Performance analysis of 3-D shape measurement algorithm with a short baseline projector-camera system

Three-dimensional (3D) shape measurement of fringe projection profilometry (FPP) with high speed and accuracy is required in many applications. The measurement speed of FPP system is mainly limited by the low frame rate of pattern projection. Although defocusing binary patterns can be used to increase the measurement speed greatly, it will decrease the measurement depth. To this end, a novel triangular pattern generation method is proposed in this paper. By designing and projecting binary strip patterns with focused projector, images of triangular patterns can be then acquired with high frame rate. Fast and accurate 3D shape measurement can be finally obtained by using phase-shifting triangular patterns. Compared with the traditional sinusoidal patterns, the proposed method can improve the projection rate more than 4 times. Moreover, the proposed method will not decrease the measurement depth. Experimental results are given to confirm the validity of the proposed method.

Blade is the key component of the aero-engine. In generally, it requires precise size and accurate shape, so the three-dimensional shape measurement of the blade is very important. Fringe projection profilometry is generally used to measure the 3D shape of an object, because of the advantages of non-contact operation, full-field acquisition, high resolution, and fast data processing. In this paper, 3D shape measurement method based on surface structured light that combination of gray-code and phase-shift projection is proposed. The wrapped phase of the blade is got by the four-step phase-shift method. In the projection process of the gray-code, due to the ambient light, different surface reflectance and surface physical discontinuous, the edge of gray-code becomes smooth, leading to decode error, so that the gray-code pattern must be binaried before decode. Through the accurate binarization of the blade gray-code pattern, the decoding cycle of the blade is achieved, and the unwrapped phase is achieved by phase unwrapping. Then the unwrapped phase difference between the blade and reference plane is got, the height of the blade can be obtained by the relationship between the phase difference and the height. The experimental and simulation results show that the proposed method can achieve a high precision, high speed and low cost 3D shape measurement of the blade. The measurement accuracy reaches 0.03 mm. The proposed method extends the reliability and practicality of the fringe projection profilometry.

Fringe projection profilometry (FPP) is a three-dimensional (3D) shape measurement method that involves projecting fringe patterns onto the object. A phase map retrieved from these fringe images is used for reconstructing the 3D surface of the object. Fourier transform and phase-shifting are two of the widely used fringe analysis techniques for performing 3D shape measurement using FPP. Fourier transform profilometry (FTP) has the advantage of performing high-speed measurement due to its single-shot nature. However, the reconstructed 3D surface has artifacts and high noise, specifically on the edges. On the other hand, phase-shifting profilometry (PSP) has the advantage of higher accuracy (relatively less noise level) but compromises on measurement speed. In this research, we propose a deep learning method to enhance the quality of the FTP phase maps using an efficient deep learning model called phase map enhancement net (PMENet). PMENet takes an FTP phase map as input and predicts a high-quality phase map in a supervised manner by using the phase maps obtained from 18-step PSP as ground truth. The training dataset was generated using a virtual FPP system. Validations were conducted on both the simulated data (generated by virtual FPP system) and the real-world data. The experimental results demonstrate that the trained neural network model can successfully improve the quality of the 3D geometric reconstruction with FTP and reduced the mean and root-mean-square error by 66% and 43%, respectively.

Model-based object recognition to measure crystal size and shape distributions from in situ video images

Fringe projection profilometry (FPP) is a widely employed technique owing to its rapid speed and high accuracy. However, when FPP is utilized to measure shiny surfaces, the fringes tend to be saturated or too dark, which significantly compromises the accuracy of the 3D measurement. To overcome this challenge, this paper proposes an efficient method for the 3D measurement of shiny surfaces based on FPP. Firstly, polarizers are employed to alleviate fringe saturation by leveraging the polarization property of specular reflection. Although polarizers reduce fringe intensity, a deep learning method is utilized to enhance the quality of fringes, especially in low-contrast regions, thereby improving measurement accuracy. Furthermore, to accelerate measurement efficiency, a dual-frequency complementary decoding method is introduced, requiring only two auxiliary fringes for accurate fringe order determination, thereby achieving high-efficiency and high-dynamic-range 3D measurement. The effectiveness and feasibility of the proposed method are validated through a series of experimental results.

Noncontacting shape measurement for 3-D objects is important in automated manufacturing, component quality control, reverse engineering, etc. Phase-shifting method effectively attains high resolution and high accuracy in analyzing phase information on a projected grating. This technique, however, is difficult to be applied to dynamic condition since usually it requires several images. We developed a digital micromirror device (DMD) camera for phase analysis. In this paper, an one-shot shape and deformation measurement method using a DMD camera is proposed. The DMD camera consists of a DMD, a CCD, and two imaging lenses. In optics of the DMD camera, individual DMD mirrors correspond to individual CCD pixels. The DMD on-off binary pattern can be changed more than 6900 times in one second using an accessory light modulator package (ALP) controller board. Individual DMD mirrors operate as controllable high-speed shutters for corresponding CCD pixels. The four phase-shifted images can be recorded within one frame of the CCD camera. Therefore, shape measurement in dynamic condition can be realized without using a high-speed camera. In order to obtain the 3-D information of shape, multiple reference planes are used to calibrate the relationship between phase value and 3D coordinates. The principle and hardware are presented. In an experiment under dynamic condition, 3D shape information can be analyzed from only one captured image.

In recent years, fringe projection profilometry (FPP), as a kind of three-dimensional shape measurement technology, has achieved the great breakthrough, due to the rapid development of the high-speed camera and high-speed projection equipment. The number-theoretical approach, as a classical method for the temporal phase unwrapping algorithm, is suitable for the binary defocusing FPP since it can avoid the acquiring of low frequency fringes. However, in order to ensure the stability of phase unwrapping, the period of fringe is generally around 20, which leads to the limited accuracy of 3D measurement. In this paper, we propose a bi-frequency number-theoretical phase unwrapping method with depth constraint. Using the principle of depth constraint, we will eliminate the period ambiguities of each pixel within a pixel-variant local period range so that the method only requires the coprime of two fringe frequencies within the local period range instead of the conventional global range. In this way, the requirement of stability of the traditional number-theoretical phase unwrapping can be adjusted from global range to local range. The stability is higher in the local period range due to containing less period ambiguities. As a result, we can realize phase unwrapping of higher frequency fringes with the same stability. Several experiments on various scenes are performed, verifying that our method can achieve high-speed and high-precision 3D measurement.

In fringe projection profilometry, system calibration is crucial for guaranteeing the measurement accuracies. Its difficulty lies in calibrating projector parameters, especially when the projector lens has distortions, since the projector, unlike a camera, cannot capture images, leading to an obstacle to knowing the correspondences between its pixels and object points. For solving this issue, this paper, exploiting the fact that the fringe phases on a plane board theoretically have a distribution of rational function, proposes an iterative calibration method based on phase measuring. Projecting fringes onto the calibration board and fitting the measured phases with a rational function allow us to determine projector pixels corresponding to the featured points on the calibration board. Using these correspondences, the projector parameters are easy to estimate. Noting that the projector lens distortions may deform the fitted phase map thus inducing errors in the estimates of the projector parameters, this paper suggests an iterative strategy to overcome this problem. By implementing the phase fitting and the parameter estimating alternately, the intrinsic and extrinsic parameters of the projector, as well as its lens distortion coefficients, are determined accurately. For compensating for the effects of the lens distortions on measurement, this paper gives two solutions. The pre-compensation actively curves the fringes in computer when generating them; whereas when using the post-compensation, the lens distortion correction is performed in the data processing stage. Both methods are experimentally verified to be effective in improving the measurement accuracies.

In fringe projection profilometry, temporal phase unwrapping is an essential procedure to recover an unambiguous absolute phase even in the presence of large discontinuities or spatially isolated surfaces. In this work, a dual-sensitivity profilometry technique is presented, which is based on defocused projection of binary and sinusoidal fringe patterns with a high and low-frequency spatial carrier, respectively. The binary defocusing techniques (based on PWM or square-wave profile patterns, whose pitch is relatively narrow) have demonstrated successful for high-quality three-dimensional shape measurement when the projector presents a nonlinear response. But they suffer if pitch fringe is wide. On the other hand, using dual sensitivity profilometry, the quality of the unwrapped phase is determined by the high-frequency carrier. Thus, working with only one binary pattern, one can use a single defocusing level (low) in order to reduce the data acquisition time and maintain the quality of the unwrapped phase. Experimental results are presented to verify the success of the proposed method.

Color-coded fringe projection profilometry (FPP) is one of the most important single-frame three-dimensional (3D) shape measurement techniques. Transverse chromatic aberration (TCA) in a color-coded FPP system yields imaging deviations, which will result in 3D shape measurement error. In this work, a TCA compensation method for color-coded FPP is proposed. The proposed method establishes the relationship among phase, pixel deviation, and imaging position for decreasing the 3D shape measurement error introduced by TCA. Compared to existing methods that use the relationship among depth, pixel deviation, and imaging position or polynomial fitting for each pixel, the proposed method offers the merits of precise and simple implementation, since it voids the cumulative error in-depth calculation and removes the time-consuming process of polynomial fitting for each pixel. For validation, a color-coded FPP system is established and calibrated. Two verification experiments, including a translation test and 3D shape measurement of a regular spherical object, are conducted with the calibrated system. Experimental results demonstrate that the proposed TCA compensation method is capable of effectively reducing the 3D shape measurement error caused by TCA.

Fringe projection profilometry (FPP) and phase measuring deflectometry (PMD) are the currently popular technologies for measuring diffuse and specular reflective surfaces respectively. Both methodologies demonstrate superior performance for single-type reflective surfaces. However, with the rapid development of advanced manufacturing and intelligent manufacturing technologies, products have seen significant improvements in complexity, diversity, and personalization, often exhibiting composite reflective characteristics on their surfaces. The aforementioned single technology cannot meet the measurement requirements for composite reflective surfaces. To address this challenge, this paper presents a composite reflective surfaces measurement method combining FPP with PMD techniques, and an optimized system calibration method based on binocular stereo vision is proposed to enhance the system's measurement accuracy. To improve the measurement efficiency, a strategy in which the LCD screen and projector project different colorful fringe patterns simultaneously is adopted. To mitigate stray light interference from the projector on specular surface profilometry, a partition projection method is presented. Instead of establishing the pixel mapping relationship between the projector and diffused surface aeras, the coordinate mapping relationship between the specular reflective region and the projector pixel is established according to the phase-height relationship to realize the accurate projection of the projector to the diffused surface. Experiments have been performed to validate the proposed method, and the results demonstrate that it can reconstruct the composite surfaces with higher accuracy. In particular, the reconstruction accuracy of specular surface can reach several tens of nanometres.

The mechanical behavior of the eardrum has previously been shown to depend critically on its shape, but accurate shape measurements have been difficult to make. Phase-shift moiré topography provides a valuable technique for measuring such shapes, and measurement in the presence of large static pressures facilitates the determination of the boundaries of the pars tensa, pars flaccida, and manubrium. New measurements of the shape of the cat eardrum are presented. The presence of hysteresis in the pressure-displacement response is demonstrated. The shapes are incorporated in individualized finite-element models for four different ears, and the variability between and within animals is examined. Fixed-manubrium low-frequency displacements are simulated and compared for the different models.

Circular fringe projection profilometry (CFPP) is a recently proposed optical three-dimensional (3D) measurement technique. Theoretically, its optimal measurement accuracy should precede that of the conventional fringe projection profilometry. In practice, the measurement accuracy is impacted by many factors, and much research remains to be done in order to make CFPP reach its optimal precision. One of the dominant factors is the zero-phase point. For the usage of the cotangent function, error near the zero-phase point will be significantly amplified. This makes the overall measurement accuracy very low for CFPP with coaxial layout. To address this critical issue, CFPP with off-axis layout (called OCFPP for simplicity) is presented in this paper. The core theory of OCFPP is briefly introduced. The zero-phase point detection problem coming with OCFPP is explained. Then, two methods, one based on a two-dimensional ruler and the other based on plane constraint, are proposed to solve this additional problem. Simulation and experiments validate the effectiveness of the proposed zero-phase point detection methods, and convince the advantage of OCFPP. This paper contributes to distinctly improving the 3D measurement capability of CFPP, and lays an indispensible foundation for its practical application.

The high precision positioning and navigation of underwater vehicles is one of the key technologies for deep-sea exploration and ocean exploration, the underwater localization systems can be categorized into two main types: Inertial Navigation System (INS) and acoustic positioning system. INS is widely used in underwater navigation on account of its autonomy, however, without the information aiding from additional sensors, the errors of inertial measurement units accumulate with time passes. The acoustic positioning system can be divided into three types: Long Base Line (LBL), Short Base Line (SBL) and Ultra Short Base Line (USBL). They are defined according to the distance between transponders. The short baseline (SBL) positioning system includes more than 3 transponders to form an acoustic array, and the formation of the array is normally triangle or quadrilateral. The distance between the transponder is accurately measured and generally more than 10m. The acoustic array coordinate system is built based on the transponder and its relationship with the carrier coordinate system of the vehicle is determined by conventional method, the main disadvantage of the SBL positioning system is that the baseline length is relatively large in order to achieve high accuracy in deep-water measurement. However, as the lateral length of the vehicles is small, it is difficult to make sure the transponders be placed way from each other, meanwhile it is difficult to calibrate multiple transponders and avoid noise. To solve this problem, this paper present an inertial navigation system and single range navigation system (SRNS) based on one acoustic transponder, the navigation system consist of an acoustic transponder, a pressure transponder and inertial sensors mounted on the vehicle and an answering device transponder which is laoid out at tens of meters deep straight under the buoy. This paper studies the measurement equation's nonlinearity effect of the INS/SRNS, establishes state equation and measurement equation of the INS/SRNS integrated system. To deal with the nonlinear noise problems of transponders, meanwhile, in view that fault detection based on traditional state chi-square hypothesis testing cannot determine the specific cause of the fault, and could only determine the validity of measure information, a new fault detection algorithm based on dual-state method is adopted. The application of this method on underwater integrated navigation system demonstrates that the algorithm can rapidly and accurately detecting and identify the faults in the system. Experiments on QIANDAO Lake show that the proposed method restrains the divergence trend error of the integrated system's navigation, which verify the effectiveness of the single range integrated navigation.

Calibration is important to perform accurate shape measurement using a grating projection. It is required to calculate spatial coordinates from the phase value of a projected grating in short time for real-time shape measurement. We propose a calibration method using multiple reference planes. This method excludes a lens distortion and intensity errors of a projected grating in measurement results theoretically. Tabulation of relationship between phase values and spatial coordinates for each pixel makes short-time measurement possible. This calibration method is applied to the real-time shape and deformation measurement.