Enhanced phase-coding method for three-dimensional shape measurement with half-period codeword.

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.

Binary coding methods have been widely used for three-dimensional (3D) shape measurement. However, traditional binary coding methods always require a sequence of binary patterns to encode the fringe order. This paper presents a spatial-temporal binary coding (STBC) method for 3D shape measurement with three binary patterns, including a spatial pattern and two temporal patterns. Specifically, the spatial pattern is used to encode a 4-bit spatial code, and the temporal patterns are used to encode the 2-bit temporal code. By combining the spatial code and the temporal code, 6-bit code words can be obtained that distinguish 26=64 fringe periods of sinusoidal phase-shifting patterns. A robust dual-region labeling decoding scheme is also developed to extract the 6-bit code word for fringe order determination, and then absolute-phase unwrapping can be carried out. Experiments have been conducted, and their results confirm that the STBC method can reliably reconstruct the 3D shapes of measured objects with only three binary patterns.

The phase-coding method is useful in 3D shape measurement due to its low sensitivity to surface contrast and camera noise. However, as the number of fringe periods increases, the wrapped phase recovered from the sinusoidal phase-shifting patterns is always misaligned with the fringe order calculated by the stair-coding patterns. To solve this, an improved dual-frequency phase-coding fringe projection method is designed to realize absolute phase retrieval. Specifically, the auxiliary fringe order determined by phase-shifting is used to get the absolute phase, which can eliminate fringe-order errors. Moreover, to increase speed and the number of codewords, this paper presents a scheme that only requires seven patterns, including a uniform gray image, two high-frequency sinusoidal fringe patterns, two low-frequency sinusoidal fringe patterns and two phase-coding fringe patterns. Therefore, this method requires fewer patterns to realize high-resolution measurement than existing methods. The success of the proposed method can be proved by experiments.

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.

In this paper, a three-dimensional (3D) shape measurement method based on structured light field imaging is proposed, which contributes to the biomedical imaging. Generally, light field imaging is challenging to accomplish the 3D shape measurement accurately, as the slope estimation method based on radiance consistency is inaccurate. Taking into consideration the special modulation of structured light field, we utilize the phase information to substitute the phase consistency for the radiance consistency in epi-polar image (EPI) at first. Therefore, the 3D coordinates are derived after light field calibration, but the results are coarse due to slope estimation error and need to be corrected. Furthermore, the 3D coordinates refinement is performed based on relationship between the structured light field image and DMD image of the projector, which allows to improve the performance of the 3D shape measurement. The necessary light field camera calibration is described to generalize its application. Subsequently, the effectiveness of the proposed method is demonstrated with a sculpture and compared to the results of a conventional PMP system.

Conventional three-dimensional (3D) shape measurement methods are typically generic to all types of objects. Yet, for many measurement conditions, such a level of generality is inessential when having the preknowledge of the object geometry. This paper introduces a novel adaptive algorithm for absolute 3D shape measurement with the assistance of the object computer-aided-design (CAD) model. The proposed algorithm includes the following major steps: (1)export the 3D point cloud data from the CAD model; (2)transform the CAD model into the camera perspective; (3)obtain a wrapped phase map from three phase-shifted fringe images; and (4)retrieve absolute phase and 3D geometry assisted by the CAD model. We demonstrate that if object CAD models are available, such an algorithm is efficient in recovering absolute 3D geometries of both simple and complex objects with only three phase-shifted fringe images.

This paper presents a novel area-modulated phase-shifting binary method for three-dimensional (3D) shape measurement. First, the defocused triangular binary pattern is introduced to obtain the high-quality sinusoidal fringe without gamma correction. Then, the modified three steps phase-shifting algorithm which includes an average intensity image is adopted to get the wrapped phase and the object mask. After that, a multi-frequency method is used to obtain the unwrapped phase. Finally, a two-step matching method is applied to get the corresponding matching points. The experiments show that the proposed method is more precise and efficient compared with the previous methods.

To solve the challenging issue of uneven reflectance of high-fidelity surface, this paper proposes a three-dimensional (3D) shape measurement method based on surface adaptation complementary colorimetry-encoded fringe projection profilometry. A complete complementary hue extraction method simulates the retina stimulation to establish the complementary conversion relationship between the projected and collected colors of the measurement system. On this basis, a surface reflectance adaptation fringe pattern encoding strategy is proposed to measure the high-fidelity surfaces. The experiments demonstrate that the proposed method is capable of efficiently balancing and adjusting the reflected light intensity of each fidelity surface, thereby suppressing the ambiguity reconstruction texture. The established complementary colorimetry relationship also improves the light wavelength discrimination, saturation avoidance, measurement accuracy and efficiency.

Fourier transform profilometry (FTP) is one of the frequently adopted three-dimensional (3D) shape measurement methods due to its ability to recover single-shot 3D shapes, yet it is challenging to retrieve the absolute phase map solely from one single grayscale fringe image. This paper presents a computational framework that overcomes this limitation of FTP with digital fringe projection (DFP). By using geometric constraints, an absolute phase map can be retrieved point-by-point from one single grayscale fringe image. Experiments demonstrate the success of our proposed framework with single-shot absolute 3D shape measurement capability.

A height estimating function is proposed based on geometric analysis for a three-dimensional (3-D) measurement system using a digital light processing (DLP) projector and a camera. The proposed 3-D shape measurement method is a hybrid method that combines the geometric parameter measuring method and the least squares method. This method uses the phase-to-height relationship for one line by plane analysis, and the related parameters are estimated using the least squares method. The proposed method has one function per image line instead of one function per image pixel. Sinusoidal fringe patterns of the projector are projected on the object, and the phase of the measuring point is calculated from the camera image. Then, the relationship between the phase by fringe patterns and the height of the measuring point is described as a parameter of the horizontal coordinate on the image plane. Thus, the 3-D shape of the object can be obtained. Our experiments show that the error of the modeling function is within ±0.1 mm when the x-z working range is 100×50 mm. Therefore, the proposed method can dramatically reduce the number of mapping functions needed for 3-D measurement using the geometric relationship between the projector and camera.

Phase unwrapping plays an important role in phase-based three-dimensional (3D) shape measurement. This paper proposes an effective pixel-wise phase unwrapping method without requiring additional fringe patterns. Firstly, compared with the geometric constraint-based (GCB) method which needs calibrate the fringe projection system and create a reference phase at the closest plane <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z_min</i> within the measurement volume, the proposed method can adaptively and directly estimate the reference phase from the wrapped phase without system calibration and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z_min</i> estimation. Secondly, based on the finding that the slope angle of the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z_min</i> plane ignored by the GCB method has significant impact on the measurement range, thus the phase gradients that highly correlates with the optimal slope angle are involved into reference phase estimation. The wrapped phase can be pixel-by-pixel unwrapped by comparing with the reference phase. Both simulations and experiments have been conducted to demonstrate the efficiency of the proposed method. Compared with traditional two-frequency method and phase-coding method, the proposed method can improve the measuring speed by 2 times. Experiment results show that the proposed method can effectively remove the phase unwrapping errors and achieve the mean absolute phase error of 0.0137 rad, which has obvious advantages relative to traditional methods.

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.

In-situ 3-D shape measurements with submicron shape uncertainty of fast rotating objects in a cutting lathe are expected, which can be achieved by simultaneous distance and velocity measurements. Conventional tactile methods, coordinate measurement machines, only support ex-situ measurements. Optical measurement techniques such as triangulation and conoscopic holography offer only the distance, so that the absolute diameter cannot be retrieved directly. In comparison, laser Doppler distance sensors (P-LDD sensor) enable simultaneous and in-situ distance and velocity measurements for monitoring the cutting process in a lathe. In order to achieve shape measurement uncertainties below 1 μm, a P-LDD sensor with a dual camera based scattered light detection has been investigated. Coherent fiber bundles (CFB) are employed to forward the scattered light towards cameras. This enables a compact and passive sensor head in the future. Compared with a photo detector based sensor, the dual camera based sensor allows to decrease the measurement uncertainty by the order of one magnitude. As a result, the total shape uncertainty of absolute 3-D shape measurements can be reduced to about 100 nm.

Codeword-assisted temporal phase unwrapping (TPU) is extensively applied in absolute phase retrieval, in which the fringe order embedded in the temporal sequence identifies the interval of the wrapped phase. However, owing to inevitable image blurring and random noise, the fringe order cannot be aligned with the interval of the wrapped phase at the pixel level and tends to fail easily under high-frequency measurements, thereby yielding abnormal jump errors. Existing approaches suffer from the limitations of universality, efficiency, and fringe frequency. To this end, this work proposes a universal self-correcting approach to remove abnormal jump errors efficiently and accurately. Specifically, the virtual fringe order is introduced by analysing the intensity changes of the phase-shifted patterns, and then it is combined with the real fringe order to form a complementary fringe order pair. Additionally, to enhance the anti-interference ability of the virtual fringe order, the fringe order histogram check technique (FOHCT) is proposed to eliminate fringe order errors. The proposed approach can efficiently conduct various codeword-assisted absolute phase retrieval without introducing additional patterns. Furthermore, benefitting from no error accumulation, our approach is applicable for high-frequency measurements, thereby improving the measurement capability. The measurement results validated the universality and efficiency of the proposed approach. High-frequency measurements demonstrated that the proposed approach outperformed the median filtering and the phase coding approach in terms of error rate (0.009% vs. 3.13% vs. 1.76%).

New method of determination of fractional part of interference fringe order is proposed and its accuracy is verified. This method is based on the calculation of the interferometric signal autoconvolution that is a version of the matched filtering method in the case the interferometric signal is an even function. The fractional part of interference order is identified by the position of the autoconvolution signal maximum. It is evaluated that measuring accuracy depends on the interference pattern parameters such as its spatial frequencies with reference to the fundamental frequency defined as an inverse value of the image extent. The high noise-immunity of the proposed method was proved experimentally: the fringe order error in typical cases was less than 0.03 when S/N ratio in interference pattern was 10. The errors of FFT algorithm were verified with reference to direct autoconvolution method.