Projected Fringe Pattern Research Articles

Single-Shot Fringe Projection Profilometry Based on LC-SLM Modulation and Polarization Multiplexing

Fringe projection profilometry (FPP) is extensively utilized for the 3D measurement of various specimens. However, traditional FPP typically requires at least three phase-shifted fringe patterns to achieve a high-quality phase map. In this study, we introduce a single-shot FPP method based on common path polarization interferometry. In our method, the projected fringe pattern is created through the interference of two orthogonal circularly polarized light beams modulated by a liquid crystal spatial light modulator (LC-SLM). A polarization camera is employed to capture the reflected fringe pattern, enabling the simultaneous acquisition of four-step phase-shifting fringe patterns. The system benefits from advanced anti-vibration capabilities attributable to the common path self-interference optical path design. Furthermore, the utilization of a low-coherence LED light source results in reduced noise levels compared to a laser light source. The experimental results demonstrate that our proposed method can yield 3D measurement outcomes with high accuracy and efficiency.

3D reconstruction with single-frame two-step phase-shift method based on orthogonal composite fringe pattern projection

Abstract In order to realize single-frame three-dimensional (3D) reconstruction, a single-frame two-step phase-shift method based on orthogonal composite pattern projection is proposed to solve the problem that the traditional N-step phase-shift profilometry needs multiple projections for 3D reconstruction. The orthogonal composite pattern uses only two carrier channels to reduce the spectrum overlapping influence on the demodulation accuracy of carrier and modulated fringes. A two-dimensional variational mode decomposition method is adopted to remove the background DC component of the sinusoidal fringe to overcome the mode overlap problem by controlling the size of the bandwidth. Thus, the two-step phase-shift method is applied to calculate the phases for 3D reconstruction. The experimental results show that, compared with the typical Fourier transform profilometry method, 3-step composite method and 2 + 1 composite method, the 3D reconstruction accuracy of the proposed method is improved by 49.1%,31.4% and 23.2% respectively according to mean absolute error, and by 73.0%, 58.4% and 56.8% respectively according to mean squared error as the evaluation index. Finally, the dynamic 3D reconstruction experiment demonstrates the good adaptability of dynamic 3D reconstruction.

Efficient and robust 3D reconstruction: Absolute phase extraction algorithm based on three gray images

The structured light three-dimensional (3D) measurement technology based on optical metrics has gained increasing applications, and there is a growing demand for capturing transient trajectory changes in dynamic scenes. Conventional temporal phase unwrapping (TPU) approaches often require multi-frequency fringe patterns for application. However, the inevitable conflict arises between the number of projected fringe patterns and the measurement speed. This paper proposes a highly accurate and robust 3D measurement method using only 3-step phase-shifting fringe patterns. To precisely reconstruct the 3D shape using the fewest fringe patterns, it is essential to extract as much information as possible from the available patterns. Therefore, we calculate the wrapped phase distribution using 3-step phase-shifting fringe patterns to ensure accuracy. Simultaneously, the trapezoidal phase-shifting method is employed to calculate the intensity ratio distribution. Through the proposed region-based indexing method, the intensity ratio map is transformed into an unwrapped phase map. Additionally, a novel self-correction method is introduced to correct the non-linear errors in the unwrapped phase map, which is then utilized for the calculation of the fringe order required for phase unwrapping. This high-speed measurement method utilizes only 3-step phase-shifting fringe patterns while retaining the advantages of TPU, meeting the requirements of high-speed and full-field measurements. Experimental results on both static and dynamic scenes validate the effectiveness and versatility of the proposed method, demonstrating its flexibility and simplicity in application. In our 3D measurement system, the method achieves 3D reconstruction of the dynamic object's trajectory at a measurement speed of 107 frames per second.

Large-field and fast super-resolution microscopic imaging method based on laser interferometry

In recent years, structured illumination microscopy (SIM) has been drawing great attention for both technique development and application. However, conventional SIM, which uses a spatial light modulator (SLM) for fringe projection, often has a limited field of view. To meet the demand for high-throughput microscopic imaging in biomedicine research, a large-field super-resolution (SR) fluorescence microscopic imaging method based on laser interferometry was proposed. The method that combines a two-dimensional (2D) grating for fringe pattern projection and an SLM for selecting fringe orientation can break the limitation of fringe number limited by the digital projection devices. A spatial-domain reconstruction algorithm was developed to improve the computational speed of super-resolution imaging. Finally, an experimental platform for SIM microscopy was established. A large-field view of 1380 μm × 1035 μm under a 20×/NA0.75 objective is experimentally demonstrated, and an enhancement of 1.8-fold resolution is realized. The spatial-domain reconstruction algorithm can significantly improve the computational speed by approximately 10 times faster compared to the traditional frequency-domain algorithm.

Fringe projector with submillimeter fringe spacing at a meter-scale field of view.

State-of-the-art fringe projection systems generate fringe patterns using digital light projectors (DLP). The axial uncertainty is limited by the smallest fringe period and is directly related to the pixel count. This results in limited accuracy of current DLP systems that affect applications such as in situ measurements for laser powder bed fusion systems, where a submillimeter fringe period is needed for field-of views larger than 500m m×500m m. This work presents a scalable fringe projection technique that enables the generation of stable fringe patterns over a large field of view spanning several meters while maintaining submillimeter fringe periods. This system uses geometric phase gratings to enable variable fringe spacing and fringe orientation capabilities. The system shears a coherent beam in the Fourier plane using a pair of geometric polarization gratings. The separation between the gratings directly affects the fringe spacing, and the orientation of the gratings affects the fringe orientation. The depth of focus is only limited by the coherence of the light source, enabling high fringe periods even on tilted planes. The system is designed with a single path configuration, making the system more robust to environmental noise. With a rotating linear polarizer, we demonstrate that phase-shifting methods could be employed to acquire phase information about the object. This paper employs a single-shot Fourier transform phase estimation technique to process the intensity maps acquired using projected fringe patterns. Further, we demonstrate the capabilities of the system to produce submillimeter fringe spacing and the ability to project fringes on larger scales for measurements.

Accurate measurement of high-reflective surface based on adaptive fringe projection technique

Fringe projection profilometry (FPP) is one of the most effective methods to obtain three-dimensional surface topography information about an object. However, for objects with large variations in surface reflectance, it is difficult to measure the saturated regions with conventional FPP. In this paper, a new adaptive fringe projection (AFP) method is proposed to solve this problem. Compared with existing methods, the proposed method can automatically generate low-intensity projected fringe patterns instead of requiring manual adjustment. First, we built a projection intensity model for the captured pixels and defined the surface reflection factor and environmental factor for saturated pixels. Then, a small number of uniform grayscale pattern sequences were projected to mark the saturated areas, while the surface reflection factor and the environment factor of individual pixels were calculated and a surface coefficient look-up table (SCLUT) was created. The low-intensity projected fringe patterns were automatically calculated and generated based on the captured uniform grayscale sequences of images to establish the mapping relationship between the camera image plane and the projector image plane. Finally, the optimal projection intensities of pixels in the saturated regions were calculated according to the SCLUT, and adaptive fringe patterns were generated. Experiments show that using the adaptive fringe patterns generated by the proposed method to measure objects can accurately adjust the projection intensity and substantially improve the measurement accuracy of high-reflective surface.

Three-dimensional measurement for specular reflection object based on adaptive fringe projection and phase measuring profilometry

ObjectiveUsing phase measuring profilometry (PMP) to measure the object with specular reflections is a very challenging task, a large deviation between the measured result and the actual data is caused by the highlights of the measured object surface. Therefore, a 3D measurement method for the object with a specular reflection based on adaptive fringe pattern projection (AFPP) is proposed in this paper. MethodsFirstly, a set of uniform grayscale images are projected to the measured object by a DLP projector. The gray level gradually decreases from 255 and stops when the number of saturated pixels in the camera image reaches 0. The masks of saturated pixels at each gray level are obtained. Secondly, the masks corresponding to two adjacent gray levels are compared respectively, and the optimal projection intensity of the camera image is obtained. Thirdly, the coordinates of the highlight pixels in the camera image are mapped to the projector image coordinate system, and the new fringe images are generated using the optimal projection intensity. Fourthly, the new fringe images are projected onto the measured object for 3D measurement. ResultsThe measurement experiments were implemented on the measured objects made of metal, plastic, and ceramic, respectively. Experiment results show that the proposed method can reduce the measurement deviation caused by the highlights and make the 3D reconstruction model more complete without additional cameras and hardware.

Few-fringe-based phase-shifting profilometry employing hilbert transform

In optical measurement techniques, when the projector works at a constant projection rate, reducing the number of projected fringe patterns is an effective way to reduce the projection time. In this paper, we propose a few-fringe-based phase-shifting profilometry employing Hilbert transform. We project only two fringe patterns for each frequency of fringes, with the phase shift between the fringes designed to be π. The Hilbert transform makes these two captured fringes phase shifted by π/2, thus transforming the original two fringes into four, and the wrapped phase can be obtained through these four fringes with a phase difference of π/2. To improve the accuracy and robustness of the method, we adopt three frequencies of fringes for phase unwrapping. Further, since different phase unwrapping methods can be used for the different frequencies of the fringes, we propose a heterodyne 2H+2 M+2 L method and a hierarchical 2H+2 M+2 L respectively. Multiple experimental results have confirmed the feasibility and effectiveness of the two 2H+2 M+2 L methods, and the different characteristics of the reconstructed shapes obtained by the two 2H+2 M+2 L methods are compared to provide useful guidance in the selection of the required method for different application scenarios. The experimental results demonstrate that when using the heterodyne and hierarchical methods for phase unwrapping, the RMSE of the 2H+2 M+2 L method is only higher than that of the three-frequency four-step phase-shifting method by 0.0056 and 0.0024 respectively, but this 2H+2 M+2 L method improves the efficiency of the three-frequency four-step phase-shifting method by 50%.

An Improved Synthesis Phase Unwrapping Method Based on Three-Frequency Heterodyne

An improved three-frequency heterodyne synthesis phase unwrapping method is proposed to improve the measurement accuracy through phase difference and phase sum operations. This method can reduce the effect of noise and increase the equivalent phase frequency. According to the distribution found in the phase difference calculation process, the Otsu segmentation is introduced to judge the phase threshold. The equivalent frequency obtained from the phase sum is more than those of all projected fringe patterns. In addition, the appropriate period combinations are also studied. The simulations and related experiments demonstrate the feasibility of the proposed method and the ability to improve the accuracy of the measurement results further.

Correction of perspective distortion and intensity errors in projected fringe patterns in phase-measuring deflectometry

The relative pose between the projector and screen in a phase-measuring deflectometry (PMD) setup can result in perspective distortion and intensity errors in the projected fringe patterns. These problems degrade the sinusoidal characteristics of the fringe patterns, thus increasing phase, slope, and height errors in the PMD measurement. To overcome these issues, inverse perspective distortion and intensity modification algorithms were developed and applied to computer-generated fringe patterns before projection. The inverse perspective distortion matrices were obtained using a single image of the projected grid distortion target. The pixel intensities in the generated fringe patterns were modified using the relationship between the generated and captured pixel intensity values in grayscale images of uniform intensity. Experiments were conducted to measure the surface topographies of spherical concave and convex mirrors using a monoscopic PMD setup. Based on the experimental results, the root-mean-squared (RMS) intensity and phase errors in the projected sinusoidal fringe patterns were reduced by about 90% after using the modified fringe patterns compared to the original fringe patterns. When comparing the measured and the theoretical heightmaps, the results in PMD measurement showed an 8% and a 14% reduction of the RMS height errors in concave and convex heightmaps, respectively. The effectiveness of the algorithms in improving the accuracy of projector-based PMD measurement was demonstrated successfully.

Metrology Benchmarking of 3D Scanning Sensors Using a Ceramic GD&T-Based Artefact.

The use of non-contact scanning equipment in metrology and in dimensional and geometric inspection applications is increasing due to its ease of use, the speed and density of scans, and the current costs. In fact, these technologies are becoming increasingly dominant in the industrial environment, thus moving from reverse engineering applications to metrological applications. However, this planned transfer requires actions to ensure the achievable accuracy by providing traceability of measurements. In the present study, a comparison between the devices is carried out and a specific standard artefact is designed, equipped with multiple ceramic optically friendly entities, and allowing a wide variety of geometric dimensioning and tolerancing (GD&T). Four different 3D scanning sensors are used in the experimentation. Three of them are based on laser triangulation, and the fourth is a structured blue light sensor (fringe pattern projection). The standard artefact is calibrated with a high accuracy, using a coordinate measuring machine (CMM) and probing sensors. With this CMM, reference values of multiple predefined GD&T are obtained. The evaluation methodology maximises the accuracy of each device in measuring the dimensions of the artefact due to the good dimensional (milling and turning), surface (control of machining variables), and the dimensional and spatial distribution characteristics. The procedure also includes the same treatment of the captured point clouds (trimming, filtering, and best-fit algorithm, etc.) in each of the four 3D scanning sensors considered. From this process, very reliable measurements of the maximum achievable accuracy of each device (deviations from the CMM measurements) are finally obtained, and a multi-characteristic comparison between the four sensors is performed, also with high reliability.

High-reflective surfaces shape measurement technology based on adaptive fringe projection

Fringe projection profilometry (FPP) is limited by the pixel depth of the camera and cannot correctly reconstruct complex objects with highly reflective surfaces. In this paper, we proposed an improved adaptive fringe technique to avoid image saturation. This method only needs to project a uniform gray level image and a set of horizontal and vertical phase-shifting fringe patterns to generate adaptive fringes. The gray level of saturated regions can be fitted by the uniform image and the coordinates of the areas are obtained by calculating the horizontal and vertical fringes. To avoid the process of recursion, we introduce the concept of the grayscale correction function. Furthermore, a modified mapping formula is adopted and refined, which enhances the mapping effect and reconstruction accuracy. Compared with the original adaptive fringe projection (AFP), the modified method further decreases the number of projected fringe patterns. We analyzed the error between the fitted value and the standard value to evaluate the performance of the method. Experimental results demonstrated that the proposed method maintains the accuracy of reconstruction while improving time efficiency compared to other high dynamic range (HDR) measurement methods. • The contribution of different fringe projection technology with highly reflective objects is investigated. • A novel adaptive fringe is proposed to measure the depth information of HDR objects. • An idea is proposed for the improvement of adaptive fringe projection.

Fast and accurate 3D face reconstruction based on facial geometry constraints and fringe projection without phase unwrapping

Phase unwrapping is a critical process and a challenging step in fringe projection profilometry. Methods employing additional auxiliary patterns or embedding signals in the projected fringe pattern can successfully address this issue, but most of them suffer from increased number of structured patterns or depressed signal-to-noise ratio (SNR) of fringe images, which are not expected in real-time high-accuracy application such as 3D face reconstruction. In this paper, a 3D face reconstruction method that completely sidesteps the phase unwrapping process is proposed. Phase order lines (POLs) are first extracted from the left and right wrapped phase map of the stereo vision system respectively, and then the left and right POLs are matched by automatically drawing polylines on the face with facial geometry constraints as prior knowledge. Finally, based on the matched POL pairs, fine matching is performed directly employing the wrapped phase to generate a dense disparity map. Compared with the conventional, the processing time of the proposed method is further improved without sacrificing accuracy. Experiments demonstrate the effectiveness and robustness of the method.

Large-field structured illumination microscopy based on 2D grating and a spatial light modulator.

Structured illumination microscopy (SIM) has been widely used in biological research due to its merits of fast imaging speed, minimal invasiveness, super-resolution, and optical sectioning imaging capability. However, the conventional SIM that uses a spatial light modulator (SLM) for fringe projection often has a limited imaging field of view. Herein, we report a large-field SIM technique that combines a 2D grating for fringe pattern projection and an SLM for selecting fringe orientation and performing phase shifting digitally. The proposed SIM technique breaks the bottleneck of fringe number limited by the digital projection devices, while maintaining the advantage of high-speed (digital) phase shifting of conventional SIM. The method avoids the pixilation and dispersion effects of the SLMs. Finally, a 1.8-fold resolution enhancement in a large field of 690 × 517 µm2 under a 20×/NA0.75 objective is experimentally demonstrated. The proposed technique can be widely applied to biology, chemistry, and industry.

LED source interferometer for microscopic fringe projection profilometry using a Gates’ interferometer configuration

The fringe projection technique is considered one of the most reliable solutions for structured light technology, developed for non-contact three-dimensional (3D) data acquisition. When working with this technique, applying it on a microscopic scale, one often encounters some problems such as the limited depth of field of the projected fringe pattern, typical of the imaging lenses, or the formation of speckle-noise when laser interferometric fringes are projected, which are problems that can cause significant errors on test surfaces whose height exceeds the depth of field, and on which, the other hand, speckle noise affects the resolution of the technique. This paper presents a Gates’ interferometer configuration with a LED source to project a fringe pattern without speckle noise and a very long field depth. We explain how a non-located sinusoidal fringe pattern can be obtained using two-beamsplitter cubes and a LED light source. Moreover, we compare measurements made using the LED and laser concerning a commercial contact profilometer.

Reconstruction of moving object with single fringe pattern based on phase shifting profilometry

Phase shifting profilometry (PSP) shifts the phase by projecting multiple fringe patterns with different initial phase values. Errors will be introduced when the dynamic object moves among the multiple fringe patterns. This paper presents a new 3D reconstruction method of moving object based on PSP by projecting single fringe pattern. The phase shift is caused by the object movement. Multiple images of the object with movement are captured. The object movement is tracked first; then, the phase variation caused by the movement in the single projected fringe pattern is analyzed and the reconstruction model describing the fringe pattern with movement is given; at last, the phase value is retrieved by utilizing the phase variation caused by the movement. The effectiveness of the proposed method is verified by the simulations and the experiment.

PMENet: phase map enhancement for Fourier transform profilometry using deep learning

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.

Indoor and Outdoor Surface Measurement of 3D Objects under Different Background Illuminations and Wind Conditions Using Laser-Beam-Based Sinusoidal Fringe Projections

In this study, both theoretical analysis and experimental validation are carried out for 3D surface measurement under different indoor/outdoor environmental conditions via combining the projected laser-beam-based sinusoidal optical signal, the optical filtering technique, and the single-shot approach based on Fourier transform profilometry. The designed optical signal generator used in this work is capable of ensuring that the projected fringe pattern is monochromatic, higher-contrast, time-invariant, and truly sinusoidal. The proposed and developed optical setup of 3D surface measurement is portable and is used for in-situ experiments of 3D surface measurements that have been carried out under different sunlight illuminations. The experimental results indicate that accurate reconstructions of measured objects with even or varying surface reflectivity can be obtained under windy conditions and strong environmental illuminations such as the background illuminance of 5600–35,000 Lux. The generated fringe-pattern signal is not sensitive to vibrations from environmental influences including the effects of the wind, which has overcome the outdoor-measurement restrictions of the traditional interferometric system and the profilometry approaches based on phase-shifting methods.

High resolution laser fringe pattern projection based on MEMS micro-vibration mirror scanning for 3D measurement

3D measurement of micro-sized components by Fringe projection profilometry (FFP) requires fringe patterns with high spatial resolution. In order to project high-resolution and fine fringe patterns, a MEMS scanning module is used to project the precise time-modulated line laser stripes into space to form high-resolution laser fringes. The micro-vibration mirror in the MEMS module works in a resonant state, and the internal position detection of the MEMS module generate precise time reference signal. The reference signal is used to project spatial fringe patterns and ensure the stability and high resolution. The high-resolution laser fringe patterns generated by MEMS scanning module are projected to micro-sized components for 3D measurement. The measurement experiment shows that the spatial resolution of the projected fringes can reach 0.47 mm and the phase shift resolution is 0.12 mm. The measurement results show that the tiny height changes of the measured components can be well measured and presented. The standard gauge block with a height of 1 mm is measured, and the root mean square error of the measured height is 0.037 mm. It has a good prospect to apply the proposed method to the 3D measurement of micro-sized components.

Fourier-Transform-Based Surface Measurement and Reconstruction of Human Face Using the Projection of Monochromatic Structured Light.

This work presents a new approach of surface measurement of human face via the combination of the projection of monochromatic structured light, the optical filtering technique, the polarization technique and the Fourier-transform-based image-processing algorithm. The theoretical analyses and experimental results carried out in this study showed that the monochromatic feature of projected fringe pattern generated using our designed laser-beam-based optical system ensures the use of optical filtering technique for removing the effect of background illumination; the linearly-polarized characteristic makes it possible to employ a polarizer for eliminating the noised signal contributed by multiply-scattered photons; and the high-contrast sinusoidal fringes of the projected structured light provide the condition for accurate reconstruction using one-shot measurement based on Fourier transform profilometry. The proposed method with the portable and stable optical setup may have potential applications of indoor medical scan of human face and outdoor facial recognition without strict requirements of a dark environment and a stable object being observed.