Jacek Kacperski

Active, LCoS based laser interferometer for microelements studies

The modification of classical Twyman-Green interferometer by implementation of Liquid Crystal on Silicon (LCoS) spatial light modulator as the reference mirror allows introducing arbitrary phase in the reference wavefront. This special capability is applied to facilitate the measurements of shape and deformation of active microelements and extend the range of such measurement. This can be realized by introducing linear or circular spatial carrier frequency into interferogram or by compensating object wavefront deformation. Moreover LCoS display can be used as an accurate phase shifter if the proper calibration is introduced. The analysis of sources of measurement errors introduced by LCoS display is presented and the ways of their elimination are discussed. The possible application of LCoS based laser interferometer for initial microelement shape determination and transient deformation monitoring as well as active reference phase modification are shown and experimentally confirmed during silicon micromembranes studies.

Active microelement testing by interferometry using time-average and quasi-stroboscopic techniques

Increasing technological capabilities to produce active microelements (incl. microbeams, micromembranes and micromirrors) and their expanding areas of application introduce unprecedented requirements concerning their design and testing. The paper presents a concept of an optical measurement system and methodology for out-of-plane displacement testing of such active microelements. The system is based on Twyman-Green microinterferometer. It gives the possibility to combine the capabilities of time average and quasi-stroboscopic interferometry methods to find dynamic behavior of active microelements (e.g., resonance frequencies and amplitude distributions in vibration modes). For mapping the zero-order Bessel function modulating the contrast of two-beam interference fringes the four-frame technique is applied. The calibration of the contrast variation in time-averaged interferograms enables quantitative evaluation of the vibration amplitude encoded in the argument of the Bessel function. For qualitative estimation of the vibration amplitude sign a simple quasi-stroboscopic technique is proposed. In this technique, laser pulses have the same frequency as the signal activating the microelement under test. This self-synchronous system enables to visualize the shape of the tested element at maximum deflection. Exemplary results of measurements performed with active micromembranes are presented.

Interferometric methods for static and dynamic characterizations of micromembranes for sensing functions

We present a methodology for static and dynamic testing of mechanical properties of microelements. The measurement path includes temporal phase shifting interferometry for quantitative static shape elements analysis. This is followed by determination of the resonance frequency by means of modified time average interferometry and transient amplitude and phase maps of vibrating micromembrane capturing and evaluation by phase shifting stroboscopic interferometry. Proper application of combination of these methods allows for quick and accurate analysis of micromembranes and optimization of their manufacturing conditions.

Multifunctional interferometric platform for static and dynamic MEMS measurement

Increasing technological capabilities to produce microelements (for example: microbeams, micromembranes and micromirrors) and their expanding areas of application introduce unprecedented requirements concerning their design and testing. Conventional two beam interferometry is one of the most popular testing methods of microelements that have reflecting surface. However the elements under test may bring additional challenges: their surface finish may be mixed i.e. reflective-diffusive which restrict their analysis by conventional interferometry; their surfaces may have complicated shape or large shape gradients which restrict their testing by means of interferometer with flat reference mirror. In this paper we propose to solve these problems by converting conventional Twyman-Green interferometer into multifunctional measurement platform by introducing different reference surfaces including: mirror (for conventional two beam interferometer); diffuser (for ESPI); Liquid Crystal On Silicon (LCOS) phase spatial light modulator (for active interferometer). Diffuser allows to implement ESPI in the same system configuration. Special software enables to combine the results of measurement by conventional interferometry (mirror-like surface) and ESPI (diffuse surface). LCOS serves as an adaptive reference mirror and phase shifter. The use of such element allows to increase measurement range of the interferometer and simplifies out-of-plane displacement measurement through object wavefront compensation. The applicability of the platform will be shown at the examples of active micromembranes testing in static and dynamic modes of their work.

Active microinterferometer with liquid crystal on silicon (LCOS) for extended range static and dynamic micromembrane measurement

Increasing technological capabilities to produce active microelements (incl. microbeams, micromembranes and micromirrors) and their expanding areas of application introduce unprecedented requirements concerning their design and testing. Conventional two beam interferometry is one of the most popular testing method of microelements that have reflecting surface. Sometimes elements under test have complicated shape or shape gradients which restricts their testing by means of interferometer with flat reference mirror. In this paper we propose to use Liquid Crystal On Silicon (LCOS) spatial light modulator which serves as an adaptive reference mirror and phase shifter in Twyman-Green interferometer applied for microelements measurement. Initial tests have been performed and results confirming applicability of LCOS in active interferometer system are presented.

Modified linear and circular carrier-frequency Fourier-transform method applied for studies of vibrating microelements

Stroboscopic interferometry is the most popular method for investigation of active, vibrating elements. The interferograms obtained in measurement steps may be analysed by temporal phase shifting method or by spatial carrier frequency methods. The first one requires sequential capturing of phase-shifted interferograms which complicates the measurement system and introduces high stability requirements for the setup. The spatial methods need a single interferogram with a proper spatial carrier frequency (SCF), so they are more suitable for dynamic events analysis. The most frequently used spatial method is based on Fourier transform of an interferogram with linear SCF and can be applied to analysis of restricted class of elements represented by quasi-linear fringes. This can be easily expanded by considering elements with circular carrier fringes (CCF). In the paper two approaches to analysis of interferograms with CCF, namely: coordinate transform Fourier transform technique and direct filtering Fourier transform technique are explained. The error analysis of both techniques applied for different classes of interferograms is presented. The methodology of CCF interferogram analysis based on FT methods applied for micromembranes is presented and several exemplary results are given.

Phase only SLM as a reference element in Twyman-Green laser interferometer for MEMS measurement

The active Twyman-Green laser interferometer for MEMS measurement equipped with Spatial Light Modulator (SLM) as a reference element is reported. The SLM is electrically addressed, reflective (made in Liquid Crystal on Silicone technology) and phase-only device which allows to actively shape of the reference beam wavefront in the interferometer. The proper use of the SLM in interferometric MEMS measurement is possible after opto-mechanical modification of the interferometer, performed calibration procedures and special interferogram processing. All these aspects are described. The use of such device benefits extension of measurement range and simplification testing procedures. Usefulness of the SLM is shown at the examples of active microelements testing. Advantages and disadvantages of SLM application are described and potential of this device for interferometry is discussed.

Direct visualization of vibration modes of microobjects using an LCoS SLM in a Twyman-Green interferometer

The paper presents the way that colour can serve solving the problem of calibration points indexing in a camera geometrical calibration process. We propose a technique in which indexes of calibration points in a black-and-white chessboard are represented as sets of colour regions in the neighbourhood of calibration points. We provide some general rules for designing a colour calibration chessboard and provide a method of calibration image analysis. We show that this approach leads to obtaining better results than in the case of widely used methods employing information about already indexed points to compute indexes. We also report constraints concerning the technique. Nowadays we are witnessing an increasing need for camera geometrical calibration systems. They are vital for such applications as 3D modelling, 3D reconstruction, assembly control systems, etc. Wherever possible, calibration objects placed in the scene are used in a camera geometrical calibration process. This approach significantly increases accuracy of calibration results and makes the calibration data extraction process easier and universal. There are many geometrical camera calibration techniques for a known calibration scene [1]. A great number of them use as an input calibration points which are localised and indexed in the scene. In this paper we propose the technique of calibration points indexing which uses a colour chessboard. The presented technique was developed by solving problems we encountered during experiments with our earlier methods of camera calibration scene analysis [2]-[3]. In particular, the proposed technique increases the number of indexed points points in case of local lack of calibration points detection. At the beginning of the paper we present a way of designing a chessboard pattern. Then we describe a calibration point indexing method, and finally we show experimental results. A black-and-white chessboard is widely used in order to obtain sub-pixel accuracy of calibration points localisation [1]. Calibration points are defined as corners of chessboard squares. Assuming the availability of rough localisation of these points, the points can be indexed. Noting that differences in distances between neighbouring points in calibration scene images differ slightly, one of the local searching methods can be employed (e.g. [2]). Methods of this type search for a calibration point to be indexed, using a window of a certain size. The position of the window is determined by a vector representing the distance between two previously indexed points in the same row or column. However, experiments show that this approach has its disadvantages, as described below. * E-mail: A.Nowakowski@ire.pw.edu.pl Firstly, there is a danger of omitting some points during indexing in case of local lack of calibration points detection in a neighbourhood (e.g. caused by the presence of non-homogeneous light in the calibration scene). A particularly unfavourable situation is when the local lack of detection effects in the appearance of separated regions of detected calibration points. It is worth saying that such situations are likely to happen for calibration points situated near image borders. Such points are very important for the analysis of optical nonlinearities, and a lack of them can significantly influence the accuracy of distortion modelling. Secondly, such methods may give wrong results in the case of optical distortion with strong nonlinearities when getting information about the neighbouring index is not an easy task. Beside this, the methods are very sensitive to a single false localisation of a calibration point. Such a single false localisation can even result in false indexing of a big set of calibration points. To avoid the above-mentioned problems, we propose using a black-and-white chessboard which contains the coded index of a calibration point in the form of colour squares situated in the nearest neighbourhood of each point. The index of a certain calibration point is determined by colours of four nearest neighbouring squares (Fig.1). An order of squares in such foursome is important. Because the size of a colour square is determined only by the possibility of correct colour detection, the size of a colour square can be smaller than the size of a black or white square. The larger size of a black or white square is determined by the requirements of the exact localisation step which follows the indexing of calibration points [3]. In this step, edge information is extracted from a blackand-white chessboard. This edge information needs larger Artur Nowakowski, Wladyslaw Skarbek Institute of Radioelectronics, Warsaw University of Technology, Nowowiejska 15/19, 00-665 Warszawa, A.Nowakowski@ire.pw.edu.pl Received February 10, 2009; accepted March 27, 2009; published March 31, 2009 http://www.photonics.pl/PLP

Active Interferometric System for Mems/Moems Measurement

Micro-Electro-Mechanical Systems are nowadays frequently used in many fields of industry. The number of their applications increases and their functions became more responsible. Therefore precise knowledge about their static (shape, deformations, stresses) and dynamic (resonance frequencies, amplitude and phase of vibration) properties is necessary. Reliability or fatigue tests or other long term examinations are also becomes important in point of view their applications and the economic reasons. 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. Such method implemented in Twyman-Green interferometer allows for full-field shape determination and out-of-plane displacement measurement, Salbut et al. [1]. However the elements under test may bring additional challenges: their surfaces 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 an active reference element may be used in an interferometer setup. “Active” means that it can manipulate of the reference beam in order to introduce phase shift or tilt and influence the wavefront shape of the reference beam to make it similar to the wavefront shape of the object beam.

Interferometric Measurements of Piezoelectrically Driven Actuators

The ability to experimentally characterize static and dynamic deformation effects is crucial to the development of actuated MEMS and MOEMS devices. Almost all technological processes have an influence on the flatness and initial shape of microstructures. The accurate metrology plays a key role in the characterization and control of critical micro machining processes. For testing of MEMS structures the interferometric platform has been proposed. It gives the possibility to combine the capabilities of interferometric methods to measure static (e.g., initial shape, static out-of-plan displacements) and dynamic parameters of samples (e.g., resonance frequencies and amplitude distributions in vibration modes). In static case we use the conventional interferometry, while for vibrating elements the stroboscopic interferometry is applied with additional reference wavefront correction by a spatial modulator, namely liquid crystal on silicon (LCOS) element. As an exemplary results, the measurement of piezoelectrically driven silicon microactuators are presented