fringes may be also easily introduced to the
interferogram through using LCoS display. This capability is applied when the Fourier Transform Method (FTM) of
interferograms analysis is used.
Fig. 4. Scheme of the measurement methodology when LCoS SLM is used as a reference element
Depending on the features of microelement under test and the physical value that should be determined different
measurement procedure ought to be used. Some of them require additional calculation or measurements to be performed at
first. The block diagram of measurement procedures is presented in Fig. 4. To simplify this diagram the correction of
systematic error introduced by beam expander aberrations and SLM nonflatness was not taken into consideration. This error
can be subtracted from the determined shape data or it can be corrected at the beginning of a measurement process
supplying special PCM to the SLM. If we want to remove shape fringes from the interferogram of any object (e.g. to measure
out-of-plane displacement) special PCM is created on the base of mod(2π) phase map of the interferogram. In such a case the
systematic error is corrected automatically because it is, similarly as shape of the object, encoded in the interferogram. An
important advantage of wavefront shaping on the base of mod(2π) map is that there is no need to calculate shape of the
object under test when one want to measure displacement of this object using compensation of the object wavefront shape
(see Fig. 4). This is convenient if there is any height step at the object which cannot be properly measured (sometimes
unwrapping process of mod(2π) map brings problems). To do this in conventional way two height maps of the object in loaded
and unloaded states have to be measured and subtracted from each other and in this case we can experience difficulties with
unwrapping procedures.
Static measurements (when object under test does not change its shape for several seconds) were performed with the use of
TPS algorithm for interferogram processing. This algorithm is considered as very accurate and quick.
In the case of varying in time objects two measurement paths are possible:
• for periodically vibrating objects: implemented stroboscopic interferometry with TPS (minimum 3 interferograms required)
or FTM (one interferogram required) algorithms;
• for nonperiodically vibrating objects: impulse interferometry with FTM only.
Measurement results
To confirm functionality of the system several tests have been performed. The exemplary experimental results are presented
and discussed below.
Static shape determination
In order to determine accurately the shape of an object under test we have to get rid of the significant systematic error brought
into the reference beam by LCoS and beam expander imperfections. The wavefront is corrected by introducing onto LCoS the
PCM calculated from the interferogram obtained in Twyman-Green arrangement with a reference flat mirror placed at the
object arm of the interferometer. The exemplary mod (2π) PCM map used for wavefront correction is shown in Fig. 5c. The
proof-of-principle experiment was performed at 0.45 mm x 0.45 mm micromembrane (Fig. 5). At first its shape was calculated
by 5-frame TPS method from an interferogram without correction (Fig. 5a, b). Next the proper PCM was introduced at LCoS
SLM, the modified interferogram was obtained and the phase (correct shape of micromembrane) was calculated (Fig. 5e).
a)
b)
d)
e)
c)
f)
RMS = 16 nm
P-V = 154 nm
Fig. 5: Interferograms and results obtained during micromembrane shape determination: a) initial interferogram, b) shape of
the membrane with systematic error, c) one of five PCM for systematic error correction, d) corrected interferogram, e) shape of
the membrane after correction, f) difference between height maps obtained in setups using flat mirror and LCoS SLM as a
reference element
To estimate accuracy of such measurement the result was compared with the one obtained in optimized conditions i.e. for the
case of flat reference mirror shifted by linear piezoelectric transducer and using 5-frame TPS algorithm. The difference
between these two results interpreted as the measurement uncertainty obtained in active interferometer is shown in Fig. 5f.
The biggest errors are caused by crosstalks regions and occur in the areas where phase of the interferogram changes rapidly.
It refers to the edges of the layers deposited onto the membrane and places corresponding with phase “jumps” in PCM.
However the overall accuracy of the shape measurement is high with RMS = 16 nm. So uncertainty of such measurement can
be estimated to ± 35 nm.
Out-of-plane displacement measurement
One of the most important advantages of using LCoS SLM as a reference element is the ability to measure directly out-ofplane deformation of an element under test. After phase correction performed by SLM in order to remove interference fringes
from the interferogram of a specimen in initial state, out-of-plane deformation of this object may be directly measured on the
basis of interference fringes that will appear in the interferogram after object loading. This can be convenient for reliability tests
when one want to measure shape changes after a series of loading cycles.
Out-of-plane displacement measurement on the basis of interferogram with mathematically designed linear, spatial frequency
introduced by LCoS SLM is presented at the example of micromembrane (Fig. 6). In such a case only one interferogram is
required for a specimen height map measurement so this algorithm is more convenient for dynamic or instable object testing.
In our experiment the PCM applied included the sum of the phases due to spatial carrier frequency, systematic error of
interferometer with LCoS SLM and the specimen initial shape. This PCM, supplied to LCoS display, is presented in Fig. 6b.
The effect of introducing this PCM into T-G interferometer is clearly seen in Fig. 6c at which the linear fringes are visible. The
fringes and phase representing out-of-plane displacement of micromembrane due to the loading by constant voltage equalled
35V are given in Fig. 6d and 6e. Such interferogram is analysed using FTM. Visible edges of the layers deposited onto the
membrane slightly disturb the interference pattern what is a source of some errors in calculated displacement. Also using FFT
method which includes heavy filtering in frequency domain we may loose the detailed information about the steps or local high
gradients in the object.
a)
b)
d)
c)
e)
P-V = 730 nm
Fig. 6. Interferograms and results obtained during micromembrane out-of-plane deformation measurement using
interferograms with linear spatial frequency: a) initial interferogram, b) PCM with the phase of the object beam, systematic
phase error compensation and mathematically added linear phase (2πf0x), c) corrected interferogram of unloaded and d)
loaded membrane with f0, e) calculated out-of-plane deformation
a)
b)
d)
c)
e)
P-V = 334 nm
Fig. 7. Interferograms and results obtained during micromembrane out-of-plane deformation measurement: a) initial
interferogram, b) PCM for the phase of the object beam and systematic error compensation, c) corrected interferogram of
unloaded and d) loaded membrane, e) calculated out-of-plane deformation
Interferograms and results of the direct displacement measurement experiment of 200 μm-long microbeam are presented in
Fig. 7. In this case interferograms were analysed using 5-frame TPS method. On the basis of mod(2π) phase map of the initial
interferograms of unloaded beam a set of PCMs is created (one of such PCM is shown in Fig. 7b). Supplying such PCMs to
the LCoS display when the object is loaded a set of phase shifted interferograms is obtained (Fig. 7d) and the out-of-plane
deformation is calculated directly from them (Fig. 7e). In our experiment microbeam was loaded by constant voltage equalled
10V. Calculated displacement map is not smooth, visible waves are caused by imperfections of phase correction with LCoS
SLM (due to crosstalk between its pixels) and by some parasitic fringes (which are hard to avoid because of high coherence of
the light source). Yet uncertainty of this measurement does not exceed ± 35 nm.
Control of the departure from an expected shape
SLM can be used to generate mathematically designed wavefront shapes. This is convenient for fast assessment (qualitatively
or quantitatively) of shape departure of object under test from an expected profile (so called null fringe interferometry). In other
words one can generate virtual gauge representing the ideal shape. Results of such process performed for 400 μm-long
microbeam testing are shown in Fig. 8. Mathematically designed PCM is presented in Fig. 8c. Phase profile along horizontal
2
direction of PCM is described by parabola equation: y = ax , where: x – pixel number in PCM, y – phase value in radians, a =
0.0015. (Map for systematic error correction should be also added to this PCM). Interferogram obtained for such shaped
reference wavefront is shown in Fig. 8d and calculated height map – in Fig. 8e. It is seen that deflections of the beams do not
agree fully with the model parabolic function and the P-V departure from the expected shape is 620 nm.
P-V = 5760 nm
a)
b)
c)
P-V = 620 nm
d)
e)
Fig. 8. Controlling the departure from an expected shape of silicon microbeams: a) initial interferogram (systematic error is
corrected), b) height map calculated from initial interferogram, c) mathematically designed PCM, d) interferogram obtained
after reference wavefront correction, e) height map calculated from corrected interferogram
Such process can be also used to decrease number of shape fringes and thanks to this measurement range of the
interferometer may be increased.
Bessel function visualization
Another application of the phase correction procedure in two-beam interferometer is the improvement of Bessel function
visualization during determination of microobjects resonance frequencies. The contrast of interference fringes in an
st
interferogram of sinusoidally vibrating object under test is modulated by Bessel function – J0 (0 order, 1 type) [14]. On the
basis of such contrast modulation fringes (Bessel fringes) one can estimate amplitude of the specimen vibration and determine
vibration mode. However the disadvantage of this method is low contrast of Bessel fringes (Fig. 9 I) disturbed additionally by
the fringes representing shape of an object. In order to overcome this drawback the Enhanced Time-Average Technique
(ETAT) is most frequently used [15] (Fig. 9 II). It allows to visualize absolute value of Bessel function on the basis of 4 or 5
mutually phase shifted interferograms.
We have found that using LCoS display for object wavefront compensation (to remove fringes from an interferogram) enable to
visualize real profile of Bessel function (even for non-flat objects). Appropriate PCM is created on the base of experimentally
determined mod(2π) phase map of an object in static state. Shifting phase of PCM supplied to LCoS SLM (and, because of
that, phase of the corrected interferogram) it is possible to get interferogram where dark fringe represents nonvibrating places
of the object. In such a case the visualisation is most effective (Fig. 9 III). In such a case the positive values of Bessel function
are visible as dark places while negative values are bright (because in these places contrast of the interference fringes is
inverted). The quality of this visualization is worse than for ETAT but the biggest advantage of this active method is that the
process is going in real time and no calculation is needed therefore it may be useful for precise resonance frequencies
searching. Exemplary images obtained using time-average, enhanced time-average and object wavefront compensation
2
st
techniques during 400 μm-long microbeam and 0.45 x 0.45 mm membrane testing, for 1 resonance mode of their vibration
are presented in Fig. 9.
I. Time-average:
II. Enhanced time-average:
III. Object wavefront compensation
a)
b)
c)
d)
e)
f)
2
Fig. 9. The results of Bessel function visualization of 200 µm-long microbeams (a, b, c) and 0.45 x 0.45 mm micromembrane
(d, e, f) vibrating at their first resonance mode (f = 148 kHz, U = 2 VPP – microbeams; f = 222 kHz, U = 3 VPP micromembrane) using different techniques. Areas where Bessel function has negative values are indicated for one
microbeam in pictures b) and c).
Conclusions
In the paper the active interferometric system for MEMS/MOEMS testing has been presented. The system bases on TwymanGreen interferometer and utilizes a phase, reflective SLM made in LCoS technology for reference wavefront shaping. The
biggest advantages of the modified system when applied to investigate MEMS/MOEMS include:
• capability to monitor and measure out-of-plane displacement;
• on-line control of the departure from the expected shape,
• real-time visualization of Bessel fringes at non-flat vibrating microobjects.
Also using LCoS SLM as the reference mirror extends the range of measurement, simplifies testing process and allows to
automate it especially in the case of long term experiments.
In future the design of the Twyman-Green interferometer with LCoS display as a reference element may be simplified and the
systematic errors may be significantly decreased when spatial light modulator with smaller pixel size (preferably 1 μm x 1 μm)
and less crosstalks between the pixels appears on the market. Implementation of a new generation of LCoS spatial light
modulators in the active interferometer will also increase the range of its applications.
Acknowledgements
LCoS SLM was provided by Liquid Crystal Institute, Kent State University within the cooperation between SPIE Student
Chapters at WUT and KSU.
th
The active micromembranes have been developed within 5 EU project OCMMM no. G1RD-CT-2000-00261, while active
microbeams have been developed within the European Network of Excellence on Micro-Optics NEMO no. FP6/2003/IST/2.
These elements have been provided for the experiments by CNRS-FEMTO-ST, Besançon, France.
The work is financially supported by Warsaw University of Technology within statutory grant and EU NoE NEMO, as well as by
the Ministry of Education and Science within project no: KBN PB 3 T10C 016 29.
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