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

Parameter selection on a multi-exposure fusion method for measuring surfaces with varying reflectivity in microscope fringe projection profilometry

As industrial and scientific advancements continue, the demand for precise measurement of three-dimensional (3D) shapes and surfaces is steadily increasing. However, accurate 3D measurement of certain surfaces, especially those with varying reflectivities, has always been a challenging issue. Multi-exposure fusion methods have shown stable, high-quality measurement results, but the selection of parameters for these methods has largely been based on experience. To address this issue, this paper has improved the multi-exposure fusion method and introduced a guided approach for parameter selection, significantly enhancing the completeness of measurement results. Additionally, a comparative model is developed to experimentally validate the specific impacts of Gaussian window variance, optimal grayscale range, and attenuation factor variance on the integrity of 3D reconstruction. The experimental results demonstrate that under the guidance of the parameter adjustment method proposed in this paper, the multi-exposure fusion for measuring the 3D topography of high-dynamic surfaces improves the restoration coverage from the original 86% (bright areas) and 50% (dark areas) to over 99%. This provides a selection strategy for parameter adjustment guidance in precise measurements based on the multi-exposure method.

Accurate 3D Measurement of Complex Texture Objects by Height Compensation Using a Dual-Projector Structure

Fringe projection profilometry is a widely used technique for 3D measurement due to its high accuracy and speed. However, the accuracy significantly decreases when measuring complex texture objects, especially in the junction of different colors. This paper analyzes the causes of errors resulting from complex textures and proposes a height compensation method to revise the error by employing a dual-projector structure. Moreover, the dual-projector is capable of acquiring a pair of errors with opposite signs, which can be utilized to calculate the accurate 3D information after determining the ratio of this pair of errors. Experiments provide significant improvement in measuring complex texture objects, demonstrating the proposed method's ability.

Enhanced Fourier-Hilbert-transform suppression for saturation-induced phase error in phase-shifting profilometry

Intensity saturation tends to induce severe errors in high dynamic range three-dimensional measurements using structured-light techniques. This paper presents an enhanced Fourier-Hilbert-transform (EFHT) method to suppress the saturation-induced phase error in phase-shifting profilometry, by considering three types of residual errors: nonuniform-reflectivity error, phase-shift error, and fringe-edge error. Background normalization is first applied to the saturated fringe patterns to suppress the effect of the nonuniform reflectivity. A self-correction method is proposed to correct the large phase-shift error in the compensated phase. The self-corrected phase error is detected to assist in locating the fringe-edge area, within which the true phase is computed based on the sub-period phase error model. Experimental results demonstrated the effectiveness of the proposed method in suppressing the saturation-induced phase error and other three types of residual errors with fewer images.

Nonlinear error reduction for phase-shifting profilometry considering periodicity and symmetry of a phase histogram

Phase-shifting profilometry is extensively utilized for three-dimensional (3D) measurement. However, because of gamma nonlinearity, the image intensities of the captured fringe patterns are regrettably distorted. An effective nonlinear error reduction method without requiring parameter estimation is presented in this paper. Differing from the traditional whole-period phase histogram equalization (PHE) method, our method takes into account not only the periodicity but also the symmetry of the phase histogram. Taking a three-step phase-shifting algorithm as an example, the phase error frequency triples the fringe frequency; thus, we first propose a 1/3-period PHE method. Moreover, since the phase error distribution is sinusoidal with symmetry, we further propose a 1/6-period PHE method. Simulations and experiments both indicate that the 1/6-period PHE method, compared with the whole-period PHE and 1/3-period PHE methods, can further reduce the nonlinear error.

Fringe Projection Profilometry Based on Saturated Fringe Restoration in High Dynamic Range Scenes

In high dynamic scenes, fringe projection profilometry (FPP) may encounter fringe saturation, and the phase calculated will also be affected to produce errors. This paper proposes a saturated fringe restoration method to solve this problem, taking the four-step phase shift as an example. Firstly, according to the saturation of the fringe group, the concepts of reliable area, shallow saturated area, and deep saturated area are proposed. Then, the parameter A related to the reflectivity of the object in the reliable area is calculated to interpolate A in the shallow and deep saturated areas. The theoretically shallow and deep saturated areas are not known in actual experiments. However, morphological operations can be used to dilate and erode reliable areas to produce cubic spline interpolation areas (CSI) and biharmonic spline interpolation (BSI) areas, which roughly correspond to shallow and deep saturated areas. After A is restored, it can be used as a known quantity to restore the saturated fringe using the unsaturated fringe in the same position, the remaining unrecoverable part of the fringe can be completed using CSI, and then the same part of the symmetrical fringe can be further restored. To further reduce the influence of nonlinear error, the Hilbert transform is also used in the phase calculation process of the actual experiment. The simulation and experimental results validate that the proposed method can still obtain correct results without adding additional equipment or increasing projection number, which proves the feasibility and robustness of the method.

Generic saturation-induced phase error correction for structured light 3D shape measurement

Intensity saturation is a challenging problem in structured light 3D shape measurement. Most of the existing methods achieve high dynamic range (HDR) measurement by sacrificing measurement speed, making them limited in high-speed dynamic applications. This Letter proposes a generic efficient saturation-induced phase error correction method for HDR measurement without increasing any fringe patterns. We first theoretically analyze the saturated signal model and deduce the periodic characteristic of saturation-induced phase error. Based on this, we specially design a saturation-induced phase error correction method by joint Fourier analysis and Hilbert transform. Furthermore, the relationship among phase error, saturation degree, and number of phase-shifting steps is established by numerical simulation. Since the proposed method requires no extra captured images or complicated intensity calibration, it is extremely convenient in implementation and is applicable to performing high-speed 3D shape measurements. Simulations and experiments verify the feasibility of the proposed method.

Intensity-Averaged Double Three-Step Phase-Shifting Algorithm with Color-Encoded Fringe Projection

Fringe projection profilometry (FPP) has been broadly employed for three-dimensional shape measurements. However, the measurement accuracy suffers from gamma nonlinearity. This paper proposes an intensity-averaged double three-step phase-shifting (IDTP) algorithm making use of color-encoded fringe projection, which does not require complex calibration processes or extra fringe patterns. Specifically, two phase maps with π/2 phase shift are encoded into the red and blue channels of color fringe patterns. The average fringe patterns of the red and blue channels are approximately in sinusoidal waveform with little harmonics, thus can be directly used for accurate phase recovery. Additionally, an adaptive weight is also estimated for average operation to suppress the effect of color crosstalk. Both simulations and experiments demonstrate that the proposed IDTP algorithm can effectively eliminate nonlinear phase errors.

Defocused binary fringe phase error modeling and compensation using depth-discrete Fourier series fitting

The binary defocus fringe projection is a widely adopted way to increase the speed of fringe projection profilemotry. However, the projected patterns may deviate from ideal ones at some depths. We propose a theoretical model and a corresponding compensation method to explain and calibrate the phase error of defocus-projected patterns. We first low-pass filter the projected patterns at different depths to obtain corresponding ideal ones. Then, we calibrate the model coefficients based on the errors between the original and ideal fringe patterns. The calibrated phase error model can be used to compensate the phase error at arbitrary depths within the calibration volume. Experiments are conducted to verify the feasibility and performance of the proposed method.

Real-time motion-induced-error compensation in 3D surface-shape measurement

Object motion can introduce unknown phase shift and thus measurement error in multi-image phase-shifting methods of fringe projection profilometry. This paper presents a new method to estimate the unknown phase shifts and reduce the motion-induced error by using three phase maps computed over a multiple measurement sequence and calculating the difference between phase maps. The pixel-wise estimation of the motion-induced phase shifts permits phase-error compensation for non-homogeneous surface motion. Experiments demonstrated the ability of the method to reduce motion-induced error in real-time, for shape measurement of surfaces with high depth variation, and moving and deforming surfaces.

Multiple-gamma-value based phase error compensation method for phase measuring profilometry

Three-dimensional measurement based on fringe projection has been widely used. However, the gamma nonlinearity and system nonlinearities usually result in significant phase error. Furthermore, there are various gamma values due to the non-uniform brightness distribution of the projector and nonlinear factors of the system, which makes the problem more complicated. To solve this problem, a sub-area compensation method based on multiple gamma values is proposed. In the beginning, a uniform image is projected on a standard whiteboard with a smooth surface. The obtained image is partitioned by using histogram statistics. Then, different phase error models are established for different regions. Finally, the phase error is compensated according to the regions. By applying this method, the accuracy of the phase algorithm is greatly improved. The method is simple and convenient compared with the existing methods.