Phase-height Mapping Research Articles

Flexible and accurate system calibration method in microscopic fringe projection profilometry.

The three-dimensional (3D) measurement task of complex microstructures holds paramount significance in the domains of precision manufacturing and inspection. The calibration of the 3D system heavily determines the final reconstruction accuracy. The widely adopted system calibration method is phase-height mapping (PHM) and stereo vision (SV) based. The former can be applied directly to the calculation without considering the imaging model of the system, but it relies on highly precise and expensive translation stages or standard blocks. The latter's accuracy cannot be guaranteed because it is difficult to accurately calibrate the projector. In this paper, we establish an optically coupled microscopic fringe projection profilometry system that consists of a Scheimpflug pinhole projector and a super-low distortion bi-telecentric camera. We introduce a simplified 3D system calibration approach that combines phase modulation transfer and ray propagation. Our method enables the simultaneous calibration of the system, including the calibration of the projector, camera, and the phase to a 3D coordinates relationship, using only a 2D target. The calibrated projector's external parameters are used to obtain the target's complete poses, and then the direct mapping coefficients of the phase to the 3D coordinates can be obtained through the optical geometry structure and phase labels. Comparable experiments verify the feasibility of the proposed method.

High-precision projection moiré measurement method based on virtual reality bridging

The projection moiré method is a high-precision optical topography measurement method. The existing moiré models calibrate the phase-height mapping relationship by setting and moving the reference plane, which introduces many system errors and reduces the usability and scanning scalability of the methods. This paper proposes a moiré model based on virtual reality bridging and the corresponding scanning method. First, we use the imaging parameters of the real moiré system and the derived moiré phase correspondence to build a virtual moiré model matching the real system. Then we use a variety of phase optimization algorithms to improve the coincidence between the virtual and the reality. In addition, we propose a method to calculate the pose between views to facilitate the reconstruction of the corresponding virtual moiré model during scanning measurement. Finally, we use the virtual moiré model and scanning method to conduct fixed position and scanning measurements. The results show that the proposed virtual moiré model has high accuracy and robustness, and the scanning method can achieve high-precision full-field three-dimensional shape measurement.

High-precision projection moiré measurement method for the large depth of field with significant distortion

The projection moiré method is a high-precision optical topography measurement method. Because the reception system has the complex characteristic of two-stage imaging, the nonlinearity of phase-height mapping is severe, and imaging errors are substantial. Therefore, many existing solutions consider measurement scenes with the small depth of field and distortion. In this paper, we propose a two-stage imaging model, which can accurately describe the imaging process of the reception system under various distortion conditions. Furthermore, we derive a strongly nonlinear moiré model based on the imaging model, which fully represents the nonlinear effects caused by the depth of field and distortion. Several experiments are conducted for measurement scenarios with varying depths of field and distortion using various imaging models and nonlinear moiré models. The outcomes demonstrate that the proposed imaging and moiré model can reduce the corresponding imaging and model errors and improve the measurement accuracy and practicality in different environments.

Method for phase-height mapping calibration based on fringe projection profilometry

Method for phase-height mapping calibration based on fringe projection profilometry

Development of three-dimensional pavement texture measurement technique using surface structured light projection

To realize active, non-contact, high-precision and full-field measurement of pavement texture, an innovative surface structured light projection (SSLP) based technique is developed in this paper. Firstly, the sinusoidal intensity encoded surface structured light is projected through the optical fiber interference, and the high-resolution industrial camera is used to capture the deformed fringe pattern modulated by the measured pavement. Then, a pre-processing method is proposed to suppress the noise and uneven background illumination in the captured fringe image. After that, a two-dimensional continuous wavelet transform method (2D-CWTM) is executed, and the wrapped phase can be demodulated accurately from the wavelet ridge. Finally, the 2π steps in the wrapped phase are removed by a phase unwrapper, and the measured pavement texture elevation can be obtained according to the phase-height mapping relationship. Both laboratory and field tests demonstrate the functionality and effectiveness of the proposed SSLP technique in pavement texture measurement.

End-to-end pattern optimization technology for 3D shape measurement.

The nonlinear errors caused by the gamma effect seriously affect the measurement accuracy of phase-measuring profilometry systems. We present a novel robust end-to-end pattern optimization technology for phase-height mapping. This method generates standard sinusoidal patterns on the reference plane on a camera image instead of on a projection image by optimizing the projection image, which can avoid phase errors due to phase conversion from projector to camera. The pixel set mapping is achieved by chessboard calibration; then the projection image is optimized with the multiscale optimization method and the dislocation optimization method based on proportional integral derivative control. The experiments show that the proposed method can effectively avoid the influence of nonlinear effect and achieve high-quality three-dimensional measurement.

A three-dimensional measuring system with stroboscopic laser grating fringe

A three-dimensional measuring system based on a line-structured laser and a high-speed rotating multi-faced prism has been designed and described in detail. The grating fringe can be produced using stroboscopic effect in the system. The phase-height mapping model is applied to 3D measurements, and the step-by-step phase shift is used to calculate phase information. Introducing the PID control algorithm make the rotating speed of the multi-faced prism stabilize, that can improve the stability of the fringe phase shift during the measurement process. In order to verify the measurement accuracy of the system, the system is applied to the measurement of the height information of the machined part. In addition, the effectiveness of the system was verified by measuring the section information of the column gypsum. The actual experiment shows that the measurement accuracy of the measurement system can reach 0.075 mm.

An accurate phase-height mapping algorithm by using a virtual reference plane

In the phase measurement profilometry, the phase-height mapping is to calibrate the system by the height and phase of several known planes. The four planes method, which only needs the four references, is widely used due to its least amount of data. But for its height reconstruction, a large reconstructed height error will be introduced when the phase difference is close to 0. An improved phase-height mapping method, which is to create a virtual reference plane with a known height along the original reference plane, is proposed. Then the coefficient tables a, b, c, which are capable to suit for the whole calibration space, will be calculated and can improve the accuracy of 3D object reconstruction as well as the efficiency. The experimental results show that the mapping height errors can be significantly reduced. The RMS error of the reconstructed object is less than 4.8μm with the proposed method, while that of the traditional method is 350μm.

Analysis of a new phase and height algorithm in phase measurement profilometry

Traditional phase measurement profilometry adopts divergent illumination to obtain the height distribution of a measured object accurately. However, the mapping relation between reference plane coordinates and phase distribution must be calculated before measurement. Data are then stored in a computer in the form of a data sheet for standby applications. This study improved the distribution of projected fringes and deducted the phase-height mapping algorithm when the two pupils of the projection and imaging systems are of unequal heights and when the projection and imaging axes are on different planes. With the algorithm, calculating the mapping relation between reference plane coordinates and phase distribution prior to measurement is unnecessary. Thus, the measurement process is simplified, and the construction of an experimental system is made easy. Computer simulation and experimental results confirm the effectiveness of the method.

Discussion on accurate phase–height mapping in fringe projection profilometry

Establishing a highly accurate phase-to-height mapping relationship is very important in fringe projection profilometry, which guarantees the accuracy of final three-dimensional reconstruction. The influence coming from lens distortion, random noises, and the nontelecentric projecting and imaging of the measurement system is analyzed in detail, followed by the exhaustive discussion of a more accurate phase-to-height mapping method. The mapping tabulation between absolute phase and height information is set up by the piecewise linear fitting method within the whole measurement range for per-pixel. Our method is compared with the previously used methods, such as linear fitting (LF), quadratic fitting (QF), and cubic fitting (CF) methods. Computer simulations and experiments verify that the reconstructed height distribution employing our method is more accurate than either LF or QF methods when the random noise is obvious. In addition, if the random noise can be controlled to low level and the lens distortion is considered, the reconstruction accuracy of our method is better than that of the CF method.

Experimental study of temporal-spatial binary pattern projection for 3D shape acquisition.

Three-dimensional (3D) acquisition of an object with modest accuracy and speed is of particular concern in practice. The performance of digital sinusoidal fringe pattern projection using an off-the-shelf digital video projector is generally discounted by the nonlinearity and low switch rate. In this paper, a binary encoding method to encode one computer-generated standard sinusoidal fringe pattern is presented for circumventing such deficiencies. In previous work [Opt. Eng.54, 054108 (2015)OPEGAR0091-328610.1117/1.OE.54.5.054108], we have developed a 3D system based on this encoding tactic and showed its prospective application. Here, we first build a physical model to explain the mechanism of how to generate good sinusoidality. The phase accuracy with respect to the conventional spatial binary encoding method and sinusoidal fringe pattern is also comparatively evaluated through simulation and experiments. We also adopt two phase-height mapping relationships to experimentally compare the measurement accuracy among them. The results indicate that the proposed binary encoding strategy has a comparable performance to that of sinusoidal fringe pattern projection and enjoys advantages over the spatial binary method under the same conditions.

Phase-3D mapping method developed from back-projection stereovision model for fringe projection profilometry.

Two major methods for 3D reconstruction in fringe projection profilometry, phase-height mapping and stereovision, have their respective problems: the former has low-flexibility in practical application due to system restrictions and the latter requires time-consuming homogenous points searching. Given these limitations, we propose a phase-3D mapping method developed from back-projection stereovision model to achieve flexible and high-efficient 3D reconstruction for fringe projection profilometry. We showed that all dimensional coordinates (X, Y, and Z), but not just the height coordinate (Z), of a measured point can be mapped from phase through corresponding rational functions directly and independently. To determine the phase-3D mapping coefficients, we designed a flexible two-step calibration strategy. The first step, ray reprojection calibration, is to determine the stereovision system parameters; the second step, sampling-mapping calibration, is to fit the mapping coefficients using the calibrated stereovision system parameters. Experimental results demonstrated that the proposed method was suitable for flexible and high-efficient 3D reconstruction that eliminates practical restrictions and dispenses with the time-consuming homogenous point searching.

High precision phase measuring profilometry based on stereo microscope

A high-precision phase measuring profilometry (PMP) based on a stereo microscope is presented. A high-quality area modulation sinusoidal grating by a LED illumination is used to produce the high-quality sinusoidal fringes. Phase-shift technique is employed to get the phase distributions, and the 3D data could be reconstructed by the phase-height mapping algorithm easily. The accuracy depends on the field of view, which at a large magnification is below 1μm. This setup will be promising for high accuracy measurement task.

Least-squares calibration method based on a universal phase and height mapping formula in Fourier transform profilometry

In Fourier transform profilometry (FTP), we perform a strict theoretical analysis of the phase–height mapping relationship and give a universal calculation formula in which the constraints on the experimental setup are removed. In that case, the projector and camera can be located arbitrarily to get better information on fringes, which makes the system easy to manipulate and improves the speed of measurement. As the relationship between the phase and height distribution depends on system parameters (such as the relative position of the projector and camera) which are difficult to obtain, we propose a least-squares calibration approach for FTP, which can avoid measuring the system parameters directly. Both the simulation and experimental results prove that the 3D shape of the tested objects can be reconstructed exactly by using the calculation formula and calibration method, and that the system has better universality.

Universal calculation formula and calibration method in Fourier transform profilometry

We propose a universal calculation formula of Fourier transform profilometry and give a strict theoretical analysis about the phase-height mapping relation. As the request on the experimental setup of the universal calculation formula is unconfined, the projector and the camera can be located arbitrarily to get better fringe information, which makes the operation flexible. The phase-height calibration method under the universal condition is proposed, which can avoid measuring the system parameters directly. It makes the system easy to manipulate and improves the measurement velocity. A computer simulation and experiment are conducted to verify its validity. The calculation formula and calibration method have been applied to measure an object of 22.00 mm maximal height. The relative error of the measurement result is only 0.59%. The experimental results prove that the three-dimensional shape of tested objects can be reconstructed exactly by using the calculation formula and calibration method, and the system has better universality.

A flexible calculation on improved Fourier transform profilometry

Here a flexible optical geometry of Fourier Transform Profilometry (FTP) is discussed, and a strict theoretical analysis about an improved phase-height mapping formula based on a new description of a reference fringe and a deformed fringe proposed based on a general case, in which the exit pupil of the projecting lens and the entrance pupil of the imaging lens are not horizontal and do not have the equal distance to the reference plane; moreover, the optical axes of the projecting device and of the imaging device are not coplanar. Compared with the traditional Fourier Transform Profilometry, it is easier for us to obtain the full-field fringe through adjusting the location of either the projector or the imaging device. Compared with the Improved Fourier Transform Profilometry (IFTP), only three length system parameters need to be measured, so the operation is simple and the result is more reliable.

A Novel Method for Human Expression Rapid Reconstruction

Human expression rapid reconstruction has many potential applications in entertainment and social security. In this work, a rapid human expression measurement system based on a digital fringe projection and phase-shift technique is developed. The measurement system consists of a digital light processing (DLP) projector and a high-speed change-coupled device (CCD) camera. The DLP projector is used to project computer-generated fringe patterns onto the human face, and the high-speed CCD camera synchronized with the projector acquires the fringe images at a frame rate of 30 frames/s. Based on a three-step phase-shifting method and an accurate phase-height mapping algorithm, each frame of the 3-D human expression can be reconstructed. The principle of the proposed method is described and some experimental results are presented to demonstrate its performance. The experiment results show that the measurement system can reconstruct accurate 3-D human expression. An obvious merit of this method is that it can reconstruct the 3-D human expression in a very short time and it is not sensitive to the movement of the face during the measurement processing.

Complex object 3D measurement based on phase-shifting and a neural network

An accurate phase-height mapping algorithm based on phase-shifting and a neural network is proposed to improve the performance of the structured light system with digital fringe projection. As phase-height mapping is nonlinear, it is difficult to find the best camera model for the system. In order to achieve high accuracy, a trained three-layer back propagation neural network is employed to obtain the complicated transformation. The phase error caused by the non-sinusoidal attribute of the fringe image is analyzed. During the phase calculation process, a pre-calibrated phase error look-up-table is used to reduce the phase error. The detailed procedures of the sample data collection are described. By training the network, the relationship between the image coordinates and the 3D coordinates of the object can be obtained. Experimental results demonstrate that the proposed method is not sensitive to the non-sinusoidal attribute of the fringe image and it can recover complex free-form objects with high accuracy.

基于神经网络的相位-高度映射算法

基于神经网络的相位-高度映射算法

Fourier transform profilometry based on a projecting-imaging model

In order to obtain the correct height reconstruction of a measured object, a projection lens and a camera lens must be placed at equal heights above the reference plane in the traditional Fourier transform profilometry (FTP) method. We propose an improved phase-height mapping formula based on an improved description of the reference fringe and the deformed fringe in FTP when the projection lens and the camera lens are not placed at equal height. With our method, it is easier to obtain the full-field fringe by moving either the projector or the imaging device. In some cases, where the required parallel condition cannot be met, the proposed method offers a flexible way to calculate the height distribution.