基于相位跳变区划分的相位展开方法

提出了一种相位跳变区域的确定方法，在此基础上提出一种基于相位跳变区划分的相位展开方法。计算机模拟和实验结果均证明：此方法对噪声有很强的抗干扰能力，能有效地实现带噪声的主值相位图的相位展开。     

Surface normal guided method for two-dimensional phase unwrapping

A novel phase unwraping method has been presented and evaluated in this paper. This method works by first constructing a quality map based on the characteristic of the active triangulation system from the wrapped phase data. The quality map is then used to guide the unwrapping. In order to reduce the execution time of phase unwrapping, we tessellate the whole wrapped phase map into blocks. Blocks with higher confidence will be unwrapped first. Experiment shows that this method can unwrap the wrapped phase map derived from the digital moiré system successfully. In data integration stage, only data with higher confidence will be reserved and used to merge together to form a complete 3D model.     

Surface normal guided method for two-dimensional phase unwrapping

A novel phase unwraping method has been presented and evaluated in this paper. This method works by first constructing a quality map based on the characteristic of the active triangulation system from the wrapped phase data. The quality map is then used to guide the unwrapping. In order to reduce the execution time of phase unwrapping, we tessellate the whole wrapped phase map into blocks. Blocks with higher confidence will be unwrapped first. Experiment shows that this method can unwrap the wrapped phase map derived from the digital moiré system successfully. In data integration stage, only data with higher confidence will be reserved and used to merge together to form a complete 3D model.     

Single fringe projection profilometry based on sinusoidal intensity normalization and subpixel fitting

A novel fringe projection profilometry using a single sinusoidal fringe pattern projected is proposed. Computer-generated sinusoidal fringe and uniform intensity patterns are firstly projected on a testing object by a liquid crystal display projector. The variable reflection intensity of a fringe pattern is then roughly normalized by division operation applied to the grabbed fringe and uniform intensity patterns projected. Fringe intensity is further normalized by employing an interpolation algorithm. The deformed sinusoidal pattern encoding object shape is converted to a wrapped phase map without using phase-shifting or Fourier transform. Computer simulation and experimental performance are evaluated to demonstrate the validity of the proposed method. The experimental results compared with those of the four-step phase-shifting and fast Fourier transform methods are also presented.     

欠采样包裹相位图的恢复方法

针对非球面光学元件面形检测中的欠采样问题,提出了一种欠采样包裹相位图的恢复方法.首先,将原始欠采样包裹相位图在水平和竖直两个方向进行一个像素的错位相减,得到两个包裹相位差图.其次,对这两个包裹相位差图进行解包裹运算,得到两个解包裹相位差图.最后,应用傅里叶变换和最小二乘法恢复出连续的相位分布.模拟结果表明该方法可以高精...     

基于快速傅里叶变换的四种相位解包裹算法

为了快速准确地对含有噪声的包裹相位图进行相位展开,采用理论分析与计算机模拟及实验验证相结合的方法,对基于快速傅里叶变换（FFT）的四种典型算法四次FFT算法(4-FFT)、二次FFT算法（2-FFT）、四次离散余弦变换算法(4-DCT)及横向剪切干涉与FFT相结合的算法(LS-FFT)作了对比研究。结果表明:2-FFT算法运行速度最快,4-FFT算法次之,LS-FFT算法速度最慢;4-FFT算法对含有较强噪声和轻微欠采样的实验数据的处理效果是最好的;LS-FFT算法对强噪声数据的处理效果最差。     

Windowed Fourier assisted two-dimensional Hilbert transform for fringes phase extraction

In this article, two-dimensional windowed Fourier assisted Hilbert transform for fringes phase extraction has been proposed. The mathematical derivations of the filtered fringes image and its Hilbert transformations are presented using windowed Fourier transform. The proposed method has been verified by calculating the wrapped and unwrapped phase of the experimental moire fringes. In comparison to the conventional fringes phase extraction methods, the proposed method is found to be effective.     

Conversion from phase map to coordinate: Comparison among spatial carrier, Fourier transform, and phase shifting methods

For full-field phase measurement methods, many algorithms have been developed to extract a phase map from fringe image(s). Both phase wrapping and unwrapping algorithms have been extensively investigated by many researchers, but few papers can be found on how to calculate the coordinates of surface points from a phase map. This paper focuses on algorithms that show how a phase map can be used to calculate coordinates. Details are given for single image methods such as Fourier transform, spatial carrier methods, and multiple image methods like traditional phase-shifting methods. Algorithms that can be used to convert a phase map to coordinates and some issues related to these conversion algorithms are discussed. An artifact is measured using these phase measurement methods. The results show that using the correct algorithm to convert a phase map to coordinates is a key to obtaining accurate measurement results.     

The use of carrier frequency shifting for the elimination of phase discontinuities in Fourier transform profilometry

This paper presents a novel application of frequency shifting in the Fourier transform fringe analysis technique applied to surface shape measurement. In recent years little use has been made of frequency shifting, although it was a feature of the method as originally proposed. The paper shows that if the angle between fringe projection and viewing is small, it is possible to employ a frequency shift to effectively eliminate the occurrence of any wraps in the resulting phase distribution. This is obviously of value in cases where the object to be measured contains several discontinuities which would lead to a highly complex, maybe unprocessable, wrapped phase distribution. The technique is presented and analysed, and its effects on measurement resolution discussed. It is illustrated with a measurement made on a populated surface mount technology printed circuit board.     

基于希尔伯特变换的干涉条纹相位解调新算法

提出了一种新的应用希尔伯特变换解调干涉条纹相位的算法,可以从单幅干涉条纹图中解调出全场相位分布.在实际应用中,常借助傅里叶变换实现希尔伯特变换算法,但是会忽略负频率成分,造成相位信息的丢失.对于相位分布非单调变化的干涉条纹,提出了一种判断函数,用来计算相位信息零频率点的分布.利用相位的零频率点分布构造了一个二元模板,使用该模板对本文提出的两次希尔伯特变换法产生的包裹相位图进行修正.对修正后的包裹相位图进行解包裹处理,可以得到连续的全场相位分布.对该方法用计算机模拟进行了验证.     

Surface profile inspection of a moving object by using dual-frequency Fourier transform profilometry

The 2π phase ambiguity caused by surface isolations and large height step can be solved by dual-frequency projection grating profilometry. However, in the Fourier transform profilometry (FTP) of a moving object, only one single deformed fringe pattern can be obtained. In order to introduce the dual-frequency technique into the FTP of moving object, a novel experimental system is designed to capture two fringe patterns with different frequency at the same time. A grating structure comprising two regions with different frequencies is projected upon the surface of the detected object. Two line-scan CCD cameras are used to capture the surface images encoded by the two kinds of patterns, respectively. By getting the corresponding image intensity at the same point of the object surface in the two acquired images, the dual-frequency technique is applied to extract the real phase without phase ambiguity. The surface profile of a specimen with a large height step is measured to prove the feasibility of the proposed method. The experimental results show that the proposed method can solve the 2π phase ambiguity problem successfully in the surface profile inspection of a moving object.     

Minute displacement and strain analysis using lensless Fourier transformed holographic interferometry

An optical system for lensless Fourier transformed holographic interferometry is constructed to enable the measurement of minute displacements from nanometers to micrometers scale and to obtain corresponding strain distributions using a CCD camera with poor spatial resolution. Since a Fourier spectrum of an object beam is recorded on a hologram in this technique, the image reconstruction is easily performed with a single pass of 2-D fast Fourier transformation. Then, the map of the phase difference over the whole field is obtained by comparing two images before and after deformation. A suitable and effective unwrapping process is, however, inevitably required since the phase difference distribution is wrapped from −π to π in this technique. For phase unwrapping, the maximum spanning tree method is adopted here, which seeks a spanning tree that maximizes overall edge weights given by the cross amplitude. In-plane and out-of-plane displacements are obtained separately from the phase difference distributions at one's request. Moreover, in-plain strain is easily calculated from the in-plane displacement distribution.     

A fast,accurate phase unwrapping method for wavelet-transform profilometry

A novel phase unwrapping method used in wavelet-transform profilometry is presented to improve the accuracy and speed of the unwrapping process. The wrapped phase of the fringe image is extracted by using wavelet transform. How to establish quality map using scale factor at wavelet ridge is discussed firstly. The proposed method can reflect the reliability of the pixels in fringe image effectively. As the consuming time of traditional flood-fill phase unwrapping algorithm is too long, an improved quality-guided method is used in phase unwrapping process. We divide the wrapped phase map into two levels following the established quality map, and process these two levels using different algorithms. Compared with the traditional flood-fill algorithm, we can get the accurate result while the consuming time of the phase unwrapping process is much less by using the proposed method. Simulation and experiment results verify that the 3D information of the measured object can be obtained rapidly and accurately by using the proposed method. Also the dynamic object can be measured too.     

Weighted least-squares phase unwrapping algorithm based on derivative variance correlation map

Among different phase unwrapping approaches, the weighted least-squares minimization methods are gaining attention. In these algorithms, weighting coefficient is generated from a quality map. The intrinsic drawbacks of existing quality maps constrain the application of these algorithms. They often fail to handle wrapped phase data contains error sources, such as phase discontinuities, noise and undersampling. In order to deal with those intractable wrapped phase data, a new weighted least-squares phase unwrapping algorithm based on derivative variance correlation map is proposed. In the algorithm, derivative variance correlation map, a novel quality map, can truly reflect wrapped phase quality, ensuring a more reliable unwrapped result. The definition of the derivative variance correlation map and the principle of the proposed algorithm are present in detail. The performance of the new algorithm has been tested by use of a simulated spherical surface wrapped data and an experimental interferometric synthetic aperture radar (IFSAR) wrapped data. Computer simulation and experimental results have verified that the proposed algorithm can work effectively even when a wrapped phase map contains intractable error sources.     

Deformation and profile measurement using the digital projection grating method

This paper presents a digital projection grating method for full field measurement of out-of-plane deformation and shape of an object. Two grating patterns on an object before and after deformation are captured by a CCD camera and stored in a computer. With the aid of Fast Fourier Transform (FFT) and signal demodulating techniques, a wrapped phase map is generated. The phases are expanded in the range of 0–2π and compared with the resulting moiré pattern. An unwrapping procedure is used to obtain a continuous phase. In addition, a digital method for fractional fringe multiplication is also developed. Results on deformation and object profile measurements are presented.     

Multi-STFT for adaptive SCPS phase determination

This paper presents a fast and reliable approach for phase modulo 2π-calculation from a single fringe pattern. It calculates correct phase values even for very complex and variable shape gradients based on a locally variable fringe period determined for the entire image. In the paper, a new two-step method for wrapped phase calculation is proposed. It is performed through the use of a method based on a multiple local fast Fourier transform for estimation of a local fringes period map and a 5-point spatial carrier phase shifting (SCPS) formula for phase modulo 2π-calculation. The described approach is verified by a correct demodulation of a real fringe pattern taken by a 3D-shape measurement system.     

An improved stair phase encoding method for absolute phase retrieval

An improved phase unwrapping method is proposed to reduce the projection fringes in three-dimensional (3D) surface measurement. Color fringe patterns are generated by encoding with sinusoidal fringe and stair phase fringe patterns in red and blue channels. These color fringe patterns are projected onto the tested objects and then captured by a color CCD camera. The recorded fringe patterns are separated into their RGB components. Two groups of four-step phase-shifting fringe patterns are obtained. One group of the stripes are four sinusoidal patterns, which are used to determine the wrapped phase. The other group of stripes are four sinusoidal patterns with the codeword embedded into stair phase, whose stair changes are perfectly aligned with the 2π discontinuities of sinusoidal fringe phase, which are used to determine the fringe order for the phase unwrapping. The experimental results are analyzed and compared with those of the method in Zheng and Da (2012. Opt Express 20(22):24139–24150). The results show that the proposed method needs only four fringe patterns while having less error. It can effectively reduce the number of projection fringes and improve the measuring speed.     

An improved windowed Fourier transform for fringe demodulation

A modified algorithm of windowed Fourier transform (WFT) for phase retrieval from electronic speckle-shearing fringe patterns with carriers is proposed. The algorithm is based on the introduction of a fast Fourier transform (FFT) in WFT to reduce computation time for fringe demodulation. Since boundary effects in FFT will influence the accuracy of phase retrieval, the Gerchberg method is employed to extrapolate the fringe pattern at the boundaries to reduce boundary effects. A theoretical analysis of the algorithm is presented. Both simulated and experimental results show that the proposed method has reduced the computation time significantly compared with the convolution method of WFT without sacrificing measurement accuracy.     

Demodulation of a single interferogram based on continuous wavelet transform and phase derivative

A novel method based on continuous wavelet transform (CWT) and guidance of phase derivative is developed to measure the phase of a single fringe pattern which contains closed fringes. Wrapped phase values are retrieved by ridge extraction algorithms based on CWT which has the capability of better noise reduction and thus increases the resolution of measurement significantly. To further reduce the noise, the scales detected by maximum ridge algorithm are filtered iteratively before retrieval of wrapped phase. The proposed method also identifies any ambiguous point in a non-monotonous fringe pattern by directly tracking an inflexion point from an unwrapped phase map without the use of a carrier. The algorithm developed is validated by computer simulation and experimental results. Based on micro interferometry the experimental results for both static and dynamic deformations of a micro structure demonstrate that the proposed method is an effective tool for the analysis of closed fringe patterns and subsequent deformation measurement. However, the proposed technique is limited to measurement of surface which is relatively smooth compared to the mean wavelength of the light source. In addition, prior knowledge of the sign of surface slope is required in cases where a spatial carrier is not available or adaptable.     

Two-step fringe pattern analysis with a Gabor filter bank

We propose a two-shot fringe analysis method for Fringe Patterns (FPs) with random phase-shift and changes in illumination components. These conditions reduce the acquisition time and simplify the experimental setup. Our method builds upon a Gabor Filter (GF) bank that eliminates noise and estimates the phase from the FPs. The GF bank allows us to obtain two phase maps with a sign ambiguity between them. Due to the fact that the random sign map is common to both computed phases, we can correct the sign ambiguity. We estimate a local phase-shift from the absolute wrapped residual between the estimated phases. Next, we robustly compute the global phase-shift. In order to unwrap the phase, we propose a robust procedure that interpolates unreliable phase regions obtained after applying the GF bank. We present numerical experiments that demonstrate the performance of our method.