Clustering of inertial particles is important for many types of astrophysical and geophysical turbulence, but it has been studied predominately for incompressible flows. Here, we study compressible flows and compare clustering in both compressively (irrotationally) and vortically (solenoidally) forced turbulence. Vortically and compressively forced flows are driven stochastically either by solenoidal waves or by circular expansion waves, respectively. For compressively forced flows, the power spectrum of the density of inertial particles is a useful tool for displaying particle clustering relative to the fluid density enhancement. Power spectra are shown to be particularly sensitive for studying large-scale particle clustering, while conventional tools such as radial distribution functions are more suitable for studying small-scale clustering. Our primary finding is that particle clustering through shock interaction is particularly prominent in turbulence driven by spherical expansion waves. It manifests itself through a double-peaked distribution of spectral power as a function of Stokes number. The two peaks are associated with two distinct clustering mechanisms; shock interaction for smaller Stokes numbers and the centrifugal sling effect for larger values. The clustering of inertial particles is associated with the formation of caustics. Such caustics can only be captured in the Lagrangian description, which allows us to assess the relative importance of caustics in vortically and compressively forced turbulence. We show that the statistical noise resulting from the limited number of particles in the Lagrangian description can be removed from the particle power spectra, allowing us a more detailed comparison of the residual spectra. We focus on the Epstein drag law relevant for rarefied gases, but show that our findings apply also to the usual Stokes drag.

Coherence scanning interferometry used in optical profilers are typically good for Z-calibration at nm-levels, but the X,Y accuracy is often left without further notice than typical resolution limits of the optics, i.e. of the order of similar to 1 mu m. For the calibration of metrology tools we rely on traceable artefacts, e.g. gauge blocks for traditional coordinate measurement machines, and lithographically mask made artefacts for microscope calibrations. In situations where the repeatability and accuracy of the measurement tool is much better than the uncertainty of the traceable artefact, we are bound to specify the uncertainty based on the calibration artefact rather than on the measurement tool. This is a big drawback as the specified uncertainty of a calibrated measurement may shrink the available manufacturing tolerance. To improve the uncertainty in X, Y we can use self-calibration. Then, we do not need to know anything more than that the artefact contains a pattern with some nominal grid. This also gives the opportunity to manufacture the artefact in-house, rather than buying a calibrated and expensive artefact. The self-calibration approach we present here is based on an iteration algorithm, rather than the traditional mathematical inversion, and it leads to much more relaxed constrains on the input measurements. In this paper we show how the X, Y errors, primarily optical distortions, within the field of view (FOV) of an optical coherence scanning interferometry microscope, can be reduced with a large factor. By self-calibration we achieve an X, Y consistency in the 175 x 175 mu m(2) FOV of similar to 2.3 nm (1 sigma) using the 50x objective. Besides the calibrated coordinate X, Y system of the microscope we also receive, as a bonus, the absolute positions of the pattern in the artefact with a combined uncertainty of 6 nm (1s) by relying on a traceable 1D linear measurement of a twin artefact at NIST.

Using dedicated stereo camera systems and structured light is a well-known method for measuring the 3D shape of large surfaces. However the problem is not trivial when high accuracy, in the range of few tens of microns, is needed. Many error sources need to be handled carefully in order to obtain high quality results. In this study, we present a measurement method based on low-cost camera and illumination solutions combined with high-precision image analysis and a new approach in camera calibration and 3D reconstruction. The setup consists of two ordinary digital cameras and a Gobo projector as a structured light source. A matrix of dots is projected onto the target area. The two cameras capture the images of the projected pattern on the object. The images are processed by advanced subpixel resolution algorithms prior to the application of the 3D reconstruction technique. The strength of the method lays in a different approach for calibration, 3D reconstruction, and high-precision image analysis algorithms. Using a 10 mm pitch pattern of the light dots, the method is capable of reconstructing the 3D shape of surfaces. The precision (1 sigma repeatability) in the measurements is < 10 mu m over a volume of 60 x 50 x 10 cm(3) at a hardware cost of similar to 2% of available advanced measurement techniques. The expanded uncertainty (95% confidence level) is estimated to be 83 mu m, with the largest uncertainty contribution coming from the absolute length of the metal ruler used as reference.

Accurate dimensional measurement of micro-milled items is a challenge and machine specifications do not include operational parameters in the workshop. Therefore, a verification test that shows the machine's overall geometrical performance over its working area would help machine users in the assessment and adjustment of their equipment. In this study, we present an optical technique capable of finding micro-milled features at submicron uncertainty over working areas > 10 cm(2). The technique relies on an ultra-precision measurement microscope combined with advanced image analysis to get the center of gravity of milled cross-shaped features at subpixel levels. Special algorithms had to be developed to handle the disturbing influence of burr and milling marks. The results show repeatability, reproducibility, and axis straightness for three micro-milling facilities and also discovered an unknown 2 mu m amplitude undulation in one of them.

Autofocus lenses are conveniently used for applications such as video metrology. In this study we investigate the stability of capturing images and show that for precision metrology applications the autofocus lenses are not as accurate as manual lenses. The investigation was done by analyzing series of seven repeated images captured from a highly accurate reference artifact using two different lenses; autofocus and manual, mounted on a same camera system.

A laser diffractometer and three image-based instruments with spatial resolutions between 0.33 and 10 mu m/pixel were compared through measurements on calibration spheres and fine fractions comprising pulp fines of various types, neat PCC filler, and a mixture of fines and fillers. The laser diffractometer was highly sensitive to the keyed in refractive index of the samples, which was calculated based on volume-based mixing rules. A high-resolution flow cytometer and a high-resolution fibre analyser were found to be complimentary for measurements on neat fines and fines/filler mixtures, and superior to the laser diffractometer. When measuring on fillers, the laser diffractometer performed as well as the high-resolution flow cytometer, which was capable of resolving single filler particles. The sizes of the calibration spheres were overestimated by the image-based instruments, and the measurement uncertainty was high. The uncertainty was mainly attributed to the unrestricted particle motion, and the low accuracy to the dissimilar optical properties of the calibration material, compared to fines. Thus, calibration materials with shape and optical properties more similar to fines should be developed.

Today several techniques are available for micro-manufacturing. Yet, it is difficult to assess the precisionand lateral X,Y accuracy of these techniques. The available accuracy information is usually based on spec-ifications given by machine suppliers. This information is based on in-house laboratory tests performedby dedicated machine operators and within an adapted environment. In practice, the accuracy is likelyto vary due to environmental conditions, materials and operator skills. In order to check the specifica-tions in realistic environments the EUMINAfab infrastructure consortium initiated a set of independenthigh precision onsite verification tests on different laser micromachining installations. In addition toproviding performance verification, it gave the participating partners real capability information of theirequipment and possibilities to improve machining performance to a higher level. In this study a compre-hensive verification test was designed and carried out by using a high precision metrology method for 2Dmeasurements based on subpixel resolution image analysis. This methodology improved our knowledgeof the capabilities of three laser micromachining installations, and showed that specifications at singlemicron levels are hard to obtain.

Micro- and nano-manufacturing is an expanding industry and many different manufacturing techniques are used, from advanced focused ion beam treatment to reasonably simple printing technologies. Common to all of them are the needs to verify the manufactured geometries and dimensions. This report presents the results of the second round of benchmarking activities within the EUMINAfab European Research Infrastructure, in order to establish more knowledge about the capabilities of a screen printing installation. To obtain a better understanding of the accuracy of the screen printing installation, a precise verification test is needed to measure the absolute performance of the machine. Predicted performance and capability information is based on specifications given for the machine installation by the machine deliverer. But, in practice the absolute performances of the installation is often off from the specification. When forming the EUMINAfab infrastructure consortium it was decided that independent high precision verification tests should be made on different installations to help the micro-manufacturers to get the real capability information of their equipment and be able to improve performance to a higher EUMINAfab level. In this study a comprehensive verification test was designed and carried out by using an ultra-precision metrology method in order to establish more knowledge about the capabilities of the screen printing equipment. The measurement results show the machine’s X,Y position accuracy, pseudo-repeatability and reproducibility. It is not as good as predicted.

We suggest a procedure for estimating Nth degree polynomial approximations to unknown (or known) probability density functions (PDFs) based on N statistical moments from each distribution. The procedure is based on the method of moments and is setup algorithmically to aid applicability and to ensure rigor in use. In order to show applicability, polynomial PDF approximations are obtained for the distribution families Normal, Log-Normal, Weibull as well as for a bimodal Weibull distribution and a data set of anonymized household electricity use. The results are compared with results for traditional PDF series expansion methods of Gram-Charlier type. It is concluded that this procedure is a comparatively simple procedure that could be used when traditional distribution families are not applicable or when polynomial expansions of probability distributions might be considered useful approximations. In particular this approach is practical for calculating convolutions of distributions, since such operations become integrals of polynomial expressions. Finally, in order to show an advanced applicability of the method, it is shown to be useful for approximating solutions to the Smoluchowski equation.

Metrology is the science of measurements; production engineering metrology is the science of applied metrology in production and in product realization. In this paper the automotive, construction equipment and aerospace industry are particularly addressed. One theoretical and practical approach to geometrical part quality assurance focusing on manufacturing processes and systematic work and use of objective, value adding production engineering metrology is proposed. This paper aims to describe a practical approach on how to carry out geometrical assurance of parts produced in manufacturing processes using traditional production methods. One example using machining, i.e. turning, of a part is used to explain this approach.