Carrier Fringes Research Articles

Heterodyne background-oriented schlieren for the measurement of thermoacoustic oscillations in flames

In aircraft engines, thermoacoustic oscillations in the combustion chamber contribute significantly to noise emissions, which, like all other emissions, must be drastically reduced. Thermoacoustic oscillations are not only a concern, they can also be beneficial in hydrogen combustion. This work demonstrates that thermoacoustic density oscillations with amplitudes at least an order of magnitude smaller than those resulting from density gradients in a turbulent flame can be detected using laser interferometric vibrometry. This improvement was made possible by heterodyning a carrier fringe system in background-oriented schlieren (BOS) recordings, which were subsequently analyzed using techniques commonly used for holographic interferometry. In comparison with other BOS evaluation techniques, the filtering of the individual frames in the Fourier domain offers a more efficient computational approach, as it allows for phase averaging of a high number of single recordings to reduce noise from turbulence. To address fringe pattern distortions and cross talk in the Fourier domain, which both have been observed by other authors, we propose background subtraction methods and an optimized background pattern. Additionally, the procedure provides a visualization tool for marking the high turbulence regions of heat release by the variations in fringe amplitude. Finally, the line-of-sight data are reconstructed using the inverse Abel transform, with the data calibrated by laser interferometric techniques, resulting in local values for density oscillations.Graphical abstract

Background-Oriented Schlieren For The Detection Of Thermoacoustic Oscillations In Flames

Thermoacoustic oscillations are well known to combustion engineers. They are not only a cause of concern, but also give hope to be able to operate aircraft engines with hydrogen, due to flame stabilization and significant reduction of NOx emissions when thermoacoustically excited. The aim of this work is to investigate the potential of using a heterodyne background-oriented schlieren (HBOS) technique to detect thermoacoustic oscillations in the density field of an acoustically excited flame. It also seeks to address the issue of accuracy due to the small amplitude of thermoacoustic oscillations compared to turbulent density fluctuations in a flame. The experiment uses an unconfined swirl-stabilized methane flame and investigates thermoacoustic oscillations at about 3.4 kW power at ambient conditions excited by a siren at 225 Hz. The HBOS technique recently presented by the authors uses a carrier fringe system in background-oriented schlieren recordings, with subsequent analysis using evaluation techniques known from holographic interferometry. These fast algorithms reduce turbulence noise by phase averaging a large number of images. To derive local data from the line-of-sight projections, an inverse Abel transform is applied. Laser interferometric vibrometry is used to calibrate to the observed oscillations. A comparison with data from chemiluminescence is also presented to better demonstrate the application of this efficient technique to the detection of heat release oscillations. Future tasks in this project will deal with full-scale test benches and machine learning tools to address the limited observations in them.

Carrier-frequency estimation for digital holograms of phase objects.

Accurate estimation of carrier fringe frequency is essential for the demodulation of off-axis digital holograms. The fringe frequency is often associated with the amplitude peak of the cross-term in the two-dimensional Fourier transform of a digital hologram. We point out that this definition of carrier frequency is not valid in general for holograms associated with phase objects. We examine the carrier-envelope representation for digital holograms from the viewpoint of Mandel's criterion [J. Opt. Soc. Am.57, 613 (1967)10.1364/JOSA.57.000613]. An appropriate definition of carrier frequency is observed to be the centroid of the power spectrum associated with the cross term. This definition is shown to apply uniformly to holograms associated with phase objects, is robust to noise, and leads to the smoothest (or least fluctuating) envelope representation for the demodulated object wave. The proposed definition is illustrated with simulated as well as experimentally recorded off-axis holograms.

State-space modeling approach for fringe pattern demodulation.

A spatial carrier fringe demodulation technique is proposed based on a state-space modeling approach for phase estimation. The fringe background intensity, carrier frequency, and phase quadrature components are considered to be the elements of the state vector, which are estimated simultaneously. The state estimation is performed using the extended Kalman filter. The simulation and experimental results are provided to demonstrate the performance comparison of the proposed method with popular and state-of-the-art methods in terms of noise robustness and phase estimation accuracy.

Development of Simultaneous Dual-Resolution Digital Holography System

This research paper is focused on the development of a digital holography system for simultaneous dual-resolution measurements. Digital holography has been widely used for deformation measurements and non-destructive testing (NDT) due to its advantages of high sensitivity, high accuracy, and whole-field, non-touch measurements. A traditional test only has one spatial resolution, which can cause a big deformation to be indistinguishable or minor defects to be ignored. Both large and small fields of view should be observed to reach a multi-spatial resolution measurement. Usually, multiple separate tests are used to observe the different sized fields of view, resulting in higher costs and longer required testing times. Furthermore, these tests may not be repeatable in some cases. This paper presents research on a novel digital holography system that achieves dual spatial resolution measurements simultaneously by testing different-sized fields of view with a single camera. The novel system has two optical channels with two optical layouts of holography to measure deformation. By changing the combined focus length, the two holographic setups have different fields of view, i.e., one has a large and the other has a small field of view. To realize a simultaneous test, the polarization technique is used to avoid cross-interference between the two optical layouts. Finally, spatial carrier fringes with different orientations are introduced into the two holographic setups by appropriately adjusting the reference beam of each setup. The different oriented spatial carrier fringes enable the spectrums of the two interferograms to be separated after a FT (Fourier transform) and the phase distributions of the two interferograms can be extracted and separated by windowing the spectrum to perform an IFT (inverse Fourier transform). The phase distributions can then be used to analyze and calculate the deformations. The experiment using this system is described in this paper and the practicability of this method is verified by the obtained experimental results.

Measuring material thickness changes through tri-aperture digital speckle pattern interferometry

A configuration for the measurement of thickness changes in materials through one-shot digital speckle pattern interferometry (DSPI) was developed. The phase maps calculation was made by adding carrier fringes by the multiple aperture principle and Fourier Transform Method (FTM). With this setup, interferometry configurations verified that the simultaneous and instantaneous visualization of two opposite faces of a surface is possible. In addition, the combination of the simultaneous results obtained from both sides of the material makes it possible to determine displacements with greater sensitivity or to identify changes in their thickness. The validation and demonstrative tests were carried out with a 1-mm-thick aluminum plate with a 5-mm diameter through hole coated. Thickness changes to 2 μm were measured.

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.

A single-frame spatial carrier phase-shifting method realized by minimizing the coefficient of variation

An advanced spatial carrier phase-shifting algorithm based on minimizing the coefficient of a variation method is proposed, which realizes the phase extraction of a single-frame spatial carrier fringe pattern. In our test, compared with the existing classical algorithms, the proposed method is proved to have the dual advantages of efficiency and accuracy. In addition, the main factors that may affect the performance of the method are analysed and discussed. The results show that the method proposed is a fast and accurate single-frame phase detection method, which can provide an effective solution for real-time phase demodulation.

Fast and in-situ correction of camera channel crosstalk based on Fourier transform of carrier fringes in multi-colour interferometry

To deal with the light intensity crosstalk between R, G and B channels of colour camera in multi-colour interferometry, we present a fast and in-situ correction method based on Fourier transform of carrier fringes. The crosstalk coefficients of camera channels are obtained in the Fourier frequency domain of captured colour carrier fringes, and the crosstalk is corrected by matrix inverse operation. Simulations and experiments verify that this method has advantages of simple implementation, fast correction speed and high measurement accuracy, and it effectively achieves in-situ correction without removing the camera.

Carrier fringe pattern analysis: Links between methods

Introducing a carrier into a fringe pattern makes the phase retrieval problem well-posed, and has become one of the pillar techniques in optical metrology. The carrier fringe pattern analysis for high-accuracy phase retrieval is hence important, for which, many well-known methods have been developed, such as the Fourier transform method, the windowed Fourier transform based methods (the windowed Fourier filtering and the windowed Fourier ridges), the spatial carrier phase-shifting method, and the sampling moiré method. These methods were developed independently and seemingly different. The purpose of this paper is to reveal the close relationships between them, and to connect these methods into a tight-knit methodology family.

Estimation of global visibility for low-quality fringe pattern using Fourier-polar transform

When the interferometers with adjustable fringe visibility is used for high precision wavefront measurement, it needs to estimate the visibility of experimental patterns so as to obtain the interference patterns with the highest visibility. A new method combining Fourier-polar transform with directional projection is developed to estimate the global visibility of carrier fringe pattern. This method can also be applied to low-quality fringe patterns such as low contrast and low signal-to-noise ratio (SNR) that often appear in the interferometer testing. Theoretical analysis shows that this method is obviously superior to the direct calculation method. In addition, an illustrative experiment based on the radial shearing interferometer is given. Results generated from this method are compared with the derived values from theoretical model of experimental system, and exemplary agreement between both is demonstrated.

Robust phase unwrapping algorithm for noisy and segmented phase measurements.

This paper proposes a robust phase unwrapping algorithm (RPUA) for phase unwrapping in the presence of noise and segmented phase. The RPUA method presents a new model of phase derivatives combined with error-correction iterations to achieve an anti-noise effect. Moreover, it bridges the phase islands in the spatial domain using numerical carrier frequency and fringe extrapolation thus eliminating height faults to enable solving segmented phase unwrapping. Numerical simulation and comparison with three conventional methods were performed, proving the high robustness and efficiency of the RPUA. Further, three experiments demonstrated that the RPUA can obtain the unwrapped phase under different noise accurately and possesses the capability to process segmented phases, indicating reliable practicality.

Automated defect identification from carrier fringe patterns using Wigner-Ville distribution and a machine learning-based method.

The paper presents a method for automated defect identification from fringe patterns. The method relies on computing the fringe signal's Wigner-Ville distribution followed by a supervised machine learning algorithm. Our machine learning approach enables robust detection of fringe pattern defects of varied shapes and alleviates the limitations associated with thresholding-based techniques that require careful control of the threshold parameter. The potential of the proposed method is demonstrated via numerical simulations to identify different types of defect patterns at various noise levels. In addition, the practical applicability of the method is validated by experimental results.

Alternative interpretation of color phase-shifting profilometry and a self-contained method for fringe analysis.

This work aims to report a robust single-shot color fringe projection method based on phase-shifting profilometry, where, to calculate the phase, is it not necessary to have knowledge of color coupling or color imbalance calibration parameters of the projector-camera system; additionally, it does not require knowledge of the phase-shifting step, nor projecting equally stepped fringe patterns. Furthermore, it does not require a high density of carrier fringes; it only requires a composite single color image. Theoretical and experimental results are provided. Its suitability to simplify absolute unwrapping is also discussed.

Suppression of artifacts in X-ray phase-contrast images retrieved by Fourier transform

Over the last two decades, the grating-based phase-contrast imaging has aroused the interest of a number of researchers. It could provide an access to three complementary signals simultaneously: the conventional absorption contrast, the differential phase contrast related to refraction of incident wave, and the dark-field contrast that relates to ultra small angle scattering in a sample. The grating-based phase-contrast signals have higher contrast sensitivity for some types of soft samples than the absorption signals. Dark-field signals have better diagnostic effects in the detection of lung tumors, pneumothorax and the identification of microcalcifications in breast. There are two main phase retrieval methods in grating-based X-ray phase-contrast imaging, i.e. phase stepping method and Fourier transform method. The phase signals retrieved by phase stepping is high precise and has low noise. But the sample suffers high dose due to at least three exposures. The phase signals retrieved by Fourier transform is low-dose due to the fact that only one image with sample is needed, but it is easily affected by artifacts when the size of the filtering window is too large. However, when the size of the filtering window is too small, the high-frequency information of the phase-contrast image will be lost, and the image will become blurred. A trade-off between definitions of the image and artifacts should be made. Since the phase-contrast signal and the dark-field signal of the sample are modulated by carrier fringes, the frequency spectrum of the detected image consists of many different harmonics. The artifacts in the retrieved signals originate from the spectrum aliasing between primary peak around zero spatial frequency and first-order harmonic peaks. Therefore, the subtraction between two images with phase difference can remove the primary peak, and the artifacts in the phase-contrast signals and dark-field signals will be suppressed. In order to further suppress the artifacts, we increase the frequency of carrier fringes, which results in a larger distance between first-order harmonic peaks in frequency domain. We finally attain artifact-free phase-contrast images and dark-field images while maintaining high definition of the images. The method proposed here is not only applicable to incoherent imaging system, but also to Talbot-Lau interferometer, and it would be useful in fast and low-dose X-ray phase-contrast and dark-field imaging.

Single-shot fringe-pattern analysis algorithm robust against abrupt phase jumps

Fringe-analysis methods, with fine carrier fringes, allow us to extract phase signals using a single-shot imaging measurement, enabling real-time observation of dynamic phenomena. However, abrupt phase jumps produced by the structural boundaries (or edges) in an object and/or object surfaces occasionally generate significant errors in the resulting images. In this paper, a new algorithm consisting of two steps is proposed to address this problem. In the first step, we computed an approximate phase map by ignoring abrupt phase jumps. In the second step, we solved a weighted least-squares problem to recover the abrupt phase jumps using the approximate phase map. The influence of several factors, such as carrier-fringe frequency and noise, was examined through simulation and experiment, and the effectiveness of the proposed method was demonstrated.

Phase demodulation from a spatial carrier fringe pattern using extended complex Kalman filter

A spatial carrier fringe pattern analysis technique is proposed for the phase demodulation using the extended complex Kalman filter. A state space model is defined based on the spatial evolution model of the fringe signal in a given row or column of the fringe pattern depending on the direction of carrier fringes. Since the state space model incorporates one of the state associated with the carrier fringe frequency, its value need not be known apriori for the phase demodulation. Furthermore, the proposed method is capable of removing carrier phase contribution from the estimated phase using the carrier fringe frequency estimate. Simulation and experimental results substantiates the applicability of the proposed method.

Adaptive carrier fringe pattern enhancement for wavelet transform profilometry through modifying intrinsic time-scale decomposition.

The uneven background illumination and random noise will degrade the quality of the optical fringe pattern, resulting in reduced accuracy or errors in phase extraction of wavelet transform profilometry (WTP). An adaptive fringe pattern enhancement method is proposed in this paper, which can effectively solve the above problems and improve the robustness of WTP. First, a modified intrinsic time-scale decomposition (MITD) algorithm is used to decompose each row of the fringe pattern adaptively, which can obtain a set of reasonable and pure proper rotation components (PRCs) with a frequency ranging from high to low and a monotonic trend. The MITD algorithm can overcome the mode mixing problem while ensuring the completeness of decomposition. Then, based on the obtained pure PRCs, an innovative background-carrier signal-noise automatic grouping strategy is proposed. Specifically, weighted-permutation entropy (WPE) is adopted to handle noise removal, and fuzzy gray correlation analysis (FGCA) is used to separate the background and carrier signal. Finally, the desired phase information can be easily and accurately extracted from the enhanced carrier signal component by a direct wavelet ridge detection method. Both the simulation and experimental results demonstrate the effectiveness and functionality of the proposed method.

High temporal and spatial resolution single-shot digital holography with Fresnel domain filtering using witch's hat illumination.

High-resolution, single-shot on-axis digital holography is proposed. Generally, an on-axis configuration samples carrier fringes with higher spatial resolution compared to an off-axis configuration. However, the reconstructed image is obtained with unnecessary images of a conjugate image and a zero-order beam. The proposed method uses a phase-modulated illumination beam and image processing to eliminate these unnecessary images. Since time-division and parallel phase-shifting methods are not required, the proposed method has higher temporal and spatial resolutions. During image processing, the conjugate image is removed by filtering on the Fresnel domain while keeping most of the information of the object image intact. The usefulness of the proposed method is confirmed by a numerical simulation and an optical experiment.

Fringe pattern analysis using deep learning

In many optical metrology techniques, fringe pattern analysis is the central algorithm for recovering the underlying phase distribution from the recorded fringe patterns. Despite extensive research efforts for decades, how to extract the desired phase information, with the highest possible accuracy, from the minimum number of fringe patterns remains one of the most challenging open problems. Inspired by recent successes of deep learning techniques for computer vision and other applications, here, we demonstrate for the first time, to our knowledge, that the deep neural networks can be trained to perform fringe analysis, which substantially enhances the accuracy of phase demodulation from a single fringe pattern. The effectiveness of the proposed method is experimentally verified using carrier fringe patterns under the scenario of fringe projection profilometry. Experimental results demonstrate its superior performance in terms of high accuracy and edge-preserving over two representative single-frame techniques: Fourier transform profilometry and Windowed Fourier profilometry.