基于复合光栅投影的快速傅里叶变换轮廓术

在实际傅里叶变换轮廓术测量中,获取条纹图的零频分量对傅里叶变换轮廓术的测量精度和测量范围有很大影响,甚至妨碍三维面形的正确重建。π相移技术常被用来消除零频分量对傅里叶变换轮廓术测量的影响,但它需要采集两帧具有π相位差的条纹图。这影响了傅里叶变换轮廓术测量方法的实时性。提出采用复合光栅投影来实现从一帧条纹图中消除零频对傅里叶变换轮廓术测量的影响,该复合光栅是由两个不同频率的载频分别调制与其方向垂直的两帧具有π相位差的条纹并叠加形成的。实验表明,同传统的π相移方法相比,提出的新方法没有明显降低π相移傅里叶变换轮廓术的的测量精度,因此能真正实现实时高速测量。     

Method for eliminating zero spectrum in Fourier transform profilometry

Windowed Fourier transform (FT) is introduced into Fourier transform profilometry (FTP) to extract zero component included in deformed fringe pattern without capturing two fringe patterns with π phase difference. First, we extract zero component of deformed fringe image using windowed FT and normalize it, then calculate the normalized Fourier spectra of deformed fringe image, finally subtract the zero component from Fourier spectra of deformed fringe image. We give the theoretical analysis of the proposed method. The experiment is carried out to demonstrate that the method can eliminate zero component and extend the measurable slope of height variation to nearly three times of the conventional FTP.     

Study on Fourier transforms profilometry based on bi-color projecting

Projecting a bicolor sinusoidal fringe pattern consisting of two interlaced RGB format base color fringe patterns with π phase difference onto an object thought digital light projector, we can capture a deformed color pattern by color digital camera, then decode two individual sinusoidal fringe patterns with π phase difference by color-separating technique. Accessing these two fringe patterns, not only are zero-order spectra eliminated, but mask function is also built to mark valid unwrapping area in FTP, automatically.Moreover, because the wrapped phase just inside the valid areas is needed unwrapping, we can mark these areas with mask function, which avoids the error transferring resulting from unwrapping the invalid areas and shortens the unwrapping time. Furthermore, in Fourier transform processing, the full-field deformed fringe pattern generally needed to guarantee measurement precision can be formed by expanding non-full-field fringe pattern captured using the mask function.     

基于双色条纹投影的快速傅里叶变换轮廓术

在实际傅里叶变换轮廓术测量中，获取的条纹图扩展的零频分量对傅里叶变换轮廓术的测量精度和测量范围有很大影响，甚至妨碍正确三维面形的恢复。π相移技术常被用来消除零频分量对测量的影响，但需要在测量系统中安装精密相移装置，并需要采集两帧具有π相位差的条纹图。传统傅里叶变换轮廓术中，完成精密相移需要较长的时间，影响了傅里叶变换轮廓术测量方法的实时性。提出了采用双色正弦光栅投影来实现从一帧条纹图中消除零频对傅里叶变换轮廓术测量的影响。该方法同传统的π相移方法相比，不需要相移装置，测量系统简单，并且能真正实现高速测量。     

Identification of nonlinear recording error in phase shifting interferometry

The phase shifting method for quantitative fringe pattern analysis provides high accuracy if stringent requirements on the component interferogram recording are met. In the paper the issue of detection and identification of error sources in the two-beam interferogram phase shifting experiment is discussed. The phase shift angle histogram and lattice-site representation are applied for that purpose. Special attention is paid to possible nonlinear recording of component interferograms in the presence of linear and nonlinear phase step errors. Four and five step phase shifting algorithms are considered. The superiority of the lattice-site representation is shown. In the case of phase steps equal to π/2, however, the lattice-site representation of shift angles for five frame algorithm does not allow to detect recording nonlinearity. The four frame counterpart shows to be very helpful in this respect. Its properties related to the fringe pattern profile under study, including a defocused Ronchi grating, are discussed.     

A phase unwrapping technique for object relief determination

Phase shifting methods are widely used in photomechanics to analyse fringe patterns obtained from interferometry, moiré, etc. The phase is determined by modulo 2π and an unwrapping process is needed. An algorithm is presented which avoids most of the inconsistency of the phase field. It can be applied to the relief determination of virtually any object shape. In this paper, two applications are performed using the projection of a parallel line grating with a pitch equal to 4 mm. The accuracy is shown to be around 0…1 mm.     

Bandwidth controllable transmission filter based on Moiré fiber Bragg grating

A new and efficient technique for fabrication of bandwidth controllable π–phase-shifted fiber Bragg grating (FBG) based on moiré grating using a uniform phase mask is demonstrated. The feasibility of writing a moiré grating into an ordinary SMF-28 fiber using stretching and double exposure by ultraviolet fringe is reported. We analyzed the relation between the initial differentia of phase of two exposures and the transmission spectrum of phase-shifted FBG. Moreover, we present a novel method to control the initial differentia of phase of two exposures. Using this technique, two kinds of resonant filters with a 3-dB line-width of 0.01 nm centered at 1553.79 nm and of 0.5 nm centered at 1554.57 nm respectively were fabricated with same uniform phase mask.     

Bandwidth controllable transmission filter based on Moiré fiber Bragg grating

A new and efficient technique for fabrication of bandwidth controllable π–phase-shifted fiber Bragg grating (FBG) based on moiré grating using a uniform phase mask is demonstrated. The feasibility of writing a moiré grating into an ordinary SMF-28 fiber using stretching and double exposure by ultraviolet fringe is reported. We analyzed the relation between the initial differentia of phase of two exposures and the transmission spectrum of phase-shifted FBG. Moreover, we present a novel method to control the initial differentia of phase of two exposures. Using this technique, two kinds of resonant filters with a 3-dB line-width of 0.01 nm centered at 1553.79 nm and of 0.5 nm centered at 1554.57 nm respectively were fabricated with same uniform phase mask.     

Phase shifting nano-moiré method with scanning tunneling microscope

In this paper, a new nano-moiré method using scanning tunneling microscope (STM) is proposed. This method is capable of measuring nanoscopic deformation of matter. The formation mechanism of the STM moiré fringe and the phase shifting technique used in STM moiré fringes are explained in details. Typical experiments are conducted with the crystal lattices of freshly cleaved highly oriented pyrolytic graphite, are used as specimen grating, to generate STM moiré fringe patterns. Phase shifting is realized in four steps from 0 to 2π by controlling the PZT in the STM system to shift the specimen in the vertical direction. This method provides a new way for disposal of moiré fringes pattern in the nano-moiré measurement.     

利用强度调制消除零频的傅里叶变换轮廓测量

采用双色正弦条纹投影的傅里叶变换轮廓术中零频分量的扩展对有用基频分量有影响,为此提出一种新型的基于强度调制的零频消除方法提高测量准确度和范围.通过采集一帧变形彩色条纹图并分离颜色通道获得两幅相位差为π的条纹图,对变形条纹做强度调制校正,进而消除零频分量,实现高度解析.理论模拟和实验测试均验证了此方法的有效性.相比传统的相移消除零频分量的方法,此方法具有显著的速度优势,适合于三维物体的实时测量.     

Error-compensating algorithms in phase-shifting interferometry: a comparison by error analysis

In this paper, two families of phase-shifting algorithms with π/2 phase steps are studied. In family I, three new algorithms are derived by using the averaging technique based on the Surrel six-sample algorithm with phase shifts of π/2. Family II includes four well-known algorithms derived by the averaging technique based on the conventional four-sample algorithm with π/2 phase steps. A polynomial model of phase-shift errors used to describe general expressions for calculation of the correct object phase via the Fourier spectra analysing method as a function of the harmonic order in the fringe signal is presented. The error-compensating properties of the algorithms in families I and II are investigated by the Fourier spectra analysing method. It is found that the averaging technique, when used in any of the algorithm with π/2 phase steps, can improve the phase-shifting algorithm property: it is insensitive to phase-shift error when the fringe signal contains the first harmonic, but it can't be used to enhance the phase-shifting algorithm properties when the fringe signal contains higher order harmonics (n2). P–V (peak–valley) phase errors are calculated by the computer simulation and tables and plots are presented, from which the algorithms in families I and II are compared. It is shown that the algorithms in family I are more insensitive to phase-shift errors when the fringe signal contains the second harmonic and the algorithms in family II are more insensitive to phase-shift errors when the fringe signal is a sinusoidal waveform.     

Josephson effect between p-wave superconductors with different orbital pairing symmetries

The Josephson effects in the ferromagnetic superconductor junctions of the equal spin pairing symmetry are investigated by a Furusaki–Tsukada-like formula. It is shown that the internal phase difference between the two different anisotropic superconductors plays an important role on the Josephson current. The current is predicted to be an oscillation function of the macroscopic phase difference with the period 2π, π, or π/2 depending on the different orbital pairing symmetries of the superconductors of the junction.     

Nanoscale deformation measurement by using the hybrid method of gray-level and holographic interferometry

This study extends the use of holographic interferometry to measure the nanoscale out-of-plane displacement with high surface resolution. It is noted that if the deformation is less than half of the optical wavelength, it is hard to find an obvious fringe pattern. Under such a situation, in general, the phase shift method is used. However, it needs to take more than 3 images for phase shifting and phase reconstruction In this paper, a more simple hybrid method of gray-level and holographic interferometry is used to extract fringe skeletons, in which it just needs to take one or two images for the normal deformation measurement directly, even if there exists no obvious fringe pattern. The displacement field with high surface resolution can also be obtained. The proposed method yielded a theoretical precision of 0.15 nm for out-of-plane displacement with a monochromatic CCD camera of 10-bit gray scale (1024 gray scales) sensitivity and microscale surface resolution for millimeter scale object with 640×480 pixels image resolution by an He–Ne LASER (632.8 nm wavelength) light source. The gray-level method is proposed to calculate the non-obvious interferometry fringe by traditional holographic interferometry hologram, and the result showed that this method works for this purpose.     

Digitally whole-field analysis of isoclinic parameter in photoelasticity by four-step color phase-shifting technique

This paper presents a whole-field method for automatic determination of the isoclinic parameter φ in photoelasticity. The method determines φ in the true phase interval (-π/2<φ+π/2) based on the four-step color phase-shifting approach and a new unwrapping method based on simple logic operations, a binary image and a gray-scale mask. A plane polariscope with a white light source is used for capturing raw photoelastic fringe images. The theoretical validation of the method is done with the problem of a circular disk under compression. Comparisons between theoretical and experimental results are also demonstrated. The experimental confirmation for the proposed method is tested with the photoelastic model having an isotropic point(s) and/or a singular point(s). The results show the method permits the reliable isoclinic parameter to be determined in the true phase interval with almost no defects of the isochromatic parameter.     

Digital speckle interferometry for assessment of surface roughness

In this work, the principle of interferometry is used to assess the surface roughness of the machined surfaces. Interferometry produces an interference fringe pattern when two or more light waves interact with each other. It is one of the important tool for precision optical metrology and testing. Well-known advantages of the phase shifting interferometry include high measurement accuracy, rapid measurement, good result even with low contrast fringes and that the polarity of the wave front can be determined. In fringe projection techniques, a known optical fringe pattern is projected onto the surface of interest. The fringe pattern on the surface is perturbed in accordance with the profile of the test surface, thereby enabling direct derivation of surface profile.In this work, an attempt has been made to assess the surface roughness using a speckle fringe analysis method of five frame phase shift algorithm for machined surface (ground surface). As these fringes are too noisy, advanced filtering technique has been used so as to reduce noise and to get improved wrapped phase map from the phase shifted fringes. A phase unwrapping software has been developed using discrete cosine transform (DCT) to generate the three-dimensional (3-D) profiles. Finally, it is compared with R_a values measured using a mechanical stylus instrument, showing good agreement.     

Development of Matlab filtering techniques in digital speckle pattern interferometry

In interferometric fringe pattern analysis, specular and speckle fringe patterns are the two main divisions. While specular fringes are characterized by quality fringes, speckle (that obtains due to the diffuse scattering of the coherent radiation from an optically rough surface) fringe patterns are characterized by noisy fringes. This paper concentrates on this aspect and the Matlab based filtering methods to improve the quality of speckle fringe patterns by developing the appropriate software. Further, the newly developed software “Macurv” will be presented which can give the second order derivative (curvature) fringe information. A software with several functions is written using Matlab. The objective of the software is to provide a more effective way for the post-processing of speckle interferometric fringes. The algorithm and functions of the developed software “Macurv” will be explained.     

Observation of record flux pinning in melt-textured NEG-123 superconductor doped by Nb, Mo, and Ti nanoparticles

Flux pinning in melt-processed (Nd_0.33Eu_0.33Gd_0.33)Ba₂Cu₃O_y “NEG-123” + 35 mol% Gd₂BaCuO₅ “NEG-211” (70 nm in size) composite doped by TiO₃, MoO₃ and Nb₂O₅ achieved record values. The optimum values of all three dopands were found to be around 0.1 mol%. Transmission electron microscope (TEM) analysis found clouds of <10 nm sized particles in the NEG-123 matrix, shifting the pinning particle size distribution to significantly lower values. TEM by energy dispersive X-ray spectroscopy (EDX) analysis clarified that these nanoparticles contained a significant amount of Nb, Mo, and Ti. Appearance of nanometer-sized defects correlated with a significantly improved flux pining at low and medium magnetic fields, which was particularly significant at high temperatures. In the Nb-doped sample, a record J_c value of 925 kA/cm² at the secondary peak field (4.5 T) was achieved at 65 K, 640 kA/cm² at zero field at 77 K, and 100 kA/cm² at 90.2 K, the last value having been up to now considered as a good standard for REBa₂Cu₃O_y “RE-123” materials at 77 K. The greatly improved J_c–B performance in Nb/Mo/Ti doped samples can be easily translated to large-scale LRE-123 (LRE = light rare earths, Nd, Eu, Gd, Sm) blocks intended for real superconducting super-magnets applications.     

Observation of Gouy phase anomaly with an interferometer

The intensity variation of bright and dark fringes in Young's double slit experiment shows that a light beam propagating through the focus of a lens experiences a phase shift (called the Gouy phase shift [Gouy CR. Acad Sci Paris 1890;110:1251]) with respect to its plane wave counterpart. The additional phase change of π introduced on focusing the light beam and then further propagating it in one arm of the interferometer changes a bright fringe into a dark fringe and vice-versa. We have, thus, made direct visualization of the Gouy phase shift by a simple experiment.     

Determination of isoclinics in photoelasticity with a fast regularized estimator

The determination of isoclinics from photoelastic fringe patterns is a key problem in photoelasticity. Dealing with this problem, however, is not a simple task when isotropic points are present which is common for most experimental situations. Because of this, few researchers have proposed effective and practical solutions. Visualizing this problem as the problem of the determination of the modulo 2π fringe orientation, in this paper it is proposed an efficient regularized algorithm to solve it. Experimental results show that the proposal is effective and can be used with either monochromatic or white light.     

A new method to preserve the c-axis growth of thick YBa2Cu3O7–δ films grown by pulsed laser deposition

YBa₂Cu₃O_7–δ (YBCO) films were prepared on (1 0 0) MgO substrates by pulsed laser deposition (PLD) method. In order to eliminate the a-axis growth, which is commonly observed in the YBCO film thicker than a critical value, we developed a new PLD target that was sintered at a temperature far below YBCO 123 phase formation. The surface analysis made by AFM technique confirmed that very fine particles of around 20 nm size could be ejected from the new target to the substrate. The fine oxide clusters could be easily moved and incorporated into the YBCO phase thus benefited the c-axis growth even in the thick films. For instance, only the c-axis growth in the new film with a thickness of about 650 nm was larger than a critical thickness of the a-axis growth. However, in the standard film of the same thickness, there is 24.5% of the a-axis growth accompanying the main c-axis growth. Therefore, the c-axis growth could be preserved in the very thick YBCO film by a non-superconducting target.