Calibration method of multi-projector display system with extra-large FOV and quantitative registration accuracy analysis.

The calibration of multi-projector display with extra-large field of view (FOV) and quantitative registration analysis for realizing perfect visual splicing is crucial and difficult. In this paper, we present a novel calibration method to realize the seamless splicing for a multi-projector display system with extra-large FOV. The display consists of 24 projectors, covering the range of 360 degrees in the longitude direction and 210 degrees in the latitude direction. A wide-angle camera fixed on a rotating optical system is used to scan the entire display scene and establish point-to-point correspondence between projector pixels and spatial points using the longitude and latitude information. Local longitude table and latitude table are established on the target of the wide-angle camera. A deterministic method is proposed to locate the North Pole of the display. The local tables corresponding to different camera views can be unified based on the image of the North Pole to form global longitude and latitude tables of arbitrary free-form surface. The mapping between the projector pixels and the camera pixels is established by inverse projection technique, and then each pixel of each projector can be appointed a pair of unique longitude and latitude values. A quantitative registration accuracy analysis method is proposed for multi-projector display system, in which, three-frequency temporal unwrapping method based on coded longitude and latitude values is applied to calculate the registration accuracy. Experiments prove that the registration error of the multi-projector system is less than 0.4 pixels.

Uniaxial 3D Measurement with Auto-Synchronous Phase-Shifting and Defocusing Based on a Tilted Grating.

Conventional uniaxial techniques generally require shifting objects or projection grating with the assistance of a high-precision mechanical moving component. To overcome this limitation, we propose a novel uniaxial 3-D shape measurement system with auto-synchronous phase-shifting and defocusing by using a tilted and fixed projection grating. The tilted focused image plane (FIP), which is reflected by a mirror at about 90 degrees, could be shifted across the measured surface by slightly rotating the mirror within a small angle range. This procedure will simultaneously introduce the change in defocusing and phase-shifting of the fringe. The modulation curve of each point can be deciphered by Fourier fringe analysis after a sequence of fringe intensities is acquired. Since both the measured object and projection grating are fixed, the proposed method could make the measurement system more compact and flexible. Both computer simulation and experiments are carried out to demonstrate the validity of this proposed system.

Flexible gamma calculation algorithm based on probability distribution function in digital fringe projection system.

The gamma effect of phase-measuring profilometry systems yields nonlinear errors, which will substantially reduce the 3D shape measurement accuracy. Here, a robust and flexible gamma correction method based on the probability distribution function (PDF) of the wrapped phase is presented. First, a series of PDF curves are generated from the simulated wrapped phase distributions with different gamma values. Second, an experimental PDF curve will be produced after obtaining the wrapped phase from the captured three-step phase-shift fringe images. Then, a correlation procedure will be used to find the most similar PDF curve from the simulated PDF curves, and the gamma value of the matched PDF curve is that of the current system. Note that the gamma value detected by this method will be smaller than the true value due to the defocusing effect of the projection system with a large aperture. Therefore, an improved PDF-based algorithm, which projects two sets of three-step phase-shifting sinusoidal fringe patterns with different pre-coded gamma values and produces two PDF curves, is also added. Then after one more correlation procedure, a more accurate systematic gamma value could be calculated. It does not need large-step phase-shift images and 2×3 fringe images are quite enough. The experimental results show that the technique is very fast, easy to use and quite accurate.

Experimental study of temporal-spatial binary pattern projection for 3D shape acquisition.

Three-dimensional (3D) acquisition of an object with modest accuracy and speed is of particular concern in practice. The performance of digital sinusoidal fringe pattern projection using an off-the-shelf digital video projector is generally discounted by the nonlinearity and low switch rate. In this paper, a binary encoding method to encode one computer-generated standard sinusoidal fringe pattern is presented for circumventing such deficiencies. In previous work [Opt. Eng.54, 054108 (2015)OPEGAR0091-328610.1117/1.OE.54.5.054108], we have developed a 3D system based on this encoding tactic and showed its prospective application. Here, we first build a physical model to explain the mechanism of how to generate good sinusoidality. The phase accuracy with respect to the conventional spatial binary encoding method and sinusoidal fringe pattern is also comparatively evaluated through simulation and experiments. We also adopt two phase-height mapping relationships to experimentally compare the measurement accuracy among them. The results indicate that the proposed binary encoding strategy has a comparable performance to that of sinusoidal fringe pattern projection and enjoys advantages over the spatial binary method under the same conditions.

Accurate and fast 3D surface measurement with temporal-spatial binary encoding structured illumination.

Balancing the accuracy and speed for 3D surface measurement of object is crucial in many important applications. Binary encoding pattern utilizing the high-speed image switching rate of digital mirror device (DMD)-based projector could be used as the candidate for fast even high-speed 3D measurement, but current most schemes only enable the measurement speed, which limit their application scopes. In this paper, we present a binary encoding method and develop an experimental system aiming to solve such a situation. Our approach encodes one computer-generated standard 8 bit sinusoidal fringe pattern into multiple binary patterns (sequence) with designed temporal-spatial binary encoding tactics. The binary pattern sequence is then high-speed and in-focus projected onto the surface of tested object, and then captured by means of temporal-integration imaging to form one sinusoidal fringe image. Further the combination of phase-shifting technique and temporal phase unwrapping algorithm leads to fast and accurate 3D measurement. The systematic accuracy better than 0.08mm is achievable. The measurement results with mask and palm are given to confirm the feasibility.

Modulation measuring profilometry with auto-synchronous phase shifting and vertical scanning.

To determine the shape of a complex object with vertical measurement mode and higher accuracy, a novel modulation measuring profilometry realizing auto-synchronous phase shifting and vertical scanning is proposed. Coaxial optical system for projection and observation instead of triangulation system is adopted to avoid shadow and occlusion. In the projecting system, sinusoidal grating is perpendicular to optical axis. For moving the grating along a direction at a certain angle to optical axis, 1D precision translation platform is applied to achieve purposes of both phase-shifting and vertical scanning. A series of fringe patterns with different modulation variations are captured by a CCD camera while scanning. The profile of the tested object can be reconstructed by the relationship between the height values and the modulation distributions. Unlike the previous method based on Fourier transform for 2D fringe pattern, the modulation maps are calculated from the intensity curve formed by the points with definite pixel coordinates in the captured fringe patterns. The paper gives the principle of the proposed method, the set-up of measurement system and the method for system calibration. Computer simulation and experiment results proved its feasibility.

Robust self-calibration three-dimensional shape measurement in fringe-projection photogrammetry.

Commonly, fringe-projection photogrammetry involves two independent stages: system calibration and measurement. The measurement accuracy largely depends on the calibration procedure. However, the results of system calibration may be unstable in different occasions. In this Letter, we propose a robust self-calibration 3D shape measurement in fringe-projection photogrammetry by combining control and measurement points. The control points with known 3D coordinates are provided on the checkerboard, and the measurement points are identified by absolute phase information in the deformed fringes. The introduction of control points in the nonlinear collinearity equations can be regarded as invariant in the optimization procedure, which enhances the measurement robustness. Compared to the binocular model in fringe-projection technique, moreover, multiple-view ray intersection is utilized to reflect the advantage of photogrammetry in the fringe-projection 3D measurement.

Using concentric circles and wedge grating for camera calibration.

This paper presents a method for camera calibration based on the orthogonal vanishing point calibration using concentric circles grating and wedge grating. This method, which we believe is new, uses the high-precision characteristics of phase extraction to obtain the feature points, thus decreasing the calibration errors caused by the traditional marker extraction errors of gray pattern. According to the simulation experiment analysis results, the concentric circles grating was designed with seven periods and the wedge grating was designed with four periods. In the real measuring experiment, the grating target and the similar gray concentric circles target were used to calibrate the camera, respectively. Through comparing the reprojective errors of the two methods, the method proposed is proven to improve the calibration accuracy and robustness for the vanishing point calibration algorithm.

Two-dimensional wavelet transform for reliability-guided phase unwrapping in optical fringe pattern analysis.

This paper theoretically discusses modulus of two-dimensional (2D) wavelet transform (WT) coefficients, calculated by using two frequently used 2D daughter wavelet definitions, in an optical fringe pattern analysis. The discussion shows that neither is good enough to represent the reliability of the phase data. The differences between the two frequently used 2D daughter wavelet definitions in the performance of 2D WT also are discussed. We propose a new 2D daughter wavelet definition for reliability-guided phase unwrapping of optical fringe pattern. The modulus of the advanced 2D WT coefficients, obtained by using a 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 that represents the reliability of the retrieved phase data. Computer simulation and experimentation show the validity of the proposed method.

Three-dimensional shape measurement of large-aperture aspheric mirrors by off-axis null Ronchi test.

An off-axis null Ronchi test is presented to measure the three-dimensional (3D) shape of a large-aperture aspheric mirror. The method designs curved fringe patterns as null sinusoidal gratings by means of phase information and ray tracing. In the process of measurement, the curved fringe patterns are displayed on a transmission-type liquid crystal display (T-LCD) screen, and a CCD camera records the fringe patterns containing the information of deviations of the mirror. The slopes of the deviations of the mirror are obtained by using the recorded fringe patterns. The deviations are restored by integrating, and then the 3D shape of the mirror can be reconstructed. Compared with the classical null Ronchi test, the method can provide enough measured data points and avoid the jagged edges of bands on the null gratings. Moreover, the method can conveniently change period and direction of the curved fringes and accurately control phase shifting. Computer simulations and a preliminary experiment are presented to show the performance of the method.

Flexible geometrical calibration for fringe-reflection 3D measurement.

System geometrical calibration is a challenging task in fringe-reflection 3D measurement because the fringe displayed on the LCD screen does not lie within the camera's field of view. Commonly, a flat mirror with markers can accomplish system geometrical calibration. However, the position of the markers must be precisely located by photogrammetry in advance. In this Letter, we introduce a calibration method by use of a markerless flat mirror. Experiments in phase measuring deflectometry demonstrate that the proposed method is simple and flexible.

Three-dimensional shape measurement of aspheric mirrors with fringe reflection photogrammetry.

Three-dimensional (3D) shape measurement of an aspheric mirror with fringe reflection photogrammetry involves three steps: correspondence matching, triangulation, and bundle adjustment. Correspondence matching is realized by absolute phase tracking and triangulation is computed by the intersection of reflection and incidence rays. The main contribution in this paper is constraint bundle adjustment for carefully dealing with lens distortion in the process of ray intersection, as compared to the well-known grating reflection photogrammetry. Additionally, a free frame is proposed to alleviate troublesome system geometrical calibration, and constraint bundle adjustment is operated in the free frame to refine the 3D shape. Simulation and experiment demonstrate that constraint bundle adjustment can improve absolute measurement accuracy of aspheric mirrors.

Measurement based on fringe reflection for testing aspheric optical axis precisely and flexibly.

A method based on fringe reflection is proposed to measure the optical axis of an aspheric mirror precisely and flexibly. In the measurement, a screen displaying a fringe pattern is moved along its normal direction, and a camera is located beside and observes the fringe pattern reflected via a tested surface. This method can test the optical axis of an aspheric mirror quantitatively before measuring the absolute height of the tested surface. And it can be combined with some presented methods that need to fit the aspheric mirror according to the optical axis to measure the surface. To validate the ability of this method, it is combined with one of the presented methods to measure absolute height of an aspheric mirror precisely and flexibly. Computer simulations and preliminary experiment validate the feasibility of this method.

Quality-guided phase unwrapping technique: comparison of quality maps and guiding strategies.

Quality-guided phase unwrapping is a widely used technique with different quality definitions and guiding strategies reported. It is thus necessary to do a detailed comparison of these approaches to choose the optimal quality map and guiding strategy. For quality maps, in the presence of noise, transform-based methods are found to be the best choice. However in the presence of discontinuities, phase unwrapping is itself unresolved and hence quality-guided phase unwrapping is not sufficient. For guiding strategies, classical, two-section, and stack-chain guiding strategies are chosen for comparison. If accuracy is the foremost criterion then the classical guiding strategy with a data structure of indexed interwoven linked list is best. If speed is of essence then the stack-chain guiding strategy is the one to use.

Fringe inverse videogrammetry based on global pose estimation.

Fringe inverse videogrammetry based on global pose estimation is presented to measure a three-dimensional (3D) coordinate. The main components involve an LCD screen, a tactile probe equipped with a microcamera, and a portable personal computer. The LCD is utilized to display fringes, a microcamera is installed on the tactile probe, and the 3D coordinate of the center of the probe tip can be calculated through the microcamera's pose. Fourier fringe analysis is exploited to complete subpixel location of reference points. A convex-relaxation optimization algorithm is employed to estimate the global camera pose, which guarantees global convergence compared with bundle adjustment, a local pose estimation algorithm. The experiments demonstrate that fringe inverse videogrammetry can measure the 3D coordinate precisely.

A novel encoded-phase technique for phase measuring profilometry.

Three-dimensional (3-D) shape measurement using a novel encoded-phase grating is proposed. The projected sinusoidal fringe patterns are designed with wrapped and encoded phase instead of monotonic and unwrapped phase. Phase values of the projected fringes on the surface are evaluated by phase-shift technique. The absolute phase is then restored with reference to the encoded information, which is extracted from the differential of the wrapped phase. To solve the phase errors at some phase-jump areas, Hilbert transform is employed. By embedding the encoded information in the wrapped phase, there is no extra pattern that needs to be projected. The experimental results identify its feasibility and show the possibility to measure the spatially isolated objects. It will be promising to analyze dynamic objects.

Universal calculation formula and calibration method in Fourier transform profilometry.

We propose a universal calculation formula of Fourier transform profilometry and give a strict theoretical analysis about the phase-height mapping relation. As the request on the experimental setup of the universal calculation formula is unconfined, the projector and the camera can be located arbitrarily to get better fringe information, which makes the operation flexible. The phase-height calibration method under the universal condition is proposed, which can avoid measuring the system parameters directly. It makes the system easy to manipulate and improves the measurement velocity. A computer simulation and experiment are conducted to verify its validity. The calculation formula and calibration method have been applied to measure an object of 22.00 mm maximal height. The relative error of the measurement result is only 0.59%. The experimental results prove that the three-dimensional shape of tested objects can be reconstructed exactly by using the calculation formula and calibration method, and the system has better universality.

Analysis and identification of phase error in phase measuring profilometry.

Both the analysis of phase errors which occur at the abrupt discontinuities in phase measuring profilometry (PMP) and the identification method are presented in this paper. The sampling effect of CCD will cause a dilution of accuracy in PMP, especially at abrupt discontinuities on the object surface. The existing methods cannot efficiently identify the abrupt discontinuities. We analyze the relationship between the phase, the height and the equivalent wavelength. By viewing the phase as the argument of a vector we find out that CCD sampling introduces errors into the measurement and the phase is nonlinear to the equivalent wavelength at the abrupt discontinuities. Therefore temporal phase unwrapping (TPU) is introduced into the measurement to identify the abrupt discontinuities. Computer simulations and practical experiment validate the feasibility of this method.

Wavelet ridge techniques in optical fringe pattern analysis.

Wavelet ridge techniques utilizing daughter wavelets under two different kinds of definitions in the optical fringe pattern analysis are theoretically clarified. The clarification reveals that the phase of the optical fringe pattern is equal to that of its wavelet transform coefficients on the ridge using both of the two wavelet definitions. The differences between the two definitions in the performance of wavelet transform algorithms are verified in theory. The strict relations between the instantaneous frequency of the fringe pattern and the scale parameter at the wavelet ridge position are also theoretically clarified for the phase gradient method. A simple method for selecting the scale vector is introduced. Computer simulations and experiments reveal the correctness of the clarification and the validity of the proposed method.

A novel phase measuring deflectometry for aspheric mirror test.

A method based on fringe reflection is presented to measure the aspheric mirror with higher precise. This method measures the absolute height of the aspheric mirror with dummy paraboloid, while the camera is located beside the optical axis of the test surface. It can be used to measure the aspheric mirror with high deviation. And for locating the camera beside the optical axis, this method doesn't have occlusion problem and can do the measurement more flexibility. Furthermore, compared with the traditional PMD, this method measures the tested surface with dummy paraboloid instead of the intersection of two straight lines, so it doesn't need to calibrate the image projection vectors. And the errors of the calibration influence this method less than the traditional method. Therefore, this method can measure the high deviation aspheric mirror with higher precise even if the calibration precise isn't very high. Computer simulations and preliminary experiment validate the feasibility of this method.