Fringe pattern demodulation by the Fourier transform method associated with fringe extrapolation by the Gerchberg
algorithm was investigated in details for its application to fast profiling of surfaces with small patterns and/or cuttings.
For such surfaces, spectral leakage is a major concern as it corrupts data in a large part of the areas of interest if
extrapolation is not carried out. Simulated fringe patterns or real interferograms recorded on micromechanical devices by
interference microscopy were used for this evaluation. Different filter shapes in the Fourier space were tested for the
determination of valid areas in the interferogram, for the fringe extrapolation stage and for the final phase demodulation.
It is demonstrated that filters with a shape adapted to the modulation sidelobe in the Fourier space allow automated
measurements without user expertise while maintaining a high accuracy. Some practical rules for the choice of
extrapolation margins, fringe density, fringe extrapolation iteration number and other parameters are clarified to reach
accurate and fast automated measurements.
Microelectromechanical systems (MEMS) are based on the generation and/or detection of deformations, motion and vibrations of thin mechanical structures having lateral dimensions in the micrometer to millimeter range. A number of technological issues commonly appear during the development of MEMS fabrication processes such as non uniform etching or deposition, surface roughening, stiction and stress-induced deformations. Likewise, as mechanical properties of thin films are difficult to predict, and are very variable with process parameters. Consequently, experimental data on the (thermo)mechanical and dynamical behaviour of MEMS and on their reliability are often required. In this paper, after a short description of the basic principles and performances of interference microscopy techniques, we review the capabilities of full field interference microscopy techniques for these applications. They are illustrated by various examples taken during the development of MEMS fabrication and packaging processes, and by results of measurements as function of temperature or under vacuum.
Interferogram analysis techniques able to compute phase or contrast maps from a single interferogram are useful for fast measurements of surface profiles, of out-of-plane displacement fields under thermal or mechanical loading, and of vibration mode shapes. Well known single interferogram techniques are Fast Fourier Transform (FFT) analysis, spatial carrier phase stepping and synchronous detection techniques. These techniques typically need a sample tilting to introduce a fringe spatial carrier and fail when the interferograms contain closed fringes. A 2D fringe pattern demodulation technique which overcomes these limitations is the Vortex Transform method proposed recently by K.G. Larkin et al. In this paper a fully automated version of this technique is described. Then it applied on real interferograms recorded on microdevices by microscopic homodyne interferometry is demonstrated.
Microscopic interferometry with monochromatic or white light stroboscopic illumination allows time-resolved measurements of out-of-plane MEMS vibration mode shapes with (sub)micron lateral resolution and a vertical resolution in the (sub)nanometer range. In this method, light pulses are synchronized with the sinusoidal excitation voltage to "freeze" microdevice vibrations, and automatic interferogram analysis techniques are used to get a 3D surface profile of the vibrating device. To obtain quantitative measurements of the vibration amplitudes, it is necessary to know in each point the phase delay between the light pulses and the microdevice vibrations. One way is first, to search manually for the phase delay tmax corresponding to an extremum of the vibration cycle, and then to perform two measurements at tmax and tmax+180°. The difference and the sum of these two measurements provide respectively the map of twice the vibration amplitudes and the map of twice the static deformations. Another way is to perform measurements while the phase delay is scanned in order to reconstitute the whole vibration cycle. We investigate herein an alternative method which enables, from only 3 measurements with different phase delays, a fully automatic mapping of the vibration phase, of the vibration amplitudes and of the static deformations. This method is illustrated by monochromatic and white light stroboscopic measurements on micromechanical devices. Factors affecting its accuracy such as the light pulse delay, the light pulse duty cycle and sample drift between acquisitions are analyzed from simulations and measurements.
Microscopic homodyne interferometry with monochromatic or white light illumination is up to now the most widely used technique for micromechanical devices and MEMS surface profiling. In the last five years its capabilities have been largely extended and this technique can now be applied to out-of-plane or in-plane vibration measurements, to micromechanical testing, to transparent film thickness mapping and to surface spectral reflectivity mapping. In this paper we will review the performances and limits of this technique and its various applications in the MEMS field from technology assessment up to final device characterization. Some guidelines are provided to achieve high frequency vibration measurements, transient response measurements as well as on wafer or in vacuum measurements. Finally, future developments needed are discussed.
Several optical methods have been developed for the measurement of in-plane vibration of microscopic objects. However most of them need a scattering surface or a specific surface structuring. A low cost method which has not these limitations is optical stroboscopic microscopy combined with image processing by optical flow techniques. Previous works have shown that a nanometric sensitivity can be obtained. In this paper, we investigated several subpixel image processing methods for in-plane vibration measurements of MEMS by this technique. Emphasis was put on whole displacement field measurements and on fast algorithms able to process a large sequence of images without the need of a multi-resolution approach to get local vibration amplitudes. It is notably shown that use of spatiotemporal regularity between images is an efficient way to reduce noise and that a resolution in the 0.01 - 0.03 pixel range can be achieved. Results are applied to in-plane vibration local measurements in two perpendicular directions at video rate as well as to full-field mapping of in-plane vibration mode of electrostatically actuated MEMS devices in SOI technology.
Interferometric optical profilometers are increasingly used for the characterization of the static deformation of micromechanical devices and Micro(Opto)Electromechanical Systems (M(O)EMS). Recent works have shown that they can also be used for full field dynamic measurements provided that a stroboscopic light source is added or that time averaging of the interferograms is performed. In this work we investigate two methods to make quantitative time-averaged microscopic interferometric measurements. Both methods are based on the calibration of the fringe contrast variation as function of the vibration amplitude. It is demonstrated from experiments on micromechanical devices that 3D vibration modes shapes can be measured at any frequency with a spatial resolution in the micrometer range and a detection limit around 5 nm.
White light fringe scanning interferometric profilometry is increasingly used for 3D full field measurements of the surface topography and of the static deformations of MEMS because it can be applied, contrary to most interferometric technique using monochromatic illumination, to surfaces having large discontinuities and patterns with a complex geometry. In this paper it is demonstrated that this technique is also well suited for 3D full field measurements of MEMS vibrations provided that a stroboscopic LED array source is used. A fast algorithm based on quadrature filtering of the interferometric signal is described to determine for each pixel the maximum of the fringe envelope when the sample is translated. 3D measurements of the vibration modes of micromechanical devices with a complex shape and/or an initial deformation are demonstrated up to 570 kHz. A spatial resolution in the micrometer range and a detection limit of 5 nm have been obtained.
An experimental set-up designed for the mechanical characterization of small-size membranes by the bulge test and blister test techniques is described. The differential pressure (0-10 bars) is applied to the membrane with a motorized microsyringe pump filled with water to minimize stored elastic energy in the system. An interferometric microscope equipped with a quasi monochromatic Na discharge lamp, a CCD camera and an apertured photomultiplier is used to get simultaneously full field interferograms of the membrane deformed shape and a point measurement of the membrane central height variation. Phase extraction by FFT and unwrapping of the photomultiplier output signal, and processing of some pixels corresponding to the substrate in the set of interferograms images allows to get, with an accuracy in the 3-30 nm range, the true membrane maximum deflection corrected from substrate bending, vertical drift and tilting. 2D or 3D profiles of the membrane deformed shape can as well be obtained with a similar accuracy and a spatial resolution of 3micrometers . The good performances of the system are illustrated from measurements on micromachined Si3N4 and Mo membranes on silicon.
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