Effective camera calibration by using phase-shifting fringe patterns

A novel phase-shifting profilometry to realize temporal phase unwrapping simultaneously with the least fringe patterns

Phase-shifting interferometry is a highly accurate technique for obtaining phase distribution from the recorded fringe patterns. Generally, phase-shifting interferometry requires recording several fringe patterns with varying phase shifts experimentally and during the acquisition, the object must be stable. Also, the atmospheric turbulence and mechanical conditions should also remain constant during this time. These requirements limit the use of these phase-shifting interferometric techniques in dynamic event studies. In the present work, we introduce Riesz transformed based digital four-step phase-shifting interferometer to obtain phase distribution from a single recorded fringe pattern. All the experimental phase-shifting setups necessary to realize the phase-shifting are removed. The idea is based on the recording of a single fringe pattern, and computes its Riesz transform at first, second and third-orders. The obtained Riesz transform components are combined to generate three π/2 phase-shifted fringe patterns, and then, the phase distribution is obtained from these phase-shifted fringe patterns. The performance of this method is demonstrated first by using numerical simulation and the quantitative appraisal is given by using image quality index. Further, we apply this technique on a real fringe pattern recorded in digital speckle pattern interferometry (DSPI). The obtained results reveal that our method provides a simple and accurate solution for phase evaluation, therefore, makes it suitable for real-time measurements.

In this paper, we propose a novel technique for quantitative phase measurements of vibrating structures based on additive-subtractive speckle interferometry. Additive fringe patterns (of poor visibility) corresponding to the object deformation are obtained by pulsing the laser illumination at times when the deformation is at its maximum and minimum amplitudes. A relative inter-pulse phase shift is introduced within each repetitive deformation cycle (e.g. +(pi) /2 for the maximum and -(pi) /2 for the minimum amplitudes respectively) to obtain two consecutive conjugate pairs of phase-shifted additive fringe patterns. Additionally, and inter-frame phase shift is introduced between the conjugate pairs of additive fringe patterns, which are then subtracted and rectified to provide a phase-shifted additive-subtractive fringe pattern of good visibility. Typically four such phase-shifted additive-subtractive fringe patterns with relative phase shift of (pi) /2 between each other are obtained, and these are used to calculate the deformation phase map from which the vibration measurement of a circular membrane. The ability of the technique to perform in relatively severe noisy environments is demonstrated.

Phase measuring deflectometry (PMD) is a well-established method for determining the topography of specular freeform surfaces. A disadvantage of the classical PMD method, however, is the sequential measurement process - it requires at least six camera images of phase-shifted sinusoidal fringe patterns for one measurement. Therefore, for moving objects in industrial production, as well as for non-fixable objects such as the human cornea, the classical PMD evaluation is not suitable anymore. To overcome this problem, single-shot methods using single-side-band demodulation have been presented, which allow for a deflectometric measurement based on just one single image capture. However, this kind of evaluation does not work for complex surface geometries that result in broadband fringe patterns, since the phase is only considered globally in the Fourier space. A new single-shot evaluation method for the phase determination using the Continuous Wavelet Transform (CWT) is presented. The advantage of the wavelet transform is that the signal can be evaluated locally in both spatial and frequency space, making it possible to measure even complex reflective surfaces in motion. First measurement results are shown and compared to the classic phase-shifting evaluation for a non-moving object. Furthermore, limits and possible enhancements of this new method are discussed. Phase measuring deflectometry (PMD) is a well-established method for determining the topography of specular freeform surfaces. A disadvantage of the classical PMD method, however, is the sequential measurement process - it requires at least six camera images of phase-shifted sinusoidal fringe patterns for one measurement. Therefore, for moving objects in industrial production, as well as for non-fixable objects such as the human cornea, the classical PMD evaluation is not suitable anymore. To overcome this problem, single-shot methods using single-side-band demodulation have been presented, which allow for a deflectometric measurement based on just one single image capture. However, this kind of evaluation does not work for complex surface geometries that result in broadband fringe patterns, since the phase is only considered globally in the Fourier space. A new single-shot evaluation method for the phase determination using the Continuous Wavelet Transform (CWT) is presented. The advantage of the wavelet transform is that the signal can be evaluated locally in both spatial and frequency space, making it possible to measure even complex reflective surfaces in motion. First measurement results are shown and compared to the classic phase-shifting evaluation for a non-moving object. Furthermore, limits and possible enhancements of this new method are discussed.

A hybrid algorithm is proposed in this study for demodulating a single spatial carrier fringe pattern (FP) of interferometric measurement, which essentially combines the spatial carrier phase shift (SCPS) method and Fourier transform (FT) method. It firstly extracts three phase-shifted FPs from a single spatial carrier FP, then employs the FT method and a subtraction operation to determine the phase shift of three phase-shifted FPs, and finally retrieves the phase map using a least-square phase shift algorithm. The subtraction operation could considerably mitigate the inherent edge error of the FT method, resulting in an increase of accuracy compared with the FT method. It also does not require the background and modulation amplitude of the spatial carrier FP to be constant; thus it is robust and quite suitable for engineering. The factors that may influence the performance of the proposed algorithm are analyzed, including the random and speckle noise, carrier frequency, shape of the background, and modulation amplitude. The feasibility of the proposed algorithm is validated by two experiments, comparing them with the temporal phase-shifted method. The proposed algorithm is expected to be used in interferometric measurement under adverse environments.

In the phase measuring deflectometry, two groups of fringe patterns in orthogonal directions are usually applied to establish the correspondences between the pixel pairs on the screen and camera. Usually, 16 phase-shifting fringe patterns with different spatial frequencies are required in order to calculate the absolute phases in the conventional temporal phase unwrapping algorithms. This requirement makes the measurement inefficient and not robust against environmental noise. In this paper, an efficient phase retrieval strategy is developed, which requires only six fringe patterns. The modulating information in one-direction is obtained by first using four fringe patterns, and then it is applied to assist the phase calculation in the other direction, so that only two extra fringe patterns are needed. Subsequently the phases are unwrapped by using the geometric constraints of the software configurable optical test system without additional image acquisition. The measurement time is saved by 5/8, compared to the conventional methods. In this way, the influence of the low-frequency disturbances can be suppressed in the workshop condition. Experiments demonstrate that the proposed method can reliably retrieve the absolute phases, and it is of significance to improve the measuring efficiency and stability of in situ deflectometry.

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.

A simple but effective filtering scheme in phase shifting interferometry is proposed. Conventionally, either the phase-shifted fringe patterns, or the resulting wrapped phase field, is chosen for filtering to remove noise. In this letter, we propose filtering the complex field resulting from the combination of the phase-shifted fringe patterns, as a third choice. The filtering can be realized by Fourier trans- form or windowed Fourier transform. Processing results of speckle fringes are given to show its effectiveness. © 2003 Society of Photo-Optical Instrumentation Engineers. (DOI: 10.1117/1.1609457)

A new fringe projection method for surface-shape measurement was developed using four high-frequency phase-shifted background modulation fringe patterns. The pattern frequency is determined using a new fringe-wavelength geometry-constraint model that allows only two corresponding-point candidates in the measurement volume. The correct corresponding point is selected with high reliability using a binary pattern computed from intensity background encoded in the fringe patterns. Equations of geometry-constraint parameters permit parameter calculation prior to measurement, thus reducing measurement computational cost. Experiments demonstrated the ability of the method to perform 3D shape measurement for a surface with geometric discontinuity, and for spatially isolated objects.

Conventional camera calibration that employs calibration targets is a commonly used method to acquire a camera’s intrinsic and/or extrinsic parameters. The calibration targets are usually designed as periodic arrays of simple high-contrast patterns that provide highly accurate world coordinate system points and the corresponding image pixel coordinate system points. The existing pixel coordinate extraction algorithms can reach a sub-pixel level; however, they treat each single pattern in one image as an independent individual, which makes it difficult to further improve extraction accuracy. In this paper, a novel method is proposed by utilizing the periodic arrangement characteristics of the calibration target pattern as a global constraint to improve the calibration accuracy. Based on a camera’s pinhole model, the intersection point of two fitted curves is used as an optimized pixel point to replace the initial one. Following the pixel coordinate optimization procedures, experiments were performed using real data from a 3D laser line scanner and a dynamic precision calibration target. Our results show that the relative errors of camera homography matrix elements obtained by the proposed optimization method were reduced compared with the commonly used method. The average coordinate measurement accuracy can be improved by nearly 0.05 mm. It is shown that the proposed optimization method can enhance the camera calibration accuracy, especially when the extracted pixels are of poorer precision.

Accurate robot camera calibration is a requirement for vision guided robots to perform precision assembly tasks. In this paper, we address the problem of doing intrinsic camera and hand-eye calibration on a robot vision system using a single point marker. This removes the need for using bulky special purpose calibration objects, and also facilitates on line accuracy checking and re-calibration when needed, without altering the robots production environment. The proposed solution provides a calibration routine that produces high quality results on par with the robot accuracy and completes a calibration in 3 minutes without need of manual intervention. We also present a method for automatic testing of camera calibration accuracy. Results from experimental verification on the dual arm concept robot FRIDA are presented.

This research addresses the challenge of camera calibration and distortion parameter prediction from a single image using deep learning models. The main contributions of this work are: (1) demonstrating that a deep learning model, trained on a mix of real and synthetic images, can accurately predict camera and lens parameters from a single image, and (2) developing a comprehensive synthetic dataset using the AILiveSim simulation platform. This dataset includes variations in focal length and lens distortion parameters, providing a robust foundation for model training and testing. The training process predominantly relied on these synthetic images, complemented by a small subset of real images, to explore how well models trained on synthetic data can perform calibration tasks on real-world images. Traditional calibration methods require multiple images of a calibration object from various orientations, which is often not feasible due to the lack of such images in publicly available datasets. A deep learning network based on the ResNet architecture was trained on this synthetic dataset to predict camera calibration parameters following the Brown-Conrady lens model. The ResNet architecture, adapted for regression tasks, is capable of predicting continuous values essential for accurate camera calibration in applications such as autonomous driving, robotics, and augmented reality.

Fringe projective 3D profile sensor can obtain dense coordinates map of object outline fast and quantitatively. Phase unwrapping technique plays an important role in the performance of the sensor when phase-shifting fringe patterns are used. The multi-period phase shift method can considerably increase the accuracy of measuring phase value. However, due to error of intensity approximation arisen from digital grating and the spatial resolution limits on the projector and cameras of the senor, the result of unwrapped phase value is still within noise only by means of temporal phase-unwrapping. A new algorithm combining the spatial and temporal phase-unwrapping methods is presented. The algorithm, which is a good compromise between the number of needed gratings and the unwrapping reliability, is especially designed for using two groups of digital phase-shifting gratings with different period. Experiments have been carried out by selecting about thirty pairs of periods to illustrate the efficiency of temporal and spatial criterions, and the results offer the tolerance of phase calculation which is unwrapped correctly. The algorithm has been implemented on a test system, and the ratio of unwrapping successfully reaches to 80% with the repeated error 0.05 rad.

This paper presents a novel method that does not reqire additional images for 3D video imaging with phase unwrapping technique using geometric constrain based on graident field. Specifically, we creat an artificial absolute phase map Φ_min at given depth z = z_min from the former frame. We optimize the z_min by validate the continuity of computed unwrapped phase with gradient field and deliver the true minimum z value z_min to next frame. The first frame is reconstructed by a static method. Experiments demonstrate that only three phase-shifted fringe patterns are required to measure moving objects.

For high-speed and high-accuracy 3D shape measurement, it has been demonstrated that using 1-bit binary patterns is advantageous over 8-bit sinusoidal phase-shifted fringe patterns especially on the digital-light-processing (DLP) projection platform. By properly defocusing the projector for specific square binary patterns, researchers have achieved the speed breakthroughs for high-accuracy 3D shape measurement, yet such a method requires carefully adjustment of the projector’s lens to within a small out-of-focus range, limiting its depth measurement capability. Optimizations based on pulse width modulation (PWM), optimal pulse width modulation (OPWM), and dithering/halftoning have substantially improved measurement quality, yet they only work well for a limited range of fringe period variations especially when a small number of phase-shifted fringe patterns are used. This paper proposes to generate high-quality phase using two sets of three phase-shifted binary patterns: the first set is generated by triangular pulse width modulation (TPWM) technique, and the second set being p shifted from the first set is also generated by TPWM technique. A three-step phase-shifting algorithm is then applied to compute the phase. Through optimizing the modulation frequency of the carrier signal, our simulation and experimental results demonstrate that high-quality phase can be generated for a wide range of fringe periods (e.g., from 18 to 1140 pixels) with only six binary patterns.