A comparison study of denoising techniques in fringe pattern analysis

Parallel computing for fringe pattern processing: A multicore CPU approach in MATLAB ® environment

Single-frame fringe pattern processing and analysis is an important task of optical interferometry, structural illumination and moire techniques. In this contribution we present several algorithmic solutions based on the notion of Hilbert-Huang transform consisting of empirical mode decomposition algorithm and Hilbert spectral analysis. EMD adaptively dissects a meaningful number of intrinsic mode functions from the analyzed pattern. Appropriately managing this set of functions results in a powerful fringe processing tool. We describe in detail especially tailored manners proposed to extend the EMD algorithm to 2D and perform Hilbert-transform-aided efficient fringe pattern denoising, detrending and amplitude/phase demodulation.

A principled approach, based on Bayesian estimation theory and complex-valued Markov random-field prior models, is introduced for the design of a new class of adaptive quadrature filters. These filters are capable of adapting their tuning frequency to the local dominant spatial frequency of the input image while maintaining an arbitrarily narrow local frequency response; therefore they may be effectively used for the accurate recovery of the phase of broadband spatial-carrier fringe patterns, even when they are corrupted by a significant amount of noise. Also, by constraining the spatial variation of the adaptive frequency to be smooth, they permit the completely automatic recovery of local phase from single closed fringe pattern images, since the spurious discontinuities and sign reversals that one obtains from the classical Fourier-based methods are avoided in this case. Although the applications discussed here come from fringe pattern analysis in optics, these filters may also be useful in the solution of other problems, such as texture characterization and segmentation and the recovery of depth from stereoscopic pairs of images.

Fringe visibility and noise removal, are key success factors in interferometric techniques, where novel deep learning techniques can be applied. We test the use U-Net deep convolutional network applied to the obtained interference images, trained with an ad-hoc generated image dataset with complex fringe patterns, computed using high order Zernike polynomials.

This work aims to define Sonine filters and introduce them for digital image processing. Their fundamental properties are described and an optimizing performance procedure is explained, exploiting the unique advantage that this kind of filters possess, which consists of having simple analytical finite Fourier transforms for circular, elliptical and rectangular domains. A comparison with various existing filters is also presented, like Gaussian, Hann, Hamming, Blackmann, etc. Some relations are provided to facilitate their applicability. Also, comprehensive optimized filter designs are provided. Finally, an experimental application for intensity normalization and noise reduction of fringe patterns is described, showing that this kind of filters could be helpful in digital image processing and particularly in the analysis of fringe patterns.

The possibility to describe interference fringes by stochastic differential equations is demonstrated. Evaluation of interference fringes is based on the idea to define the interference fringe intensity variation as a nonlinear transform of supposed dynamic system evolution, where the system parameters like fringe amplitude, frequency and phase are described by the discrete stochastic differential equations. It allows realizing the optimal recurrence prediction-correction algorithms for dynamic fringe processing, in which fringe signal is predicted to a following discretization step using full information available before this step, and fringe signal prediction error is used for step-by-step dynamic correcting the fringe parameters. This approach has been applied to low-coherence interference fringe processing and 2-D fringe pattern analysis with the 2-D prediction procedure that increases the noise-immunity and data processing speed of fringe evaluation in non-destructive optical testing and material science.

A new method for derivation of phase-shifting algorithms is presented. The cost function is defined and it is minimized using descending gradient method. The family of algorithms is derived as the result. The properties of the algorithms do not change within the family. Examples of algorithms for constant phase-step as well as for randomly disturbed phase- steps are given and analyzed.

Application of fourier analysis to the laser based interferometric strain/displacement gage

A real-time extension of a recently developed optical holographic interferometry method [J. A. Clark, J. Sound Vib. 56(2) (1978)] is reported. In this extension of the basic method, a single hologram of the visualization region in an acoustic test facility is recorded. Then the hologram is developed and reinserted into its original position in the optical system. If the visualization region is illuminated for a short duration while an acoustic wave is propagating through the region, interference fringes can be observed—even directly by eye! —which can be quantitatively interpreted as contours of equal instantaneous pressure. These fringe patterns can also be photographed with a still or motion picture camera. The measurement method is used to investigate scattering of sound at a pressure release boundary such as a free liquid surface or a bubble screen. Motion picture records of the scattering process observed as a function of time, frequency, and source strength will be shown. It is demonstrated for the first time that the instantaneous pressure field can be observed in the region immediately adjacent to a free acoustic boundary. [Research supported by ONR.]

A fringe analysis method, which combines the Fourier transform with the fractional fringe order method for measuring the absolute thickness of a block gauge, is presented. An approximate integer part of the fringe order is estimated by mechanical measurements, and the fractional part is determined by Fourier analysis of the interferometric fringe patterns. The fringe patterns are obtained with a Michelson interferometer by illumination of several selected wavelengths, respectively. The use of the fractional fringe order method can determine accurately more than 2ϖ phase jumps. The measured thickness of a block gauge is 5999115.0 ± 0.7 nm, which is comparable with the standard thickness of 6 mm. The influence of wavelength and approximate integer part of fringe order on the measurement accuracy is discussed.

This paper introduces a novel uniaxial fringe projection profilometry (FPP) called active shape from projection defocus profilometry (ASPDP), which utilizes the sharpness analysis of binary fringe patterns to quantify the defocus level. Compared with previous uniaxial FPP methods, our work first utilizes a pinhole defocus model to account for three-dimensional reconstruction. Since defocused fringe pattern can be modeled as the original pattern convoluted with a point spread function (PSF), pixel-wise defocus level can be quantified with this PSFs kernel using temporal Fourier analysis. In this research, calibration is achieved by using a mechanical translation device, and determined by rational polynomial fitting to establish defocus-depth relationship. The experiment demonstrates that this method can provide an accurate reconstructed 3D geometry without shadows.

Windowed Fourier transform (WFT) is used to analyze fringe patterns observed from optical measurements. The space-frequency resolution of the WFT is limited, which affects the analyzing performance. In this Letter, we propose to apply the two-dimensional synchrosqueezing transform (SST) for analyzing fringe patterns. The SST is a technique used to overcome the limitation of the space-frequency resolution of the WFT, which sharpens the WFT representation using the derivative of the WFT phase. Numerical experiments confirm the effectiveness of the SST in denoising the fringe pattern and estimating the local frequency from the observed fringe pattern.

Optical full-field measurement techniques have been widely studied in academia and applied to many actual fields of automated inspection, reverse engineering, cosmetic surgery, and so on. With the advent of color CCD cameras and DMD (Digital Micromirror Device) based color DLP (Digital Light Processing) projectors, their major red, green, and blue channels have been used as a carrier to code fringe patterns. Since three fringe patterns can be simultaneously projected and captured at one shot, the acquisition time reduces to 1/3 of the value by the gray fringe pattern projection. This chapter will introduce two kinds of applications of red, green, and blue as a carrier: 1) modulation and demodulation method of coding sinusoidal fringe patterns into RGB channels of a composite color image; and 2) modulation and demodulation method of coding sinusoidal and binary fringe patterns into RGB channels of multiple composite color images. Experiments on testing the two kinds of applications were carried out by measuring the shape of objects’ surface. The results confirm that red, green, and blue channels can be used as a carrier to reduce the acquisition time.

Analysis of closed-fringe patterns with quadratic phase that are often encountered plays an important role in optical interferometry. But because the frequency spectra of the two exponential signals that compose closed-fringe patterns overlap in the Fourier domain while one is clearly distinct from the other in the fractional Fourier domain, fractional Fourier transform (FRFT) is a useful method for analyzing the images to provide parameter estimation. However, when the fringe pattern has varying background and/or modulation due to non-uniform illumination, parameter estimation accuracy based on FRFT is affected, which lacks theoretical justification. Thus, the impact of varying background and/or modulation on the FRFT is studied with theoretic analysis and presented in this paper. Key factors that contribute to the optimal results are discussed when employing three kinds of fringe normalization methods to eliminate the impact. Here, the fringe pattern is first processed by the normalization technique. Then the cosine-only term is used to estimate parameter by use of the FRFT-based method. Physical quantities are then obtained by parameter estimation. In comparison with our previous method based on FRFT, more accurate results are achieved. The feasibility and applicability of the proposed approach are demonstrated using simulation and experimental results.

A new technique for fringe pattern demodulation using a linear digital phaselocked loop (DPLL) is presented. The phase components of a fringe pattern arecalculated using a way similar to the Fourier fringe analysis technique and awrapped phase map is produced. The linear DPLL demodulates, tracks and unwrapsthe wrapped phase map simultaneously. Consequently, the proposed algorithm hasgood noise immunity. The proposed algorithm is tested using real fringepatterns and its suitability for demodulating real fringe patterns isconfirmed. Also, the proposed algorithm is compared with the Fourier fringeanalysis technique. The implementation of the linear DPLL in real time on acommercial parallel image processing system is described. Fringe patterns aregrabbed, processed and the resultant phase maps are displayed concurrently.The parallel system is capable of analysing 25 images per second. There is atwo-image delay between grabbed fringe patterns and displayed phase maps.