Some practical considerations in fringe projection profilometry

Journal of Optics, 2011

In this paper, we propose a high-speed three-dimensional (3-D) shape measurement technique for dynamic scenes using geometry-constraint-based number-theoretical phase unwrapping. As a classical algorithm for temporal phase unwrapping (TPU), the number-theoretical approach is suitable for the binary defocusing fringe projection system since it can retrieve an absolute phase without using low-frequency fringe patterns. However, the conventional number-theoretical TPU approach cannot provide sufficient stability to unwrap a high-frequency phase since it requires the two fringe frequencies to be coprime within the global range of the projector coordinate. In contrast, using low-frequency fringe patterns tends to make phase unwrapping more reliable, but at the expense of the measurement precision. By introducing depth constraint into the traditional number-theoretical TPU, we only need to eliminate the phase ambiguity of each pixel within a small period range defined by the depth range, which means that our method just requires the two fringe frequencies to be coprime within the local period range instead of the conventional global range. Due to the reduction of fringe order candidates and the unambiguous phase range, the reliability of phase unwrapping can be significantly improved compared with the traditional number-theoretical TPU approach even when high-frequency fringe patterns are used. The proposed method has been successfully implemented on a high-frame-rate fringe projection system, achieving high-precision, robust, and absolute 3-D shape measurement at 3333 frames per second.

Optik, 2018

Fringe projection profilometry is an efficient approach for shape reconstruction. An essential step in fringe projection profilometry is the calibration of both the transverse (axial) and longitudinal (depth) directions. In the present work, a longitudinal calibration method for fringe projection profilometry is proposed. In the proposed approach a stepped board is used to calibrate the measurement system in a single scan. Each step of the board represents a different position and therefore only a single scan is required to calibrate the measurement system. The proposed approach neither requires a translating stage nor taking multiple scans of a reference board at various positions, as in traditional techniques. The proposed approach was validated by reconstructing a real object and evaluating its main dimension. Experimental results show the reliability and effectiveness of the proposed method. Measurement errors evaluated for a system calibrated using the proposed approach are relatively smaller than those obtained using a traditional calibration approach. The proposed approach is considerably faster than traditional calibration methods besides being much simpler to implement for onsite measurements.

Optics express, 2011

Fringe projection profilometry is generally used to measure the 3D shape of an object. In oblique-angle projection, the grating fringe cycle is broadened on the reference surface. A well-fitted, convenient, and quick cycle correction method is proposed in this study. Based on the proposed method, an accurate four-step phase shift method is developed. Comparative experiments show that the fringe projection profilometry based on the novel phase shift method can eliminate cycle error and significantly improve measurement accuracy. The relative error of the measurement is less than 1.5%. This method can be widely employed for measuring large objects.

Measurement Science & Technology, 2006

We present a whole-field, 3D optical digitizer based on phase profilometry and on absolute calibration, which performs shape measurement through the projection of a single pattern of Ronchi fringes, and an absolute calibration of the optical head. A suitably developed procedure, based on accurate fringe analysis, implements phase extraction and allows univocal indexing of the field of view. Accurate models express, in a global reference system, both extrinsic and intrinsic parameters of the camera-projector pair. Proper calibration is performed for lens distortion compensation, and to obtain the absolute measurement of the shapes within a global reference system. The technique requires the acquisition of a single image, shows good robustness against fine variations of the fringe period and adapts well to the measurement of free-form shapes in a very short time. The system is portable, fully reconfigurable depending on the measurement requirements and suitable for a low-cost implementation. In this paper, we present the phase extraction method and the system calibration, and highlight the measurement performance of the digitizer in different set-ups, using free-form objects requiring multi-view acquisition.

A predistortion-based 3-D phase mapping method with linear epipolar constraints for fringe projection system calibration and measurement is reported. Hybrid system calibration methods have been developed recently to provide accurate measurement, high speed, and flexibility for fringe projection profilometry (FPP). However, these methods still have significant limitations. With projector distortion, for example, rigorous post-undistortion often results in low efficiency in computation. Conversely, simple, approximated undistortion is only effective for low levels of distortion. As a result, projector undistortion is usually not prioritized in practice. Aiming to achieve high-accuracy 3-D reconstruction with FPP, an easily implementable projector undistortion method is proposed in this article. Theoretical analyses and simulations confirm that the proposed method is rigorous. Experiments validate that the pixelwise root-mean-square reconstruction error is 0.042 mm, a 24% reduction from that of a simple post-undistortion method. The proposed method is also efficient computationally. Finally, a 3-D phase mapping lookup table is built. The results show that the proposed method is effective for achieving high accuracy and speed in 3-D surface measurement.

Applied Measurement Systems, 2012

An extensive survey over coded structured light techniques to solve the correspondence problem which is the basis for 3D surface reconstruction is given by Battle (Battle et al., 1998). www.intechopen.com Determining Exact Point Correspondences in 3D Measurement Systems Using Fringe Projection-Concepts, Algorithms and Accuracy Determination 213 A model describing the random error of the resulting 3D measurement data was developed and confirmed by the results of simulation experiments and real data measurements obtained by two different measuring devices. The results are analysed and discussed and an outlook to future work is given. 2. Situation and measuring principles Recently several fringe projection systems for 3D surface determination for different measurement objects were developed at our institute (

Optics and Lasers in Engineering, 2006

A precise interferometric method for three-dimensional surface measurements in a wide dynamic range is presented. The method is based on symmetrical two-spacing projection phase-stepping interferometry. Two approaches are proposed-one with double symmetrical illumination and the other with double symmetrical observation-which reduce influence of shadowing at investigation of complex surfaces and allow absolute coordinates estimation. The theoretical background, experimental check as well as accuracy and sensitivity assessment of the method are discussed. The proposed technique is especially useful for remote, non-destructive in-situ measurements of real objects-for example historical objects and monuments. r (J. Harizanova), [email protected] (V. Sainov).

Optics Letters, 2010

Fringe-projection profilometry is one of the most commonly used noncontact methods for acquiring the threedimensional (3D) shape information of objects. In practice, the luminance nonlinearity caused by the gamma effect of a digital projector and a digital camera yields undesired fringe intensity changes, which substantially reduce the measurement accuracy. In this Letter, we present a robust and simple scheme to eliminate the intensity nonlinearity induced by the gamma effect by combining a universal phase-shifting algorithm with a gamma correction method. First, by using three-step and large-step phase-shifting techniques, the gamma value involved in the measurement system can be detected. Then, a gamma pre-encoding process is applied to the system for actual 3D shape measurements. With the proposed technique, high accuracy of measurement can be achieved with the conventional smallstep phase-shifting algorithm. The validity of the technique is verified by experiments.

Optics Letters, 2010

Fringe-projection-based (FPB) three-dimensional (3D) imaging technique has become one of the most prevalent methods for 3D shape measurement and 3D image acquisition, and an essential component of the technique is the calibration process. This paper presents a framework for hyper-accurate system calibration with flexible setup and inexpensive hardware. Owing to the crucial improvement in the camera calibration technique, an enhanced governing equation for 3D shape determination, and an advanced flexible system calibration technique as well as some practical considerations on accurate fringe phase retrieval, the novel FPB 3D imaging technique can achieve a relative measurement accuracy of 0.010%. The validity and practicality are verified by both simulation and experiments.

Experimental Techniques, 1999

Optik - International Journal for Light and Electron Optics, 2014

Three-dimensional profile measurement Fringe projection profilometry Look-up table a b s t r a c t Fringe projection profilometry is widely used for three-dimensional shape measurement. In an obliqueangle projection, the fringe cycle is broadened on the reference plane. Phase errors are mainly caused by the nonlinear gamma of the projector and fringe cycle broadening. This study describes a phase error compensation method to eliminate these phase errors. A look-up table that stores phase errors is constructed for phase error compensation. Based on it, a new height equation is proposed. The experimental results show that the proposed method can compensate for the phase errors of the fringe projection profilometry, thereby improving the measurement accuracy significantly.

Smaller objects reconstruction using three dimensional techniques is one among the challenged tasks from the decade. Researchers in graphical designing and professionals of photography are continuously working on the reconstruction of 3D object techniques to meet the demand of real time applications of almost all in every walk of real life. Reconstruction of 3D objects has a major role in the reverse engineering applications too. The major challenges in successful 3D object reconstruction are high computational costs and lack of accuracy. Fringe projection has come into view as a propitious 3D reconstruction mechanism with low computational cost for high precision and resolutions. It makes use of Digital projection, structured light systems and phase analysis on fringed images. Its performance is shown as acceptable in the research analysis carried out on the implementation of it and its insensitiveness to ambient light. An overview of some of the fringe projection techniques are presented in this paper and also propose a new simple fringe projection system which can yield the more accurate and acceptable results with different objects.

Optics Express, 2012

Fringe-projection-based (FPB) three-dimensional (3D) imaging technique has become one of the most prevalent methods for 3D shape measurement and 3D image acquisition, and an essential component of the technique is the calibration process. This paper presents a framework for hyper-accurate system calibration with flexible setup and inexpensive hardware. Owing to the crucial improvement in the camera calibration technique, an enhanced governing equation for 3D shape determination, and an advanced flexible system calibration technique as well as some practical considerations on accurate fringe phase retrieval, the novel FPB 3D imaging technique can achieve a relative measurement accuracy of 0.010%. The validity and practicality are verified by both simulation and experiments.

Applied Optics - APPL OPT, 2010

Three-dimensional (3D) surface shape measurement is a vital component in many industrial processes. The subject has developed significantly over recent years and a number of mainly noncontact techniques now exist for surface measurement, exhibiting varying levels of maturity. Within the larger group of 3D measurement techniques, one of the most promising approaches is provided by those methods that are based upon fringe analysis. Current techniques mainly focus on the measurement of small and mediumscale objects, while work on the measurement of larger objects is not so well developed. One potential solution for the measurement of large objects that has been proposed by various researchers is the concept of performing multipanel measurement and the system proposed here uses this basic approach, but in a flexible form of a single moveable sensor head that would be cost effective for measuring very large objects. Most practical surface measurement techniques require the inclusion of a calibration stage to ensure accurate measurements. In the case of fringe analysis techniques, phase-to-height calibration is required, which includes the use of phase-to-height models. Most existing models (both analytical and empirical) are intended to be used in a static measurement mode, which means that, typically, a single calibration is performed prior to multiple measurements being made using an unvarying system geometry. However, multipanel measurement strategies do not necessarily keep the measurement system geometry constant and thus require dynamic recalibration. To solve the problem of dynamic recalibration, we propose a class of models called hybrid models. These hybrid models inherit the basic form of analytical models, but their coefficients are obtained in an empirical manner. The paper also discusses issues associated with all phase-to-height models used in fringe analysis that have a quotient form, identifying points of uncertainty and regions of distortion as issues affecting accuracy in phase maps produced in this manner.

Applied Optics, 1999

A spatiotemporal phase-unwrapping method is presented that combines the dynamic fringe-projection method and the phase-shifting technique and extends the phase-unwrapping method, which measures two phase maps at different sensitivities. The most important feature of the method is that it makes possible the automatic three-dimensional shape measurement of discontinuous objects with large dynamic range limits and high precision because the effective wavelength of the fringe-projection profilometry can be continuously varied over several orders of magnitude by rotation of the projection grating in its own plane. Only one grating and several steps of rotating the grating are required; therefore the method is inherently simple, fast, and robust. In the experiment, choosing the rotation angle was crucial for optimizing the measurement speed and the measurement accuracy. A criterion is presented for the choice of the minimum number of rotational steps for a given accuracy. The experimental results demonstrate the validity of the proposed method.