Bernd Gutmann

Phase unwrapping with the branch-cut method : Role of phase-field direction

Phase unwrapping with the branch-cut method has been successfully used in many different applications in recent years. Most methods to set the branch cuts minimize the overall cut length. However, this technique fails in different cases, since this criterion is based mainly on statistical examinations. We show how the orientation and direction of the phase map help to create additional physical criteria that can be used to optimize the setting of the branch cuts. We show how these new criteria can be implemented into an energy function that will be minimized by a simulated annealing algorithm in order of a correct setting of the branch cuts. Finally, we present experimental results from electronic speckle pattern interferometry and digital holography phase maps.

Phase unwrapping with the branch-cut method: clustering of discontinuity sources and reverse simulated annealing

The branch-cut method is a powerful tool for correct unwrapping of phase maps in optical metrology. However, this method encounters the problem of the correct setting of the cuts, which belongs to the class of nondeterministic-polynomial-time-complete problems. Simulated annealing is an algorithm used to solve problems of this kind in a polynomial-time execution. However, the algorithm still requires an enormous calculation time if the number of discontinuity sources and thus the number of branch cuts is high. We illustrate the motivation for the use of this algorithm and show how the running time can be severely reduced by use of reverse simulated annealing, starting from the nearest-neighbor solution to find a proper initial configuration, and by clustering of discontinuity sources.

Phase-shifter calibration and error detection in phase-shifting applications: a new method

The phase-shifting technique is used in optical metrology to evaluate the local phase of a fringe pattern. Accurate calibration of the shifting device is often essential but sometimes hardly possible because of deviations of the fringe pattern from the ideal sinusoidal shape and because of a nonconstant phase shift between consecutive frames. We introduce a new technique for calculating the phase shift between frames even in the presence of high noise and nonsinusoidal fringe patterns. In addition, this technique permits the identification of different error sources such as low signal-to-noise ratio, higher harmonics contained in the fringe pattern, and nonconstant phase shift.

Optical in situ measurement of dust cake thickness distributions on rigid filter media for gas cleaning

Abstract Rigid barrier filters are one of the options for particulate removal from gas streams by means of surface filtration. Non-uniform gas flow through the filter, possibly caused by inhomogeneities from the manufacturing process, affects the filtration behavior of such media, is suspected of causing an inhomogeneous dust cake build-up, and may influence regeneration adversely, resulting in an instable operating cycle. So far little is quantitatively known about the distribution of cake properties (e.g., porosity, thickness, etc.) across the filter surface, possible variations of this distribution over a number of filtration cycles, and how such variations may be connected with the distribution of residual cake patches after regeneration. This paper introduces an optical in situ technique to measure dust cake height distributions across a flat area of filter surface of 14 cm in diameter. Distributions are recorded by an image acquisition process with a lateral resolution of about 280 μm (1 pixel) and a vertical resolution of about 50 μm. Sample data of a partially regenerated ceramic filter medium are presented to illustrate the capabilities of the technique. The experiments were performed with quartz dust at ambient temperature and pressure on a filter test rig according to VDI Standard 3926 [VDI Richtlinie 3926, Prufung von Filtermedien fur Abreinigungsfilter, VDI Handbuch Reinhaltung der Luft, Band 6, 1991]. The data can be used to determine point-by-point growth rates of the filter cake during filtration and residual cake thickness after pressure pulse or reverse gas flow regeneration.

Application of fuzzy-rule-based postprocessing to correlation methods in pattern recognition

The use of fuzzy-logic techniques on the correlation output plane is analyzed as a method to improve the discrimination capabilities of pattern-recognition procedures. The study is divided into two parts: one recounts a computer-simulated example corresponding to pattern recognition by the use of input images that may be defocused, tilted, or corrupted by additive Gaussian noise, and the second part describes an experimental setup in which the deformation of foam material is studied.

Some Improvements of the Phase Unwrapping Process by the use of simulated Annealing

Phase unwrapping is an essential process in many different applications in optical metrology. Measurement methods like fringe projection, electronic speckle pattern interfero-metry, or digital holography, provide their measurement information through fringe patterns. To receive the phase value of the fringes at each point, the phase has to be unwrapped. This process is very difficult in the presence of different error sources like speckle noise, aliasing effects and others. This paper shows, how the branch-cut method together with the simulated annealing algorithm can be used successfully for a robust phase unwrapping.

Improvement of the discrimination capability of correlation techniques by the use of fuzzy logic

The use of correlation methods in pattern recognition is a well known technique to detect the absence, presence and even the spatial or temporal position of any signal within another signal embedded in a complex background. Blurring, rotation, scaling, and noise often lead to false alarms in the correlation plane when working with images. Simple thresholding algorithms then might give the wrong correlation peak. Often, however, the human user can easily define the correct peak by taking into account the shape and surrounding of those local maxima that could represent the correlation peak. Sometimes less obvious factors have influence on the users decision to discriminate between wrong and false peaks. These factors have to be interrogated and transferred into quantities that can be accessed by the computer. For example, it is possible in some applications (e.g., stress analysis in experimental mechanics) to predict the peaks location to be within a certain area of the correlation plane. Thus, this quantity could be used as well. In many cases, however, it is not easy to define mathematical relations between these input variables that lead to a quantity that helps to distinguish between wrong and correct peaks. All these facts lead to the introduction of fuzzy logic to be used on the correlation plane to decide which of the local maxima corresponds to the correct correlation peak. Fuzzy logic simplifies the way in which input quantities and rules that connect these quantities have to be defined. This way the discrimination capability of different correlation methods could be greatly improved.

Fuzzy logic: a new tool for 3D displacement measurements

For comparison to model predictions, measurement of the true response of weak polymeric materials requires that a non- contacting method be used. In particular, for compression tests on weak polymers it is necessary to obtain the full 3D displacement field for the specimen. In this work, the full 3D displacement field was measured using a combination of white light speckle correlation and projected fringes. To obtain the out-of-plane displacement field, a fringe pattern with frequency of 0.30 lpmm was projected onto the specimen surface using a standard slide projector. A phase-stepping algorithm was used to convert the optical fringe pattern in a contour map for the surface. Due to reflections and noise in the fringe pattern, the authors developed a robust phase unwrapping methodology based on fuzzy logic principles. Baseline tests have shown that the algorithm produces accurate contour maps even when noise and poor fringe contrast are present. For the measurements of the in-plane displacement field the polymer foam materials was illuminated with a white light source and the natural character of the reflected light was used to obtain speckle images of the polymer. The images were acquired at various load levels and stored in digital form. The digital images were correlated to obtain the speckle deformation field. To increase the range of measurement and to deal with high strain, additional processing of the images using fuzzy logic algorithms was completed.

Ein Fuzzy geregeltes optisches Meßsystem zur Messung von 3D-Verformungn

Es wird ein optischer Mesplatz zur beruhrungslosen Verformungsmessung an Proben aus Polymerschaum vorgestellt. Dabei werden zwei bewahrte optische Mesmethoden, ein als digitale Specklephotographie bezeichnetes Korrelationsverfahren und das Projektionsstreifenverfahren miteinander kombiniert, um das dreidimensionale Verschiebungsvektorfeld auf der Probenoberflache zu ermitteln. Grose Dehnungen fuhren bei der Verwendung der digitalen Specklephotographie zu Dekorrelationen, die die Anwendbarkeit des Mesverfahrens beschranken. Durch die Verarbeitung von Vorinformationen und den Einsatz von Fuzzylogik ist es gelungen, den Anwendungsbereich fur beide Mesverfahren zu erweitern.