Status, challenges, and future perspectives of fringe projection profilometry

In traditional phase measuring profilometry (PMP) setup, the connecting line between the exit pupil center of projector and entrance pupil center of CCD camera must parallel to the reference plane and the optical axes of projector and CCD camera must intersect at the same point on the reference plane. At this condition, the coefficients of phase-to-height mapping are constants because they are proved to be only dependent on the structural parameters. But lots of experimental results show that some of coefficients are not constants. Further analyzing this phenomenon, it is found that the above two restricted conditions can hardly to be guaranteed due to the invisible of the exit pupil, the entrance pupil and the optical axes. The more popular situation is that the above connecting line may not parallel to the reference plane and the above optical axes do not intersect on the reference plane. So a new universal mapping algorithm is derived at this situation. It reveals some of coefficients of the mapping really remain constants which are dependent on only the structural parameters, while some of coefficients are really not constants which are dependent on not only the structural parameters but also the phase distribution of the reference plane. It also reveals that the traditional mapping algorithm is just a special case of the derived mapping algorithm. Furthermore, it reveals that the accuracy of PMP can be improved distinctly by calibrating the phase of the reference plane. Experimental results have shown the feasibility and validity of the derived phase-to-height mapping algorithm.

Intrinsic feature revelation of phase-to-height mapping in phase measuring profilometry

Establishing a highly accurate phase-to-height mapping relationship is very important in fringe projection profilometry, which guarantees the accuracy of final three-dimensional reconstruction. The influence coming from lens distortion, random noises, and the nontelecentric projecting and imaging of the measurement system is analyzed in detail, followed by the exhaustive discussion of a more accurate phase-to-height mapping method. The mapping tabulation between absolute phase and height information is set up by the piecewise linear fitting method within the whole measurement range for per-pixel. Our method is compared with the previously used methods, such as linear fitting (LF), quadratic fitting (QF), and cubic fitting (CF) methods. Computer simulations and experiments verify that the reconstructed height distribution employing our method is more accurate than either LF or QF methods when the random noise is obvious. In addition, if the random noise can be controlled to low level and the lens distortion is considered, the reconstruction accuracy of our method is better than that of the CF method.

Discussion on accurate phase–height mapping in fringe projection profilometry

Flexible and high-accuracy method for uni-directional structured light system calibration

Whole-field high precision point to point calibration method

In phase measurement profilometry (PMP), the projector can be regarded as another camera according to the reversibility of the light path principle. The relationship of projecting spatial points to image plane of camera and projector is studied, and the phase–height mapping equation without projector distortion is obtained. The equation is then expanded to a polynomial for the convenience of calibration. Furthermore, the relation between the distortion value and the phase is investigated. Finally the phase–height mapping algorithm considering projector distortion and its polynomial expression are acquired. The accuracy of approximation is studied and compared with another two existing algorithms by computer simulation. It is revealed that the absolute error of the new algorithm expressed with quartic polynomial reaches 5.380× 10−3 mm and its standard deviation reaches 3.354× 10−4 mm under general lens distortion. The accuracy of the new algorithm is the highest among the three algorithms. In experiment, t...

Accurate phase–height mapping algorithm for PMP

The measurement of transparent objects has always been regarded as one of the difficult problems in 3D reconstruction technology. For transparent objects conforming to the birefringence model, we propose a method for measuring the parameters of transparent objects based on multi-wavelength incident light. This paper analyzes the transparent objects where light enters the birefringence model. Because the transparent objects refract light of different wavelengths differently, when the lights with different wavelengths emitted from the same point and same direction passes through the transparent objects, the position and direction of light with different wavelength will come out differently. The position and direction of these outgoing rays are related to the refractive index and surface topography of the transparent objects. By obtaining the equations of these outgoing rays, we can derive the equations of the refractive index and surface topography of the transparent objects. In this paper, the incident light obtained by computer simulation is used as the initial data, and the simulated annealing algorithm is used to verify the model. The final results show that within the range of random error values given by the computer, the surface shape, curvature, thickness and refractive index of transparent objects with small error values can be obtained. At the same time, this paper introduces the Ceres Solver C++ nonlinear optimization library into the simulated annealing algorithm, which improves the speed and accuracy of the algorithm and greatly enhances the robustness of the algorithm.

Qingyang Wu

Papers

Accurate phase–height mapping algorithm for PMP

Research on transparent object measurement based on multi-wavelength ray tracing technology