Igor P. Gurov

Analysis of low-coherence interference fringes by the Kalman filtering method

Interferometers with low-coherence illumination allow noncontact measurement of rough-surface relief with a wide range of measurement definition by locating the visibility maxima of interference fringes. The problem is light scattering by the surface to be measured, which can cause distortion of low-coherence interferometric signals. We propose to use a stochastic fringe model and a Kalman filtering method for processing noisy low-coherence fringes dynamically. Prediction of the fringes signal value at each discretization step is based on all the information available before this step; the prediction error is used for dynamic correction of the estimates of the fringe envelope and phase. The advantages of the Kalman filtering method consist in its immunity to noise, optimal fringe evaluation, and data-processing speed.

White-light spectral interferometric technique to measure the wavelength dependence of the spectral bandpass of a fibre-optic spectrometer

Abstract A spectral-domain white-light interferometric technique with channelled spectrum detection is used to measure the wavelength dependence of the spectral bandpass of a fibre-optic spectrometer. In an experimental setup comprising a halogen lamp, a non-dispersive Michelson interferometer and the spectrometer to be measured, spectral interferograms are recorded for different optical path differences (OPDs) between interfering beams. By processing the recorded spectral interferograms using discrete filtering and a fringe amplitude demodulation method, spectral fringe visibilities, first, as a function of the wavelength for given OPDs, and second, as a function of the OPD at given wavelengths, are obtained. It is confirmed, in accordance with theory, that the latter spectral fringe visibility functions are Gaussian functions with maxima and widths dependent on the wavelength. From the widths of the Gaussian spectral fringe visibility functions the wavelength dependence of the spectrometer bandpass is determined over a wide spectral range.

Full-field high-speed optical coherence tomography system for evaluating multilayer and random tissues

Testing the condition of art subjects plays important role in reservation of Cultural Heritage. Optical Coherence Tomography (OCT) is a promising tool for nondestructive cross-sectional evaluating internal structure of material samples like varnish layer of paintings. It is important to use high-speed OCT systems for testing subsurface structure of objects with large area. In the paper, comparison of OCT systems from viewpoint of information capacity is given to select the most appropriate OCT system variant for evaluating 3D multilayer and random tissues. The method of sub- Nyquist sampling of OCT signals is considered that is used to decrease sampling speed in a few times. To provide high noise-immunity and stability when processing OCT signals with randomly variable parameters, the Kalman filtering method has been applied for evaluating sub-Nyquist sampled OCT signals. Experimental results of evaluating materials like varnish layer of paintings are presented and discussed.

Interferometric data analysis based on Markov nonlinear filtering methodology

For data processing in conventional phase shifting interferometry, Fourier transform, and least-squares-fitting techniques, a whole interferometric data series is required. We propose a new interferometric data processing methodology based on a recurrent nonlinear procedure. The signal value is predicted from the previous step to the next step, and the prediction error is used for nonlinear correction of an a priori estimate of the parameters phase, visibility, or frequency of interference fringes. Such a recurrent procedure is correct on the condition that the noise component be a Markov stochastic process realization. The accuracy and stability of the recurrent Markov nonlinear filtering algorithm were verified by computer simulations. It was discovered that the main advantages of the proposed methodology are dynamic data processing, phase error minimization, and high noise immunity against the influence of non-Gaussian noise correlated with the signal and the automatic solution of the phase unwrapping problem.

Fringe analysis for moiré interferometry by modification of the local intensity histogram and use of a two-dimensional Fourier transform method

A noise-immune method for phase retrieval of a single moire interferometric fringe pattern is presented and discussed. The method is shown to provide accurate recovery of the phase information by a combined method based on modification of the local intensity histogram and use of a two-dimensional Fourier transform of the enhanced moire fringe pattern. The principle of the method is described and the experimental results of moire interferometric measurements with submicrometre sensitivity of the in-plane displacement fields of thick carbon fibre/PEEK composite laminates are presented as an example of the application of the technique.

Evaluation of spectral modulated interferograms using a Fourier transform and the iterative phase-locked loop method

Spectral modulated interference fringes are observed in the form of the periodical modulation of a broadband spectrum at the output of an interferometer provided with a subsequent spectrometer. The group optical path difference of interfering light waves corresponding to the distance from the surface to be measured is characterized by the spectral fringe phase function. To recover the phase functions, a standard, Fourier-transform method, or parametric methods like a phase-locked loop (PLL) method, can be used. In the former case, the Fourier spectrum in the wavelength domain is computed and filtered out to obtain the reference spectrum and the overall phase information using a phase-unwrapping algorithm. In the latter case, the fringe phase deviations are traced dynamically in the independent variable domain, i.e. in the wavelength domain when the PLL method is applied to spectral interferometry. The PLL method was used to demodulate spectral fringes iteratively. A spectral fringe signal with a priori unknown carrier fringe frequency is considered and at the first iteration step a fringe phase equal to zero is supposed. The second iteration takes the demodulated phase found from the first iteration etc. As a result, the unwrapped phase function of the spectral fringes is found.

Spectral interferograms including equalization wavelengths processed by autoconvolution method

The processing of the recorded spectral interferograms including the equalization wavelengths is extended by using autoconvolution method to determine the equalization wavelengths precisely. The equalization wavelength determination is used to estimate the spectral fringe phase function in a two-beam interference experiment with the compensated Michelson interferometer and an optical sample inserted in it under the knowledge of both dispersion in the interferometer and the displacement of the interferometer mirror. The interferometer dispersion is given by the thickness of fused-silica optical sample and its refractive index, which can be evaluated from the Sellmeier dispersion relation. Good agreement between the recorded and theoretical spectral interferograms is confirmed and a new method of determining the optical path differences between beams of the interferometer is proposed.

Fringe Evaluation and Phase Unwrapping of Complicated Fringe Patterns by the Data-Dependent Fringe Processing Method

Evaluation of noisy fringe patterns is important for solving problems of nondestructive testing and is widely used in moire, holographic, and speckle interferometry. In this paper, a new method of fringe pattern analysis has been proposed based on iterative estimation of local fringe amplitude, spacing, and orientation. Fringe parameter evaluation at each iteration step allows the formation of a two-dimensional (2-D) data-dependent anisotropic impulse response of a spatial filter that allows suppression of the noise influence without decreasing the fringe visibility. When the local fringe parameters are obtained, it is possible to find the phase difference at each point of the fringe pattern and at any other one within the local 2-D area. These local phase differences are utilized to recover the wrapped fringe phase at the point using a local model of the fringe pattern fitted under the criterion of root-mean-square error minimization. The high noise immunity of the proposed method was verified experimentally when processing complicated fringe patterns with 2-D fringe phase unwrapping

Dynamic Wavefront Evaluation in Phase Shifting Interferometry Based on Recurrence Fringe Processing

The method of recovering 3D unwrapped phase distribution in phase shifting interferometry is investigated. The method is based on dynamic recurrence processing of a set of fringe patterns involving the Kalman filtering algorithm with 3D spatial‐temporal prediction of fringe parameters. The advantage of the suggested algorithm consist in dynamic evaluation of wavefront full phase with highest phase accuracy at the last phase shift step.

Wavefront aberration analysis in two-beam reversal shearing interferometry by elliptical Zernike polynomials

We present a modal phase-reconstruction method for analyzing wave front aberrations of rotationally symmetric optical components in two beam shearing interferometry. The optical configuration requires only two mutually coherent off-axis plane wave fronts transmitted through or reflected by the optical component under test. Finite moire beating between the interferograms and the CCD array is used to subtract the linear carrier introduced by defocus and the tilt making the presense of high order aberrations more evident. The difference wave front is described by elliptical Zernike polynomials as a function of the amount of lateral displacement between the two aberrated wave fronts. The method allows for accurate wave front reconstruction inside the quasi-elliptical overlap area between the laterally sheared interfering beams. Results of numerical experiments and applications of the technique for measuring aberrations of simple biconvex spherical lenses are presented.