Hubing Du

Color fringe-projected technique for measuring dynamic objects based on bidimensional empirical mode decomposition

A triple-frequency color fringe-projected technique is presented to measure dynamic objects. Three fringe patterns with a carrier frequency ratio of 1:3:9 are encoded in red, green, and blue channels of a color fringe pattern and projected onto an objects surface. Bidimensional empirical mode decomposition is used for decoupling the cross talk among color channels and for extracting the fundamental frequency components of the three fringe patterns. The unwrapped phase distribution of the high-frequency fringe is retrieved by a three-step phase unwrapping strategy to recover the objects height distribution. Owing to its use of only a single snapshot, the technique is suitable for measuring dynamically changing objects with large discontinuity or spatially isolated surfaces.

Algorithm for phase shifting shadow moiré with an unknown relative step

We report our experimental results of phase shifting shadow moire with a constant but unknown phase step to estimate both the wavefront phases and the phase step. The method allows phase retrieval from phase shifting interferograms even though the calibration data of the phase shifter are unknown. Compared with the traditional shifting shadow moire method, the proposed algorithm is insensitive to the height dependent effects, which is the main systematic source of error in phase shift shadow moire when reconstructing surfaces from fringe patterns. Experiments show that the proposed method can effectively minimize the effects of the phase shifting errors and possesses a superior performance to existing typical phase shifting algorithms in the shifting shadow moire technique.

Three frames phase-shifting shadow moiré using arbitrary unknown phase steps

A method combining the spatial and temporal fringe analysis techniques is proposed to extract the phase from shadow moire interferogram with random phase shift. The proposed method first determines the grating translation difference based on the spiral phase transform technique. Then the initial phase shift is estimated. After that a generalized iterative least-squares method is developed to retrieve the accurate phase map using three interferogram frames. The proposed method relaxes the restriction on phase shift calibration between frames and provides stable and correct convergence in a fast way. Simulation and experiment demonstrate the effectiveness of this method. It shows our method possesses a superior performance than the existing typical phase-shifting algorithm. The proposed method is suitable for phase-shifting shadow moire.

Phase-shifting shadow moiré based on iterative self-tuning algorithm

We proposed a general algorithm for phase-shifting shadow moiré by an iterative self-tuning algorithm. In our proposed system, the grating is translated in equal distance to introduce phase shifts across the field of view. The proposed algorithm produces accurate phase information with five interferograms and can calibrate the precise phase step during the process of the height demodulation. Compared with the traditional method, the proposed algorithm is insensitive to the height dependent effects, which is the main systematic source of error in phase-shift shadow moiré when reconstructing surfaces from fringe patterns. Numerical simulations and optical experiments show that the proposed method can eliminate the nonuniform phase-shift error and possesses a superior performance to existing typical phase-shifting algorithms.

2D phase unwrapping algorithm for interferometric applications based on derivative Zernike polynomial fitting technique

We propose a phase unwrapping method for general interferometric applications. The proposed method relies on a derivative Zernike polynomial fitting (DZPF) technique where the phase is approximated as a combination of Zernike polynomials. The fitting coefficients are then estimated using the least squares method. Thus the phase unwrapping problem is reduced to the calculation of these coefficients. Because of the full field operation, the proposed method is fast and efficient. In addition, the method directly provides the desired phase without the need to compute the misalignment errors further. The method combines the phase unwrapping and the wavefront fitting process. Simulation and experimental results are presented to validate the methods potential.

Non-null testing for aspheric surfaces using elliptical sub-aperture stitching technique

We propose an elliptical sub-aperture stitching (ESAS) method to measure the aspheric surfaces. In our method, the non-null configuration is used to overcome the disadvantages of the null testing. By adding the dynamic tilt, the different local nearly null fringe patterns are obtained and the corresponding phase data in the elliptical masks is extracted with negligible retrace errors. In order to obtain the full aperture result, a stitching algorithm is developed to stitch all the phase data together. We firstly show the principle of our method. Then the performance of the proposed method is analyzed by simulation experiments. In the end, practical examples are given to demonstrate the correctness of the proposed method. The stitching result shows a good agreement with the full-aperture null testing result.

Shadow moiré technology based fast method for the measurement of surface topography.

We present a fast phase-shifting shadow moiré device for surface topography measurement. In our setup, multiple light sources located at different positions are controlled to illuminate the grating sequentially. Therefore, the phase shift across the field of view shadow moiré is introduced by changing the distance between the light source and the camera. Thanks to the necessity for mechanical movement being omitted here, the proposed setup can capture the phase-shifting fringe patterns at a high speed. However, affected by the bias modulation and amplitude modulation of the captured fringe patterns, the phase of interest cannot be demodulated by the standard phase-shifting algorithm directly. Thus the principal component analysis (PCA) demodulation approach is used to extract the wrapped phase map. In addition, we develop an iterative procedure to reduce the detuning error introduced by the PCA algorithm. The proposed method implements a fast way to determine the topography of a surface through a simple experimental setup. It is applied to obtain an external surface of a specimen. Both the simulation results and the experimental results show the validity of the proposed technique.

Study of sub-aperture stitching interferometry based on topography data

Sub-aperture stitching testing method is an effective way to extend the lateral and vertical dynamic range of a conventional interferometer. In this paper, the global stitching method based on topography data is studied. The influence of the weight coefficient and the positioning accuracy on the stitching result is investigated. On this basis, the lateral parameters optimization method is introduced. Finally, a 152.4 mm parabolic surface is tested to validate the effectiveness of the proposed method.

Fast phase shifting shadow moiré by utilizing multiple light sources

We present a fast phase shifting shadow moiré device for the measurement of surface topography. In our set-up, the phase shift across the field of view shadow moiré is introduced by using two light sources illuminate the grating sequentially. Therefore, it is possible to capture the two fringe patterns at high speed. Due to the effect of bias modulation, the proposed phase demodulation method first removes the DC term of the sampling data. Then a spiral phase transform (SPT) based technique is developed to determine the introduced phase shift pointwisely. After that, the tunable two-frame algorithm is used to extract the wrapped phase map with no spatially non-uniform phase shift error. We implemented a fast technique to determine the topography of a surface by a simple experimental set-up. The proposed technique was applied to obtain an external surface of a specimen. The experimental results show the validity of this technique.

Phase extraction from random phase-shifted shadow moiré fringe patterns using stereovision technique

The measurement accuracy of phase shifting shadow moiré is limited by the spatially non-uniform and random phase shift error. Substantial work has been developed to overcome this difficulty. But few works are proposed to deal with the two error sources above simultaneously. In the presented paper, we describe a solution that can compensate the both error sources at the same time. In our proposed method, a binocular stereovision system is integrated into our test configuration. By measuring the coordinates of marks attached to the measurement grating, the stereovision system obtains the position and the setting parameters are calibrated. Then, the acquiring three fringe patterns are analyzed by iterative least squares method in temporal and the phase shift is calibrated by the least squares fitting in spatial. Because a local cost function is used, the proposed calibration technique is insensitive to spatial variations in detector response. Numerical simulations and optical experiments show that the proposed method can effectively minimize the two phase-shift error sources and possess a superior performance than the existing typical phase shifting algorithm.