Captured Fringe Images Research Articles

Recognition and separation of fringe patterns in deflectometric measurement of transparent elements based on empirical curvelet transform

In the deflectometric measurement of transparent elements, it is critical to separate the superposed fringes reflected from the front and rear surfaces to establish the pixel correspondences between the camera and screen pixels. But it is a challenging task due to the low reflectivity and uneven background of transparent elements. A reliable fringe separation method is proposed based on the empirical curvelet transform. The captured fringe images are decomposed into different modes according to their directions, periods, curvatures or modulation coefficients, and then a weighted-permutation-entropy-based fusing algorithm is developed to automatically aggregate those over-separated patterns. By employing the proposed method, the measurement accuracy is significantly improved, the number of demanded images is effectively reduced, and high-precision, automatic, and rapid measurement is thereby achieved. The measurement accuracy of spherical and cylindrical lenses can achieve 73 nm and 332 nm Root-of-Mean-Squares-Error, respectively.

Error compensation for phase retrieval in deflectometry based on deep learning

Fringe patterns are widely applied in optical metrology, and phase retrieval is an essential process for decoding surface information. In the field of phase measuring deflectometry (PMD), phase errors in the phase retrieval process have more significant effects for PMD is a slope-based technique and is more sensitive to low-frequency errors. The main factors affecting the quality of the captured fringe images include the gamma effect of the liquid crystal display screen, the random noise from the charge-coupled device camera, and the random noise amplified by the defocused fringe patterns. Conventional methods compensated the phase errors of these factors separately with different methods, which are inefficient in handling the errors from coupling factors effectively. In this paper, we propose a deep neural network to compensate for the phase errors resulting from the combination of the factors. Experimental results demonstrate that the proposed network can significantly suppress the errors in phase retrieval with non-ideal fringe images. The phase errors can be reduced in both simulated and authentic data for deflectometry, which verifies the robustness and effectiveness of the proposed method.

Wavefront-coded phase measuring deflectometry for the all-focused measurement.

Phase measuring deflectometry is a powerful measuring method for complex optical surfaces, which captures the reflected fringe images encoded on the screen under the premise of focusing the measured specular surface. Due to the limited depth of field of the camera, the captured images and the measured surface cannot be focused at the same time. To solve the position-angle uncertainty issue, in this Letter, the wavefront coding technology is used to modulate the imaging wavefront of the deflectometry, thereby making the measuring system insensitive to the defocus and other low-order aberration including astigmatism, field curvature, and so on. To obtain the accurate phase, the captured fringe images are deconvoluted using the modulated point spread function to reduce the phase error. Demonstrated with a highly curved spherical surface, the measurement accuracy can be improved by four times. Experiments demonstrate that the proposed method can successfully reconstruct the complex surfaces defocusing the captured images, which can greatly release the focusing requirement and improve measurement accuracy.

Development of three-dimensional pavement texture measurement technique using surface structured light projection

To realize active, non-contact, high-precision and full-field measurement of pavement texture, an innovative surface structured light projection (SSLP) based technique is developed in this paper. Firstly, the sinusoidal intensity encoded surface structured light is projected through the optical fiber interference, and the high-resolution industrial camera is used to capture the deformed fringe pattern modulated by the measured pavement. Then, a pre-processing method is proposed to suppress the noise and uneven background illumination in the captured fringe image. After that, a two-dimensional continuous wavelet transform method (2D-CWTM) is executed, and the wrapped phase can be demodulated accurately from the wavelet ridge. Finally, the 2π steps in the wrapped phase are removed by a phase unwrapper, and the measured pavement texture elevation can be obtained according to the phase-height mapping relationship. Both laboratory and field tests demonstrate the functionality and effectiveness of the proposed SSLP technique in pavement texture measurement.

A Fast Self-Correction Method for Nonlinear Sinusoidal Fringe Images in 3-D Measurement

Phase-shifting profilometry (PSP) is a method used to establish the pixel correspondence between a projector and a camera using phase-shifting fringe patterns. Due to the nonlinear intensity response of the captured images, nonlinear errors will be induced into the calculated phase and thus decrease the accuracy of 3-D measurement. In this article, we propose a fast self-correction algorithm to reduce the nonlinear phase error without the need for additional projections or precalibration. In this study, we derived an average intensity expression of the captured fringe images that contain the nonlinear response parameters. We can establish a set of equations with the known projection fringe information and unknown nonlinear parameters based on the captured fringe images at different frequencies used in the multifrequency heterodyne algorithm. Based on the equation set, the nonlinear response parameters can be solved for each pixel in the captured images, and the inverse function of the system response can thus be obtained and used to correct the actual nonlinear gray value. This pointwise correction algorithm can reduce the nonlinear phase error corresponding to different frequency fringe images without increasing the number of projections and with no excessive calculation time. Furthermore, this method can use small-pitch fringe patterns to improve the measurement accuracy while maintaining the reliability of the phase unwrapping. Experimental results show that the proposed method can eliminate the nonlinear phase error, improve phase unwrapping robustness, and achieve a high measurement quality for fast 3-D measurement through PSP.

A two-step phase-shifting algorithm dedicated to fringe projection profilometry

Improving the time efficiency of fringe projection profilometry (FPP) is an attractive problem. For FPP using phase-shifting, it is desired to improve the efficiency by reducing the step number for phase retrieval. This paper proposes a two-step phase-shifting algorithm dedicated to FPP. Considering the physical process of FPP, the captured fringe image is formulated with two variables, i.e. surface reflectance and phase value. And a phase shift is introduced to get the two equations, which lead to the close-form solution for phase calculation. Then the phase error due to ambient light is analyzed via a line-circle model, and an algorithm of refining the phase calculation is proposed based on the estimation of the actual fringe contrast. The validity of the proposed approach is demonstrated with experiments.

An improved background segmentation algorithm for fringe projection profilometry based on Otsu method

In fringe projection profilometry, there always exist background and shadow areas in the captured fringe images. To improve the data quality, these areas should be recognized and deleted before the point cloud is reconstructed. For the existing algorithms, it is a nontrivial task to obtain a reasonable threshold to recognize the background and shadow areas from the fringe images. An inappropriate threshold usually leads to a misclassification of the object and background/shadow areas. In this paper, an improved adaptive thresholding method is built to address this problem. Instead of the gray level histogram, the modulation level histogram is utilized to compute the threshold. The modulation image is computed from all the captured images in the projection sequence. A novel objective function with a Gaussian weighted factor is proposed to improve Otsu’s method. With this weighted factor, the between-class variance between the object and background/shadow is intensified. The new built objective function also makes the objective function plot much smoother, which makes the proposed method more suitable for noise image segmentation. Additionally, the weighted factor changes adaptively with the input images. Experiment results illustrate that the proposed scheme performs better than existing methods. The scan for an area on a car body rear demonstrates the effectiveness and feasibility of the proposed method in structured light measurement of real metal components.

A novel 3D measurement technique for rigid moving objects with a determined movement trajectory and constant movement speed

When phase-shifting (PS) and temporal-phase-unwrapping algorithms are employed for three-dimensional (3D) shape measurement, the measured object must be kept static during the projection and acquisition. If the measured object is moving, deviation among multiple fringe images will inevitably occur, which results in the 3D measurement error. In this paper, a novel 3D measurement technique for rigid moving objects obtained by using the PS algorithm and the three-pitch heterodyne-unwrapping (TPHU) algorithm is proposed, which consists of six steps. First, the pixel offset is estimated based on a centroid deviation calculation. Second, the phase offsets among multiple fringes are calculated. Third, a novel set of fringes for the projection is generated. Fourth, we offset the captured fringe images according to the pixel offsets to generate a new set of captured fringe images for the phase calculation. Fifth, the wrapped phase is calculated by the PS algorithm. Finally, the unwrapped phase is calculated by the TPHU algorithm. The proposed method can be applied to the 3D shape reconstruction of a rigid movement object with a determined movement trajectory and constant movement speed. This approach not only greatly improves the measurement efficiency but also inherits the high accuracy and robustness of the PS and TPHU algorithms.

Robust Single-shot Fringe Projection Profilometry Based on Morphological Component Analysis.

In a fringe projection profilometry (FPP) process, the captured fringe images can be modeled as the superimposition of the projected fringe patterns on the texture of the objects. Extracting the fringe patterns from the captured fringe images is an essential procedure in FPP; but traditional single-shot FPP methods often fail to perform if the objects have a highly textured surface. In this paper, a new single-shot FPP algorithm which allows the object texture and fringe pattern to be estimated simultaneously is proposed. The heart of the proposed algorithm is an enhanced morphological component analysis (MCA) tailored for FPP problems. Conventional MCA methods which use a uniform threshold in an iterative optimization process are inefficient to separate fringe-like patterns from image texture. We extend the conventional MCA by taking advantage of the low-rank structure of the fringe's sparse representation to enable an adaptive thresholding process. It ends up with a robust single-shot FPP algorithm that can extract the fringe pattern even if the object has a highly textured surface. The proposed approach has a side benefit that the object texture can be simultaneously obtained in the fringe pattern estimation process, which is useful in many FPP applications. Experimental results have demonstrated the improved performance of the proposed algorithm over the conventional single-shot FPP approaches.

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.

Robust Fringe Projection Profilometry via Sparse Representation.

In this paper, a robust fringe projection profilometry (FPP) algorithm using the sparse dictionary learning and sparse coding techniques is proposed. When reconstructing the 3D model of objects, traditional FPP systems often fail to perform if the captured fringe images have a complex scene, such as having multiple and occluded objects. It introduces great difficulty to the phase unwrapping process of an FPP system that can result in serious distortion in the final reconstructed 3D model. For the proposed algorithm, it encodes the period order information, which is essential to phase unwrapping, into some texture patterns and embeds them to the projected fringe patterns. When the encoded fringe image is captured, a modified morphological component analysis and a sparse classification procedure are performed to decode and identify the embedded period order information. It is then used to assist the phase unwrapping process to deal with the different artifacts in the fringe images. Experimental results show that the proposed algorithm can significantly improve the robustness of an FPP system. It performs equally well no matter the fringe images have a simple or complex scene, or are affected due to the ambient lighting of the working environment.

Filter Dependence on the Phase Error of Fourier Transform Profilometry

In phase measuring fringe reflection Fourier transform profilometry, it gets the captured image data from the projected sinusoidal fringe patterns by using the CCD cameras. Added white noise in captured fringe images and its low contrast levels affect the accuracy of three-dimensional surface profile measurements induced the phase errors. In this work, we present a phase error reduction method using the low pass spatial image filter and median filter. Experimental results have shown to validate the low pass filter and median filter. Although the effect of the filter is to be smoothed the fringe, white noise included in the pattern was able to remove effectively. In case of the median filter, it showed negative influence to the phase error, but the low-pass filter evidently reduced the phase error about 30%.

Effective bias removal for fringe projection profilometry using the dual-tree complex wavelet transform

When reconstructing the three-dimensional (3D) object height profile using the fringe projection profilometry (FPP) technique, the light intensity reflected from the object surface can yield abruptly changing bias in the captured fringe image, which leads to severe reconstruction error. The traditional approach tries to remove the bias by suppressing the zero spectrum of the fringe image. It is based on the assumption that the aliasing between the frequency spectrum of the bias, which is around the zero frequency, and the frequency spectrum of the fringe is negligible. This, however, is not the case in practice. In this paper, we propose a novel (to our knowledge) technique to eliminate the bias in the fringe image using the dual-tree complex wavelet transform (DT-CWT). The new approach successfully identifies the features of bias, fringe, and noise in the DT-CWT domain, which allows the bias to be effectively extracted from a noisy fringe image. Experimental results show that the proposed algorithm is superior to the traditional methods and facilitates accurate reconstruction of objects' 3D models.

Efficient fringe image enhancement based on dual-tree complex wavelet transform

In optical phase shift profilometry (PSP), parallel fringe patterns are projected onto an object and the deformed fringes are captured using a digital camera. It is of particular interest in real time three-dimensional (3D) modeling applications because it enables 3D reconstruction using just a few image captures. When using this approach in a real life environment, however, the noise in the captured images can greatly affect the quality of the reconstructed 3D model. In this paper, a new image enhancement algorithm based on the oriented two-dimenional dual-tree complex wavelet transform (DT-CWT) is proposed for denoising the captured fringe images. The proposed algorithm makes use of the special analytic property of DT-CWT to obtain a sparse representation of the fringe image. Based on the sparse representation, a new iterative regularization procedure is applied for enhancing the noisy fringe image. The new approach introduces an additional preprocessing step to improve the initial guess of the iterative algorithm. Compared with the traditional image enhancement techniques, the proposed algorithm achieves a further improvement of 7.2 dB on average in the signal-to-noise ratio (SNR). When applying the proposed algorithm to optical PSP, the new approach enables the reconstruction of 3D models with improved accuracy from 6 to 20 dB in the SNR over the traditional approaches if the fringe images are noisy.

Absolute phase technique for the Fourier transform method

The phase-to-coordinate conversion is an important step for accurate 3-D shape measurement by use of structured light methods. We propose to use an absolute phase map in the Fourier transform method to achieve better accuracy in the phase-to-coordinate conversion. A cross-shaped marker is embedded in the fringe pattern that is projected onto the object. The position of the marker in the captured fringe image is detected and utilized to calculate the absolute phase map. For phase analysis of the fringe image, the marker is removed and the sinusoidal intensity distribution of the fringe pattern is restored before the forward and inverse Fourier transforms are applied. Experimental results of absolute phase retrieval and 3-D reconstruction are presented to show the feasibility of the proposed method.

Fly Height Measurement Based on Phase Comparison Michelson Interferometry Using Low-Coherence Light Source

We present a method for measuring head fly height in hard disk drives using phase comparison Michelson interferometry (PCMI), which compares the phases of two interference fringe patterns formed respectively on the inner surface of a glass disk and the air-bearing surface of a fly head slider through the glass disk. To suppress interference noise and further enhance measurement accuracy, we adopted a low-coherence light source as an illumination source to replace a high-coherence laser. The captured fringe images enabled us to extract ridge lines much more accurately than with a laser. We compared our measurements in the sub-10 nm spacing range with calculations and found excellent agreement.

Generic nonsinusoidal phase error correction for three-dimensional shape measurement using a digital video projector

A structured light system using a digital video projector is widely used for 3D shape measurement. However, the nonlinear gamma of the projector causes the projected fringe patterns to be nonsinusoidal, which results in phase error and therefore measurement error. It has been shown that, by using a small look-up table (LUT), this type of phase error can be reduced significantly for a three-step phase-shifting algorithm. We prove that this algorithm is generic for any phase-shifting algorithm. Moreover, we propose a new LUT generation method by analyzing the captured fringe image of a flat board directly. Experiments show that this error compensation algorithm can reduce the phase error to at least 13 times smaller.