Blind color isolation for color-channel-based fringe pattern profilometry using digital projection

We present an algorithm for estimating the color demixing matrix based on the color fringe patterns captured from the reference plane or the surface of the object. The advantage of this algorithm is that it is a blind approach to calculating the demixing matrix in the sense that no extra images are required for color calibration before performing profile measurement. Simulation and experimental results convince us that the proposed algorithm can significantly reduce the influence of the color cross talk and at the same time improve the measurement accuracy of the color-channel-based phase-shifting profilometry.     

An online triple-frequency color-encoded fringe projection profilometry for discontinuous object

Abstract

An online triple-frequency color-encoded fringe projection profilometry is proposed to measure the complex and discontinuous object at straight-line movement. N frames of color fringe patterns are specially designed. Three grayscale sinusoidal grating patterns with geometric progression frequency growth are encoded into red (R), green (G), and blue (B) channels separately to compose a color-encoded fringe pattern. If these three grayscale sinusoidal grating patterns are phase-shifted N steps with an equivalent shift phase of 2π/N, they can compose the corresponding N frames of color-encoded fringe patterns as above respectively. In order to avoid the movement’s interference to the phase shifting, position adjustment should be done to guarantee the phase-shifting direction to be perpendicular to the moving direction. While these N frames of specially designed color-encoded fringe patterns are projected onto the moving object one by one, the corresponding deformed color patterns are captured by a CCD camera in real time. By color separating, color crosstalk compensation, pixel matching, and phase calculation, three wrapped phase at different frequencies can be extracted. The unwrapped phase can be solved by a simplified algorithm based on temporal phase unwrapping method from the relationship of the three wrapped phase at the same pixel. Thus, it is very suitable to measure the online complex and discontinuous objects at straight-line movement. The experimental results show the feasibility and the validity of the proposed method.     

Two-step phase-shifting fringe projection profilometry: intensity derivative approach

A new two-step phase-shifting fringe projection profilometry is proposed. The slowly variable background intensity of fringe patterns is removed by the use of an intensity differential algorithm. The high-resolution differential algorithm is achieved based on global interpolation of fringe gray level on a subpixel scale. Compared with the traditional three- or four-step phase-shifting method, the profile measurement is sped up with this approach. Computer simulation and experimental performance are evaluated to demonstrate the validity of the proposed measurement method. The experimental results compared with those of the four-step phase-shifting method are presented.     

Precise and fast phase wraps reduction in fringe projection profilometry

Phase wraps in a 2D wrapped phase map can be completely eliminated or greatly reduced by frequency shifting. But it usually cannot be optimally reduced using conventional fast Fourier transform (FFT) because the spectrum can be shifted only by a integer number in the frequency domain. In order to achieve a significant phase wrap reduction, we propose a fast and precise two-step method for phase wraps reduction in this paper, which is based on the iterative local discrete Fourier transform (DFT). Firstly, initial estimate of the frequency peak is obtained by FFT. Then sub-pixel spectral peak with high resolution is determined by iteratively upsampling the local DFT around the initial peak location. Finally, frequency shifting algorithm that operates in the spatial domain is used to eliminate phase wraps. Simulations and experiments are conducted to demonstrate the superb computing efficiency and overall performance of the proposed method.     

双色正弦投影傅里叶变换轮廓术方法研究

提出双色正弦条纹投影方法来提高 FTP 的测量范围并保持其实时特点。只需采集一帧双色变形条纹,从中分离出两个有 π 位相差的分量,通过背景和对比度校正,得到一帧消零频的变形条纹图,并且自动生成物体轮廓的二元模板。此模板结合调制度信息相可以生成可靠性模板,指导相位展开,避免物体轮廓以外相位展开误差的传递;结合参考条纹可以完成变形条纹的扩充,提高频域的分辨率。     

Effective bias removal for fringe projection profilometry using the dual-tree complex wavelet transform

When reconstructing the three-dimensional (3D) object height profile using the fringe projection profilometry (FPP) technique, the light intensity reflected from the object surface can yield abruptly changing bias in the captured fringe image, which leads to severe reconstruction error. The traditional approach tries to remove the bias by suppressing the zero spectrum of the fringe image. It is based on the assumption that the aliasing between the frequency spectrum of the bias, which is around the zero frequency, and the frequency spectrum of the fringe is negligible. This, however, is not the case in practice. In this paper, we propose a novel (to our knowledge) technique to eliminate the bias in the fringe image using the dual-tree complex wavelet transform (DT-CWT). The new approach successfully identifies the features of bias, fringe, and noise in the DT-CWT domain, which allows the bias to be effectively extracted from a noisy fringe image. Experimental results show that the proposed algorithm is superior to the traditional methods and facilitates accurate reconstruction of objects' 3D models.     

Improved speckle projection profilometry for out-of-plane shape measurement

An improved speckle projection profilometry that combines the projection of computer generated random speckle patterns using an ordinary LCD projector and the two-dimensional digital image correlation technique for in-plane displacements measurement is proposed for accurate out-of-plane shape and displacement measurements. The improved technique employs a simple yet effective calibration technique to determine the linear relationship between the out-of-plane height and the measured in-plane displacements. In addition, the iterative spatial domain cross-correlation algorithm, i.e., the improved Newton-Raphson algorithm using the zero-normalized sum of squared differences correlation criterion and the second-order shape function was employed in image correlation analysis for in-plane displacement determination of the projected speckle patterns, which provides more reliable and accurate matching with a higher correlation coefficient. Experimental results of both a regular cylinder and a human hand demonstrate that the proposed technique is easy to implement and can be applied to a practical out-of-plane shape and displacement measurement with high accuracy.     

Lens curvature measurements by shadow projection profilometry

A technique is described for measuring spherical and aspherical lens curvature independent of surface contact or dependence on surface smoothness. The shadow of a lens profile is projected onto a CCD pixel array, and its silhouette edge-traced by computer video-image analysis. Nonlinear regression analysis, with correction for axial tilt, calculates lens curvature.     

Optical roughness measurements with fringe projection

The characterization of roughness of engineering surfaces over an area is an important task for different applications as well as for manufacturing processes. The surface roughness is in particular an important factor in determining the performance of a workpiece. We demonstrate that the fringe projection technique allows very fast three-dimensional surface inspections. The inspection time for an entire measurement is reduced to less than 5 s with standard hardware. Based on a zoom stereo microscope setup, we demonstrate a modular measuring instrument. The magnification-dependent vertical resolution can be as high as 0.1 microm. The special properties for roughness measurements are demonstrated, especially the comparability with a tactile sensor and with other optical sensors, which is discussed in connection with amplitude parameters.     

Three-dimensional profilometry based on shift estimation of projected fringe patterns

This paper presents a new approach to fringe pattern profilometry. In this paper, a generalized model describing the relationship between the projected fringe pattern and the deformed fringe pattern is derived, in which the projected fringe pattern can be arbitrary rather than being limited to being sinusoidal, as are those for the conventional approaches. Based on this model, what is believed to be a new approach is proposed to reconstruct the three-dimensional object surface by estimating the shift between the projected and deformed fringe patterns. Additionally, theoretical analysis, computer simulation, and experimental results are presented, which show how the proposed approach can significantly improve the measurement accuracy, especially when the fringe patterns are distorted by unknown factors.     

Application of S-transform profilometry in eliminating nonlinearity in fringe pattern

The S-transform, conceptually viewed as an extension of the short-time Fourier transform and the wavelet transform, features a time-frequency representation known for its local spectral property and multiresolution strategy. It has been introduced in optical three-dimensional shape measurement based on a fringe projection technique recently. In this paper, an application of S-transform for demodulating fringe patterns affected by the nonlinearity has been discussed. Two methods based on the S-transform, called S-transform ridge method and S-transform filtering method, are used to eliminate the phase errors caused by nonlinear factors of the projector and CCD camera. The theoretical representations of S-transform ridge method and S-transform filtering method in fringe analysis are given. The computer simulation and experiment are carried out to verify our research. Compared with the reconstructions of the windowed Fourier transform, the wavelet transform and the S-transform ridge method, the S-transform filtering method gives a better result under considering the influence of the fringe nonlinearity.     

光学三维测量中结构光栅投影系统的开发

为解决结构光三维测量系统中的光栅投影质量问题,提出并实现了以物理光栅为核心的结构光栅投影系统。该系统以现代光栅制造技术制造的精密光栅元件为核心,基于幻灯投影原理实现高质量的光栅条纹投影,利用步进电机带动高精密滚轴丝杆进行平移实现投影光栅的切换。实验结果表明,基于该系统实现的光学三维测量系统的可以达到1：100以上的对比度,具有较大的光强和良好的景深,同时能获得连续的强度分布及较好的正弦性,测量误差小于0．04mm,测量精度约为0．03mm,满足工业应用的要求。     

Microshape and rough-surface analysis by fringe projection

A fringe-projection system for microscopic applications, fringe-projecting microscopy, is developed and analyzed. Projection of the grating and imaging of the fringe system, modulated by the surface, are accomplished by the same high-aperture objective. The spectrum of the grating is spatially filtered and projected into the aperture with a lateral shift, which leads to a telecentric projection under oblique incidence and telecentric imaging. Topographies of specularly as well as diffusely reflecting surfaces can be obtained. The measurement of highly rough surfaces is described together with preprocessing steps. The resulting intensity distribution of the fringes is analyzed. Formulas for vertical and lateral resolution, measuring range, and dynamic range, based on noise considerations, are presented and verified by topographies of technical surfaces.     

Generic nonsinusoidal fringe model and gamma calibration in phase measuring profilometry

Gamma distortion is a dominant error source of phase measuring profilometry. It makes a single frequency for the ideal sinusoidal waveform an infinite width of spectrum. Besides, the defocus of the projector-camera system, like a spatial low-pass filter, attenuates the amplitudes of the high-frequency harmonics. In this paper, a generic distorted fringe model is proposed, which is expressed as a Fourier series. The mathematical model of the harmonic coefficients is derived. Based on the proposed model, a robust gamma calibration method is introduced. It employs the multifrequency phase-shifting method to eliminate the effect of defocus and preserve the influence of gamma distortion. Then, a gamma correction method is proposed to correct the gamma distortion with the calibrated gamma value. The proposed correction method has the advantage of high signal-to-noise ratio. The proposed model is verified through experiments. The results confirm that the phase error is dependent on the defocus and the pitch. The proposed gamma calibration method is compared with the state of the art and proves to be more robust to pitch and defocus variations. After adopting the proposed gamma correction method, the phase precision is much enhanced with higher quality in the measured surfaces.     

采用双频光栅投影的快速傅里叶变换轮廓术

傅里叶变换轮廓术中通过反正切计算出的相位是截断的,如果被测物高度变化引起的相邻点的非截断相位变化过大,就无法直接进行正确的相位展开。故提出一种采用双频光栅的快速傅立叶变换轮廓术：从一帧条纹图中获取同一物体对应于不同等效波长的两组截断相位,先展开对应于低频的低精度截断相位,并以此为参考,根据双频光栅两个频率之间的关系,展开对应于高频的高精度相位。经过模拟比较,在误差范围内比传统方法恢复的图形有了较大的改善,相对误差率由2．26％下降到1．79％。     

Discrete cosine transform-based shift estimation for fringe pattern profilometry using a generalized analysis model

What is believed to be a new analysis algorithm to carry out profile measurement with low computational complexity and less noise sensitivity is presented. First, a discrete cosine transform (DCT)-based representation method is introduced to express the height distribution of a 3D surface. Then a novel shift estimation algorithm, called the DCT-based shift estimation (DCT-SE), is presented to reconstruct 3D object surfaces by using the proposed expression and the generalized analysis model. The advantage of DCT-SE is that without loss of measurement precision it provides lower computational complexity to implement 3D reconstruction from nonlinearly distorted fringe patterns and, at the same time, survives the random noise. Simulations and experiments show that the proposed DCT-SE is a fast, accurate, and efficient reconstruction algorithm for digital projection- based fringe pattern profilometry techniques.     

Photogrammetric endoscope for measurement of inner cylindrical surfaces using fringe projection

We present a photogrammetric endoscope to measure three dimensional (3D) shapes of inner cylindrical surfaces by fringe projection. The basic configuration includes two identical cameras aligned with the optical axis and facing each other, conical lenses, and a 360 degrees helical fringe projector. The helical fringe pattern is phase shifted and acquired by both cameras. The phase patterns are used to acquire data from the surface in a regular cylindrical mesh. A prototype was built, calibrated, and tested. We present the results and an application to inspect internal welding seams and misalignment of welded joints in 150 mm (6 in.) diameter pipelines.     

一种数字投影式顶焦度测量仪

提出一种数字投影式顶焦度测量的技术方案。根据此方案设计的焦度测量仪,通过精密机械传动,嵌入以单片微型计算机为核心的硬件控制系统和软件处理系统,对眼镜镜片球镜顶焦度、球柱镜顶焦度及轴位角等进行了测量。它通过光学投影的方式进行对焦,测量活动标尺的平动量和转动量来计算相应参数,并利用液晶 LCD 显示结果。采用一种动态基准存储技术,通过预先存储的动态基准来计算顶焦度,可以有效消除系统误差,提高测量精度。对产品样机的试验结果表明,顶焦度的测量精度达到±0.03D。     

Topometry of technical and biological objects by fringe projection

Fringe projection is a fast and accurate technique for obtaining the topometry of a wide range of surfaces. Here some features of the principle are described, together with the possibilities of adapting this technique for the measurement of vaulted surfaces. We discuss various methods of phase evaluation and compare them with simulated computer data to obtain the resolution limits. Under certain restrictions a semispatial algorithm, called the modified Fourier analysis algorithm, gives the best results. One special subject of interest is the application of fringe projection for the measurement of the three-dimensional surface of the cornea. First results of in vivo measurements are presented.