Framework for gradient integration by combining radial basis functions method and least-squares method
TL;DR: A framework with a combination of the radial basis functions method and the least-squares integration method is proposed to improve the integration process from gradient to shape and is accurate, automatic, easily implemented, and robust.
Abstract: A framework with a combination of the radial basis functions (RBFs) method and the least-squares integration method is proposed to improve the integration process from gradient to shape. The principle of the framework is described, and the performance of the proposed method is investigated by simulation. Improvement in accuracy is verified by comparing the result with the usual RBFs-based subset-by-subset stitching method. The proposed method is accurate, automatic, easily implemented, and robust and even works with incomplete data.
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TL;DR: The stitching result is compared to the result of a one-dimensional angular-measurement-based stitching method to discuss the merits and limitation of the proposed method.
Abstract: In this paper, a two-dimensional stitching interferometry system using two tiltmeters is proposed During the scanning and the measurement, one tiltmeter stays with the interferometer and the other one is attached to the translation stage where the surface under test is placed The differences of the x- and y-tilt readings between these two tiltmeters are recorded as the relative tilt between interferometer and surface under test The relative tilt in both x- and y-directions are used to correct the surface tip/tilt of each subset, and then the piston is adjusted to get the final stitching surface map As an example, a stitching result of a 125mm-long mirror surface is presented The repeatability of our current stitching system is about 148 nm RMS The stitching result is compared to the result of a one-dimensional angular-measurement-based stitching method to discuss the merits and limitation of the proposed method
15 citations
TL;DR: In this article, a new direct phase measuring deflectometry technique has been developed to measure the three-dimensional shape of specular objects that have discontinuous and/or isolated surfaces.
Abstract: Phase measuring deflectometry has been widely studied as a way of obtaining the three-dimensional shape of specular objects. Recently, a new direct phase measuring deflectometry technique has been developed to measure the three-dimensional shape of specular objects that have discontinuous and/or isolated surfaces. However, accurate calibration of the system parameters is an important step in direct phase measuring deflectometry. This paper proposes a new calibration method that uses phase information to obtain the system parameters. Phase data are used to accurately calibrate the relative orientation of two liquid crystal display screens in a camera coordinate system, by generating and displaying horizontal and vertical sinusoidal fringe patterns on the two screens. The results of the experiments with an artificial specular step and a concave mirror showed that the proposed calibration method can build a highly accurate relationship between the absolute phase map and the depth data.
2 citations
TL;DR: The results show that the developed method can compensate for the tilt uncertainty without the help of the precision apparatus and exhibits improved performance in comparison with conventional methods.
2 citations
TL;DR: This paper presents an attempt to summarize the status of deflectometry, and to map relations between its notable ”spin-off” branches to provide a common communication basis for practitioners and at the same time to offer a convenient entry point for those interested in learning and using the method.
Abstract: Deflectometry as a technical approach to assessing reflective surfaces has now existed for almost 40 years. Different aspects and variations of the method have been studied in multiple theses and research articles, and reviews are also becoming available for certain subtopics. Still a field of active development with many unsolved problems, deflectometry now encompasses a large variety of application domains, hardware setup types, and processing workflows designed for different purposes, and spans a range from qualitative defect inspection of large vehicles to precision measurements of microscopic optics. Over these years, many exciting developments have accumulated in the underlying theory, in the systems design, and in the implementation specifics. This diversity of topics is difficult to grasp for experts and non-experts alike and may present an obstacle to a wider acceptance of deflectometry as a useful tool in other research fields and in the industry. This paper presents an attempt to summarize the status of deflectometry, and to map relations between its notable"spin-off"branches. The intention of the paper is to provide a common communication basis for practitioners and at the same time to offer a convenient entry point for those interested in learning and using the method. The list of references is extensive but definitely not exhaustive, introducing some prominent trends and established research groups in order to facilitate further self-directed exploration by the reader.
1 citations
TL;DR: This paper introduces the approach for the 3D measurement of specular surfaces by means of Experimental Ray Tracing and Radial Basis Functions integration, and presents simulations and discusses the reconstructed surface and the resulting reconstruction error results.
Abstract: Optical deflectometric methods with their inherent potential of high channel capacity with regard to information theory has been of great interest for specular surface topography measurement, where the limited dynamic range needs to be considered in the detection plane. Achieving a final smooth reconstructed surface is the next challenge, because the 2Dintegration methods for the interpolation of the derived data from such sensors are prone to various sources of error such as path dependency, large data sets and secondary reflections. On the other hand, Radial Basis Functions have been studied in this respect for the last years and their characteristics have been widely discussed. In this paper, we introduce our approach for the 3D measurement of specular surfaces by means of Experimental Ray Tracing and Radial Basis Functions integration. We present simulations and discuss the reconstructed surface and the resulting reconstruction error results.
1 citations
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TL;DR: An overview of 3-D shape measurement using various optical methods, and a focus on structured light tech- niques where various optical configurations, image acquisition technology, data postprocessing and analysis methods and advantages and limitations are presented.
Abstract: We first provide an overview of 3-D shape measurement us- ing various optical methods. Then we focus on structured light tech- niques where various optical configurations, image acquisition tech- niques, data postprocessing and analysis methods and advantages and limitations are presented. Several industrial application examples are presented. Important areas requiring further R&D are discussed. Finally, a comprehensive bibliography on 3-D shape measurement is included, although it is not intended to be exhaustive. © 2000 Society of Photo-Optical Instrumentation Engineers. (S0091-3286(00)00101-X)
1,481 citations
"Framework for gradient integration ..." refers background in this paper
...Optical 3D shapemetrology is widely used for inspection purposes in industrial applications [1,2]....
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TL;DR: In this paper, the problem of wavefront estimation from wave-front slope measurements has been examined from a least-squares curve fitting model point of view, and a new zonal phase gradient model is introduced and its error propagator, which relates the mean square wavefront error to the noisy slope measurements, has been compared with two previously used models.
Abstract: The problem of wave-front estimation from wave-front slope measurements has been examined from a least-squares curve fitting model point of view. It is shown that the slope measurement sampling geometry influences the model selection for the phase estimation. Successive over-relaxation (SOR) is employed to numerically solve the exact zonal phase estimation problem. A new zonal phase gradient model is introduced and its error propagator, which relates the mean-square wave-front error to the noisy slope measurements, has been compared with two previously used models. A technique for the rapid extraction of phase aperture functions is presented. Error propagation properties for modal estimation are evaluated and compared with zonal estimation results.
958 citations
10 Sep 2004
TL;DR: In this paper, a stereo-based enhancement of phase measuring deflectometry (PMD) is proposed to measure the height and the slope of specular free-form surfaces within seconds.
Abstract: We present a new method to measure specular free-form surfaces within seconds. We call the measuring principle `Phase Measuring Deflectometry' (PMD). With a stereo based enhancement of PMD we are able to measure both the height and the slope of the surface. The basic principle is to project sinusoidal fringe patterns onto a screen located remotely from the surface under test and to observe the fringe patterns reflected via the surface. Any slope variations of the surface lead to distortions of the patterns. Using well-known phase-shift algorithms, we can precisely measure these distortions and thus calculate the surface normal in each pixel. We will deduce the method's diffraction-theoretical limits and explain how to reach them. A major challenge is the necessary calibration. We solved this task by combining various photogrammetric methods. We reach a repeatability of the local slope down to a few arc seconds and an absolute accuracy of a few arc minutes. One important field of application is the measurement of the local curvature of progressive eyeglass lenses. We will present experimental results and compare these results with the theoretical limits.
463 citations
10 Sep 2004
TL;DR: In this paper, the authors proposed to switch from fringe projection to fringe reflection, which can reach a depth resolution of about one by 10.000 of the measurement field size (e.g. 100 μm for a 1 m sized field).
Abstract: Accurate 3D shape measurement is of big importance for industrial inspection. Because of the robustness, accuracy and ease of use optical measurement techniques are gaining importance in industry. For fast 3D measurements on big surfaces fringe projection is commonly used: A projector projects fringes onto the object under investigation and the scattered light is recorded by a camera from a triangulation angle. Thus, it is possible reaching a depth resolution of about one by 10.000 of the measurement field size (e.g. 100 μm for a 1 m sized field). For non- or low scattering objects it is common to put scattering material like particle spray onto the object under investigation. Objects where this is not allowed are often regarded as problematic objects for full field non-coherent optical measurement techniques. The solution is to switch from fringe projection to fringe reflection. The fringe reflection technique needs a simple setup to evaluate a fringe pattern that is reflected from the surface under investigation. Like for fringe projection the evaluated absolute phase identifies the location of the originating fringe. This allows identifying the reflection angles on the object for every camera pixel. The results are high resolution local gradients on the object which can be integrated to get the 3D shape. The achievable depth resolution compared to fringe projection is much better and reaches to a depth resolution down to 1 nm for smooth surfaces. We have proven the ability, robustness and accuracy of the technique for various technical objects and also fluids. A parallel paper of this conference 'Evaluation Methods for Gradient Measurement Techniques' picks up further processing of the evaluated data and explains in more detail the performed calculations. This paper mainly concentrates on the fringe reflection principle, reachable resolution and possible applications.
156 citations
TL;DR: A generalized method for reconstructing the shape of an object from measured gradient data based on an approximation employing radial basis functions that can be applied to irregularly sampled, noisy, and incomplete data, and it reconstructs surfaces both locally and globally with high accuracy.
Abstract: We present a generalized method for reconstructing the shape of an object from measured gradient data. A certain class of optical sensors does not measure the shape of an object but rather its local slope. These sensors display several advantages, including high information efficiency, sensitivity, and robustness. For many applications, however, it is necessary to acquire the shape, which must be calculated from the slopes by numerical integration. Existing integration techniques show drawbacks that render them unusable in many cases. Our method is based on an approximation employing radial basis functions. It can be applied to irregularly sampled, noisy, and incomplete data, and it reconstructs surfaces both locally and globally with high accuracy.
116 citations