Optical metrology is a driving force in advancing industries ranging from consumer electronics to components for energy and transportation. Despite this progress, there is considerable wasted effort attributable to misleading instrument specifications, inconsistent calibrations, and ambiguous data processing procedures. Confusing statements of accuracy and uncertainty, inconsistencies in filtering and parameter calculations, and misunderstandings about measurement principles and limitations undermine confidence in measurement results. A greater awareness and use of international standards documents can improve the situation, leading to a wider adoption of optical methods. At the same time, there is a critical need for stronger engagement in the development of new standards by experts in optics and photonics.
Normally, roughness measurements are carried out with a rather high uncertainty ranging to a few percent up to 10%. This is a rather bad situation considering the accuracy of primary length standards (1:5•10^11) and common dimensional measurements(1:106). In this paper we show that with laser interferometer calibration techniques and extensive uncertainty evaluations this situation can be improved. As the probe of a roughness measuring instrument moves dynamically, a probe calibration should be carried out dynamical as well, in the same frequency range as in which the probe normally operates. For this, a simple yet very effective dynamic probe calibration device has been designed, where the traceability is achieved by a laser interferometric read-out with 30 kHz and 10 nm resolution. With this device a probe can be fully characterized for various amplitudes and frequencies. It is shown that for a Mitutoyo roughness measuring machine the deviations stay well within 1%. Uncertainty estimations for roughness measurements are not straightforward, therefore one takes for safety often quite high estimates for effects like probe size and measurement force. With the VFM ('Virtual Form Measurement') concept this problem is treated by simulating the measurement on the same surface as actually measured, while varying probe diameter, filtering, probe angle, noise etc. and estimating the influence of all these circumstances on the calculated parameter. In this way a task-specific uncertainty estimation is obtained with an outcome which is mostly lower than expected. This is shown with some examples. With improved noise reduction techniques the basic uncertainty can be reduced to the nm-level for the roughness tester used.
In this study, the non-linear errors in a commercial heterodyne interferometer are investigated. There are two types of cyclic nonlinearities present in heterodyne interferometers and it is desirable to be able to measure these nonlinearities in order to quantify the uncertainty of the interferometer setup. The current study investigates whether the nonlinearities can be detected by measuring the optical power of the interferometers output signal as a function of its phase. In theory, the optical power can be described as a perfect circle in polar coordinates in the absence of cyclic errors. The cyclic errors present, then manifest themselves as ellipticity of this circle and a translation of its centre. In this study large cyclic nonlinearities were deliberately introduced into a standard heterodyne interferometer setup, making them large enough to
measure directly from the displacement data. Comparison with predicted nonlinearities calculated from the optical power data showed a good fit, indicating that it is possible to predict cyclic nonlinearities by reading the optical power from the measurement board.
For beam delivery in a single-fiber-fed heterodyne laser interferometer with nanometer uncertainty, the use of polarization-maintaining (PM) fibers is investigated. The PM properties of the light emerging from the fiber determine the achievable measurement accuracy. Measurements of the polarization-mixing properties of several different PM-fiber types as well as a range of fiber lengths were described in part I of this paper. In this part, a model and analysis of the fiber are presented. By means of the analytical model, a quick selection method is given, which can also be used to precisely align the fiber with respect to the other optical components of the interferometer. The presented model, based on Jones matrices, allows the investigation of local and global disturbances within the fiber and their location. As in part I, the dominant effect of the connector in the fiber assembly is shown. The effects of imperfections in fiber material are shown for longer fibers; they change the dominating connector effect slightly.
New measurement techniques and methods for characterizing the quality of optical fibers are presented. The fibers are to be used in a single-fiber-fed heterodyne laser interferometer with nanometer uncertainty. The polarization-mixing properties of several different polarization-maintaining fiber types, as well as the effects of fiber lengths on high-precision length measurements, is investigated for the first time. Mixing ratio and polarization orthogonality were measured using three different methods. The measured mixing ratios varied between 1:100 and 1:1650 (intensity). Also the influence of the fiber assembly on the polarization-mixing properties is shown.
Since the wafer industry is using an increasing amount of double side polished wafers, the future of wafer metrology is very likely to shift from capacitance gauging techniques to optical measurement techniques. Participating in an international project the Technical University of Eindhoven is developing a self calibrating, traceable double side wafer flatness and thickness measurement device. By using proper measurement principles and advanced software a robust and traceable wafer thickness and flatness measurement instrument is created which combines high lateral resolution, nanometer accuracy, high speed and low cost.
Laser interferometer systems are known for their high resolution, and especially for their high range/resolution ratio. In dimensional metrology laboratories, laser interferometers are popular workhorses for the calibration of displacements. The uncertainty is usually limited to about 10 nm due to polarization- and frequency mixing. For demanding applications however nanometer uncertainty is desired.
We adapted a commercially available heterodyne laser interferometer by feeding the measurement signal into a fast lock-in amplifier and use the laser interferometer reference signal as a reference. By measuring both the in-phase and quadrature component an uncorrected phase can be directly measured. By recording both components while the phase changes between 0 and 2π a typical ellipse is recorded from which the first and second harmonics of periodic deviations can be derived. These can be corrected independent of their origin. Measurements show that this method can reduce severe non-linearities (40 nm top-bottom) to a standard deviation of about 0.02 nm. Also, optical set-ups can be analysed to predict the non-linearities when a non-compensated standard interferometer is used.
In form and roughness measurements, often surfaces are measured which are approximately straight, round, or smooth. Measuring such surfaces often gives measurement results in which noise plays a role. This noise may give an offset in measurement parameter as the noise makes the parameter, e.g. the flatness deviation of the Ra-value, deviate away from zero. In this paper we propose a method to correct for this noise bias for the roughness parameter Rq which is equivalent to the standard deviation. By considering the decrease in Rq once an average over multiple measurements is made, an unbiased value for Rq is estimated by extrapolating the value to an infinite amount of measurements. It is shown that using this method for two profile measurements only, the true measurand is approached better than with averaging dozens of measurements. This principle is extended to obtain a complete 'noise-corrected' profile by considering the power spectrum and the change of each Fourier component with averaging. As for each Fourier component few estimations are available, the method only has advantages when many measurements are taken. Combining the two methods and considering the statistical significance of each Fourier component enables a further reduction. Simulation and measurement examples are shown for roughness and roundness measurments.
For the calibration of length standards and instruments, various methods are available for which usually an uncertainty according to the GUM [1] can be set up. However, from calibration data of a measuring instrument it is not always evident what the uncertainty will be in an actual measurement (or calibration) using that calibrated instrument. Especially where many measured data are involved, such as in CMM measurements, but also in typical dimensional geometry measurements such as roughness, roundness and flatness measurements, setting up an uncertainty budget according to the GUM for each measurement can be tedious and even impossible. On the other hand, international standards require that for a proof of the conformance to specifications, the measurement uncertainty must be taken into account. Apart from this it is not so consistent that a lot is invested in the calibration of instruments where it is still unclear what the uncertainty is of measurements carried out with these 'calibrated' instruments. In this paper it is shown that the 'standard' GUM-uncertainty budget can be modified in several ways to accommodate more complicated measurements. Also, it is shown how this budget can be generated automatically by the measuring instrument, by the simulation of measurements by instruments with alternative metrological characteristics, so called virtual instruments. This can lead to a measuring instrument where, next to the measured value, also the uncertainty is displayed. It is shown how these principles are already used for roughness instruments, and how they can be used as well for e.g. roundness, cylindricity, flatness and CMM measurements.
KEYWORDS: Calibration, Monte Carlo methods, 3D modeling, Temperature metrology, Computer simulations, Metrology, Interferometers, Signal generators, 3D metrology, Laser development
In coordinate measurement metrology, assessment of the measurement uncertainty of a particular measurement is not a straight forward task. A feasible way for calculation of the measurement uncertainty seems to be the use of a Monte Carlo method. In recent years, a number of Monte Carlo methods have been developed for this purpose, we have developed a Monte Carlo method that can be used on CMM's that takes into account, among other factors, the auto correlation of the error signal. We have separated the errors in linearity errors, rotational errors, straightness errors and squareness errors. Special measurement tools have been developed and applied to measure the required parameters. The short-wave as well as the long-wave behavior of the errors of a specific machine have been calibrated. A machine model that takes these effects into account is presented here. The relevant errors of a Zeiss Prismo were measured, and these data were used to calculate the measurement uncertainty of a measurement of a ring gauge. These calculations were compared to real measurements.
Nanosensors are a new class of sensors that has recently appeared. These sensors are characterized by nanometer or sub-nanometer resolution over a range of at least several micrometers. The most well known examples are capacitive and inductive sensors but also laser interferometers, holographic scales, and scanning probe microscopes (SPM's) belong to the class of nanosensors. The accuracy of these nanosensors is not necessarily of the same level as the resolution. Effects like sensitivity errors, non-linearity, hysteresis and drift may cause deviations of many nanometers. In order to determine these errors in a traceable way, a new measuring instrument was developed. The heart of the system is a Fabry-Perot interferometer, which consists of two parallel mirrors separated by a distance L from each other. Light of a so-called slave laser is directed into this Fabry-Perot cavity and stabilized to the cavity length L. When one of the mirrors of this cavity is displaced the frequency of the slave-laser will follow its movement. The frequency of this slave-laser is then compared to the frequency of a primary length standard. In this way the displacement of the mirror is measured. When a nanosensor is placed on top of the mirror it will also follow the movement of the mirror. In this way the nanosensor is calibrated. The range of the instrument is 300 micrometers and the uncertainty is approximately 1 nm. Measurements of different sensors, such as an inductive and a capacitive sensor as well as a laserinterferometer will be presented. A detailed description of the uncertainty budget will also be given.
The mechanical probing system is often one of the limiting factors in the calibration of length standards. It has been shown, that for highly accurate applications a particular effect, which is often not considered, has to be taken into account: a spherical probe on a stylus undergoes a small rotation due to the angular stylus deflection, which creates friction and potentially stick slip during the probing process and may thus lead to non-reproducible probing. A novel probe has been built which avoids this effect by an additional degree of freedom, providing a small vertical movement of the stylus. The probe is of a monolithic flexure hinge design with a ridge connection of the stylus and the mirror reflector for the plane mirror interferometer, which measures the displacement. Them measurement force, which is proportional to the deflection of the hinges, is measured with a capacitive probe. The probing procedure generates the force/deflection curve and allows for the measurement force to be extrapolated to zero. The presented test results show the system's capability for a probing accuracy in the nanometer range.
An instrument for the measurement of ball diameters in the 0.5-20 mm range in a gauge block interferometer is realized. The measurement principle is that the ball is positioned between an optical flat and a calibrated gauge block. The total length is measured in a gauge block relative to the optical flat and proper measurement of the deformations due to the measuring force. The parallelism is adjusted while viewing the interference patterns on the gauge block and the optical flat. The measuring force can be varied in the 0.03- 2.35 N range. The applied force is calibrated. Experiments show that commonly used formulas to calculate the ball indentation as a function of the applied force are approximately correct; this instrument however provides a direct means to measure this dependence and to apply a proper extrapolation to zero measuring force. The design is rather compact so it will fit in commonly used gauge block interferometers. The uncertainty which can be achieved is less than 0.1 micrometer.
An interferometer is realized, based on the Twyman-Green Interferometer principle for the calibration of long gauge blocks and length bars in the 100-1000 mm range with an uncertainty of 0.02 micrometers + 0,1 micrometers /m. Also the expansion coefficient of gauge blocks and even of rod-shaped materials with non-optical flat faces can be calibrated in the 18-22 degrees C range with an uncertainty below 1 X 10-7/K. The set-up basically follows the most commonly used interferometer arrangements for long gauge blocks as they are described by Darnedde, Ikonen and Lewis where the most similarities with the latter occur. The set- up has some peculiarities which make the measurement straightforward, accurate and reliable.
The relations between the optical, electrical and structural properties of
pyrolytically sprayed, Fluorine-doped tinoxide coatings have been examined by
analyzing coatings having a different Fluorine doping, different preparation
temperature and different coating thickness. The results show that doping
tinoxide coatings with fluorine increases the electron density and the
mobility ii the coating. The maximum electron density which can be obtained is
about 410 6/m . The maximum mobility of about 45 cm /Vs which has been
obtained, roughly equals the maximum mobility predicted by the theory for
ionized impurity scattering. This leads to a minimum attainable thermal
emittance of about 0. 15. When the maximum mobility has not been reached, this
can be due to a too weak preferential orientation in the (200) direction or
to a small electron density in the coating.
Recent Developments in Traceable Dimensional Measurements III
31 July 2005 | San Diego, California, United States
Recent Developments in Traceable Dimensional Measurements II
4 August 2003 | San Diego, California, United States
Course Instructor
SC562: Accuracy of Interferometric Measurements for Nano-Metrology
This course gives the attendees insight into the physical principles that enable and limit the possibilities of metrology at the nm-uncertainty level. An overview will be given of measurement techniques and principles that are available, with emphasis on their suitability for accurate measurements. Special attention will be given to laser-interferometry. This technique for measuring displacements can be used in several ways as part of a nanometer measuring- or manufacturing device. Another important measuring technique is the measurement of flatness and form deviations by Fizeau or similar interferometers. It will be demonstrated where the limits are and how these can be established for this technique. Examples will be given in the measurement of nanostructures.
Access to the requested content is limited to institutions that have purchased or subscribe to SPIE eBooks.
You are receiving this notice because your organization may not have SPIE eBooks access.*
*Shibboleth/Open Athens users─please
sign in
to access your institution's subscriptions.
To obtain this item, you may purchase the complete book in print or electronic format on
SPIE.org.
INSTITUTIONAL Select your institution to access the SPIE Digital Library.
PERSONAL Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.