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Journal ArticleDOI

Improvement of high-order least-squares integration method for stereo deflectometry.

01 Dec 2015-Applied Optics (Optical Society of America)-Vol. 54, Iss: 34, pp 10249-10255
TL;DR: A modified easy-implementation integration method based on HFLI (EI-HFLI), which can work in arbitrary domains, and can directly and conveniently handle incomplete gradient data is proposed.
Abstract: Stereo deflectometry is defined as measurement of the local slope of specular surfaces by using two CCD cameras as detectors and one LCD screen as a light source. For obtaining 3D topography, integrating the calculated slope data is needed. Currently, a high-order finite-difference-based least-squares integration (HFLI) method is used to improve the integration accuracy. However, this method cannot be easily implemented in circular domain or when gradient data are incomplete. This paper proposes a modified easy-implementation integration method based on HFLI (EI-HFLI), which can work in arbitrary domains, and can directly and conveniently handle incomplete gradient data. To carry out the proposed algorithm in a practical stereo deflectometry measurement, gradients are calculated in both CCD frames, and then are mixed together as original data to be meshed into rectangular grids format. Simulation and experiments show this modified method is feasible and can work efficiently.
Citations
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Journal ArticleDOI
TL;DR: The fundamental principle and the basic concepts of PMD technique are introduced and followed by a brief overview of its key developments since it was first proposed to provide some suggestions for potential future investigations.

133 citations

Journal ArticleDOI
07 Dec 2017-Sensors
TL;DR: This work presents a review of the relevant techniques regarding classical and improved phase-measuring deflectometry, and discusses the challenges and future research directions to further advance PMD techniques.
Abstract: The fast development in the fields of integrated circuits, photovoltaics, the automobile industry, advanced manufacturing, and astronomy have led to the importance and necessity of quickly and accurately obtaining three-dimensional (3D) shape data of specular surfaces for quality control and function evaluation. Owing to the advantages of a large dynamic range, non-contact operation, full-field and fast acquisition, high accuracy, and automatic data processing, phase-measuring deflectometry (PMD, also called fringe reflection profilometry) has been widely studied and applied in many fields. Phase information coded in the reflected fringe patterns relates to the local slope and height of the measured specular objects. The 3D shape is obtained by integrating the local gradient data or directly calculating the depth data from the phase information. We present a review of the relevant techniques regarding classical PMD. The improved PMD technique is then used to measure specular objects having discontinuous and/or isolated surfaces. Some influential factors on the measured results are presented. The challenges and future research directions are discussed to further advance PMD techniques. Finally, the application fields of PMD are briefly introduced.

59 citations


Cites methods from "Improvement of high-order least-squ..."

  • ...proposed a modified easy-implementation integration method called EI-FLI based on finite-difference-based least-squares integration [79], which could work in arbitrary domains, and could directly and conveniently handle incomplete gradient data....

    [...]

Journal ArticleDOI
TL;DR: This work considers the height increment as a more general connector to establish the height-slope relations for least-squares regression and presents a new idea for the zonal methods for quadrilateral geometry, which preserve many good aspects of the classical ones.
Abstract: There are wide applications for zonal reconstruction methods in slope-based metrology due to its good capability of reconstructing the local details on surface profile. It was noticed in the literature that large reconstruction errors occur when using zonal reconstruction methods designed for rectangular geometry to process slopes in a quadrilateral geometry, which is a more general geometry with phase measuring deflectometry. In this work, we present a new idea for the zonal methods for quadrilateral geometry. Instead of employing the intermediate slopes to set up height-slope equations, we consider the height increment as a more general connector to establish the height-slope relations for least-squares regression. The classical zonal methods and interpolation-assisted zonal methods are compared with our proposal. Results of both simulation and experiment demonstrate the effectiveness of the proposed idea. In implementation, the modification on the classical zonal methods is addressed. The new methods preserve many good aspects of the classical ones, such as the ability to handle a large incomplete slope dataset in an arbitrary aperture, and the low computational complexity comparable with the classical zonal method. Of course, the accuracy of the new methods is much higher when integrating the slopes in quadrilateral geometry.

40 citations

Journal ArticleDOI
TL;DR: A new LSI method is proposed to integrate gradient data, based on an approximation that the normal vector of one point is perpendicular to the vectors connecting points at either side, which is effective and accurate at handling deflectometry measurement.
Abstract: Least-squares integration (LSI) and radial basis function integration (RBFI) methods are widely used to reconstruct specular surface shapes from gradient data in a deflectometry measurement. The traditional LSI method requires gradient data having a rectangular grid, and the RBFI method is effective at handling small size measurement data sets. Practically, the amount of gradient data is rather large, and data grids are in quadrilateral shapes. With this in mind, a new LSI method is proposed to integrate gradient data, which is based on an approximation that the normal vector of one point is perpendicular to the vectors connecting points at either side. A small measurement data set integrated by the RBFI method is employed as a supplementary constraint of the proposed method. Simulation and experimental results show that this proposed method is effective and accurate at handling deflectometry measurement.

35 citations


Cites methods from "Improvement of high-order least-squ..."

  • ...Ren [4] introduced an easy implementation integration method (EI-HFLI) based on HFLI to reconstruct gradient data locating at arbitrary domains....

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  • ...Currently, least-squares integration (LSI) method [1-4] and radial basis function integration (RBFI) method [5, 6] are widely used to reconstruct specular surface shape when gradient data is obtained by deflectometry, and many attempts at improvement have been researched....

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  • ...Though these measurement data can be interpolated into rectangular format [4] and then integrated via traditional LSI methods, this implementation is not so convenient....

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Journal ArticleDOI
TL;DR: In this article, a spline integration method is proposed to fit the measured slope data with piecewise polynomials and uses the analytical polynomial functions to represent the height changes in a lateral spacing with the pre-determined spline coefficients.

35 citations


Cites methods from "Improvement of high-order least-squ..."

  • ...proposed an easy implementation of Li's method for incomplete dataset or even in arbitrary domain [16]....

    [...]

References
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Journal ArticleDOI
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


"Improvement of high-order least-squ..." refers background in this paper

  • ...Various optical techniques, such as triangulation, structured light and interferometry are widely used to measure 3D shape of objects in industrial applications [1]....

    [...]

Journal ArticleDOI
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

Proceedings ArticleDOI
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

Proceedings ArticleDOI
TL;DR: A comparative assessment of the strengths and weaknesses of both measurement principles from the current perspective will show that deflectometry is now heading to become a serious competitor to interferometry.
Abstract: Deflectometric methods that are capable of providing full-field topography data for specular freeform surfaces have been around for more than a decade. They have proven successful in various fields of application, such as the measurement of progressive power eyeglasses, painted car body panels, or windshields. However, up to now deflectometry has not been considered as a viable competitor to interferometry, especially for the qualification of optical components. The reason is that, despite the unparalleled local sensitivity provided by deflectometric methods, the global height accuracy attainable with this measurement technique used to be limited to several microns over a field of 100 mm. Moreover, spurious reflections at the rear surface of transparent objects could easily mess up the measured signal completely. Due to new calibration and evaluation procedures, this situation has changed lately. We will give a comparative assessment of the strengths and – now partly revised – weaknesses of both measurement principles from the current perspective. By presenting recent developments and measurement examples from different applications, we will show that deflectometry is now heading to become a serious competitor to interferometry.

126 citations

Journal ArticleDOI
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