Jeremias Seppä

A method for linearization of a laser interferometer down to the picometre level with a capacitive sensor

This paper describes methods for dynamic measurement and correction of laser interferometer periodic nonlinearity down to the picometre level. A capacitive sensor is used as an external reference for measuring and calculating the periodic interferometer nonlinearity correction function. The experimental interferometer setup is a heterodyne interferometer with symmetrical paths to detectors and time-interval-based phase detection. The periodic nonlinearity is represented as harmonic Fourier components. The time evolution of the nonlinearity function is tracked during measurement. The method is verified by spatial and temporal repeatability of the measured nonlinearity. Linearization repeatability in the 10 pm range is observed.

High-precision diode-laser-based temperature measurement for air refractive index compensation

We present a laser-based system to measure the refractive index of air over a long path length. In optical distance measurements, it is essential to know the refractive index of air with high accuracy. Commonly, the refractive index of air is calculated from the properties of the ambient air using either Ciddor or Edlén equations, where the dominant uncertainty component is in most cases the air temperature. The method developed in this work utilizes direct absorption spectroscopy of oxygen to measure the average temperature of air and of water vapor to measure relative humidity. The method allows measurement of temperature and humidity over the same beam path as in optical distance measurement, providing spatially well-matching data. Indoor and outdoor measurements demonstrate the effectiveness of the method. In particular, we demonstrate an effective compensation of the refractive index of air in an interferometric length measurement at a time-variant and spatially nonhomogeneous temperature over a long time period. Further, we were able to demonstrate 7 mK RMS noise over a 67 m path length using a 120 s sample time. To our knowledge, this is the best temperature precision reported for a spectroscopic temperature measurement.

Measurement strategies and uncertainty estimations for pitch and step height calibrations by metrological atomic force microscope

Gratings and step height standards are useful transfer standards for lateral and vertical length scale calibration of atomic force microscopes (AFMs). In order to have traceability to the SI-meter, the standards must have been calibrated prior to use. Metrological AFMs (MAFMs) with online laser interferometric position measurements are versatile instruments for the calibrations. The developed task-specific measurement strategies for step height and pitch calibrations with the Centre for Metrology and Accreditations (MIKESs) metrological AFM are described. The strategies were developed to give high accuracy and to reduce measurement time. Detailed uncertainty estimations for step height and grating pitch calibrations are also given. Standard uncertainties are 0.016 and 0.018 nm for 300 and 700 nm pitch standards, respectively, and 0.21 and 0.44 nm for 7 and 1000 nm step height standards.

High accuracy laser diffractometer: angle-scale traceability by the error separation method with a grating

Laser diffractometer constructed at MIKES for calibration of pitches of 1D and 2D gratings is based on the Littrow configuration. The grating is rotated by a rotary table. In order to obtain optimal beam quality a fibre-coupled frequency-doubled stabilized Nd:YAG laser is used as a light source and a CCD without internal reflections is used to detect the diffracted beam position. The angle corresponding to the Littrow null position is calculated using a linear fit to equidistantly spaced angles around the null position, which reduces the effect of nonlinearity of the angle encoder scale. Pitch is calculated as a weighted average of the diffraction orders. Novel use of an uncalibrated 1D grating applied to classical error separation methods for angle calibration by full-circle subdivision is described. Diffraction angle measurements are repeated in many sample holder alignments rotated relative to the absolute angle scale. The sequences overlap so that the full circle of the angle scale is covered with multiple evenly distributed sequences, needed for circle-subdivision metrology. The average grating pitch over all sequences is used to separate angle scale errors and a correction table for the rotary table is calculated. The method was verified using a calibrated polygon and an autocollimator. Uncertainty estimates for the grating pitch calibration are given, e.g. the standard uncertainty of 9 pm for 2 µm grating.

Quasidynamic calibration of stroboscopic scanning white light interferometer with a transfer standard

Abstract. A stroboscopic scanning white light interferometer (SSWLI) can characterize both static features and motion in micro(nano)electromechanical system devices. SSWLI measurement results should be linked to the meter definition to be comparable and unambiguous. This traceability is achieved by careful error characterization and calibration of the interferometer. The main challenge in vertical scale calibration is to have a reference device with reproducible out-of-plane movement. A piezo-scanned flexure guided stage with capacitive sensor feedback was attached to a mirror and an Invar steel holder with a reference plane—forming a transfer standard that was calibrated by laser interferometry with 2.3 nm uncertainty. The moving mirror vertical position was then measured with the SSWLI, relative to the reference plane, between successive mirror position steppings. A light-emitting diode pulsed at 100 Hz with 0.5% duty cycle synchronized to the CCD camera and a halogen light source were used. Inside the scanned 14 μm range, the measured SSWLI scale amplification coefficient error was 0.12% with 4.5 nm repeatability of the steps. For SWLI measurements using a halogen lamp, the corresponding results were 0.05% and 6.7 nm. The presented methodology should permit accurate traceable calibration of the vertical scale of any SWLI.

Intercomparison of lateral scales of scanning electron microscopes and atomic force microscopes in research institutes in Northern Europe

An intercomparison of lateral scales of scanning electron microscopes (SEM) and atomic force microscopes (AFM) in various research laboratories in Northern Europe was organized by the local national metrology institutes. In this paper are presented the results of the comparison, with also an example uncertainty budget for AFM grating pitch measurement. Grating samples (1D) were circulated among the participating laboratories. The participating laboratories were also asked about the calibration of their instruments. The accuracy of the uncertainty estimates seemed to vary largely between the laboratories, and for some laboratories the appropriateness of the calibration procedures could be considered. Several institutes (60% of all results in terms of En value) also had good comprehension of their measurement capability. The average difference from reference value was 6.7 and 10.0 nm for calibrated instruments and 20.6 and 39.9 nm for uncalibrated instruments for 300 nm and 700 nm gratings, respectively. The correlation of the results for both nominally 300 and 700 nm gratings shows that a simple scale factor calibration would have corrected a large part of the deviations from the reference values.

Traceable characterization of a bending millimetre scale cantilever for nanoforce sensing

We have developed and characterized a force measuring system that is able to measure small forces down to 50 nN. The force measuring system and the characterizing method are described, thoroughly tested and analysed. The force measuring system consists of a linear positioner, a bending cantilever and an optical detection system for detecting the bending of the cantilever displacement. Characterization was carried out with a microbalance and a laser interferometer. The characterized measurement range of the system is from 50 nN to 1.5 mN. The performance of the system is limited by the linearity of the positioner and the noise of the optical sensor detecting the cantilever bending. The characterization system was found to be adequate for force sensors in the nanonewton range. The results are traceable to mass and acceleration of gravity, which makes the measurements reliable and comparable to other force measurements and applications.

Interference cancellation for hollow-core fiber reference cells

Doppler-free spectroscopy of gases in hollow-core fiber (HCF) -based cells can be used for realizing new compact, robust and portable frequency standards. In this summary a method for cancelling interferences resulting from splices between standard telecom fiber and HCF using two piezoelectric stack actuators is presented. Both HCF and mirror-side standard fiber are modulated by stretching. The performance of the cancellation scheme was tested with a HCF yielding 99 % interference amplitude reduction.

Traceable Quasi-dynamic Stroboscopic Scanning White Light Interferometry

We addressed the question of how to assign confidence limits to the measured trajectory of a moving MEMS membrane. This was done by calibrating our SSWLI setup using a traceable piezoelectric transducer as a transfer standard. We calibrated our SSWLI setup for quasi-dynamic measurements of vertical movements up to 14 μm with standard uncertainty of 9.4 nm.