Reference Fringe Research Articles

Multi-color two-photon scanning structured illumination microscopy imaging of live cells.

Multi-color two-photon microscopy imaging of live cells is essential in biology. However, the limited diffraction resolution of conventional two-photon microscopy restricts its application to subcellular organelle imaging. Recently, we developed a laser scanning two-photon non-linear structured illumination microscope (2P-NLSIM), whose resolution improved three-fold. However, its ability to image polychromatic live cells under low excitation power has not been verified. Here, to improve the reconstruction super-resolution image quality under low excitation power, we increased the image modulation depth by multiplying the raw images with the reference fringe patterns in the reconstruction process. Simultaneously, we optimized the 2P-NLSIM system to image live cells, including the excitation power, imaging speed, and field of view. The proposed system could provide a new imaging tool for live cells.

An Improved Circular Fringe Fourier Transform Profilometry.

Circular fringe projection profilometry (CFPP), as a branch of carrier fringe projection profilometry, has attracted research interest in recent years. Circular fringe Fourier transform profilometry (CFFTP) has been used to measure out-of-plane objects quickly because the absolute phase can be obtained by employing fewer fringes. However, the existing CFFTP method needs to solve a quadratic equation to calculate the pixel displacement amount related to the height of the object, in which the root-seeking process may get into trouble due to the phase error and the non-uniform period of reference fringe. In this paper, an improved CFFTP method based on a non-telecentric model is presented. The calculation of displacement amount is performed by solving a linear equation instead of a quadratic equation after introducing an extra projection of circular fringe with circular center translation. In addition, Gerchberg iteration is employed to eliminate phase error of the region close to the circular center, and the plane calibration technique is used to eliminate system error by establishing a displacement-to-height look-up table. The mathematical model and theoretical analysis are presented. Simulations and experiments have demonstrated the effectiveness of the proposed method.

FFT swept filtering: a bias-free method for processing fringe signals in absolute gravimeters

Absolute gravimeters, based on laser interferometry, are widely used for many applications in geoscience and metrology. Although currently the most accurate FG5 and FG5X gravimeters declare standard uncertainties at the level of $$2{-}3\,{\upmu }\hbox {Gal}$$ , their inherent systematic errors affect the gravity reference determined by international key comparisons based predominately on the use of FG5-type instruments. The measurement results for FG5-215 and FG5X-251 clearly showed that the measured g-values depend on the size of the fringe signal and that this effect might be approximated by a linear regression with a slope of up to $$0.030\,{\upmu }\hbox {Gal/mV}$$ . However, these empirical results do not enable one to identify the source of the effect or to determine a reasonable reference fringe level for correcting g-values in an absolute sense. Therefore, both gravimeters were equipped with new measuring systems (according to Křen et al. in Metrologia 53:27–40, 2016. https://doi.org/10.1088/0026-1394/53/1/27 applied for FG5), running in parallel with the original systems. The new systems use an analogue-to-digital converter HS5 to digitize the fringe signal and a new method of fringe signal analysis based on FFT swept bandpass filtering. We demonstrate that the source of the fringe size effect is connected to a distortion of the fringe signal due to the electronic components used in the FG5(X) gravimeters. To obtain a bias-free g-value, the FFT swept method should be applied for the determination of zero-crossings. A comparison of g-values obtained from the new and the original systems clearly shows that the original system might be biased by approximately $$3{-}5\,{\upmu }\hbox {Gal}$$ due to improperly distorted fringe signal processing.

3-D shape measurement of rail achieved by a novel phase measurement profilometry based on virtual reference fringe generated by image interpolation

The 3-D measurement of rail shape is important for the safety of railway transportation. Phase Measurement Profilometry (PMP) is chosen to measure rail shape in this paper for its advantages of non-contact, high accuracy and fast speed. In traditional Phase Measurement Profilometry (T-PMP), the setting of the reference plane plate plays an important role, and it is a critical step to capture the reference fringe pattern projected onto the reference plane plate. However, it is sometimes difficult to choose or place the physical reference plane plate in practical applications with complex environments, such as in rail shape measurement. In this paper, a novel PMP based on virtual reference fringe (VRF-PMP) is proposed to deal with the problem. The virtual reference fringe is obtained through extending a partial undeformed fringe pattern intercepted from the whole fringe pattern using image interpolation methods, including Nearest Interpolation, Bilinear Interpolation, Bicubic Interpolation and a proposed One-dimensional New Edge-directed Interpolation (ONEDI). Simulation and experimental results show that VRF-PMP can reconstruct the 3-D shape of rail effectively without a physical reference plane plate. This paper provides a new suggestion for actual detection by PMP.

Carbon Sequestration and Sedimentation in Mangrove Swamps Influenced by Hydrogeomorphic Conditions and Urbanization in Southwest Florida

This study compares carbon sequestration rates along two independent tidal mangrove creeks near Naples Bay in Southwest Florida, USA. One tidal creek is hydrologically disturbed due to upstream land use changes; the other is an undisturbed reference creek. Soil cores were collected in basin, fringe, and riverine hydrogeomorphic settings along each of the two tidal creeks and analyzed for bulk density, total organic carbon profiles, and sediment accretion. Radionuclides 137Cs and 210Pb were used to estimate recent sediment accretion and carbon sequestration rates. Carbon sequestration rates (mean ± standard error) for seven sites in the two tidal creeks on the Naples Bay (98 ± 12 g-C m−2·year−1 (n = 18)) are lower than published global means for mangrove wetlands, but consistent with other estimates from the same region. Mean carbon sequestration rates in the reference riverine setting were highest (162 ± 5 g-C m−2·year−1), followed by rates in the reference fringe and disturbed riverine settings (127 ± 6 and 125 ± 5 g-C m−2·year−1, respectively). The disturbed fringe sequestered 73 ± 10 g-C m−2·year−1, while rates within the basin settings were 50 ± 4 g-C m−2·year−1 and 47 ± 4 g-C m−2·year−1 for the reference and disturbed creeks, respectively. These data support our hypothesis that mangroves along a hydrologically disturbed tidal creek sequestered less carbon than did mangroves along an adjacent undisturbed reference creek.

Flexible Distributed Pressure Sensing Strip for a Urethral Catheter.

A multi-sensor flexible strip is developed for a urethral catheter to measure distributed pressure in a human urethra. The developed sensor strip has important clinical applications in urodynamic testing for analyzing the causes of urinary incontinence in patients. There are two major challenges in the development of the sensor. First, a highly sensitive sensor strip that is flexible enough for urethral insertion into a human body is required and second, the sensor has to work reliably in a liquid in-vivo environment in the human body. Capacitive force sensors are designed and micro-fabricated using polyimide/PDMS substrates and copper electrodes. To remove the parasitic influence of urethral tissues which create fringe capacitance that can lead to significant errors, a reference fringe capacitance measurement sensor is incorporated on the strip. The sensing strip is embedded on a catheter and experimental in-vitro evaluation is presented using a bench-top pressure chamber. The sensors on the strip are able to provide the required sensitivity and range. Preliminary experimental results also show promise that by using measurements from the reference parasitic sensor on the strip, the influence of parasitics from human tissue on the pressure measurements can be removed.

Broadband interferometric characterization of divergence and spatial chirp.

We demonstrate a spectral interferometric method to characterize lateral and angular spatial chirp to optimize intensity localization in spatio-temporally focused ultrafast beams. Interference between two spatially sheared beams in an interferometer will lead to straight fringes if the wavefronts are curved. To produce reference fringes, we delay one arm relative to another in order to measure fringe rotation in the spatially resolved spectral interferogram. With Fourier analysis, we can obtain frequency-resolved divergence. In another arrangement, we spatially flip one beam relative to the other, which allows the frequency-dependent beamlet direction (angular spatial chirp) to be measured. Blocking one beam shows the spatial variation of the beamlet position with frequency (i.e., the lateral spatial chirp).

X-ray Moiré deflectometry using synthetic reference images

Moiré fringe deflectometry with grating interferometers is a technique that enables refraction-based x-ray imaging using a single exposure of an object. To obtain the refraction image, the method requires a reference fringe pattern (without the object). Our study shows that, in order to avoid artifacts, the reference pattern must be exactly matched in phase with the object fringe pattern. In experiments, however, it is difficult to produce a perfectly matched reference pattern due to unavoidable interferometer drifts. We present a simple method to obtain matched reference patterns using a phase-scan procedure to generate synthetic Moiré images. The method will enable deflectometric diagnostics of transient phenomena such as laser-produced plasmas and could improve the sensitivity and accuracy of medical phase-contrast imaging.

Three-dimensional information security combined fringe projection with double random phase encoding

Three-dimensional (3D) information security with optical fringe projection encoding is proposed. The 3D information about an object, which is encoded into two-dimensional (2D) deformed and reference fringes by optical fringe projection, are encrypted by use of double random phase encoding (DRPE). Deformed and reference fringes, regarded as phase and amplitude respectively, are simultaneously modulated by random phase keys. The key-space is enlarged, because the keys for decryption are not only the random phase masks, but also the calibration parameters of the fringe projection system. The proposed method is robust to noise. Experiment is performed to obtain the reference and deformed fringes. Numerical simulations are employed to verify the validity of the proposed method.

A flexible calculation on improved Fourier transform profilometry

Here a flexible optical geometry of Fourier Transform Profilometry (FTP) is discussed, and a strict theoretical analysis about an improved phase-height mapping formula based on a new description of a reference fringe and a deformed fringe proposed based on a general case, in which the exit pupil of the projecting lens and the entrance pupil of the imaging lens are not horizontal and do not have the equal distance to the reference plane; moreover, the optical axes of the projecting device and of the imaging device are not coplanar. Compared with the traditional Fourier Transform Profilometry, it is easier for us to obtain the full-field fringe through adjusting the location of either the projector or the imaging device. Compared with the Improved Fourier Transform Profilometry (IFTP), only three length system parameters need to be measured, so the operation is simple and the result is more reliable.

2-D crack growth measurement using circular grating moiré fringes and pattern matching

A two-dimensional (2-D) crack growth measurement method that uses moire fringes generated by circular gratings and pattern matching was developed in this work for application in structural health monitoring. The moire fringe patterns were extracted by transforming the circular gratings into linear gratings using polar-radius transformation and applying a one-dimensional average filter. The filtered image was inversely transformed to recover the moire fringes. Pattern matching was performed by comparing the absolute difference between an input fringe pattern caused by an unknown displacement and a series of reference fringe patterns of known displacements in one direction. The matching of the moire fringes caused by displacement at 90° to that in the reference patterns and combination of the two orthogonal directions was carried out after applying a rotational angle search algorithm. Demonstration using a crack model showed the applicability of the proposed system for the measurement of relative displacement of crack development along two directions with a sensitivity of 0.02 mm. The measured displacements were found to have high correlation with the actual displacements with a R2 value of 0.9985. Copyright © 2010 John Wiley & Sons, Ltd.

Investigation of the accuracy of different methods of interferogram analysis for calculation of local free convection heat transfer coefficient on axisymmetric objects

An experimental study using a Mach–Zehnder interferometer has been carried out in order to investigate the accuracy of four different methods of interferogram analysis for obtaining free convection heat transfer coefficient on heated axisymmetric objects. Different methods of reference fringe interferogram analysis can be categorized as classical and transform methods. In transform methods, a mathematical transform method is applied to solve the governing integral equation while in the classical methods the integral equation is approximated by a finite summation. Classical methods are also divided into two groups according to the equations which are based upon. Experiments have been carried out on a vertical isothermal cylinder in air with three different surface temperatures. Four methods of interferogram analysis which are three classical and a transform method have been used to calculate the temperature distributions and the local free convection heat transfer coefficients at different cross sections. In order to investigate the accuracy of the methods, experimental values of the local heat transfer coefficient have been compared with the numerical solution and the mean relative error of each method has been obtained. Results show that the transform method is the most accurate one with the shortest solution time. It is also shown that assuming more complex functions for variation of index of refraction in the classical methods could lead to more accurate results.

Global Doppler frequency shift detection with near-resonant interferometry

The recent development in measuring 2D Doppler shift distributions for flow velocimetry using the dispersive properties of atomic line filters is presented. On the basis of velocity field measurements on a subsonic jet flow and a tip vortex flow in a medium-sized wind tunnel, the technique was assessed. Atomic line filters near a resonant transition combine imaging capabilities with a sharp frequency cutoff and an associated region of strong anomalous dispersion. While conventional Doppler global velocimetry relies on the absorption of the filter to convert frequency shifts to intensity variations, near-resonant interferometry uses its dispersion to detect frequency shifts as phase changes in an interference pattern. In the present setup, an iodine vapor cell in an imaging Michelson interferometer is used. With the illuminating laser frequency tuned near a resonant transition, the cell’s dispersion converts the frequency content of the field of view into a distortion of the carrier-fringe pattern recorded at the image plane of the interferometer. The phase distribution in the fringe images is reconstructed by filtering the individual images with a 2D Gabor filter pair tuned to the spatial frequencies of the basic carrier-fringe pattern. The post-processing is concluded with subsequent phase-unwrapping and subtraction of the carrier reference fringe phase. The method and the setup were demonstrated and calibrated experimentally on a rotating disc. The capability of the technique to operate in a real experimental environment was validated in a free subsonic jet and a tip vortex flow behind a wing section in a medium-sized wind tunnel facility. The measurements were found to be in generally good agreement with the theoretically predicted system characteristics and the reference measurements. As with other Doppler global techniques, the stability of the pulsed laser system and the secondary scattering in the test volume were identified as the main error sources.

Wavefront sensing using speckles with fringe compensation

Wavefront sensing with numerical phase-error correction system is carried out using a random phase plate and phase retrieval using multiple intensity measurements of axially-displaced speckle patterns and the wave propagation equation. Various wavefronts with smooth curvatures incident on the developed phase plate (DPP) are examined: planar, spherical, cylindrical, and a wavefront passing through the side of a bare optical fiber. Spurious fringe pattern in the wavefront reconstructions due to a small tilt (Delta theta=0.212 degrees) in the plane illumination wave is detected and numerically corrected for. Fringe pattern of the illumination wave obtained for the setup without the phase object being investigated is used as reference fringe pattern. Fringe compensation yields wavefronts with the correct shape and numerical value based on the specifications of the setup. The numerical phase-error correction system described in this study can be extended to other types of phase errors such as those due to aberrations if optical elements are present in the setup or due to perturbations in the environment.

Fourier transform profilometry based on a projecting-imaging model

In order to obtain the correct height reconstruction of a measured object, a projection lens and a camera lens must be placed at equal heights above the reference plane in the traditional Fourier transform profilometry (FTP) method. We propose an improved phase-height mapping formula based on an improved description of the reference fringe and the deformed fringe in FTP when the projection lens and the camera lens are not placed at equal height. With our method, it is easier to obtain the full-field fringe by moving either the projector or the imaging device. In some cases, where the required parallel condition cannot be met, the proposed method offers a flexible way to calculate the height distribution.

Real-time holographic interferometry using superposed compensating holograms

Superposed compensating holograms are shown to be a promising tool for solving a number of problems in real-time holographic interferometry, in particular, obtaining of interference patterns with fixed parameters of reference fringes and adjustment of the measurement sensitivity. The proposed approach is tested through visualization of the melting of a PMMA planar sample by means of lateral shear holographic interferometry.

Holographic reverse shearing interferometry with high measurement sensitivity

The possibility of studying phase objects by reverse shearing interferometry with high measurement sensitivity is demonstrated. Phase objects are studied in two stages. In the first stage, holographic reverse shear interferograms are measured with and without an object under nonlinear conditions with tuning to frequent reference fringes. In the next stage, these interferograms are optically processed to obtain two interference patterns. The behavior of the interference fringes is the same as in the case of conventional double-beam interferometry with a standard reference wave. The increase in the measurement sensitivity in the thus-obtained interference patterns is due to the use of higher diffraction orders reconstructed from the holographic interferograms. A possibility of controlling the width of interference fringes is considered. The results of experimental approval of this technique are presented.

General approach to residual stresses determination in thin-walled structures by combining the hole drilling method and reflection hologram interferometry

Main questions, which are connected with a determination of residual stresses by combining the hole-drilling method and whole-field displacement measurements, are considered in detail. The relations, which are needed for converting initial experimental data into stress values of interest, are presented for thin-walled plane structures. Required input data are obtained by simultaneous measurements of probe hole distortions in two principal strain directions on opposite sides of thin plane specimen. Emphasis is made on a careful quantitative formulation of the inverse problem, a solution of which is capable of deriving both membrane and bending residual stress components with the highest possible accuracy. It is shown that an availability of two-side initial data is both an essential and a necessary condition of such formulation. Detailed analysis of accuracy of the results obtained is performed proceeding from three different criteria. All presented considerations are supported with a set of high-quality actual interferograms and analogous reference fringe patterns related to weld-induced residual stress fields.

Classification of holographic fringe patterns inherent in through hole drilling in residual stress field

Comparative analysis of actual fringe patterns, which are induced by combined implementing the hole drilling method and reflection hologram interferometry for residual stresses determination, is presented. Involved considerations are related to plane thin-walled structural elements. A set of interferograms of perfect (ideal) form is selected proceeding from one-side measurements. A base for recognising each specific ideal configuration is a fine coincidence between actual interferograms and analogous reference fringe patterns constructed for the same stress state. Perfect (ideal) both actual and reference fringe patterns are defined as a response of pure membrane 2D stress field on through hole drilling between exposures. Main principles of creating the regular catalogue of reference fringe patterns inherent in through hole drilling in thin-walled components are formulated. Emphasis is made on a careful collecting and classifying actual interferograms with clear indications of bending stress presence in total residual stress field. Evidences needed for a reliable classification of the type of residual stresses field of interest are established and verified. A response of superimposed residual stress field, which consists of both membrane and bending components, is characterised by various deviations of each specific fringe pattern from an ideal form. More deep analysis of fringe patterns related to superimposed residual stress field is based on specially designed technique. The main essence of the approach developed is simultaneous measurements of through hole distortions in two principal strain directions on opposite sides of thin plane specimen. These sides are faces of the drill entrance and exit. Sophisticated optical set-up that is capable of obtaining high-quality fringe patterns in the course of two-side measurements is developed and implemented. Typical set of fringe patterns obtained for single probe hole on opposite specimen faces is presented.

Residual stresses deriving from holographic interferometry data on a base of inverse problem solution

A transition model, which is capable of obtaining both membrane and bending residual stress components from initial experimental information, is developed for thin-walled plane structures. The determination of residual stresses is based on the combined implementing of the hole-drilling method and reflection hologram interferometry. Required input data are obtained by simultaneous measurements on through hole distortions in two principal strain directions on opposite sides of thin plane specimen. These sides are faces of the drill entrance and exit. Superimposed residual stresses field, which consists of both membrane and bending components, is a reason for the various deviations of each specific fringe pattern from an ideal form. This fact is a clear experimental indication of the bending stress contribution in a total stress field. Two ways of decomposition of superimposed residual stresses field are proposed and analysed in detail. Emphasis is laid on a careful quantitative formulation of the inverse problem needed for an accurate deriving both membrane and bending residual stress components. It is shown that an availability of two-side initial data is both an essential and necessary condition of such a formulation. Detailed analysis of an accuracy of the results obtained is performed. This analysis is based on a wide set of both actual interferograms and analogous reference fringe patterns related to superimposed residual stress field under study. Comparing residual stress values obtained proceeding from one-side and two-side data are presented for different types of superimposed field of interest.