Method For Absolute Phase Retrieval Research Articles

Absolute phase retrieval based on fringe amplitude encoding without any additional auxiliary pattern

An absolute phase retrieval method based on fringe amplitude encoding is proposed. Different from the conventional intensity coding methods which are based on time division multiplexing with multiple additional auxiliary patterns, the proposed fringe order encoding strategy is codeword overlapping interaction based on space division multiplexing. It just directly encodes different fringe amplitudes for different periods in corresponding sinusoidal phase-shifting patterns to generate space division multiplexing composite sinusoidal phase-shifting patterns and quantifies the fringe amplitudes into four levels as encoding strategy, so it can retrieve absolute phase without any additional auxiliary patterns. To improve the anti-interference capability of the proposed method, a codeword extraction method based on image morphological processing is proposed to segment the grayscale. Consequently, both the phase-shifting sinusoidal deformed patterns and the single frame space division multiplexing four gray-level codewords for fringe order recognition can be extracted respectively from the captured composite deformed patterns. Then, a half-period single-connected domain correction method is also proposed to correct the codewords. Moreover, in order to suppress the effect of jump errors, the phase zero points are constructed to segment the positive and negative ranges of the phase, making the phase unwrapping process segmented. The experimental results demonstrate the feasibility and effectivity of the proposed method.

Anti-crosstalk absolute phase retrieval method for microscopic fringe projection profilometry using temporal frequency-division multiplexing.

In microscopic fringe projection profilometry (MFPP), the traditional absolute phase retrieval method using composite frequency fringe has the shortcomings of low accuracy and poor robustness due to mutual crosstalk of harmonic from the different channels of frequency-division multiplexing. In this study, an absolute phase retrieval method that avoids the inter-channel crosstalk is proposed. By introducing guard bands to accommodate the frequency channels corresponding to the second harmonic that dominate the high order harmonics, the aliasing between the second harmonic and the fundamental is eliminated. Consequently, phase maps without crosstalk can be demodulated using appropriate phase-shifting algorithms. The proposed method is well-suited for high-precision three-dimensional shape measurement scenarios in many fields such as integrated circuit manufacturing process control and micro-electro-mechanical system quality inspection. The experiment results demonstrate that the anti-crosstalk method is effective and can realize three-dimensional reconstruction for discontinuous planar surface and spherical surface.

A novel phase-shifting segmented phase coding method for absolute phase retrieval

The phase-coding method is widely used during 3D measurement for attaining absolute phase retrieval. However, traditional the phase-coding method still suffers from low accuracy and insufficient reliability. To address these issues, a phase-shifting segmented phase coding method was proposed in this work for absolute phase retrieval in complex object measurements, which specifically improved upon the segmented method of phase coding. Coding patterns with different phase-shifting were obtained by embedding the codeword into the phase-shifting phase. These patterns were also combined and arranged to create novel segmented coding patterns. In addition, this segmented encoding can be self-connected based on its different phase-shifting information to obtain the complete fringe order, achieving thus absolute phase retrieval of over 36 codewords. To solve the problem of the periodic misalignment of the wrapped phase and fringe order, the complementary phase coding method was encoded by the bidirectional coding method, and the separation method of the bidirectional coding was improved. From experimental results, it was demonstrated that the proposed method has high measurement accuracy and reliability.

Hue-indexing-based absolute phase retrieval method using a discrete hue sequence

To achieve an effective phase unwrapping for hue-based fringe projection profilometry, this paper proposes a hue-indexing-based absolute phase retrieval method using a discrete hue sequence. First, the hue component is extracted as the wrapped phase for 3D reconstruction by projecting a programmed hue fringe pattern. Afterward, a hue-indexing sequence with a random combination of six unique hues from the hue map is designed for hue unwrapping. By assigning a hue index of the fringe geometric center, the defocusing effect in the hue unwrapping is corrected, where the fringe order of the wrapped hue is then uniquely identified. The simulations show that the root mean square (RMS) of the residual error is 2.2185×10-4 r a d, and the effectiveness of the proposed method is further verified through experiments using a plaster statue and a compressor blade. The measurement comparison of the proposed method and the coordinate measuring machine is provided, where the RMS error of the measured deviation is 4.09×10-2 m m.

Half-Period Gray-Level Coding Strategy for Absolute Phase Retrieval

N-ary gray-level (nGL) coding strategy is an effective method for absolute phase retrieval in the fringe projection technique. However, the conventional nGL method contains many unwrapping errors at the boundaries of codewords. In addition, the number of codewords is limited in only one pattern. Consequently, this paper proposes a new gray-level coding method based on half-period coding, which can improve both these two deficiencies. Specifically, we embed every period with a 2-bit codeword, instead of a 1-bit codeword. Then, special correction and decoding methods are proposed to correct the codewords and calculate the fringe orders, respectively. The proposed method can generate n2 codewords with n gray levels in one pattern. Moreover, this method is insensitive to moderate image blurring. Various experiments demonstrate the robustness and effectiveness of the proposed strategy.

Optimized phase-coding method for absolute phase retrieval based on K-means algorithm

The phase-coding method for absolute phase measurement possesses a strong robustness because its codewords are encoded into phase domain rather than intensity. However, a misalignment problem arises between fringe order and wrapped phase in this method owing to random noises and image blurring, especially in the high-frequency fringes situation. Therefore, the measurement result is unavailable. To overcome this problem, an optimized phase-coding algorithm is proposed in the study. We use the sinusoidal patterns to generate two opposite binary masks, which can locate half of each codeword. Then, the K-means algorithm is used to correct the codewords errors. The accurate fringe order is obtained by merging two halves of codewords and the absolute phase is recovered afterward. The used method is experimentally verified by an established measurement system, and the results show the proposed method is robustness and efficiency.

Absolute phase retrieval for colored objects based on three phase-shifting amount codes.

We propose an absolute phase retrieval method based on three phase-shifting amount codes (3-PSA-codes) to measure the colored object with one additional pattern. 3-PSA-codes adopt the coding concept of 3-digit-codes, in which the code elements of three consecutive periods are treated as a unique code word for one period. However, to measure the colored object more effectively in the proposed method, each code element is embedded into the PSA domain and retrieved from the phase difference. Fringe patterns for the wrapped phase are artfully employed in the code element retrieval. Hence, for the first time, to the best of our knowledge, the code element related to the phase can be determined by one additional pattern. It breaks the constraint that temporal methods require multiple additional patterns to overcome the adverse effect of the surface color of objects on absolute phase retrieval. Experimental results demonstrate that the proposed 3-PSA-codes have strong robustness in the measurement of the colored object.

An improved phase-coding method for absolute phase retrieval based on the path-following algorithm

Although the traditional phase-coding method for absolute phase retrieval possesses strong robustness, the method leads to unwrapping artifacts as a mass of codewords required. To solve this problem, a novel improved method is proposed in this paper. The incorrect points in the recovered phase via the traditional method are located using a computational framework, and the path-following algorithm is adopted as an aid to correct the unwrapping artifacts. The effectiveness of the proposed method is experimentally verified by an established measurement system. The reconstructed geometry of standard sphere has sufficient accuracy and the absolute phase retrieval of a complex star object has high quality.

High-speed 3D shape measurement using the optimized composite fringe patterns and stereo-assisted structured light system.

In this paper, we propose a high-speed 3D shape measurement technique based on the optimized composite fringe patterns and stereo-assisted structured light system. Stereo phase unwrapping, as a new-fashioned method for absolute phase retrieval based on the multi-view geometric constraints, can eliminate the phase ambiguities and obtain a continuous phase map without projecting any additional patterns. However, in order to ensure the stability of phase unwrapping, the period of fringe is generally around 20, which limits the accuracy of 3D measurement. To solve this problem, we develop an optimized method for designing the composite pattern, in which the speckle pattern is embedded into the conventional 4-step phase-shifting fringe patterns without compromising the fringe modulation, and thus the phase measurement accuracy. We also present a simple and effective evaluation criterion for the correlation quality of the designed speckle pattern in order to improve the matching accuracy significantly. When the embedded speckle pattern is demodulated, the periodic ambiguities in the wrapped phase can be eliminated by combining the adaptive window image correlation with geometry constraint. Finally, some mismatched regions are further corrected based on the proposed regional diffusion compensation technique (RDC). These proposed techniques constitute a complete computational framework that allows to effectively recover an accurate, unambiguous, and distortion-free 3D point cloud with only 4 projected patterns. Experimental results verify that our method can achieve high-speed, high-accuracy, robust 3D shape measurement with dense (64-period) fringe patterns at 5000 frames per second.

Optimal pulse width modulation technique combined with stair phase-coding method for absolute phase retrieval with projector defocusing

The accurate three-dimensional shape measurement of a complex surface is significantly important in industrial testing. However, three-dimensional profilometry by conventional sinusoidal fringe projection using a phase-shifting algorithm performs suboptimally because of the nonlinear intensity response of projectors. To overcome this problem, the present paper proposes using a combined optimizing sinusoidal pulse width modulation (SPWM) technique and stair phase-coding approach to obtain the unwrapped phase. Properly optimizing SPWM with a small degree of a defocusing projector to generate sinusoidal fringe patterns can overcome the undesired harmonics and nonlinear gamma effect. Two groups of four-step phase-shifting fringe patterns are used. One group of the stripes contains four sinusoidal patterns generated by the SPWM technique, which is used to determine the wrapped phase. The other group of stripes contains four sinusoidal patterns with the codeword embedded into the stair phase, whose stair changes are perfectly aligned with the 2π discontinuities of the sinusoidal fringe phase, which is used to determine the fringe order for the phase unwrapping. Moreover, for the defocusing projection, because the frequency of the phase-coding fringe increases, the fringe order decision becomes less reliable. Thus, a self-correction phase unwrapping method is applied for phase retrieval. Experiments were conducted to verify the performance of the proposed method.

Absolute Phase Retrieval Using One Coded Pattern and Geometric Constraints of Fringe Projection System

Fringe projection technologies have been widely used for three-dimensional (3D) shape measurement. One of the critical issues is absolute phase recovery, especially for measuring multiple isolated objects. This paper proposes a method for absolute phase retrieval using only one coded pattern. A total of four patterns including one coded pattern and three phase-shift patterns are projected, captured, and processed. The wrapped phase, as well as average intensity and intensity modulation, are calculated from three phase-shift patterns. A code word encrypted into the coded pattern can be calculated using the average intensity and intensity modulation. Based on geometric constraints of fringe projection system, the minimum fringe order map can be created, upon which the fringe order can be calculated from the code word. Compared with the conventional method, the measurement depth range is significantly improved. Finally, the wrapped phase can be unwrapped for absolute phase map. Since only four patterns are required, the proposed method is suitable for real-time measurement. Simulations and experiments have been conducted, and their results have verified the proposed method.

Enhanced reference-plane-based dual-frequency absolute phase retrieval for depth measurement

Digital fringe projection is one of the most widely adopted optical non-contact methods used for high-precision depth measurement in industry. Nevertheless, new approaches with less measurement complexity and higher accuracy are still emerging in the research field. In this paper, we first analyze the efficiency of the reference-plane-based dual-frequency (RDF) pixel-by-pixel absolute phase retrieval method. The RDF method is able to provide a high-precision phase measurement, but the constraint of measurement depth range limits its application. We therefore propose an enhanced reference-plane-based dual-frequency (ERDF) pixel-by-pixel absolute phase retrieval method. The proposed ERDF method overcomes the constraint of measurement depth range and preserves the merits of the RDF method. In the ERDF method, the lower-frequency phase map is completely unwrapped with reference-plane-based single-frequency method, and the higher-frequency phase map is completely unwrapped using the lower-frequency unwrapped phase. The ERDF method is suitable for measuring objects with step-height surface discontinuities. Experiments have been conducted to demonstrate the advantages of the proposed ERDF method as compared to the RDF method.

An effective assessment method for absolute phase retrieval in digital fringe projection profilometry

In this paper, we propose an effective method for assessing absolute phase retrieval quality in digital fringe projection profilometry (DFPP). The method provides a quantitative analysis of the phase retrieval quality with a new integrated quality metric. The phase map of the measured object is pre-defined on the imaging plane and called the inverse ground truth. To obtain the measurement result of the inverse ground truth, object-adapted patterns are projected onto the object and the phase map of the object is retrieved by a phase retrieval technique. Subsequently, the retrieved phase map of the object is compared with the inverse ground truth to assess the phase retrieval quality. The structural similarity between the measurement result and the inverse ground truth is quantified by the proposed quality metric in terms of mean, contrast and structure comparisons. Experiments are carried out to evaluate the effectiveness of the proposed method from two aspects: comparing the accuracies of different phase retrieval techniques and evaluating the influence of different setup parameters on the accuracy. Experimental results show that the analysis by the proposed quality metric is well consistent with the existing findings for the phase retrieval quality in DFPP.

Modified Gray-Level Coding Method for Absolute Phase Retrieval.

Fringe projection systems have been widely applied in three-dimensional (3D) shape measurements. One of the important issues is how to retrieve the absolute phase. This paper presents a modified gray-level coding method for absolute phase retrieval. Specifically, two groups of fringe patterns are projected onto the measured objects, including three phase-shift patterns for the wrapped phase, and three n-ary gray-level (nGL) patterns for the fringe order. Compared with the binary gray-level (bGL) method which just uses two intensity values, the nGL method can generate many more unique codewords with multiple intensity values. With assistance from the average intensity and modulation of phase-shift patterns, the intensities of nGL patterns are normalized to deal with ambient light and surface contrast. To reduce the codeword detection errors caused by camera/projector defocus, nGL patterns are designed as n-ary gray-code (nGC) patterns to ensure that at most, one code changes at each point. Experiments verify the robustness and effectiveness of the proposed method to measure isolated objects with complex surfaces.

Quantized phase coding and connected region labeling for absolute phase retrieval.

This paper proposes an absolute phase retrieval method for complex object measurement based on quantized phase-coding and connected region labeling. A specific code sequence is embedded into quantized phase of three coded fringes. Connected regions of different codes are labeled and assigned with 3-digit-codes combining the current period and its neighbors. Wrapped phase, more than 36 periods, can be restored with reference to the code sequence. Experimental results verify the capability of the proposed method to measure multiple isolated objects.

High speed implementation of a three-dimensional shape profiler with submillimeter precision using a digital light processing device and a new efficient algorithm for absolute phase retrieval

The processing of structured light images in real time is a challenging task for the development of three-dimensional (3-D) shape measurement methods. This paper presents a high speed and low-cost optical profiler implemented using a projection method based on the use of a digital light-processing device to illuminate the object to be measured. The image processing of the reflected structured light pattern allows potential real-time capabilities. The proposed method of absolute phase retrieval for unwrapping the relative phase uses a single additional staircase intensity pattern to determine and correct 2π discontinuities in the phase. Good results are obtained when the method is compared to another which uses three additional fringe patterns to determine the stair phase and then the absolute phase. Since the proposed technique uses only one extra pattern instead of three, it is less costly in terms of computation complexity and is thus faster. The hardware of the developed fringe projection system for a 3-D macroscopic reconstruction is presented and the performance of the method is evaluated. Simulated and experimental results are presented and compared to the other absolute phase-retrieval method. The proposed method is suitable for measuring 3-D object surfaces for a possible implementation in real time.

Phase coding method for absolute phase retrieval with a large number of codewords

A recently proposed phase coding method for absolute phase retrieval performs well because its codeword is embedded into phase domain rather than intensity. Then, the codeword can determine the fringe order for the phase unwrapping. However, for absolute phase retrieval with a large number of codewords, the traditional phase coding method becomes not so reliable. In this paper, we present a novel phase coding method to tackle this problem. Six additional fringe images can generate more than 64(2(6)) unique codewords for correct absolute phase retrieval. The novel phase coding method can be used for absolute phase retrieval with high frequency. Experiment results demonstrate the proposed method is effective.