Innovative calibration technique for fringe projection based 3D scanner

A new approach to 3D scanners calibration, based on Fourier Transform Profilometry method, is proposed and verified by experiments. Commonly used calibration techniques require that a calibration plane is placed in different and known positions in the scanner measuring volume; an optimization procedure iteratively change the value of some calibration parameters in order to minimize the discrepancy between the height distributions of the measured planes and the reference ones. The main limit of this type of calibration techniques is the necessity to guarantee a high accuracy in the placement of the planes used as calibration references. The innovation of the method proposed in this paper is the complete removal of any device for the accurate plane placement by assigning the task of the plane positions estimation to the camera, which is part of the scanner. The well known camera calibration algorithm proposed by Zhang permits at the same time to calibrate the camera and to estimate the positions and orientations of the plane used for the calibration itself. The knowledge of the plane position allows to use them as a reference of the scanner calibration. The obtained results show that this method provides accuracy values for the scanner parameters estimation comparable with other calibration techniques, but the advantage is that no particular device is needed.     

Unstable resonator alignment based on the fringe analysis

The existing cavity mirrors alignment method aligns cavities according to the symmetry of the near-field interference fringes of the guided lights by the unstable resonator. Its precision is restricted due to the lack of objective criterion for the fringe symmetry. This article proposes a high-precision cavity mirrors alignment method using the grey projection of fringe patterns as a solution to the problem. First, vertical and horizontal grey projection on the concerned fringe patterns; then an evaluation function for the cavity mirrors alignment is established using the distances between peak/valley values of all the levels in the projection curve as variables; finally, the function value is employed to characterize the fringe symmetry and thus to provide an objective criterion for the alignment effect of the stable resonator cavity mirrors. Experiments show that the proposed method is able to give effective evaluation for the symmetry of the near-field interference fringes of the guided lights and improve the alignment precision greatly.     

Testing a large aspheric surface based on analysis of scanning 3D interferogram

A new method based on new reconstruction algorithm and new interferogram fringe analysis was proposed for testing a large aspheric surface. In the testing process, firstly, the interferometer or the tested aspheric surface was shifted relatively for measurement of the whole aperture of the tested aspheric surface to obtain a series of interferograms. Then these interferograms were analyzed to extract the best matching point, where the annular sub-surface was tangent with the corresponding reference sphere of the reference wavefront. Finally, the wavefront aberration of the whole aperture was figured out to describe the deformation information of the tested surface. Without any additional null optical elements, this method can perform the measurement directly. So, this method provides an effective and convenient means of testing the large-aperture aspheric surface. The mathematical model of this method is described, and the results of simulation tests are presented to verify it.     

Performance analysis of a 3D full-field sensor based on fringe projection

This article analyzes the measurement performance of a 3D full-field imaging system based on the projection of grating and active triangulation. We first explore the exact mathematical relationship that exists between the height of an object's surface, the phase and the parameters of the experimental setup, which relationship can be used to obtain the precise shape of an object. We then investigate in detail the influence on the measurement results of the introduction of an inaccuracy into the determination of the system's parameters. Finally, using simulated data, we conduct experiments to evaluate the measurement performance.     

Examination of the upper measurement limit in displacement measurement using fringe compensation in digital holography

Digital holography is a widely used method for displacement measurement in coherent optical metrology. An obvious limit of the method is that too large displacements result in dense fringes, so the fringes are practically invisible. The maximum number of contour fringes in displacement measurement is limited, because the cameras are discrete devices and sampling theory plays an important role. Because of the limited measurement range, compensation methods are promising tools for practical measurements. It can be shown that the practical measurement range can be extended above the Nyquist sampling limit. Compensation methods can be digital, because digital holographic interferometry operates with images recorded with a digital camera. In our research work the upper measurement range of fringe compensation method was examined. Our goal was to perform automatic compensation even if the displacement is higher than the measurement range of the basic method. The operation of the automatic fringe compensation method was based on the combination of two types of out-of-plane displacement measurements with different sensitivities.     

Phase retrieval of non-continuous fringe patterns by a genetic data reduction algorithm

In this work we focus on the possibilities of recovering the phase from a single fringe pattern that do not have a fringe order sequence or whose fringes are broken. The phase is obtained with a polynomial fitting method whose coefficients are calculated with a genetic algorithm technique that constrains the smoothness of the solutions of a merit function. It is explained how conjugate gradient methods fail in the solution of the proposed merit function. Experimental results are presented using discontinuous fringe patterns obtained from a grazing incidence interferometer while testing a polishing tool.     

Transformation of phase to (x,y,z)-coordinates for the calibration of a fringe projection profilometer

In this work we present a phase to (x,y,z)-coordinates transformation method for the calibration of a fringe projection profilometer. Our technique is divided in two parts: (1) phase to z transformation (for axial calibration) based on the typical polynomial fitting which uses a flat plane placed at several z positions to measure the phase of the projected fringes. (2) Phase to x and y transformation (for transverse calibration) based on the use of a crossed gratings pattern and a Fourier phase measurement method to determine x and y coordinates at several z positions. As will be shown the use of the crossed gratings pattern and the Fourier phase measurement method for transverse calibration is advantageous in several aspects: an unique image can give us x and y information at once. It provides x and y coordinates at each pixel in the image avoiding the use of interpolation methods. We present some experimental results and explain the viability of the proposed technique.     

Orthogonal projection technique for resolution enhancement of the Fourier transform fringe analysis method

The spatial resolution of the phase map in the Fourier transform fringe analysis method is determined by the size of the filter’s window in frequency domain. This article reports a straightforward technique to improve the method’s resolution by a factor of nearly two. The technique requires capturing a second image with a fringe pattern orthogonal to the first one, therefore using the information from both patterns to eliminate the central component in frequency space. The resulting spectrum supports double sized filter windows for removal of the carrier frequency without leaking into adjacent orders. The overall spatial resolution of the method is thus increased. In the following, the Fourier fringe analysis method is briefly reviewed, the new technique is described and analyzed and the experimental results are shown and discussed.     

The study and application of a new filtering method on electronic speckle pattern interferometric fringe

It is important for the study of digital image processing to remove noises and enhance images because of various noises in images. The article is concerned with the recursive algorithm-filtering technique, which is capable of effectively removing noise and rapidly leading to a continuous gray-level distribution of a random image. By applying the method on speckle images of defects of rubber material, it is shown that this technique is the most effective and speedy method for the filtering of ESPI fringe patterns. Comparing the images before and after filtering, we can see the advantages of the novel technique clearly. It can increase the accuracy of measurement both in phase measurement and in quantitative evaluations of defects.     

Lens distortion elimination for improving measurement accuracy of fringe projection profilometry

Fringe projection profilometry (FPP) is a powerful method for three-dimensional (3D) shape measurement. However, the measurement accuracy of the existing FPP is often hindered by the distortion of the lens used in FPP. In this paper, a simple and efficient method is presented to overcome this problem. First, the FPP system is calibrated as a stereovision system. Then, the camera lens distortion is eliminated by correcting the captured images. For the projector lens distortion, distorted fringe patterns are generated according to the lens distortion model. With these distorted fringe patterns, the projector can project undistorted fringe patterns, which means that the projector lens distortion is eliminated. Experimental results show that the proposed method can successfully eliminate the lens distortions of FPP and therefore improves its measurement accuracy.     

Accurate carrier-removal technique based on zero padding in Fourier transform method for carrier interferogram analysis

Based on interferogram zero padding and fast Fourier transform (FFT) methods, an effective, straightforward and stable carrier-removal approach in Fourier transform (FT) based method for carrier interferogram analysis is proposed. The spatial carrier interferogram is firstly extrapolated by zero padding method, and the carrier-frequency values within a small fraction of an integral (or a pixel) are estimated from the extrapolation interferogram with FFT method. Then the carrier-phase component is removed by subtracting a pure carrier-frequency phase constructed by the estimated carrier-frequencies in the spatial domain. Numerical simulations and experiments are given to demonstrate the performance of the proposed method and the results show that the proposed method is effective and stable for suppressing the carrier-removal error in the FT method for carrier interferogram analysis.     

Study on an automatic processing technique of the circle interference fringe for fine interferometry

The fringe center method (FCM) is an important digital processing technique of fringe patterns analysis for interferometry. In this paper, an improved automatic processing technique based on FCM was presented, which correlated the processing link and the looped feature of the circle fringe pattern. It also integrated several techniques including noise removal, the fringe thinning, the fringe patching, assignment of the fringe orders and wavefront reconstruction and can be executed orderly and automatically. Based on the new the algorithms of the fringe patching and assignment of the fringe orders, the fringe feature information was extracted automatically and the interference wavefront was reconstructed by Zernike polynomial fitting method. With the automatic processing technique, the circle interference fringe of the fine polished aluminum disks surface captured by the Twyman-Green interferometer was processed, and the surface profile and the parameters of the disk were obtained automatically. The experiments show that the improved automatic processing technique was more accurate and fast in measurement than the conventional one. It was convenient to use it in in-situ industry inspection.     

Applications of windowed Fourier fringe analysis in optical measurement: A review

The applications of windowed Fourier fringe analysis in the past decade are reviewed. Because fringe patterns from different optical measurement systems are similar, the reviewed applications are classified according to the functions of the windowed Fourier transform being used in fringe pattern analysis: denosing exponential phase fields, demodulating carrier fringe patterns, getting phase derivatives, and utilizing local properties. From these applications, the windowed Fourier transform is shown to be effective and versatile for fringe pattern analysis.     

The leveling of mask and wafer in proximity nanolithography using fringe pattern phase analysis

The fringe pattern phase analysis method is proposed for the leveling of mask and wafer in proximity lithography. The tilt between mask and wafer in the space is reflected in the tilted fringe pattern. The method combining the 2-D Fourier transform and 2-D Hanning window is proposed for processing the tilted fringe pattern. The offset and angle of tilt are extracted through phase analysis. Computer simulation and experiment are both performed to verify this method. The results indicate that the tilt of the mask and wafer in the space can be extracted with high accuracy through this method.     

Surface profile measurement of low-frequency vibrating objects using temporal analysis of fringe pattern

A simple and accurate algorithm (phase scanning method) is proposed for 3D surface contouring and dynamic response determination of a vibrating object. A sinusoidal fringe pattern is projected onto a low-frequency vibrating object by a programmable liquid crystal display projector. The fringe patterns are captured by a high-speed CCD camera with a telecentric gauging lens. Phase values are evaluated point by point using phase scanning method. From the phase values of each point on the object, the contour of the specimen at different instants of vibration can be retrieved. In this paper, a small vibrating coin is used to demonstrate the validity of the method and the experimental results are compared with test results on a stationary coin using four-step phase shifting and fast Fourier transform methods. The technique is especially useful in applications where the vibrating object has a complicated shape.     

A derivative based simplified phase tracker for a single fringe pattern demodulation

In this paper, a novel fringe demodulation method for the estimation of phase and its first-order derivative from a closed-fringe interferogram is proposed. The proposed method determines the phase derivatives in both x&y directions from fringe orientation and density. The phase derivatives are subsequently used to determine phase values using a novel simplified phase tracker. In the phase tracking model, the complexity of the cost function is reduced using predetermined derivatives so computation time required for phase tracking is reduced considerably. The proposed model is more robust while dealing with saddle points in fringes than the conventional phase tracker model. Hence it does not require any specialized scanning strategy. The proposed method is validated with simulated and experimental fringe patterns (obtained using electronic speckle pattern interferometry and optical holographic interferometry) and a comparison study is carried out with conventional regularized phase tracker. The simulation results show that the proposed method has good accuracy and requires less computation time than existing phase-tracking algorithms. The experimental results demonstrate the robustness of the proposed method against speckle noise and its practical applicability for static and dynamic applications.     

A new wavelet transform for reliability-guided phase unwrapping of optical fringe patterns

A new daughter wavelet definition for reliability-guided phase unwrapping of the optical fringe pattern is introduced. The new daughter wavelet definition is given by normalized mother wavelet with a new factor including a Gaussian function. The modulus of the wavelet transform coefficients, obtained by using daughter wavelet under this new daughter wavelet definition, includes not only modulation information but also local frequency information of the deformed fringe pattern. Therefore, it can be treated as a good parameter which represents the reliability of the reconstructed phase data. Mathematical demonstration of this parameter is given. Both the computer simulation and experiment reveal the validity of the proposed method.     

Fringe analysis by phase shifting technique for birefringent fluid studies

We have developed a new optical method to evaluate the tensio-optic behaviour of a fluid in a Couette cell. This method is based on the analysis of the phenomenon of light scattered from a laser beam passing through a sheared fluid. A phase shifting technique was added to increase the measurement accuracy and the range of possible applications. For example, with this modification the problem of low shear stresses can be analysed. This improvement enables measurements to be made even if there is less than one visible fringe. This method also allows the determination of local stresses within the fluid. For a classical Newtonian or shear thinning fluid, a linear correlation between fringe order and shear stresses is observed and the tensio-optic coefficient may then be calculated. A yield stress thixotropic fluid is also analysed to demonstrate the relevance of the developed method. This test shows two distinctive behaviours with two different tensio-optic coefficients relative to a solid state and a liquid state.