Binary Fringes Research Articles

Deep learning based measurement accuracy improvement of high dynamic range objects in fringe projection profilometry

One of the key factors affecting the accuracy of three-dimensional (3D) measurement in fringe projection profilometry (FPP) is the phase retrieve accuracy. In the 3D measurement of high dynamic range (HDR) objects, fringe saturation and/or low contrast are difficult to avoid. A greater number of fringe images are needed for 3D measurement of HDR objects by traditional methods, which is unfavorable for the measurement of moving objects. In this paper, what we believe to be a new method to solve the phase demodulation problem of HDR objects using deep learning is proposed. In this method, a “many-to-one” mapping relationship is established using an improved UNet deep neural network. In addition, in order to obtain more saturated fringe information, π-shifted binary fringes were also used. This allows us to retrieve the wrapped phase of HDR objects quickly and accurately. Experimental results demonstrate the effectiveness and reliability of the proposed method.

Three-dimensional measurement based on equal spacing binary fringe coding

Abstract Binary fringe projection technology can effectively avoid the measurement error caused by nonlinearity in structured light three-dimensional measurement system. In this paper, a binary fringe projection coding based on equal spacing is proposed firstly, the image sequence projected by binary fringes with equal spacing is corresponding to the sinusoidal intensity values in the same period one by one, and then the sinusoidal fringes are generated by weighted superposition. The experimental results show that, compared with the traditional four-step and 12-step phase shifting methods, the mean square error of the synthesized sinusoidal pattern is reduced by 36.74% and 18.24% respectively, and the mean square error of the distance between the obtained spherical point cloud of the standard sphere and the center of the fitting standard sphere is reduced by 89.36% and 77.27% respectively.

Enhanced accuracy in 3D structured illumination microscopy through binary encoding with accelerated speed using sampling Moiré

Structured Illumination Microscopy (SIM) is widely recognized as a precise and stable technique for three-dimensional inspection. However, efficiently achieving precise results still poses a challenge to be addressed. This research paper presents significant advancements aimed at enhancing the precision and efficiency of the SIM system. We leverage the defocus sensitivity of binary fringes, which yields more accurate height mapping, reducing the error by an outstanding 5% to 20%. Additionally, we introduce a novel technique called sampling Moiré (SM) for modulation decoding from a single shot, resulting in a reduction of camera exposure time by (N−1)/N compared to the N-step phase shift technique and a minimum 20% reduction in error compared to the Fourier transform (FT). These advancements elevate the system's precision and increase efficiency, making SIM an even more powerful tool for high-quality three-dimensional (3D)inspections.

A phase error compensation method for three-dimensional shape measurement using improved iteration algorithm

The binary defocusing has been extensively studied in the three-dimensional measurement. But if the projector is slightly defocused, the binary fringes after defocusing still contain high-order harmonics compared with the ideal sinusoidal fringes, so the phase error caused by the nonlinear response is not negligible. In this paper, two models are proposed to calculate and compensate phase error, which include a double-precision iterative compensation model (DPICM) and a dual-domain iterative compensation model (DDICM). These two models obtain accurate phase errors by fusing the phases at different precision and domains. DPICM is composed of the double precision method and the improved iterative algorithm, and DDICM consists of the dual-domain method and the improved iterative algorithm. This improved iterative algorithm is used to compensate phase error, which can improve phase accuracy. DPICM and DDICM reduce the RMS error by 25.5% and 13.5% respectively.

Robust binary fringe generation method with defocus adaptability

Current binary defocus technology mainly focuses on fringe generation suitable for specific frequencies without considering fringe adaptability for defocus-degree variation, which decreases the measuring accuracy for this scenario. To achieve a high-quality measurement, we propose a robust binary fringe generation method to minimize the phase error caused by changes in defocus and the random error in measurement. In the method, we establish a complete phase error model and construct a novel objective function, to the best of our knowledge, to optimize the binarization threshold of each pixel. Through derivation of the threshold gradient calculation formula, we quickly obtain optimal binary fringes that can adapt to different fringe pitches and various degrees of defocus. The experimental results verify that the proposed method can generate robust binary fringes adaptive to different fringe pitches and defocus degree variation, and thus achieve high-quality 3D measurements.

High-quality 3D shape measurement with binary half truncated sinusoidal fringe pattern

Digital fringe projection (DFP) with defocused binary fringe patterns could overcome the projector nonlinearity and achieve a high-speed 3D measurement. Most of the binary defocusing techniques take sinusoidal fringe as the target of binarization, hoping the binary fringes can become “quasi-sinusoidal” after defocusing. However, considering that the phase-shifting algorithm (PSA) has an inherent resistance to certain order harmonics components, it is not the best choice to make the defocused binary fringe become more sinusoidal. This paper proposed a new kind of fringe called half truncated sinusoidal (ht-sinusoidal) fringe, which has the same phase result as the sinusoidal fringe with 4-step PSA theoretically. And this kind of fringe is easier to be binarized for the reason that half of it has 0 intensity values already. Therefore it can achieve significant phase quality improvements compared with the binary sinusoidal fringe. We mainly verified that the ht-sinusoidal fringe will help substantially improve the measurement accuracy of different error diffusion methods through both simulations and experiments.

Performance Enhancement Scheme for RSE-Based Underwater Optical Camera Communication Using De-Bubble Algorithm and Binary Fringe Correction

Optical camera communications (OCC) has been growing rapidly in recent years, which offers a flexible and low-cost way to achieve underwater wireless optical communication (UWOC). However, the existence of underwater bubbles and suspended impurities will greatly decrease the signal quality. In this paper, we propose a de-bubble algorithm and a sampling scheme based on binary fringes correction (BFC) to enhance the communication quality. The experimental results demonstrate that a robust transmission can be achieved in the harsh bubble environment by applying the proposed two algorithms.

Depth range enhancement of binary defocusing technique based on multi-frequency phase merging.

Binary defocusing technique has demonstrated various merits for high-speed and high-accuracy three-dimensional measurement. However, the existence of excessive defocusing zone (EDZ) limits the depth range of binary defocusing system. To overcome this problem, this paper proposes a multi-frequency phase merging (MFPM) approach, which makes it possible to measure the object surface in large depth range (LDR). The method is based on our finding that for different fringe frequencies, the associated EDZs of binary defocusing system are different and not totally overlapped. Thus by merging the phase maps of multiple binary fringes, we could effectively enhance the measurement depth range. Meanwhile, a strategy to determine the optimal combination of fringe frequencies is also proposed by analyzing the phase error distribution under different defocusing degrees. Both simulations and experiments verify the effectiveness and robustness of the proposed method.

Three-dimensional shape measurement based on binary fringe conventional projection

A three-dimensional (3D) shape measurement method based on binary fringe conventional projection is proposed. In traditional 3D shape measurement methods based on binary fringe projection, the binary fringe is used as an approximate sinusoidal fringe by defocusing projection or even directly used as an approximate sinusoidal fringe by nonlinear error suppression feature of large-step phase measuring profilometry (PMP). In the proposed method (Prop), neither defocusing projection is needed nor large-step PMP must be used. When the binary fringe is conventionally projected on the measured object, just by filtering operation in spatial frequency domain from the captured deformed pattern, the nearly unbroken sinusoidal deformed pattern can be extracted efficiently. While N ( N≥3) frames binary fringes with 1/ N period misalignment between each adjacent fringe are conventionally projected onto the measured object sequentially, the corresponding nearly unbroken N-step sinusoidal deformed patterns extracted from the N frames captured deformed patterns can be used to reconstruct the 3D shape of the measured object with N-step PMP algorithm. The experimental results show the feasibility and validity of the Prop. It is more flexible for its optional fringe period and optional phase-shifting steps. It has potential application in the real-time 3D shape measurement.

Real-time three-dimensional shape measurement based on color binary fringe projection

A real-time three-dimensional (3-D) shape measurement based on single-shot color binary fringe (CBF) projection is proposed. In the traditional 3-D shape measurement methods based on binary fringe projection, the duty cycle of the binary fringe is always set to 1/2, so as to approximate the sinusoidal fringe by defocusing projection. In the proposed method, the binary fringe with a duty cycle of 1/3 is introduced. It is found that although the duty cycle is not 1/2, a nearly unbroken sinusoidal fringe pattern can be extracted from the captured fringe pattern by a filtering operation in the spatial frequency domain. In order to realize real-time 3-D shape measurement, a composite CBF was designed, in which three monochromatic binary fringes share the same duty cycle of 1/3 but misaligned 1/3 periods one by one are encoded in red (R), green (G), and blue (B) channels. When this composite CBF is projected onto the measured object, only one color-deformed pattern (CDP) needs to be captured and three monochromatic sinusoidal deformed patterns with a phase-shifting of 2π / 3 one another can be extracted from the single-shot captured CDP. So the 3-D shape of the measured object can be reconstructed with three-step phase measuring profilometry. The experimental results show the feasibility and validity of the proposed method. It can either effectively avoid the color overlapping in traditional color sinusoidal fringe or avoid the grayscale nonlinearity of sinusoidal fringe caused by the effect of gamma.

Dynamic Phase Measuring Profilometry Based on Tricolor Binary Fringe Encoding Combined Time-Division Multiplexing

A dynamic phase measuring profilometry (PMP) based on tricolor binary fringe combined time-division multiplexing principle is proposed. Only one tricolor binary fringe combined by red (R), green (G), and blue (B) binary fringes with the same fringe width but without any color overlapping one another is needed and sent into the flash memory of a high-speed digital light projector (HDLP) in advance. A specialized time-division multiplexing timing sequence is designed to control the HDLP to project the tricolor binary fringe saved in the flash memory onto the measured dynamic object separately and sequentially at 234 fps, at the same time, the projected light source mode is set as monochrome mode which means that all the RGB LEDs remain lighting. Meanwhile, it also triggers a high frame rate monochrome camera synchronized with the HDLP to capture the corresponding deformed patterns in R, G and B channels. By filtering, the nearly unbroken phase-shifting sinusoidal deformed patterns for three-step PMP can be extracted from the captured deformed patterns. It is equivalent to the three-dimensional (3D) shape reconstruction of the measured dynamic object at 78 fps. Experimental results verify the feasibility and the validity of the proposed method. It is effective for measuring the dynamic object and can avoid the color cross-talk effectively.

High-speed three-dimensional measurement technique for object surface with a large range of reflectivity variations.

It is a challenge for any optical method to measure object surfaces with a large range of reflectivity variations. Dark or saturated regions on fringe images may lead to phase and measurement errors. At present, the main defect of the existing methods is the low measurement efficiency. This paper presents a high-speed three-dimensional (3D) measurement for object surfaces with a large range of reflectivity variations. First, we set the intensity of the projected fringes to the maximum, which ensures a better signal-to-noise ratio (SNR) of fringe images compared to the traditional methods. Second, in order to achieve high-speed projection, we transform 12 fringes with 256 gray-value cosine variations to binary fringes and defocus the digital light procession to filter out the higher harmonics. Third, since manually adjusting the camera lens or exposure time is much more time-consuming and not conducive to improving the SNR, we use the color light projection of the projector itself to get multiple groups of fringe sequences with different brightnesses. Finally, the final group of fringe images, used for 3D reconstruction, are formed by choosing the brightest but unsaturated corresponding pixels from multiple groups of fringe images. Experiments verified that the proposed method has the advantages of high-speed measurement, low cost in hardware, high measurement accuracy, a simple algorithm, and ease of extending to several applications.

Dual-sensitivity profilometry with defocused projection of binary fringes.

A dual-sensitivity profilometry technique based on defocused projection of binary fringes is presented. Here, two sets of fringe patterns with a sinusoidal profile are produced by applying the same analog low-pass filter (projector defocusing) to binary fringes with a high- and low-frequency spatial carrier. The high-frequency fringes have a binary square-wave profile, while the low-frequency binary fringes are produced with error-diffusion dithering. The binary nature of the binary fringes removes the need for calibration of the projector's nonlinear gamma. Working with high-frequency carrier fringes, we obtain a high-quality wrapped phase. On the other hand, working with low-frequency carrier fringes we found a lower-quality, nonwrapped phase map. The nonwrapped estimation is used as stepping stone for dual-sensitivity temporal phase unwrapping, extending the applicability of the technique to discontinuous (piecewise continuous) surfaces. We are proposing a single defocusing level for faster high- and low-frequency fringe data acquisition. The proposed technique is validated with experimental results.

3D shape from phase errors by using binary fringe with multi-step phase-shift technique

A three-dimensional shape measurement method is presented, which is a uniaxial measurement by measuring phase errors instead of the well-known phase, modulation or contrast. A sequence of exposures are captured by using a multi-step phase-shift technique with the binary fringes. Then the high-accuracy phases can be obtained by using all the exposures, meanwhile, a set of low-accuracy phases can be calculated by dividing those exposures into a set of four-step phase-shift measurements. For each pixel there will be a set of phase errors by subtracting low-accuracy phases from the high-accuracy ones. And the weighted phase error of every pixel can be calculated. Meanwhile the phase error caused by the improperly defocused binary fringes has a unique relationship with the depth z. Therefore, the 3D information of every pixel can be obtained by analyzing the phase errors. It will be promising for a uniaxial measurement, such as deep holes.

Temporal-spatial encoding binary fringes toward three-dimensional shape measurement without projector nonlinearity

Projector nonlinearity is a common problem for digital structured light-based three-dimensional (3-D) shape measurement techniques. A temporal-spatial binary encoding method is presented for the purpose of eluding it. We build a 3-D shape measurement scheme by combining our proposed method with phase measurement profiling. A standard sinusoidal fringe pattern is divided into more than two binary fringe patterns using specially designed temporal and spatial binary encoding rule based on intensity hierarchic quantification, and then are in-focus projected onto the measured object at a time sequence to reconstruct a frame phase-shifting fringe image. On account of the projected binary fringe pattern strictly consisting of zeros and ones, the influence of the projector nonlinearity on the measurement result can be effectively ruled out and simultaneously enables high-quality sinusoidality. In-depth investigations by theoretical analysis and experiments are conducted to demonstrate the performance of this method.

离焦条纹投影三维测量中正弦光栅的二值化方法研究

The non-linear intensity response of digital projector can be eliminated in 3D shape measurement using defocused binary fringe projection technique.The speed of projecting can be increased and it is possible to realize high speed measurement as well.Typical binary fringes used in digital projection were adopted as a study subject.The relation between the fundamental frequency,higher harmonics and fringe period of binary fringe was studied through the theoretical analysis and experiments. According to suitable phase shifting algorithm,the performance of various binary fringes was measured using the measurement error of phase as its target.The results showed that sinusoidal fringe with high performance could be generated by defocusing the Ronchi grating and pattern generated using 2Derror diffusion algorithm under the condition that fringe with short period was adopted.The measurement accuracy of defocused Ronchi grating was higher than that of other pattern,when the algorithm of odd step phase-shifting with equal interval in one period was used for 3D measurement;the highest measurement accuracy was obtained by using defocused optimal pulse width modulation fringe,when the period of fringe was long.The research results provide the evidence for selection of binary grating in the 3Dmeasurement based on defocused projection.

Color encoding of binary fringes for gamma correction in 3-D profiling

Three-dimensional profiling by sinusoidal fringe projection using PSI-algorithms are distorted by the nonlinear response of digital cameras and commercial video projectors. To solve the problem, we present a fringe generation technique that consists of projecting and acquiring a temporal sequence of strictly binary color patterns, whose (adequately weighted) average leads to sinusoidal fringe patterns with the required number of bits, which allows for a reliable three-dimensional profile using a PSI-algorithm. Validation experiments are presented.

Three-dimensional profiling with binary fringes using phase-shifting interferometry algorithms

Three-dimensional shape measurements by sinusoidal fringe projection using phase-shifting interferometry algorithms are distorted by the nonlinear response in intensity of commercial video projectors and digital cameras. To solve the problem, we present a method that consists in projecting and acquiring a temporal sequence of strictly binary patterns, whose (adequately weighted) average leads to a sinusoidal fringe pattern with the required number of bits. Since binary patterns consist of "ones" and "zeros"--and no half-tones are involved--the nonlinear response of the projector and the camera will not play a role, and a nearly unit contrast gray-level sinusoidal fringe pattern is obtained. Validation experiments are presented.

Obtención del relieve digital mediante proyección de luz estructurada en modelos analógicos de extensión

We present the results of using a projected structured light technique to obtain a digital topographic map in analogue models of deformation during extension. The analogue models simulate extensional processes occurring in the uppermost part of the earth crust. The technique to obtain the relief consists in the projection of a structured light (binary fringes produced by light and shadows) on the surface of the model. The model is deformed and a digital photograph of the surface is obtained for each deformation increment. The deformation apparatus is squeeze-box type and consists of a Plexiglas box in which models are constructed using materials that simulate the mechanical behavior of the earth crust. A vertical moving wall is displaced within the box at a constant and low velocity allowing the extension of the model. The optical array was constructed in Centro de Investigaciones en Optica. Results obtained illustrate the convenience of the optical techniques to analyze the surface deformation on the physical experiments.