Synthetic Fringe Research Articles

Correcting etaloning fringes in hyperspectral image cubes of Jupiter using sensor thickness modeling with flat-field data fitting

Evidence of “fringing” due to optical etaloning was observed in narrowband hyperspectral image cubes of Jupiter collected prior to 2018 at the Apache Point Observatory 3.5-m telescope with the New Mexico State University Acousto-optic Imaging Camera. The etaloning resulted from the use of a back-illuminated, high quantum efficiency CCD. Otherwise successful flat-field correction was ineffective in removing fringes at some wavelengths associated with Jupiter’s absorption regions. We describe an etaloning correction method based on a mathematical interference model that assumes a single detection layer. A two-dimensional thickness function for the sensor layer was derived and found to have an overall “dish-shaped” variation along with some finely spaced surface polishing marks. Synthetic fringe frames corresponding to the flat-field and science images were created using the thickness function. Optimized contrast values were found for the synthetic frames and defringed images of Jupiter were generated by separately correcting flat-field and science images using the synthetic fringe frames before applying the final flat-field division. Quantitative analyses of defringed flat-field images showed fringe contrast reductions by factors of 2 to 8 on average and a disk-averaged spectrum of defringed Jupiter data compared favorably with an established spectrum. This defringing approach is applicable to other detectors that can be modeled with a single detection layer and where a sequence of spectral images with adequate wavelength resolution is available.

Two-step phase shifting algorithms: Where are we?

Two steps phase shifting interferometry has been a hot topic in the recent years. We present a comparison study of 12 representative self–tunning algorithms based on two-steps phase shifting interferometry. We evaluate the performance of such algorithms by estimating the phase step of synthetic and experimental fringe patterns using 3 different normalizing processes: Gabor Filters Bank (GFB), Deep Neural Networks (DNNs) and Hilbert Huang Transform (HHT); in order to retrieve the background, the amplitude modulation and noise. We present the variants of state-of-the-art phase step estimation algorithms by using the GFB and DNNs as normalization preprocesses, as well as the use of a robust estimator such as the median to estimate the phase step. We present experimental results comparing the combinations of the normalization processes and the two steps phase shifting algorithms. Our study demonstrates that the quality of the retrieved phase from of two-step interferograms is more dependent of the normalizing process than the phase step estimation method.

Augmented Lagrangian method for a total variation-based model for demodulating phase discontinuities

In this work, we reformulate the method presented in App. Opt. 53:2297 (2014) as a constrained minimization problem using the augmented Lagrangian method. First we introduce the new method and then describe the numerical solution, which results in a simple algorithm. Numerical experiments with both synthetic and real fringe patterns show the accuracy and simplicity of the resulting algorithm.

Fringe pattern denoising using spatial oriented gaussian filters

In this paper, it is proposed a gaussian convolution-based fringe pattern denoising method. As will be shown, this method is robust enough compared with some of the most outstanding methods in the literature. Additionally, the proposed method overcomes the problem of underperformance in low-frequency fringes that is common in most oriented filtering methods, while keeping the great advantages of convolution-based filters. The advantages of the proposed denoising method will be demonstrated with experiments realized over synthetic and real fringe patterns, and comparing the performance with four representative methods, already reported.

Enhancing single-shot fringe pattern phase demodulation using advanced variational image decomposition

In many full-field optical metrology techniques, i.e. interferometry, moiré, and structured light, the information about the measurand, e.g. displacement, strain, or 3D shape, is stored in the phase distribution of a recorded two-dimensional intensity pattern—the fringe pattern. Its analysis (phase demodulation) therefore plays a crucial role in the measurement procedure, significantly affecting the total accuracy of the optical system. Phase demodulation methods based on just a single fringe pattern are especially interesting, due to their robustness to environmental disturbances and ability to examine dynamic events. However, the calculated phase map is easily spoiled by errors, which appear mainly because of fringe pattern imperfections, i.e. random noise, parasitic interferences, a nonsinusoidal fringe pattern profile or a non-uniform image background. In this contribution, an advanced variational image decomposition scheme is proposed to reduce these phase demodulation errors. The reported purely phase domain method can be easily adopted to aid virtually any fringe analysis method, including single-frame and multi-frame phase-shifting, possibly enhancing retrieved phase distribution without the need for hardware manipulation. We employed it to improve single-frame Hilbert–Huang transform-based fringe analysis. The remarkable efficiency and versatility of the developed algorithm are verified by processing synthetic and experimental fringe patterns and phase maps. The demonstrated approach compares favorably with the very capable 2D empirical mode decomposition reference method.

Variational phase recovering without phase unwrapping in phase-shifting interferometry

ABSTRACTWe present a variational method for recovering the phase term from the information obtained from phase-shifting methods. First we introduce the new method based on a variational approach and then describe the numerical solution of the proposed cost function, which results in a simple algorithm. Numerical experiments with both synthetic and real fringe patterns show the accuracy and simplicity of the resulting algorithm.

ABSOLUTE DISTANCE MEASUREMENT USING FREQUENCY SCANNING INTERFEROMETRY

Absolute distance measurement is necessary for many applications where the distance to a fixed-target is required. In this paper, frequency scanning interferometry is implemented with an external cavity tunable diode laser, which has a wavelength scanning range of (665-675 nm), to measure distances up to 5 m absolutely (achieved by multi-reflection system). An ultra-low expansion (ULE) Fabry-Perot (FP) cavity has been used as a reference to measure the tunable-laser scanning range. Absolute distance is determined by counting the synthetic fringes and FP peaks simultaneously while scanning the laser frequency. A fringe processing technique is developed to perform online distance measurement even though the tunable laser is not mode-hop free. This fringe processing method enables simple, fast and accurate distance measurements with repeatability ±3.9×10-6 L and combined uncertainty ±38.9×10-6 L which is limited by the calibration system used.

Two-shot fringe pattern phase-amplitude demodulation using Gram-Schmidt orthonormalization with Hilbert-Huang pre-filtering.

Gram-Schmidt orthonormalization is a very fast and efficient method for the fringe pattern phase demodulation. It requires only two arbitrarily phase-shifted frames. Images are treated as vectors and upon orthogonal projection of one fringe vector onto another the quadrature fringe pattern pair is obtained. Orthonormalization process is very susceptible, however, to noise, uneven background and amplitude modulation fluctuations. The Hilbert-Huang transform based preprocessing is proposed to enhance fringe pattern phase demodulation by filtering out the spurious noise and background illumination and performing fringe normalization. The Gram-Schmidt orthonormalization process error analysis is provided and its filtering-expanded capabilities are corroborated analyzing DSPI fringes and performing amplitude demodulation of Bessel fringes. Synthetic and experimental fringe pattern analyses presented to validate the proposed technique show that it compares favorably with other pre-filtering schemes, i.e., Gaussian filtering and continuous wavelet transform.

High dynamic range fringe acquisition: A novel 3-D scanning technique for high-reflective surfaces

This paper presents a novel 3-D scanning technique for high-reflective surfaces based on phase-shifting fringe projection method. High dynamic range fringe acquisition (HDRFA) technique is developed to process the fringe images reflected from the shiny surfaces, and generates a synthetic fringe image by fusing the raw fringe patterns, acquired with different camera exposure time and the illumination fringe intensity from the projector. Fringe image fusion algorithm is introduced to avoid saturation and under-illumination phenomenon by choosing the pixels in the raw fringes with the highest fringe modulation intensity. A method of auto-selection of HDRFA parameters is developed and largely increases the measurement automation. The synthetic fringes have higher signal-to-noise ratio (SNR) under ambient light by optimizing HDRFA parameters. Experimental results show that the proposed technique can successfully measure objects with high-reflective surfaces and is insensitive to ambient light.

Fringe counting method for synthetic phase with frequency-modulated laser diodes

Fringe counting method with laser diodes (LDs) for displacement measurement has been constructed. Two LDs are frequency modulated by mutually inverted sawtooth currents on an unbalanced two-beam interferometer. The mutually inverted sawtooth-current modulation of LDs produces interference fringe signals with opposite signs for respective wavelengths. The two fringe signals are fed to an electronic mixer to produce a synthetic fringe signal with a reduced sensitivity to the synthetic wavelength. Synthetic fringe pulses derived from the synthetic fringe signal make a fringe counting system possible for faster movement of the tested mirror.

Critical Examination of the Use of Coherent Gradient Sensing in Measuring Fracture Parameters in Functionally Graded Materials

Specific relations for out-of-plane deformation near crack tips of linearly graded materials are introduced and used with the optical method of coherent gradient sensing (CGS) to interpret experimentally obtained fringes. Stress intensity factors are thus derived and used to reconstruct synthetic fringes that are then compared to experimental ones. An error function is used with sets of 2-6 terms in the asymptotic solution to gage the incremental accuracy contributed by using these additional terms with the experimental results. The study reveals the necessity of using up to the sixth higher-order term to obtain a precise agreement between the analytical solution and the experimental interferograms. Specimen configurations with cracks consecutively positioned at the stiffer, and then at the more compliant end of the gradient are used. Distinct features of the interferograms indicate the benefits of having the crack on the compliant side of the elastic modulus variation.

Phase retrieval in digital speckle pattern interferometry by application of two-dimensional active contours called snakes

We propose a novel approach to retrieving the phase map coded by a single closed-fringe pattern in digital speckle pattern interferometry, which is based on the estimation of the local sign of the quadrature component. We obtain the estimate by calculating the local orientation of the fringes that have previously been denoised by a weighted smoothing spline method. We carry out the procedure of sign estimation by determining the local abrupt jumps of size pi in the orientation field of the fringes and by segmenting the regions defined by these jumps. The segmentation method is based on the application of two-dimensional active contours (snakes), with which one can also estimate absent jumps, i.e., those that cannot be detected from the local orientation of the fringes. The performance of the proposed phase-retrieval technique is evaluated for synthetic and experimental fringes and compared with the results obtained with the spiral-phase- and Fourier-transform methods.

Denoising of conoscopic holography fringe patterns with orientational filters: a comparative study

One of the most important problems to address when applying interferometric techniques to industrial applications is the prevalence of noise, which results in poor fringe patterns and thus poor measurements. One of the techniques that suffers most from this problem is conoscopic holography. Though this interferometric technique is ideal for industrial inspection, the poor quality of fringe patterns obtained in adverse environments may make measurement impossible. Classical filtering techniques based on one-dimensional filters or general speckle removal filters, such as the Frost or the gamma, may not suffice in adverse conditions. Therefore, a new approach, based on the nature of the fringe pattern information itself, is worth looking into. In this paper we propose the use of orientational filters to develop a filtering method that not only removes noise of any nature, but also enhances the fringe-pattern information. Several approaches to these algorithms are implemented and evaluated using synthetic conoscopic fringe patterns under different noise conditions, showing how they clearly outperform classical filters with negligible distortion even in the worst conditions. Examples with real data acquired with the latest prototype of a conoscopic long-standoff profilometer are also provided.

Measuring the thickness of opaque plane-parallel parts using an external cavity diode laser and a double-ended interferometer

This investigation proposes a method, which is based on an external cavity diode laser (ECDL) and a double-ended interferometer, for directly measuring the thickness of opaque plane-parallel parts. The test part does not need to be wrung on a platen because a ring-like configuration enables the interferometer to view both surfaces of the part simultaneously. The optical path difference (OPD) of the interferometer is sequentially measured at a series of descending synthetic wavelengths to eliminate interference fringe order ambiguity. Every synthetic wavelength is a combination of a varied wavelength and the initial wavelength of the ECDL. The thickness of the part is finally determined following a succession of OPD calculations in terms of synthetic wavelengths and measured synthetic fractional fringes. The uncertainty in the measurement is gradually reduced as the measuring synthetic wavelength is progressively reduced. The results of performance testing indicate that the accuracy is about 0.5 μm for a 10 mm gauge block.

Measuring large step heights by variable synthetic wavelength interferometry

Many mechanical and optical components contain step features whose surfaceheight changes far exceed the optical wavelength. Therefore, this work presents aninterferometer based on variable synthetic wavelength interferometry (VSWI) anddifferential heterodyne configuration to measure large step heights directly andunambiguously. This largely common-path configuration can substantially reducethe influence of environmental disturbances, which are the main sources of error inthe VSWI. Only one external cavity diode laser (ECDL) is employed to synthesizea series of synthetic wavelengths in descending order. The wavelengthsare combinations of the varied wavelengths and the initial wavelengthof the ECDL. In contrast to wavelength scanning interferometry, thismethod does not require the laser wavelength to be continuously tuned.The step height is sequentially measured at these synthetic wavelengthsand a lock-in amplifier resolves the corresponding synthetic fractionalfringes. The step height is determined following a succession of opticalpath difference calculations, in terms of the synthetic wavelengths andmeasured synthetic fractional fringes. Three known step heights, verifiedby a gauge block interferometer, were used to confirm the performanceof the proposed system. The results reveal that the uncertainty in themeasurement is approximately 80 nm when the measured height is up to 25 mm.

Synchronous detection technique for temporal fringe pattern analysis

An alternative method for temporal evaluation of fringe patterns is proposed. The method is based on the application of a synchronous detection system for processing the temporal irradiance fluctuations generated when the sensitivity of the optical set-up is changed. The technique requires an easy computing implementation and presents good noise rejection characteristics. In particular, the proposed method does not require to store the whole set of fringe images as it happens with Fourier techniques which allows for a faster data processing. Results of this method proved on synthetic fringe images as well as in real experiments are presented.

A Study of the Fracture Behavior of Unindirectional Fiber- Reinforced Composite Using Coherent Gradient Sensing (CGS) Interferometry

The feasibility of using Coherent Gradient Sensing (CGS) interferometry for studying the fracture behavior of unidirectional fiber-reinforced composites is investigated in this paper. First, the solution for the deformation field surrounding the tip of a crack in an orthotropic material is summarized. Specifically, the most singular term in the asymptotic expansion is explicitly presented. Then, the quantities that relate to the CGS measurements are derived in terms of the spatial position, stress intensity factors, and material constants. Based on these results, synthetic CGS fringe patterns are plotted numerically, and the effects of material anisotropy and crack-tip mixity on the shape of CGS fringe pattern are investigated. In addition, a finite difference interpretation of CGS fringes caused by the finite spacing of the CGS diffraction gratings is taken into account in the simulation. Finally, the initiation fracture toughness and the subsequent resistance curve behavior of a particular unidirectional graphite/epoxy composite are measured using the CGS method. The optically measured stress intensity factors compare successfully to values obtained from the load measurements and the available analytical solutions.

Fringe detection in noisy complex interferograms

A new algorithm to estimate the two-dimensional local frequencies of phase interferometric data is described. With a complex sine-wave model, demonstration is given that a conventional multiple-signal classification (MUSIC) algorithm can be used in spite of multiplicative noise perturbations. A faster algorithm dedicated to the processing of interferograms is developed and a measure of confidence in the estimate is proposed. We studied numerical performances using synthetic fringes. As a result of the frequency estimation, knowledge of the fringe local width and orientation can be applied to restore noisy phase data. Results of a complex phase filter are presented for real interferograms obtained from synthetic aperture radar images.

Absolute Positioning of Scanning Probe Microscope Tip by Two-Wavelength Synthetic Method

In this paper, we describe the absolute positioning of a probe tip in a scanning Wiener fringe optical microscope (SWOM) using a synthetic wavelength method. Two laser beams with different wavelengths are superimposed and are incident on a sample surface. A synthetic fringe which has a longer period than that of the Wiener fringe obtained with a single wavelength is formed on the surface. The order of Wiener fringe which is utilized as a feedback signal in the microscope can be determined by the synthetic fringe. A sample with known structure was observed for various defined fringe orders using the SWOM.

Displacement Measurement by Image-processed Speckle Patterns

Abstract The use of a commercial image-processing system in digital speckle-pattern interferometry is demonstrated. The possibilities of electronic-noise suppression and speckle-noise smoothing are discussed. Synthetic speckle patterns have been created and are shown to be useful in software development. Fringe skeletons have been extracted automatically from both synthetic and experimental correlation fringes giving accurate quantitative results.