Surface micro topography measurement (e.g., form, waviness, roughness) is a precondition to assess the surface quality
of technical components with regard to their applications. Well defined, standardized measuring devices measure and
specify geometrical surface textures only under laboratory conditions. Laser speckle-based roughness measurement is a
parametric optical scattered light measuring technique that overcomes this confinement. Field of view dimensions of
some square millimeters and measuring frequencies in the kHz domain enable in-process roughness characterization of
even moving part surfaces. However, camera exposure times of microseconds or less and a high detector pixel density
mean less light energy per pixel due to the limited laser power. This affects the achievable measurement uncertainty
according to the Heisenberg uncertainty principle. The influence of fundamental, inevitable noise sources such as the
laser shot noise and the detector noise is not quantified yet. Therefore, the uncertainty for speckle roughness
measurements is analytically estimated. The result confirms the expected inverse proportionality of the measurement
uncertainty to the square root of the illuminating light power and the direct proportionality to the detector readout noise,
quantization noise and dark current noise, respectively. For the first time it is possible to quantify the achievable
measurement uncertainty u(Sa) < 1 nm for the scattered light measuring system. The low uncertainty offers ideal
preconditions for in-process roughness measurements in an industrial environment with an aspired resolution of 1 nm.
KEYWORDS: Light scattering, Radium, Speckle, Scattering, Speckle pattern, Near field, Laser scattering, Near field optics, Finite element methods, Computer simulations
This paper deals with an efficient computation method for scattered light intensity distributions, which occur, if a nanostructured surface is illuminated with a monochromatic laser beam of several millimeters in diameter. The minimization of the computational amount is an essential precondition in connection with the development of powerful design tools for laser optical surface measuring methods, which derive structure characterizing attributes from structure dependent scattering effects.
The presented approach differs from concepts based on near-field solutions of the Maxwell equations (finite element methods (FEM), finite difference time domain methods (FDTD)) or approximation methods for the near-field (Discrete Dipole Approximation (DDA), Generalized Multipole Technique (GMT)) as the near-field is not computed. Instead, an electrically equivalent model based on pre-computed radiation sources like Huygens point sources, dipoles, quadrupoles, etc. is used, which for standard geometrical nanostructures (cylindrical holes, spheres and ellipsoids) leads to the same far-field distributions as the conventional methods. In order to simulate the scattered light by an arbitrary surface it is divided into subwavelength geometries, which can be substituted by electrically equivalent dipole radiation sources. The far-field is calculated with a numerical scalar method. The computational effort is much smaller compared to algorithms based on the solution of Maxwell's equations.
This paper presents a simulation approach for light scattering from surfaces containing spherical and elliptical nanoparticles. For this approach an electrically equivalent macro model is derived based on the analytical solutions of Maxwell's equations (e.g. Mie's solution of a sphere). These macro models do not necessarily fulfill the boundary conditions or give the correct near-field but they provide a suitable far-field solution. The benefit of this approach is an abstract model for the far-field computation that is much more efficient than known solutions like FEM. The radiation sources at the surface are reduced to a maximum like a single source for a whole particle, which gives the correct far-field but does not fulfill the boundary conditions. For the set of radiation sources used for the macro models the approach presented here reverts to the accurate computation of simple geometries. In this special case of spherical and elliptical particles the solution of the Mie theory can be used. In this paper it is shown that in the case of nanostructures the far-field of a sphere and an ellipse can be replaced by the radiation field from a set of dipoles. Based on these results it is possible to approximate an equivalent macro model of the surface containing spherical and elliptical elements. The presented macro model provides a very reasonable simulation approach with acceptable simulation times for large surface areas of several square millimeters.
Parallel kinematics machines (PKM) present a promising new formation of machine kinematics. But, their application is limited due to insufficient positioning accuracy, caused by errors of the transformation model and indirect position measurements. The theoretically attainable machining accuracy of machine tools is further decreased by unsolved calibration problems, which are the most important obstacles concerning the introduction of new machine tools with parallel or hybrid kinematics. This paper presents a conceptual improvement based on a direct position measurement in Cartesian coordinates, which overcomes these problems.
Fringe Projection systems generate phase distributions of an object illuminated with a specific fringe pattern. These phase correspond to the object coordinates. It is mostly necessary to transform the dimension-less phases to a metric dimension. Until today this is realized by photogrammetric techniques, which are subdivided into three main processes. At first a reference plane is defined. Then a grid within this plane is fixed. In the third step, the height axis is calibrated by different methods, for example, by use of a single height step or another well defined base object. This article describes a new method to calibrate the measuring volume by a multi-value calibration algorithm. As a first step, the fringe projection systems detects the phase distribution of a plane, denoted as reference plane. The, the plane moves stepwise in z-direction. In each step the phase distribution is detected, while an interferometer measures the distance of the z-coordinate form the reference plane. Together with the discrete x-y-coordinates of a CCD- detection unit, a 3D measuring volume is defined. The volume calibration is performed by separate polynomials for each x- y-coordinate, which are derived from the corresponding values of the phase distributions and the interferometric height values. With this method some problems of the conventional 'single value calibration' can be solved. This contribution describes the theoretical solution of the problem and presents first experimental results.
The nitration process influences the mechanical and chemical properties of steel and changes the near-surface characteristics. The nitrided surfaces are less sensitive to corrosive fluids and show a better stability against abrasion. Unfortunately, during treatment pores emerge at the surface. In general this is not desired, since the pores reduce the wear stability. The change of the near-surface characteristics also leads to a remodeling of the surface topography. For example, ground, smooth surfaces show an increased but isotropic roughness after nitration. During the recent years, various speckle techniques for an in-process characterization of surface topography have been improved significantly. One of these promising techniques is the method of trichromatic speckle autocorrelation. Its measuring principle is based on trichromatic light scattering and enables to determine an integral parameter of the surface roughness by the evaluation of the speckle elongation. Especially in the case of nitration, where the specimen is located in a stove filled with ammonia at a temperature of 580 degrees Celsius, this technique offers an in-processing monitoring of surface topography changes from outside the stove. In this paper, the in-process characterization of surface topography by speckle autocorrelation will be introduced. In this context an algorithm has been developed, which allows to estimate the position of the optical axis within the speckle pattern and therefore to determine the surface roughness as well as the local inclination of isotropic surfaces. An important goal of the current research is to realize a reliable process control based on the speckle autocorrelation, that is necessary to produce nitrided surfaces without pores in the compound layer and with good abrasive and corrosive resistance.
A method for determining surface roughness of engineering surfaces that is applicable to in-process measurements under harsh circumstances of industrial production plants (e.g. vibrations, humidity) is introduced. The rough surface is illuminated with polychromatic laser light. The angular distribution of scattered light intensities, i.e. a polychromatic speckle pattern, is the result of an incoherent superposition of monochromatic speckle intensities. The angular dispersion leads to increasing speckle widths with an increasing distance to the optical axis an effect called speckle elongation. This gives rise to a radial structure of the speckle pattern. However, with increasing surface roughness the radial structure vanishes because of a decreasing similarity of the monochromatic speckle patterns of the different wavelengths. The markedness of this effect is analyzed by digital image processing algorithms, e.g. the procedure of polychromatic speckle autocorrelation. The latest approach to an in-process roughness measurement device was made by the use of singlemode fiber-pigtailed laser diodes in order to supply a trichromatic, temporally partially coherent laser beam. A brief introduction to the theoretical background is followed by the presentation of the experimental setup. The image processing algorithms for calculating an optical roughness measure from digitalized speckle patterns are explained, and first results of surface roughness determination are presented.
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.