Three-dimensional measurement based on optimized circular fringe projection technique.

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.

Fringe projection profilometry has emerged as a widely used non-contact three-dimensional (3D) measurement technique due to its full-field acquisition, high precision, and rapid measurement capabilities. However, its performance degrades significantly when measuring objects with complex surface reflection characteristics, as light undergoes inter-reflection and subsurface scattering during measurement, generating indirect light signals that lead to reconstruction errors. Dual profilometry, a computational 3D profilometry based on dual photography theory, overcomes this limitation by treating each camera pixel as a single-pixel detector to isolate the direct light signals. While theoretically effective, existing implementations need the reconstruction of millions of dual images. To overcome this limitation, we present an efficient reconstruction method that avoids dual image reconstruction. Experimental validation demonstrates that the reconstruction speed can be substantially improved compared to existing dual profilometry implementations, achieved without compromising reconstruction accuracy. The proposed method effectively resolves the efficiency bottleneck that has hindered the practical adoption of dual profilometry, enabling its deployment in practical applications such as industrial inspection and high-resolution biomedical surface characterization.

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) 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.

Fringe projection profilometry is a widely used three-dimensional (3D) optical measurement technique. However, it is quite challenging to quickly obtain the 3D information of objects. Minimizing the number of patterns for phase unwrapping is an efficient way to address the above problem, and many methods have been proposed. This paper reports a period-wise phase unwrapping method with only two gray level coding patterns. Due to a hybrid coding strategy implemented, the number of patterns used in the proposed method reduces by one in comparison with conventional gray level method when generating the same number of codewords. A robust decoding scheme is also developed to determine the fringe order, and its accuracy is guaranteed by using the self-correcting method to remove the phase errors. Some experiments have been conducted, and their results confirm that the success of the proposed method.

Three-Dimensional droplet splashing dynamics measurement with a stereoscopic shadowgraph system

Fringe projection technology is usually used for three-dimensional (3D) measurement, but there will be large errors when the measurement is overexposed or the surface is too dark. Polarizing filters can be used to eliminate the highlights of the image, but they may also cause the image to be too dark and affect the measurement accuracy. Otherwise, to ensure measurement accuracy, the complexity of the operation of the polarization system will be increased. In order to ensure the measurement accuracy and improve the measurement efficiency, a 3D measurement method of quantified exposure time is proposed in this paper, and the intensity response function of the light intensity captured by the camera and the exposure time is established, and more meaningful variable value intervals can be selected by the method of this paper. It can avoid the complex polarization bidirectional reflectance distribution function model, and the required exposure time can be calculated quantitatively within the already screened intervals. Then it is combined with the image fusion algorithm to generate the optimal fringe pattern. Experimental results demonstrate that this method significantly eliminates the effects of highlights in the image. The fuzzy transition area between the black and white fringes is effectively reduced, and the edge information of the fringes is correctly restored.

Fringe projection technology is often used for three-dimensional (3D) measurement, but it is difficult to measure highlight surfaces. Polarization systems are usually used to remove highlight surfaces. Polarizing filters can be used to eliminate the highlights of the image, but they may also cause the image to be too dark and affect the measurement accuracy. Otherwise, to ensure measurement accuracy, the complexity of the operation of the polarization system will be increased. A method of polarization-based camera intensity response function for 3D measurement is proposed. The intensity response function of the camera under the polarization system is established. It can avoid the complicated polarized bidirectional reflectance distribution function model and directly and quantitatively calculate the required angle between the transmission axes of the two polarizing filters. Then it is combined with the image fusion algorithm to generate the optimal fringe pattern. Experimental results demonstrate that this method significantly eliminates the effects of highlights in the image. The fuzzy transition area between the black and white fringes is effectively reduced, and the edge information of the fringes is correctly restored. Moreover, the high signal-to-noise ratio and contrast of the image are retained when the polarization filters are added.

Fringe projection profilometry (FPP) has been widely used for three-dimensional shape measurement because of its simple hardware and high measurement accuracy. However, the use of most FPP systems to measure complex surfaces such as stepped height objects can result in severe occlusion and shadow. To alleviate this problem, a coaxial measurement method based on dual biprisms is presented in this paper. The system is low-cost and easy to implement, and does not require the introduction of mechanical moving parts. Only dual biprisms are introduced into the coaxial system to provide the geometric constraints required for reconstruction. Experimental results on the reconstruction of a surface with significant height changes demonstrate that the proposed method can achieve shadow-free measurements.

Single-shot fringe projection profilometry (FPP) offers significant advantages for dynamic three-dimensional (3D) measurement. However, existing deep learning-based single-shot methods still struggle to simultaneously and accurately extract the wrapped phase and fringe order. Because the former is a continuous physical quantity while the latter is a discrete integer label, their joint estimation from a single periodic pattern is inherently ambiguous, especially for isolated objects lacking spatial continuity. To address this problem, a deep learning-enabled single-shot FPP method is proposed by integrating inner shifting-phase encoding with a physically constrained dual-network architecture. The fringe order is embedded into the phase-shifting component of a single high-frequency fringe pattern, and two lightweight convolutional neural networks are then employed: one regresses the numerator and denominator of the wrapped phase, while the other classifies the inner shifting-phase value to recover the fringe order. This physically consistent decoupled design avoids the optimization conflicts of end-to-end regression and enables unambiguous absolute phase recovery. Experiments show that the proposed method could achieve high-accuracy absolute phase recovery comparable to traditional multi-frame techniques for measurements of complex and isolated objects, while maintaining low computational complexity. The dynamic experimental results demonstrate its application potential for dynamic 3D measurement.

In-situ areal inspection of powder bed for electron beam fusion system based on fringe projection profilometry

This study aimed to evaluate whether the coronal plane alignment of the knee (CPAK) classification between three-dimensional (3D) measurement using computed tomography (CT) and two-dimensional (2D) measurement using long leg radiographs (LLR) match. A retrospective radiographic study compared pre-operative CT and LLR measurements in 69 patients undergoing primary total knee arthroplasty. The arithmetic hip-knee-ankle angle (aHKA), joint line obliquity (JLO), and CPAK types were calculated. A match in the CPAK classification was defined as "complete agreement" and agreement was considered partial if the CPAK was located in an adjacent column. If the discrepancy was more than one column, then it was recorded as no agreement. The mean aHKA was -0.6° ± 4.4° in 3D measurement and -1.1° ± 4.3° in 2D measurement (p = 0.42). The mean JLO was 174.2° ± 3.5° in 3D measurement and 175.2° ± 3.6° in 2D measurement (p = 0.07). There was no statistically significant difference in either aHKA or JLO obtained by the two measurement methods, each within 1°. However, the complete agreement was confirmed in only 60.8% of cases. After incorporating even partial agreements including neighboring columns, the agreement rate was 91.2%. The disagreement was noticed in 8.8% of the cases. The 3D measurement method enables aHKA and JLO calculations similar to those of 2D measurements. However, complete agreement with the CPAK classification in all cases was not obtained. On the other hand, 2D measurement has the advantage that JLO can be easily appreciated and remais more intuitive for surgeons. III.

3D measurement system based on divergent multi-line structured light projection, its accuracy analysis

Fringe projection profilometry (FPP) has been one of the most popular non-contact methods for 3D surface measurement in recent years. In FPP, the quality of the fringe pattern determines the measurement accuracy and measurement range to a great extent. In this paper, we proposed a high-quality fringe projection method using a biaxial MEMS scanning mirror and a laser diode (LD). The fringe pattern is produced by a very low NA (numerical aperture) scanning laser beam. Compared with pixel array based fringe pattern generation method, such as DLP and LCOS, the generation method can produce higher performance fringe pattern, which is high contrast, narrow pitch and long depth. In this paper, we also did a contrast between different fringe pattern generation methods.

Single-shot fringe projection profilometry (FPP) is essential for retrieving the absolute depth information of the objects in high-speed dynamic scenes. High-precision 3D reconstruction using only one single pattern has become the ultimate goal in FPP. The frequency-multiplexing (FM) method is a promising strategy for realizing single-shot absolute 3D measurement by compounding multi-frequency fringe information for phase unwrapping. In order to solve the problem of serious spectrum aliasing caused by multiplexing schemes that cannot be removed by traditional spectrum analysis algorithms, we apply deep learning to frequency multiplexing composite fringe projection and propose a composite fringe projection deep learning profilometry (CDLP). By combining physical model and data-driven approaches, we demonstrate that the model generated by training an improved deep convolutional neural network can directly perform high-precision and unambiguous phase retrieval on a single-shot spatial frequency multiplexing composite fringe image. Experiments on both static and dynamic scenes demonstrate that our method can retrieve robust and unambiguous phases information while avoiding spectrum aliasing and reconstruct high-quality absolute 3D surfaces of objects only by projecting a single composite fringe image.