An improved Fourier transform profilometry and phase coding for 3D shape measurement

In-situ 3-D shape measurements with submicron shape uncertainty of fast rotating objects in a cutting lathe are expected, which can be achieved by simultaneous distance and velocity measurements. Conventional tactile methods, coordinate measurement machines, only support ex-situ measurements. Optical measurement techniques such as triangulation and conoscopic holography offer only the distance, so that the absolute diameter cannot be retrieved directly. In comparison, laser Doppler distance sensors (P-LDD sensor) enable simultaneous and in-situ distance and velocity measurements for monitoring the cutting process in a lathe. In order to achieve shape measurement uncertainties below 1 μm, a P-LDD sensor with a dual camera based scattered light detection has been investigated. Coherent fiber bundles (CFB) are employed to forward the scattered light towards cameras. This enables a compact and passive sensor head in the future. Compared with a photo detector based sensor, the dual camera based sensor allows to decrease the measurement uncertainty by the order of one magnitude. As a result, the total shape uncertainty of absolute 3-D shape measurements can be reduced to about 100 nm.

In this paper, a three-dimensional (3D) shape measurement method based on structured light field imaging is proposed, which contributes to the biomedical imaging. Generally, light field imaging is challenging to accomplish the 3D shape measurement accurately, as the slope estimation method based on radiance consistency is inaccurate. Taking into consideration the special modulation of structured light field, we utilize the phase information to substitute the phase consistency for the radiance consistency in epi-polar image (EPI) at first. Therefore, the 3D coordinates are derived after light field calibration, but the results are coarse due to slope estimation error and need to be corrected. Furthermore, the 3D coordinates refinement is performed based on relationship between the structured light field image and DMD image of the projector, which allows to improve the performance of the 3D shape measurement. The necessary light field camera calibration is described to generalize its application. Subsequently, the effectiveness of the proposed method is demonstrated with a sculpture and compared to the results of a conventional PMP system.

Rapid and automatic optimal exposure control for digital fringe projection technique

Color-coded fringe projection profilometry (FPP) is one of the most important single-frame three-dimensional (3D) shape measurement techniques. Transverse chromatic aberration (TCA) in a color-coded FPP system yields imaging deviations, which will result in 3D shape measurement error. In this work, a TCA compensation method for color-coded FPP is proposed. The proposed method establishes the relationship among phase, pixel deviation, and imaging position for decreasing the 3D shape measurement error introduced by TCA. Compared to existing methods that use the relationship among depth, pixel deviation, and imaging position or polynomial fitting for each pixel, the proposed method offers the merits of precise and simple implementation, since it voids the cumulative error in-depth calculation and removes the time-consuming process of polynomial fitting for each pixel. For validation, a color-coded FPP system is established and calibrated. Two verification experiments, including a translation test and 3D shape measurement of a regular spherical object, are conducted with the calibrated system. Experimental results demonstrate that the proposed TCA compensation method is capable of effectively reducing the 3D shape measurement error caused by TCA.

Binary coding methods have been widely used for three-dimensional (3D) shape measurement. However, traditional binary coding methods always require a sequence of binary patterns to encode the fringe order. This paper presents a spatial-temporal binary coding (STBC) method for 3D shape measurement with three binary patterns, including a spatial pattern and two temporal patterns. Specifically, the spatial pattern is used to encode a 4-bit spatial code, and the temporal patterns are used to encode the 2-bit temporal code. By combining the spatial code and the temporal code, 6-bit code words can be obtained that distinguish 26=64 fringe periods of sinusoidal phase-shifting patterns. A robust dual-region labeling decoding scheme is also developed to extract the 6-bit code word for fringe order determination, and then absolute-phase unwrapping can be carried out. Experiments have been conducted, and their results confirm that the STBC method can reliably reconstruct the 3D shapes of measured objects with only three binary patterns.

Fourier transform profilometry (FTP) is one of the frequently adopted three-dimensional (3D) shape measurement methods due to its ability to recover single-shot 3D shapes, yet it is challenging to retrieve the absolute phase map solely from one single grayscale fringe image. This paper presents a computational framework that overcomes this limitation of FTP with digital fringe projection (DFP). By using geometric constraints, an absolute phase map can be retrieved point-by-point from one single grayscale fringe image. Experiments demonstrate the success of our proposed framework with single-shot absolute 3D shape measurement capability.

Blade is the key component of the aero-engine. In generally, it requires precise size and accurate shape, so the three-dimensional shape measurement of the blade is very important. Fringe projection profilometry is generally used to measure the 3D shape of an object, because of the advantages of non-contact operation, full-field acquisition, high resolution, and fast data processing. In this paper, 3D shape measurement method based on surface structured light that combination of gray-code and phase-shift projection is proposed. The wrapped phase of the blade is got by the four-step phase-shift method. In the projection process of the gray-code, due to the ambient light, different surface reflectance and surface physical discontinuous, the edge of gray-code becomes smooth, leading to decode error, so that the gray-code pattern must be binaried before decode. Through the accurate binarization of the blade gray-code pattern, the decoding cycle of the blade is achieved, and the unwrapped phase is achieved by phase unwrapping. Then the unwrapped phase difference between the blade and reference plane is got, the height of the blade can be obtained by the relationship between the phase difference and the height. The experimental and simulation results show that the proposed method can achieve a high precision, high speed and low cost 3D shape measurement of the blade. The measurement accuracy reaches 0.03 mm. The proposed method extends the reliability and practicality of the fringe projection profilometry.

Conventional three-dimensional (3D) shape measurement methods are typically generic to all types of objects. Yet, for many measurement conditions, such a level of generality is inessential when having the preknowledge of the object geometry. This paper introduces a novel adaptive algorithm for absolute 3D shape measurement with the assistance of the object computer-aided-design (CAD) model. The proposed algorithm includes the following major steps: (1)export the 3D point cloud data from the CAD model; (2)transform the CAD model into the camera perspective; (3)obtain a wrapped phase map from three phase-shifted fringe images; and (4)retrieve absolute phase and 3D geometry assisted by the CAD model. We demonstrate that if object CAD models are available, such an algorithm is efficient in recovering absolute 3D geometries of both simple and complex objects with only three phase-shifted fringe images.

Three-dimensional (3D) shape measurement of fringe projection profilometry (FPP) with high speed and accuracy is required in many applications. The measurement speed of FPP system is mainly limited by the low frame rate of pattern projection. Although defocusing binary patterns can be used to increase the measurement speed greatly, it will decrease the measurement depth. To this end, a novel triangular pattern generation method is proposed in this paper. By designing and projecting binary strip patterns with focused projector, images of triangular patterns can be then acquired with high frame rate. Fast and accurate 3D shape measurement can be finally obtained by using phase-shifting triangular patterns. Compared with the traditional sinusoidal patterns, the proposed method can improve the projection rate more than 4 times. Moreover, the proposed method will not decrease the measurement depth. Experimental results are given to confirm the validity of the proposed method.

Three-dimensional (3D) shape measurement based on fringe pattern projection techniques has been commonly used in various fields. One of the remaining challenges in fringe pattern projection is that camera sensor saturation may occur if there is a large range of reflectivity variation across the surface that causes measurement errors. To overcome this problem, a novel fringe pattern projection method is proposed to avoid image saturation and maintain high-intensity modulation for measuring shiny surfaces by adaptively adjusting the pixel-to-pixel projection intensity according to the surface reflectivity. First, three sets of orthogonal color fringe patterns and a sequence of uniform gray-level patterns with different gray levels are projected onto a measured surface by a projector. The patterns are deformed with respect to the object surface and captured by a camera from a different viewpoint. Subsequently, the optimal projection intensity at each pixel is determined by fusing different gray levels and transforming the camera pixel coordinate system into the projector pixel coordinate system. Finally, the adapted fringe patterns are created and used for 3D shape measurement. Experimental results on a flat checkerboard and shiny objects demonstrate that the proposed method can measure shiny surfaces with high accuracy.

Three-dimensional (3D) shape measurement systems based on diffuse reflection of projected structured light do not deliver reliable data when measuring glossy, transparent, absorbent, or translucent objects. In recent years, we have developed a method based on stereo recording with infrared cameras and projection of areal aperiodic sinusoidal thermal patterns to detect such objects. However, the measurements took longer than 10 s, up to minutes; moreover, the measurement accuracy was improvable. Now, we have succeeded in both drastically reducing measurement time and significantly increasing measurement quality. This finally provides a technique for reliably measuring transparent objects, e.g., in series production. We demonstrate measurement examples achieved within 1 s and with 3D standard deviations less than 10 µm.

Fringe projection profilometry (FPP) is a three-dimensional (3D) shape measurement method that involves projecting fringe patterns onto the object. A phase map retrieved from these fringe images is used for reconstructing the 3D surface of the object. Fourier transform and phase-shifting are two of the widely used fringe analysis techniques for performing 3D shape measurement using FPP. Fourier transform profilometry (FTP) has the advantage of performing high-speed measurement due to its single-shot nature. However, the reconstructed 3D surface has artifacts and high noise, specifically on the edges. On the other hand, phase-shifting profilometry (PSP) has the advantage of higher accuracy (relatively less noise level) but compromises on measurement speed. In this research, we propose a deep learning method to enhance the quality of the FTP phase maps using an efficient deep learning model called phase map enhancement net (PMENet). PMENet takes an FTP phase map as input and predicts a high-quality phase map in a supervised manner by using the phase maps obtained from 18-step PSP as ground truth. The training dataset was generated using a virtual FPP system. Validations were conducted on both the simulated data (generated by virtual FPP system) and the real-world data. The experimental results demonstrate that the trained neural network model can successfully improve the quality of the 3D geometric reconstruction with FTP and reduced the mean and root-mean-square error by 66% and 43%, respectively.

3D shape measurement based on structured light system is a field of ongoing research for the past two decades. For 3D shape measurement using commercial projector and digital camera, the nonlinear gamma of the projector and the nonlinear response of the camera cause the captured fringes having both intensity and phase errors, and result in large measurement shape error. This paper presents a simple intensity error correction process for the phase-shifting method. First, a white flat board is projected with sinusoidal fringe patterns, and the intensity data is extracted from the captured image. The intensity data is fitted to an ideal sine curve. The difference between the captured curve and the fitted sine curve are used to establish an intensity look-up table (LUT). The LUT is then used to calibrate the intensities of measured object images for establishing 3D object shapes. Research results show that the measurement quality of the 3D shapes is significantly improved.

In this paper, a whole-field and high-speed optical three-dimensional (3D) shape measurement for the vibration pattern of a drumhead based on Fourier Transform Profilometry (FTP) is presented and verified by experiment. A projected sinusoidal fringe pattern on the surface of measured drumhead is dynamically deformed with the vibration of the membrane and grabbed by a high-speed camera. The 3D shape deformation of the drumhead at each sampling instant can be recovered from demodulating the phase of this obtained sequence of fringe patterns. The vibration of the membrane of a Chinese drum has been measured with a high-speed sampling rate (1,000 fps) and a standard deviation (0.075 mm). This method should be helpful in studying the acoustic characteristic and the manufacture technique of the percussion instrument.

A height estimating function is proposed based on geometric analysis for a three-dimensional (3-D) measurement system using a digital light processing (DLP) projector and a camera. The proposed 3-D shape measurement method is a hybrid method that combines the geometric parameter measuring method and the least squares method. This method uses the phase-to-height relationship for one line by plane analysis, and the related parameters are estimated using the least squares method. The proposed method has one function per image line instead of one function per image pixel. Sinusoidal fringe patterns of the projector are projected on the object, and the phase of the measuring point is calculated from the camera image. Then, the relationship between the phase by fringe patterns and the height of the measuring point is described as a parameter of the horizontal coordinate on the image plane. Thus, the 3-D shape of the object can be obtained. Our experiments show that the error of the modeling function is within ±0.1 mm when the x-z working range is 100×50 mm. Therefore, the proposed method can dramatically reduce the number of mapping functions needed for 3-D measurement using the geometric relationship between the projector and camera.