Phase-shifting Profilometry Research Articles

Suppression of the nonlinear phase error in phase shifting profilometry: considering non-smooth reflectivity and fractional period.

Hilbert transform (HT) has been employed to compensate phase error arising from the nonlinear effect in phase shifting profilometry (PSP). However, in most common situations, pure HT may lead to a significant system error, which has a negative impact on subsequent phase error compensation. In this paper, system error from HT of non-stationary and non-continuous fringe is analyzed, and then a novel phase error suppression approach is presented. The cosine fringe without direct current (DC) component is reconstructed to eliminate the influence of non-smooth reflectivity, and the fractional periods at both ends of the reconstructed fringe are extended to generate fringe with integer number of periods. And then the HT is applied to the reconstructed and extended fringe. Finally, a revised phase-shifting algorithm is employed to calculate the phase with the fringe after HT. The proposed approach is suitable for PSP of the surface with non-smooth reflectivity (e.g. texture of complex colors), which is demonstrated in a series of experiments.

Motion-induced error compensation for phase shifting profilometry.

This paper proposes a novel method to substantially reduce motion-introduced phase error in phase-shifting profilometry. We first estimate the motion of an object from the difference between two subsequent 3D frames. After that, by leveraging the projector's pinhole model, we can determine the motion-induced phase shift error from the estimated motion. A generic phase-shifting algorithm considering phase shift error is then utilized to compute the phase. Experiments demonstrated that proposed algorithm effectively improved the measurement quality by compensating for the phase shift error introduced by rigid and nonrigid motion for a standard single-projector and single-camera digital fringe projection system.

Instability of projection light source and real-time phase error correction method for phase-shifting profilometry.

The time-dependent phase error induced by the instability of projection light source (IPLS) is systematically studied for phase-shifting profilometry (PSP). The IPLS of the projection device is investigated by a specially designed experimental setup. Based on the results of the investigation, a new mathematical model to analyze the time-dependent phase error induced by IPLS is established and verified. Two real-time phase error correction methods using a new designed three-dimensional shape measurement system are proposed for the effect of IPLS. Experimental results demonstrate the two methods can effectively eliminate the induced time-dependent phase error with a good robustness and high accuracy. The two real-time correction methods for PSP will be promising for high-accuracy measurements.

Fringe shaping for high-/low-reflectance surface in single-trial phase-shifting profilometry

This study describes a novel fringe-shaping technique developed to alleviate the fringe truncation problem engendered by the acquired saturated and/or weak fringe images from high-/low-reflectance surfaces of three-dimensional (3D) objects in phase-shifting profilometry. The particle swarm optimization algorithm is employed to perform the recovery of the truncated fringes with optimal fitting for compensation after single-trial acquisition. The results show that the proposed method improves phase recovery accuracy to accomplish 3D surface reconstruction with only one set of phase-shifting fringes under different truncation sceneries.

Robust dynamic 3-D measurements with motion-compensated phase-shifting profilometry

Phase-shifting profilometry (PSP) is a widely used approach to high-accuracy three-dimensional shape measurements. However, when it comes to moving objects, phase errors induced by the movement often result in severe artifacts even though a high-speed camera is in use. From our observations, there are three kinds of motion artifacts: motion ripples, motion-induced phase unwrapping errors, and motion outliers. We present a novel motion-compensated PSP to remove the artifacts for dynamic measurements of rigid objects. The phase error of motion ripples is analyzed for the N-step phase-shifting algorithm and is compensated using the statistical nature of the fringes. The phase unwrapping errors are corrected exploiting adjacent reliable pixels, and the outliers are removed by comparing the original phase map with a smoothed phase map. Compared with the three-step PSP, our method can improve the accuracy by more than 95% for objects in motion.

High-precision real-time 3D shape measurement based on a quad-camera system

Phase-shifting profilometry (PSP) based 3D shape measurement is well established in various applications due to its high accuracy, simple implementation, and robustness to environmental illumination and surface texture. In PSP, higher depth resolution generally requires higher fringe density of projected patterns which, in turn, lead to severe phase ambiguities that must be solved with additional information from phase coding and/or geometric constraints. However, in order to guarantee the reliability of phase unwrapping, available techniques are usually accompanied by increased number of patterns, reduced amplitude of fringe, and complicated post-processing algorithms. In this work, we demonstrate that by using a quad-camera multi-view fringe projection system and carefully arranging the relative spatial positions between the cameras and the projector, it becomes possible to completely eliminate the phase ambiguities in conventional three-step PSP patterns with high-fringe-density without projecting any additional patterns or embedding any auxiliary signals. Benefiting from the position-optimized quad-camera system, stereo phase unwrapping can be efficiently and reliably performed by flexible phase consistency checks. Besides, redundant information of multiple phase consistency checks is fully used through a weighted phase difference scheme to further enhance the reliability of phase unwrapping. This paper explains the 3D measurement principle and the basic design of quad-camera system, and finally demonstrates that in a large measurement volume of 200 mm × 200 mm × 400 mm, the resultant dynamic 3D sensing system can realize real-time 3D reconstruction at 60 frames per second with a depth precision of 50 μm.

Black-Box Phase Error Compensation for Digital Phase-Shifting Profilometry

Due to the nonlinear response of digital phase-shifting profilometry (PSP), phase errors are inevitable in the retrieved 3-D profiles and result in negative impacts on the measurement accuracy of the PSP system. A novel method is presented in this paper to reduce the impact. Instead of compensating phase errors in the retrieved 3-D profile, specific harmonics are superimposed upon the initial fringe pattern actively to adjust the amplitudes of the harmonics in the captured fringe image with the intention to suppress the phase error, and all nonlinear response of the PSP system can be compensated in theory. Furthermore, it does not consume additional time in the 3-D profile reconstruction process. Experimental results are shown to demonstrate the validity of the method.

Optimal defocus selection based on normed Fourier transform for digital fringe pattern profilometry.

Owing to gamma-effect robustness and high-speed imaging capabilities, projector defocusing of binary-coded fringe patterns is by far the most widely used and effective technique in generating sinusoidal fringe patterns for three-dimensional optical topography measurement with digital fringe projection techniques. However, this technique is not trouble-free. It is borne with uncertainty and challenges mainly because it remains somewhat difficult to quantify and ascertain the level of defocus required for desired fidelity in sinuousness of the projected fringe pattern. Too much or too little defocusing will affect the sinuosity accuracy of fringe patterns and consequently jeopardize the quality of the measurement results. In this paper, by combining intrinsic phase spectral sensitivities and normed Fourier transform, a method to quantify the amount of defocus and subsequently select the optimal degree of sinuosity for generating digital sinusoidal fringe patterns with projector defocusing for fringe pattern optical three-dimensional profilometry is proposed. Numerical simulations plus experiments give evidence of the feasibility and validity of the proposed method in enabling an improved digital binary defocusing technique for optical phase-shift profilometry using the digital fringe projection technique.

Microsphere-assisted phase-shifting profilometry.

In the present work, we have investigated the combination of a superresolution microsphere-assisted 2D imaging technique with low-coherence phase-shifting interference microscopy. The imaging performance of this technique is studied by numerical simulation in terms of the magnification and the lateral resolution as a function of the geometrical and optical parameters. The results of simulations are compared with the experimental measurements of reference gratings using a Linnik interference configuration. Additional measurements are also shown on nanostructures. An improvement by a factor of 4.7 in the lateral resolution is demonstrated in air, thus giving a more isotropic nanometric resolution for full-field surface profilometry in the far field.

Phase-shifting profilometry combined with Gray-code patterns projection: unwrapping error removal by an adaptive median filter.

Phase-shifting profilometry combined with Gray-code patterns projection has been widely used for 3D measurement. In this technique, a phase-shifting algorithm is used to calculate the wrapped phase, and a set of Gray-code binary patterns is used to determine the unwrapped phase. In the real measurement, the captured Gray-code patterns are no longer binary, resulting in phase unwrapping errors at a large number of erroneous pixels. Although this problem has been attended and well resolved by a few methods, it remains challenging when a measured object has step-heights and the captured patterns contain invalid pixels. To effectively remove unwrapping errors and simultaneously preserve step-heights, in this paper, an effective method using an adaptive median filter is proposed. Both simulations and experiments can demonstrate its effectiveness.

Motion-induced error reduction by combining Fourier transform profilometry with phase-shifting profilometry.

We propose a hybrid computational framework to reduce motion-induced measurement error by combining the Fourier transform profilometry (FTP) and phase-shifting profilometry (PSP). The proposed method is composed of three major steps: Step 1 is to extract continuous relative phase maps for each isolated object with single-shot FTP method and spatial phase unwrapping; Step 2 is to obtain an absolute phase map of the entire scene using PSP method, albeit motion-induced errors exist on the extracted absolute phase map; and Step 3 is to shift the continuous relative phase maps from Step 1 to generate final absolute phase maps for each isolated object by referring to the absolute phase map with error from Step 2. Experiments demonstrate the success of the proposed computational framework for measuring multiple isolated rapidly moving objects.

Fast three-dimensional measurements for dynamic scenes with shiny surfaces

This paper presents a novel fringe projection technique for fast three-dimensional (3-D) shape measurements of moving highly reflective objects. By combining the standard three-step phase-shifting fringe patterns with a digital speckle image, dynamic 3-D reconstructions of shiny surfaces can be efficiently achieved with only four projected patterns. The phase measurement is performed by three-step phase-shifting algorithm as it uses the theoretical minimum number of fringe patterns for phase-shifting profilometry. To avoid the camera saturation, a dual-camera fringe projection system is built to measure shiny objects from two different directions. The erroneous phase obtained from a saturated pixel is corrected by the phase of its corresponding pixel in the other view which is free from the saturation problem. To achieve high measurement accuracy, the corresponding high light intensity areas in cameras are found by sub-pixel matches of the speckle pattern in either view. Benefited from the trifocal tensor constraint, the corresponding points in the two wrapped phase maps can be directly established, and thus, the difficulties in determining the correct fringe order for the discontinuous or isolated surfaces can be effectively bypassed. Experimental results indicate that the proposed method is able to successfully measure highly reflective surfaces for both stationary and dynamic scenes.

Phase error analysis and compensation for phase shifting profilometry with projector defocusing

Phase shifting profilometry (PSP) using binary fringe patterns with projector defocusing is promising for high-speed 3D shape measurement. To obtain a high-quality phase, the projector usually requires a high defocusing level, which leads to a drastic fall in fringe contrast. Due to its convenience and high speed, PSP using squared binary patterns with small phase shifting algorithms and slight defocusing is highly desirable. In this paper, the phase accuracies of the classical phase shifting algorithms are analyzed theoretically, and then compared using both simulation and experiment. We also adapt two algorithms for PSP using squared binary patterns, which include a Hilbert three-step PSP and a double three-step PSP. Both algorithms can increase phase accuracy, with the latter featuring additional invalid point detection. The adapted algorithms are also compared with the classical algorithms. Based on our analysis and comparison results, proper algorithm selection can be easily made according to the practical requirement.

Applying innovative stripes adaptive detection to three-dimensional measurement of color fringe profilometry

This study developed a 3D software and hardware measurement system, and proposes an innovative stripes adaptive detection algorithm. The fringe intensity is regulated automatically according to the reflection coefficient of different analytes, in order to avoid overexposure. For the measurement of the object in discontinuously changing height, a novel intensity difference coding unwrapping phase technology is used, thus overcoming the technological bottleneck of traditional phase unwrapping. In order to increase the measurement efficiency, the stripe pattern is combined with intensity coding pattern by three-channel color information, in order to generate an adaptive compound color stripe pattern. The measurement efficiency is increased by approximately two times compared with traditional gray stripe pattern. In order to increase the measurement accuracy, the uneven brightness is corrected by using brightness gain function. The three-channel intensity nonlinear response is corrected by cubic spline interpolation system response inverse function. The three-channel image is corrected by color cross-talk correction technology. The experiment proved that the system repeatability is 20µm. The traditional phase-shifting profilometry is improved successfully, overcoming the technical measurement bottleneck of discontinuous change in the analyte height, so as to attain low cost, high measurement accuracy, efficiency and measurement reliability.

Three-dimensional surface imaging by multi-frequency phase shift profilometry with angle and pattern modeling for system calibration

In this paper, we present a 3D surface imaging system based on the well-known phase shift profilometry. To yield the analytical solutions, four shifted phases and three high carrier frequencies are used to compute the phase map and reduce the noises that are caused by the inherent optical aberrations and external influences, e.g. different illumination light sources, uneven intensity distribution and automatic image processing algorithms. To reduce the system noise, we propose to model the pattern of the calibration grid in a virtual space. To obtain the modeled pattern, we use a plane to intercept the rays that are modeled by the proposed angle modeling method. In the world coordinate system, the angle and the pattern are computed based on the calibration data. A registration method is used to transform the modeled pattern in the virtual space to the ideal pattern in the world coordinate system by computing the least squared errors between the true points in the modeled pattern and the measured points in the practical pattern. The modeled (true) points are used for re-calibration of the 3D imaging system. Experimental results showed that the measurement accuracy increases considerably and the MSE is reduced from 0.95 mm to 0.65 mm (32% average error decrease) after replacing the measured points with the true points for calibration.

Recovery of absolute phases for the fringe patterns of three selected wavelengths with improved anti-error capability

In a recent published work, we proposed a technique to recover the absolute phase maps of fringe patterns with two selected fringe wavelengths. To achieve higher anti-error capability, the proposed method requires employing the fringe patterns with longer wavelengths; however, longer wavelength may lead to the degradation of the signal-to-noise ratio (SNR) in the surface measurement. In this paper, we propose a new approach to unwrap the phase maps from their wrapped versions based on the use of fringes with three different wavelengths which is characterized by improved anti-error capability and SNR. Therefore, while the previous method works on the two-phase maps obtained from six-step phase-shifting profilometry (PSP) (thus 12 fringe patterns are needed), the proposed technique performs very well on three-phase maps from three steps PSP, requiring only nine fringe patterns and hence more efficient. Moreover, the advantages of the two-wavelength method in simple implementation and flexibility in the use of fringe patterns are also reserved. Theoretical analysis and experiment results are presented to confirm the effectiveness of the proposed method.

Digital multi-step phase-shifting profilometry for three-dimensional ballscrew surface imaging

A digital multi-step phase-shifting profilometry for three-dimensional (3-D) ballscrew surface imaging is presented. The 3-D digital imaging system is capable of capturing fringe pattern images. The straight fringe patterns generated by software in the computer are projected onto the ballscrew surface by the DLP projector. The distorted fringe patterns are captured by the CCD camera at different detecting directions for reconstruction algorithms. The seven-step phase-shifting algorithm and quality guided path unwrapping algorithm are used to calculate absolute phase at each pixel position. The 3-D calibration method is used to obtain the relationship between the absolute phase map and ballscrew shape. The angular dependence of 3-D shape imaging for ballscrews is analyzed and characterized. The experimental results may provide a novel, fast, and high accuracy imaging system to inspect the surface features of the ballscrew without length limitation for automated optical inspection industry.

An improved two-step phase-shifting profilometry

An improved two-step phase-shifting profilometry is put forward in three-dimensional (3D) shape measurement. Firstly, two phase-shifted randomly sinusoidal fringe patterns are projected onto the tested object by digital-light-processing (DLP) projector. The fringe patterns modulated with the object's surface are captured by a CCD camera. Secondly, the background and modulation components are obtained by parameter estimation using the least square method; fringe normalization is accomplished by the background bias removal and modulation normalization of a given deformed fringe. Then based on the statics characteristics of fringe gray, the phase step between two phase-shifted randomly sinusoidal fringe patterns is determined by using the inverse cosine function. Then, the phase is extracted from the two frame's normalized patterns and the step value. Finally, the experimental evaluation is conducted to prove the validity and performance of the proposed method. The experimental result is analyzed and compared with that of the method by reference 16. The effectiveness and superiority of the proposed method has been demonstrated.

Flexible phase error compensation based on Hilbert transform in phase shifting profilometry.

This paper makes use of Hilbert transform to analyze and compensate the phase error caused by the nonlinear effect in phase shifting profilometry (PSP). The characteristics of the phase error distribution in Hilbert transform domain was analyzed and compared with spatial domain. A simple and flexible phase error compensation method was proposed to directly process the phase-shifting fringe images without any auxiliary conditions or complicated computation. Experimental results demonstrated that the phase error can be reduced by about 80% in three-step PSP, and more than 95% in four or more step PSP, which verified the effectiveness, flexibility, robustness and automation of the proposed phase error compensation method.

Phase unwrapping method based on multiple fringe patterns without use of equivalent wavelengths

In order to decrease the noise enhancement in the process of phase unwrapping, we present a new phase unwrapping approach for multiple wavelength phase shift profilometry. In this approach, a series of fringe images with only three wavelengths are captured by the 3D measurement system, and it does not need to calculate the equivalent wavelengths and the equivalent phases. As a result, the noise enhancement is avoided, leading to improved precision in the absolute phase map recovery. Experiment results demonstrate that the proposed method is more robust and effective compared to the existing TWPSP method.