Photorefractive moiré-like patterns for the multifringe projection method in Fourier transform profilometry.

We describe a method of obtaining optically scanned fluorescence images in a widefield conventional microscope by interfering two beams on an object so as to illuminate it with a single spatial frequency fringe pattern. Images taken at three spatial positions of the fringe pattern are processed in real time to produce optically sectioned images which are substantially similar to those obtained with confocal microscopes.© (1998) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

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.

This paper proposes the use of the two‐dimensional continuous Paul wavelet transform to extract the phase of spatial carrier fringe patterns. The proposed algorithm has been tested using computer‐generated and real fringe patterns, and these tests have demonstrated the suitability of the proposed technique for the phase demodulation of fringe patterns. Additionally, this algorithm is compared to three two‐dimensional continuous wavelet algorithms that have figured prominently in the literature, specifically the Morlet, advanced Morlet and fan mother wavelets. This comparison has revealed that the proposed algorithm outperforms the other three mother wavelets in terms of its suitability for extracting the phase of fringe patterns that exhibit large phase variations.

This paper presents an absolute phase calculation method from one composite RGB fringe pattern image by using Wavelet transform algorithm and the optimum fringe number selection. Three fringe patterns having optimum fringe numbers are projected simultaneously onto an object surface via the red, green and blue channels of a DLP (Digital Light Processing) projector. From a different viewpoint, a CCD camera captures the deformed fringe patterns with respect to the object shape to get a composite RGB image. After compensating for the crosstalk and chromatic aberration between color channels, three fringe patterns are extracted from the composite color image. Wavelet Transform algorithm is studied to calculate wrapped phase from one fringe pattern. Therefore, three wrapped maps are obtained from the three extracted fringe patterns. An absolute phase map is calculated pixel by pixel after applying the optimum three-fringe numbers selection method to the three obtained wrapped phase maps. Simulated and experimental data demonstrate the algorithm's validity of calculating the absolute phase and shape information. The proposed method can measure 3D shape information of moving objects since the system needs only one RGB fringe pattern image.

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.

Although there are various methods to measure the modulation transfer function (MTF) of charge-coupled devices (CCD), the interferometric fringe pattern method has advantages over others, such as canted slit sources, bar targets, knife-edge, laser-speckle patterns, random noise pattern, etc. Our interferometric method is relatively simple and versatile: It requires no critical optics and no focusing or precision alignment, the entry array is tested, the contrast ratio of the test pattern is high enough, the spatial frequency of the fringe pattern can vary continuously. Our method generates the formation of a sinusoidal intensity fringe pattern by the interference of two monochromatic plane waves, and straightforward projects it onto the CCD array under test. The construction of the experimental device is based on the Fresnel Double-Mirror structure. A 2.5 mw He-Ne laser with the wavelength of 632.8 nm is used as the light source, the laser beam is spatially filtered by a 10 μm pinhole and expanded to a diameter of 30 mm, and the resulting wave front is divided by two mirrors, which incline to each other at a small angle, and interfered. One of the mirrors is rotatable to vary the frequency of the pattern. The CCD array is mounted on a stage, which is also rotatable to make that the CCD array takes different angle with the fringe pattern direction, to receive the patterns. With the method we provided, the spatial frequency can be extended to some 2 times the Nyquist frequency of the CCD array to study the aliasing effect. In the Cartesian coordinates, the x- and y- axis MTFs (at angle 0° and 90°) of the CCD array were measured, the other three MTFs (at angle 26.56°, 45° and 63.44°), which nobody has done before, were also tested offering a more comprehensive characterization of the CCD array.

Holographic interference fringes, in general, contain information about the whole -field surface deformation of the test object over the entire surface. In order to analyse the fringe patterns, it is necessary that the centre of fringes should be well-defined so that accurate results could be extracted from the fringe pattern. Hence, it is necessary to process a poor quality fringe pattern by removing the noise before it is used for further analysis. The image degradation occurs due to (i) Non-Uniform light intensity used for illumination, (ii) Object surface and background characteristics and (iii) Presence of speckle noise. Hence, we need a special technique to improve the fringe quality i.e., contrast and visibility. This will enable extraction of central line of the fringes and the fringe order more accurately. In this paper, various processes used to achieve the improvement of fringe pattern stored in digital forn are presented. Different types of filters are evaluated to identify their performance. An interactive image processing software package has been described. In this package, the user has the option to choose different combinations of processes till an acceptable quality of fringe patterns are obtained. Results of sample images of different qualities are shown to highlight the improvement of fringe quality.

A novel Hilbert transform algorithm for detecting phase from fringe pattern is proposed.Only one interference pattern is required for the phase evaluation.In practice,the Hilbert transform based on the Fourier transformation eliminates all negative frequency components,and any phase variation in the fringe pattern having negative local spatial frequency can not be correctly reconstructed.A procedure for detection of regions having zero spatial frequency in the fringe pattern is proposed by an estimation function for complicated phase distribution.A binary matrix is used for modifying wrapped phase of complicated phase distribution fringe pattern, and a method for removing the bias component by twice Hilbert transform is proposed.The correct values of phase is obtained by an unwrapping process.The performance of the proposed method is evaluated by computer simulation.

In this paper, a novel methodology to process fringe pattern is presented. The core of the signal processing technique is the use of the direction information, a modulo 2pi quantity that locally informs about the direction along which fringes grow with maximum rate. By using this information, it was possible to perform adaptive, direction- and orientation-based operations on fringe images in order to remove unwanted effects, to enhance the contrast and to extract the phase information encoded. The method has been applied on shadow moire interferograms with carrier fringes in order to measure the surface of small objects. The developed algorithm allows to process fringes whose phase information is not monotonically increasing everywhere and to more accurately estimate the phase itself. Results from two experimental fringe patterns are presented. Results are compared with measurements performed by means of a conoscopic system used as a reference. Hence, it was possible to calculate the uncertainty of the performed measurements. Besides the possibility to decode fringe patterns presenting closed fringes, the proposed method provides measurements characterized by an uncertainty more than halved compared to Fourier-based methods

In the present work we present a simple comparative analysis of the results in the optical Fourier transform profilometry which fringe projection is produced by two different methods, dynamic moiré-like patterns and Michelson interferometer. First, the Fourier transform profilometry technique is applied in the projected moiré fringe pattern onto an object surface. Then, this result is compared to the Michelson fringe pattern projection in the same method of profilometry that is applied using the same test object. We have conclude that dynamic moiré-like fringe patterns could be used with some advantages, comparatively to the results obtained by the classical Michelson fringe patterns.

Two practical computer-aided optical techniques for full-field surface shape measurement are presented, one for diffuse surfaces and the other for specularly reflective surfaces. The former technique is based on projecting a computer-generated fringe pattern onto a diffuse surface, and the latter is based on reflecting the fringe pattern from a specularly reflective surface. The fringe pattern is perturbed in accordance with the object surface with the fringe phase bearing information on the depth/slope of the object surface. The computer-generated fringe pattern conveniently enables the fringe phase to be manipulated, and hence the determination of the phase distribution using a phase extraction algorithm. Instead of deriving the mathematical relationship between the fringe phase distribution and the surface depth/slope, this relationship is obtained by calibration. The techniques described can be easily implemented for rapid measurement of 3-D surface shapes in an industrial setting.

We have developed a one-dimensional theory and a computer model for synthetically imaging scenes using a novel fringe scanning/Fourier transform technique. Our method probes a scene using two interfering beams of slightly different frequency. These beams form a moving fringe pattern which scans the scene and resonates with any spatial frequency components having the same spatial frequency as the scanning fringe pattern. A simple, non-imaging detector above the scene observes any scattered radiation from the scene falling onto it. If a resonance occurs between the scanning fringe pattern and the scene, then the scattered radiation will be modulated at the difference frequency between the two probing beams. By changing the spatial period of the fringe pattern and then measuring the amplitude and phase of the modulated radiation that is scattered from the scene, the Fourier amplitudes and phases of the different spatial frequency components making up the scene can be measured. A synthetic image of the scene being probed can be generated from this Fourier amplitude and phase data by taking the inverse Fourier transform of this information. This technique could be used to image objects using light, ultrasonic, or other electromagnetic or acoustic waves.

Adaptive filter for enhancement of fringe patterns

With the development of science and technology and industrial production, the application of three-dimensional shape measurement technology in the fields of machine vision, industrial monitoring, mechanical engineering and medical testing has become increasingly widespread. The optical three-dimensional shape measurement technology is a method that uses a series of optical methods to obtain the three-dimensional information of the measured object, and the structured light measurement method is a widely used measurement method. In the structured light measurement method, the generation of fringe patterns is a very important link. Here, we use holographic method to generate a fringe pattern whose period and phase can be easily modulated. First, a black and white fringe pattern with a certain spatial frequency is generated according to the cosine structured light period and phase. The spatial frequency of the black and white fringe is determined by the spatial frequency of the structured light to be generated and the magnification of the projection system. A prism phase that can cause lateral movement is applied to the black part of the black and white stripes, so that the light incident on the black area deviates from the optical axis to the first order of diffraction, while the light incident on other parts (without being modulated) continues to travel along the optical axis. In this way, the deviated beam is bright and dark, and finally structured illumination is obtained. Theories and experiments verify the effectiveness of the method. The method to generate fringe patterns is simple, fast, accurate and can be conveniently controlled, and can be well applied to three-dimensional shape measurement technology.

Deflectometry is a well-known method to characterize pure phase objects by measuring the deformation of fringes. In principle, the retrieved magnitude is the partial derivative of the phase along the coordinate orthogonal to the fringes. In order to recover the phase it is necessary to know the derivatives in two orthogonal directions, which is usually achieved by rotating 90° the original fringes and acquiring a new deformed pattern. This "time-multiplexed" two-dimensional deflectometry is a time-consuming operation if the goal is to characterize phase objects in real time. In the present paper we propose a kind of two-dimensional deflectometry that allows acquisition of fringe patterns in two orthogonal directions in a single frame. The proposed procedure utilizes a two-dimensional ("additive") fringe pattern that allows the application of Takeda's method to each coordinate independently. The advantage of the method (with respect to the traditional one) is that it simplifies the setup and reduces the acquisition time. Validation experiments are presented.