Phase-shifting Fringe Projection Profilometry Research Articles

Color crosstalk compensation method for color phase-shifting fringe projection profilometry based on the phase correction matrix.

Color phase-shifting fringe projection profilometry is one of the single-shot three-dimensional shape measurement techniques. The color crosstalk of the projector-camera system yields undesired phase errors when using phase-shifting method. In this paper, a color crosstalk compensation method based on phase correction matrix is proposed. In this method, the phase correction matrix is established to compensate the deviations between the actual phase-shift values in the acquired fringes and the standard ones in the ideal fringes. Only two fringe patterns are utilized to obtain the phase correction matrix. The quadratic equations for calculating the actual phase-shift values of the fringes in the three color channels are derived. The actual phase-shift values and the corresponding standard ones are employed to form the equilibrium equations for computing the phase correction coefficients in the matrix. Experimental results demonstrate the feasibility of the proposed method and it can effectively reduce the induced overall phase error caused by the color crosstalk.

High-Speed Phase Structured Light Integrated Architecture on FPGA

Phase-shifting fringe projection profilometry (FPP) in three-dimension (3D) structured light measurement is widely applied in high-accuracy 3D shape measurement scenarios. But motion objects or other dynamic scenarios make the traditional phase-shifting FPP hard to deal with due to its sizable CPU-based execution time. Therefore, an embedded high-speed and high-accuracy phase-shifting FPP system is designed and implemented on FPGAs. The system implements a three-frequency four-step phase-shifting hardware algorithm with RTL-level caching, multi-frame image ping-pong buffering, and data handling, etc. The system exhibits fully-parallel and pipeline processing while behaving with lower resource and power consumption. Measurement experiments indicate that the proposed method can reach high-accuracy real-time 3D shape measurement with a 3D decoding speed of 40.15 fps when the clock frequency is 200MHz, and the image size is 2432×2048.

Least-squares method constrained by phase smoothness for correcting illumination fluctuation errors in phase-shifting profilometry

Phase-shifting fringe projection profilometry usually suffers from the errors induced by illumination fluctuations. As a result, ripple-like artifacts that have the same periods as fringes appear on the phase map. Because the illumination fluctuations cannot be simply modeled using fringe harmonics, their induced errors are difficult to remove by use of a phase-shifting algorithm. To solve this problem, this paper suggests a least-squares method constrained by phase smoothness. This method calculates fringe phases using the generalized phase-shifting algorithm and estimates coefficients related to illumination fluctuation by use of smoothed phase map. Alternately implementing these two steps enables one to eliminate effects of illumination fluctuations on the measurement results. Experimental results demonstrate that this proposed algorithm is helpful for improving measurement accuracy.

Harmonics elimination in phase-shifting fringe projection profilometry by use of a non-filtering algorithm in frequency domain.

In phase-shifting fringe projection profilometry, fringe harmonics caused by device nonlinearities as well as other factors may badly ruin the measurement results. Generally, the used phase-shifting algorithm enables restraint of effects of harmonics below a certain order depending on the number of phase shifts. When reducing the number of phase shifts for efficiency, high order harmonics will affect the phase-measuring results because of aliasing caused by insufficient sampling rate. To overcome this issue, this paper suggests a non-filtering technique operating in frequency domain, that enables improvement of measurement accuracy by eliminating effects of high order harmonics. With this technique, the phase-shifting algorithm is restated as a process of retrieving the fundamental complex fringes from the phase-shifted fringe patterns. Implementing a Fourier transform to this calculated complex fringe pattern, the actual fundamental signals and the aliased harmonics have their own lobes with separated peaks in the frequency domain. We reconstruct each order of the aliased harmonics by exploiting their relations with the fundamental signals and then estimate their magnitudes by using the spectral peaks. Instead of directly filtering the fringe spectrum, we subtract spectra of the harmonics from Fourier transform of the just calculated complex fringes, so that the Fourier spectrum of the fundamental fringes without harmonics is recovered through an iterative operation. Further, the phase map is measured accurately. Simulation and experimental results confirm that this proposed method can significantly suppress effects of fringe harmonics. Meanwhile, by taking advantage of non-filtering, it effectively preserves the edges and details of the measured surfaces from being blurred.

Phase error model and compensation method for reflectivity and distance discontinuities in fringe projection profilometry.

Phase shifting fringe projection profilometry is a widely used optical 3D surface measurement method due to its high resolution, high speed, and full-field inspection. However, the measurement accuracy decreases in regions with a reflectivity or distance discontinuity. To this end, first, a general continuous quasi-one-dimensional phase error model is proposed for discontinuity representation. Second, the discontinuities are further divided into degenerate and nondegenerate discontinuities to improve the computational speed. Third, a phase error compensation algorithm is proposed with a parameter estimation method to improve the measurement accuracy. Simulations and experiments demonstrate that the proposed methods are effective.

Multi-scale band-limited illumination profilometry for robust three-dimensional surface imaging at video rate.

Dynamic three-dimensional (3D) surface imaging by phase-shifting fringe projection profilometry has been widely implemented in diverse applications. However, existing techniques fall short in simultaneously providing the robustness in solving spatially isolated 3D objects, the tolerance of large variation in surface reflectance, and the flexibility of tunable working distances with meter-square-level fields of view (FOVs) at video rate. In this work, we overcome these limitations by developing multi-scale band-limited illumination profilometry (MS-BLIP). Supported by the synergy of dual-level intensity projection, multi-frequency fringe projection, and an iterative method for distortion compensation, MS-BLIP can accurately discern spatially separated 3D objects with highly varying reflectance. MS-BLIP is demonstrated by dynamic 3D imaging of a translating engineered box and a rotating vase. With an FOV of up to 1.7 m × 1.1 m and a working distance of up to 2.8 m, MS-BLIP is applied to capturing full human-body movements at video rate.

Suppressing motion-induced phase error by using equal-step phase-shifting algorithms in fringe projection profilometry.

Phase-shifting fringe projection profilometry is a widely used and important technique for three-dimensional surface measurement, where N-step fixed-step phase-shifting algorithms are commonly used. With a pressing need to apply this technique for dynamic object/scene measurement, the motion-induced error poses a challenge in achieving high measurement accuracy. A few correction methods have been developed by involving physical markers or complicated algorithms. In this paper, the equal-step phase-shifting algorithms are proposed as a simpler yet more effective solution. By approximating the phase variations as unknown but linear phase shifts, the equal-step algorithms are naturally immune to object motion. In particular, two classical algorithms, including the four-step Carré algorithm and the five-step Stoilov algorithm, are adopted. Furthermore, a novel three-step gradient-based equal-step phase-shifting (GEPS) algorithm is proposed. These equal-step algorithms are studied through comprehensive simulations and experiments, showing that, (i) the equal-step algorithms are all effective in greatly suppressing the motion-induced errors in both ideal and noisy situations; and (ii) among the three algorithms, the Stoilov algorithm is more robust to handle the object motion and the harmonics simultaneously, while the GEPS requires a least number of frames. This study will urge the use of the equal-step algorithms for phase extraction in dynamic profilometry for immediate motion-error suppression by merely implementing a single phase-calculation equation.

Blind Crosstalk Correction for Color Fringe Projection Profilometry Combining the Sine and Cosine Phase-Shifting Patterns

Color crosstalk is challenging for color fringe projection profilometry, which will cause color imbalance and phase-shift deviation, thus resulting in phase error. To address this challenge, this paper presents a blind crosstalk correction method for color phase-shifting fringe projection profilometry without crosstalk calibration. Three channels of the color fringe are firstly normalized to resolve color imbalance. The phase error induced by phase-shift deviation between three channels doubles the frequency of the color fringe. Therefore, the original cosine color fringe is shifted by quarter period to generate another sine color fringe to compensate the periodic phase error. Both simulations and experiments were carried out, and their results confirmed the effectiveness and accuracy of the proposed method.

Phase-Shifting Projected Fringe Profilometry Using Binary-Encoded Patterns

A phase unwrapping method for phase-shifting projected fringe profilometry is presented. It did not require additional projections to identify the fringe orders. The pattern used for the phase extraction could be used for phase unwrapping directly. By spatially encoding the fringe patterns that were used to perform the phase-shifting technique with binary contrasts, fringe orders could be discerned. For spatially isolated objects or surfaces with large depth discontinuities, unwrapping could be identified without ambiguity. Even though the surface color or reflectivity varied periodically with position, it distinguished the fringe order very well.

Single-shot 4-step phase-shifting multispectral fringe projection profilometry.

Phase-shifting profilometry (PSP) is considered to be the most accurate technique for phase retrieval with fringe projection profilometry (FPP) systems. However, PSP requires that multiple phase-shifted fringe patterns be acquired, usually sequentially, which has limited PSP to static or quasi-static imaging. In this paper, we introduce multispectral 4-step phase-shifting FPP that provides 3D imaging using a single acquisition. The method enables real-time profilometry applications. A single frame provides all four phase-shifted fringe patterns needed for the PSP phase retrieval algorithm. The multispectral nature of the system ensures that light does not leak between the spectral bands, which is a common problem in simultaneous phase-shifting with color cameras. With the use of this new concept, custom composite patterns containing multiple patterns can be acquired with a single acquisition.

A practitioner’s guide to fringe projection profilometry

Many techniques exist for 3D digitization of cultural heritage objects. Paintings, manuscripts, and other near-planar objects are especially challenging to digitize because of their minute surface variations. Of the existing techniques, fringe projection profilometry (FPP) is one of the most promising approaches for measuring the surface shape of such objects. In practical implementations of FPP, one needs to understand and control various sources of error due to system hardware and environmental conditions. It is difficult to find information on this in one place in the literature, which discourages application of the technique. In this paper we present a practitioner’s guide to phase-shifting fringe projection profilometry that covers critical but often omitted implementation details required for successful application of the technique.

Error-corrected fringe discrimination using nonary-encoded patterns for phase-shifting projected fringe profilometry

Most 3D profile measurements based on phase-shifting techniques require additional projected patterns to identify fringe orders for the task of phase unwrapping. The total number of projections is usually more than that used for phase extraction. For surfaces with low signal-to-noise ratios, these approaches might further encounter challenges in phase unwrapping. In this study, an error-corrected scheme for fringe discrimination using nonary-encoded patterns is presented. There is no need to take additional projections for phase unwrapping. The fringe patterns used for phase extraction can be analyzed to obtain the absolute phase directly. Any two adjacent fringes on the inspected surface can be discerned. To identify fringes for surfaces which are projected by only two fringes is available. Even though one of the projected fringes is decoded incorrectly, the error-corrected scheme can detect such a mistake and recover the fringe order.

High-speed dual-view band-limited illumination profilometry using temporally interlaced acquisition

We report dual-view band-limited illumination profilometry (BLIP) with temporally interlaced acquisition (TIA) for high-speed, three-dimensional (3D) imaging. Band-limited illumination based on a digital micromirror device enables sinusoidal fringe projection at up to 4.8 kHz. The fringe patterns are captured alternately by two high-speed cameras. A new algorithm, which robustly matches pixels in acquired images, recovers the object’s 3D shape. The resultant TIA–BLIP system enables 3D imaging over 1000 frames per second on a field of view (FOV) of up to 180 mm × 130 mm (corresponding to 1180 × 860 pixels ) in captured images. We demonstrated TIA–BLIP’s performance by imaging various static and fast-moving 3D objects. TIA–BLIP was applied to imaging glass vibration induced by sound and glass breakage by a hammer. Compared to existing methods in multiview phase-shifting fringe projection profilometry, TIA–BLIP eliminates information redundancy in data acquisition, which improves the 3D imaging speed and the FOV. We envision TIA–BLIP to be broadly implemented in diverse scientific studies and industrial applications.

Fringe harmonics elimination in multi-frequency phase-shifting fringe projection profilometry.

In fringe projection profilometry, the purpose of using two- or multi-frequency fringe patterns is to unwrap the measured phase maps temporally. Using the same patterns, this paper presents a least squares algorithm for, simultaneously with phase-unwrapping, eliminating the influences of fringe harmonics induced by various adverse factors. It is demonstrated that, for most of the points over the measured surface, projecting two sequences of phase-shifting fringe patterns having different frequencies enables providing sufficiently many equations for determining the coefficient of a high order fringe harmonic. As a result, solving these equations in the least squares sense results in a phase map having higher accuracy than that depending only on the fringe patterns of a single frequency. For the other few points which have special phases related to the two frequencies, this system of equations becomes under-determined. For coping with this case, this paper suggests an interpolation-based solution which has a low sensitivity to the variations of reflectivity and slope of the measured surface. Simulation and experimental results verify that the proposed method significantly suppresses the ripple-like artifacts in phase maps induced by fringe harmonics without capturing extra many fringe patterns or correcting the non-sinusoidal profiles of fringes. In addition, this method involves a quasi-pointwise operation, enabling correcting position-dependent phase errors and being helpful for protecting the edges and details of the measurement results from being blurred.

High-accuracy 3D shape measurement of translucent objects by fringe projection profilometry.

Acquiring complete and accurate 3D shape measurement results of translucent objects by fringe projection profilometry (FPP) is difficult because of the subsurface scattering effect. The phase offset introduces geometric errors, and the degraded image contrast leads to incomplete measurement results and random errors. In this research, a high-accuracy 3D shape measurement method for translucent objects based on phase-shifting FPP is proposed. The relationship between fringe period and phase error is investigated to determine the fringe periods. Random errors are suppressed by temporal noise reduction, and the robustness of multi-frequency heterodyne phase unwrapping is improved by increasing the interval of fringe periods along with temporal noise reduction. Geometric errors are compensated for by projecting multi-frequency fringe patterns to establish the relationship between fringe period and depth offset. Experimental results show that the proposed method can acquire complete measurement results and significantly reduce the overall error for measuring translucent objects.

Directly recognizing and removing the projector nonlinearity errors from a phase map in phase-shifting fringe projection profilometry

Abstract In phase-shifting fringe projection profilometry, the projector nonlinearity has been recognized as one of the main error-inducing factors, especially when only very few fringe patterns are available. For solving this issue, this paper presents a simple and effective method, that allows us to recognize and remove, directly from a calculated phase map, the nonlinearity-induced errors without calibrating the projector luminance or the phase errors in advance. In implementation, after filtering the phase map using a low-pass filter, we estimate the phase error coefficients by exploiting the dependence between the isolated artifacts and the smoothed phases under 3-sigma criterion. Furthermore, using the phase error function just estimated, the phase errors are corrected in a pointwise way through fixed-point iterations. Experimental results demonstrated that this method offers some advantages over others, such as being independent of a special nonlinearity model, being easy to implement and not requiring a prior calibration, protecting the edges and details of the measured shape from being blurred, and enabling dealing with time-variant projector nonlinearities.

Correction of projector nonlinearity in multi-frequency phase-shifting fringe projection profilometry.

In fringe projection profilometry, the original purpose of projecting multi-frequency fringe patterns is to determine fringe orders automatically, thus unwrapping the measured phase maps. This paper presents that using the same patterns, simultaneously, allows us to correct the effects of projector nonlinearity on the measured results. As is well known, the projector nonlinearity decreases the measurement accuracies by inducing ripple-like artifacts on the measured phase maps; and, theoretical analysis reveals that these artifacts, depending on the number of phase shifts, have multiplied frequencies higher than the fringe frequencies. Based on this fact, we deduce an error function for modeling the phase artifacts and then suggest an algorithm estimating the function coefficients from a couple of phase maps of fringe patterns having different frequencies. As a result, subtracting out the estimated phase errors yields the accurate phase maps with the effects of the projector nonlinearity on them being suppressed significantly. Experiment results demonstrated that this proposed method offers some advantages over others, such as working without a photometric calibration, being applicable when the projector nonlinearity varies over time, and having satisfied efficiency in implementation.

Phase accuracy evaluation for phase-shifting fringe projection profilometry based on uniform-phase coded image

Phase-shifting fringe projection profilometry (PSFPP) is a three-dimensional (3D) measurement technique widely adopted in industry measurement. It recovers the 3D profile of measured objects with the aid of the fringe phase. The phase accuracy is among the dominant factors that determine the 3D measurement accuracy. Evaluation of the phase accuracy helps refine adjustable measurement parameters, contributes to evaluating the 3D measurement accuracy, and facilitates improvement of the measurement accuracy. Although PSFPP has been deeply researched, an effective, easy-to-use phase accuracy evaluation method remains to be explored. In this paper, methods based on the uniform-phase coded image (UCI) are presented to accomplish phase accuracy evaluation for PSFPP. These methods work on the principle that the phase value of a UCI can be manually set to be any value, and once the phase value of a UCI pixel is the same as that of a pixel of a corresponding sinusoidal fringe pattern, their phase accuracy values are approximate. The proposed methods provide feasible approaches to evaluating the phase accuracy for PSFPP. Furthermore, they can be used to experimentally research the property of the random and gamma phase errors in PSFPP without the aid of a mathematical model to express random phase error or a large-step phase-shifting algorithm. In this paper, some novel and interesting phenomena are experimentally uncovered with the aid of the proposed methods.

Regional fringe analysis for improving depth measurement in phase-shifting fringe projection profilometry

This study proposes a regional fringe analysis (RFA) method to detect the regions of a target object in captured shifted images to improve depth measurement in phase-shifting fringe projection profilometry (PS-FPP). In the RFA method, region-based segmentation is exploited to segment the de-fringed image of a target object, and a multi-level fuzzy-based classification with five presented features is used to analyze and discriminate the regions of an object from the segmented regions, which were associated with explicit fringe information. Then, in the experiment, the performance of the proposed method is tested and evaluated on 26 test cases made of five types of materials. The qualitative and quantitative results demonstrate that the proposed RFA method can effectively detect the desired regions of an object to improve depth measurement in the PS-FPP system.

Self-correction of projector nonlinearity in phase-shifting fringe projection profilometry

In phase-shifting fringe projection profilometry, the luminance nonlinearity of the used projector has been recognized as one of the most crucial factors decreasing the measurement accuracy. To solve this problem, this paper presents a self-correcting technique that allows us to suppress the effect of the projector nonlinearity in the absence of any calibration data regarding the projector intensities or regarding the phase errors. In its first step, the standard phase-shifting algorithm is used to recover the phases, as well as the background intensities and the modulations. Using these results enables normalizing the fringe patterns, for ridding them of the effects of the background and modulations. Second, we smooth the calculated phase map by use of a low-pass filter in order to remove the ripple-like phase errors induced by the projector nonlinearity. Third, we determine a polynomial representing the projector nonlinearity by fitting the curve of the normalized fringe intensities against the cosine values of the smoothed phases. Finally, we correct the phase errors using the curve just obtained. Doing these steps in an iterative way eventually results in a phase map and, further, a 3D shape with their artifacts induced by the projector nonlinearity suppressed significantly. Experimental results demonstrate that this technique offers some advantages over others. It does not require a prior calibration of the projector, thus being suitable for dealing with a time-variant nonlinearity; its pointwise operation protects the edges and details of the measurement results from being blurred; and it works well with very few fringe patterns and is efficient in image capturing.