Optical surface topography measurements sometimes suffer from systematic errors. In order to predict such deviations, modeling of optical profilers is a substantial part of the European project TracOptic (Traceable Optics). Within the framework of this project, we recently developed the UFO (Universal Fourier Optics) model, which simulates virtual CSI measurements of surface topographies that fulfill the requirements of the scalar Kirchhoff approximation. The model enables a fast computation of ‘measured’ surface topographies as it is based on discrete Fourier transforms. It treats the surface under investigation as a two-dimensional phase object assuming a linear dependence of the interference phase on surface height and axial spatial frequency. The scattered light field is transferred to the Fourier domain and multiplied by a partial two-dimensional transfer function (TF) representing a horizontal cross section of the three-dimensional TF at a certain axial spatial frequency or evaluation wavelength, respectively. The TF includes parameters of the interference microscope and the reference field distribution. Inverse Fourier transform enables the reconstruction of the phase object. The coherence peak position of an interference signal results from numerical differentiation with respect to the axial spatial frequency and is generally used to overcome the 2π ambiguity of the phase profile. Parameters affecting final results of reconstructed surface topographies are the central wavelength and the spectral bandwidth of the illuminating light as well as the numerical aperture of the objective lens and the chosen evaluation wavelength. We discuss results of the UFO model with respect to the prediction of systematic deviations of measured surface topographies.
Annular subaperture stitching interferometry (ASSI) is a common approach for the measurement of aspherical surfaces. A common obstacle of ASSI is the occurrence of lateral displacement errors when the sensor or specimen is repositioned between the subaperture measurements. Our contribution focuses on modeling of the statistical displacement errors. A virtual experiment is presented simulating the propagation of the displacement errors through a cumulative and a global stitching algorithm to the retrieved surface form. For the considered experimental setup, the uncertainty in lateral position depends on the positioning uncertainties of the employed motion system and the uncertainty in the absolute distance measurement between the sensor and specimen. The lateral displacement uncertainty is determined experimentally employing a calibratable lateral grating. Thus, it is traceable to the SI unit of the length (meter). The experimental results show that the lateral displacement errors may be modeled by a normal distribution, and the results of the virtual experiment indicate that the statistical lateral displacement errors transfer linear through the stitching procedure and also cause a normal distributed topography error. This enables the assignment of an expanded uncertainty to each individual sample point employing the Zernike polynomial expression of the topography measurement.
Positioning an interferometric sensor with respect to the specimen requires a precise and expensive motion system to retain the sensors accuracy. A cost-efficient and precise setup requires a compensation of any run-out that the motion system induces. This contribution demonstrates that run-outs of a rotational axis can be compensated by implementing a low-cost interferometric point sensor to a previously presented interferometric line-scan system. Furthermore, the setup is extended by an evaluating algorithm that is capable of evaluating the line-sensor’s measurement data in real-time, using either a CPU or a GPU. An improved mechanical design of the interferometric sensor is introduced. It consists of fewer mechanical parts compared to previous versions, thus making the sensor more efficient in production and more robust against vibrations. An up-to-date high-speed line camera with a length of 4,000 pixels and line rate of up to 200 kHz increases the measurement rate of the sensor to up to 2,000 height values per second per camera pixel, enabling the sensor to evaluate 8 million height values per second.
Due to its outstanding depth resolution capabilities vertical scanning low-coherence or white-light interferometry is one
of the most used optical techniques in the field of 3D micro-metrology. Unfortunately, step height structures often lead to
disturbing effects known as batwings in SWLI measurement that overlay the real profile heights of a rectangular
structure. As a consequence, the lateral resolution capabilities and the transfer characteristics of white-light interference
microscopes are difficult to characterize. In general, the lateral resolution of such instruments is assumed to agree with
the lateral resolution of a conventional light microscope for 2D imaging and the measurement process of an optical
profiler is assumed to be linear similar to a microscopic imaging process.
Our results show that there are significant discrepancies between the instrument transfer function of a white-light
interferometer and the optical transfer function of a conventional microscope. In this paper we analyze the transfer
characteristics of current white-light interferometers based on theoretical considerations, simulation studies, and
experimental investigations. It turns out that under certain conditions a correct measurement of a rectangular profile is
possible even if only the first order diffraction component is captured by an objective lens with a given numerical
aperture.
In addition to the discussion of current instruments new approaches to overcome existing limits will be introduced: In
order to reduce the batwing effect we combine a Mirau white-light interferometer with a confocal illumination system.
Furthermore, it is shown that proper adaption of the evaluation wavelength of the low-coherent light can improve the
measurement accuracy significantly if rectangular profiles are obtained from the phase information inherent in WLI
signals.
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