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Fringe Pattern Denoising Using Two-Dimensional Variational Mode Decomposition (2D-VMD) Method for Inspection of Flatness of Reduced Surfaces

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Abstract

The flatness is a major element for any functional precision surface. It becomes extremely important in the miniaturization of the systems, which require the components of reduced sizes. There is a need to develop appropriate methods to solve measurement problems in industrial design, manufacturing of production and process monitoring. In this work, we used an optical method based on the moiré interferometry for topography in full-field and to control the flatness of the reduced surfaces having a size of 30 mm2 and more. This technique makes it possible to palpate optically the surface and to give an instantaneous topography of surface in real-time. We have developed an optical set-up which it is possible to inspect in a nondestructive way and without contact, the surface quality. Unfortunately, the moiré fringes taken by camera contain excessive noise. That is why we proposed to use the Two-Dimensional Variational Mode Decomposition (2D-VMD) method to reduce the random noise from the fringe patterns and to ameliorate the profiles and the residual images from which we can control the presence of defects flatness of reduced surfaces. We have also used three objective image quality evaluation methods (PSNR, SNR and correlation coefficient) to compare between the denoising results given by 2D-VMD with those obtained by the Bidimensional Empirical Mode Decomposition (BEMD).

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Abbreviations

BEMD:

Bidimensional Empirical Mode Decomposition

CCD:

Charge-Coupled Device

D:

Diaphragm

1D:

One-Dimensional

2D:

Two-dimensional

2D-VMD:

Two-Dimensional Variational Mode Decomposition

EMD:

Empirical Mode Decomposition

EEMD:

Ensemble Empirical Mode Decomposition

FT:

Fourier Transformation

IFT:

Inverse Fourier Transformation

IMF:

Intrinsic Mode Functions

Ma:

Magnification

MSE :

Mean Squared Error

na :

Additive noise

OP:

Observation Plane

PSNR :

Peak Signal-to-Noise Ratio

SF:

Spatial Filter

WT:

wavelet Transform

d:

Moiré fringe spacing

dp:

Moiré fringe spacing on the observation plane

f :

Image, signal

\( \overline{M},\overline{f} \) :

The mean values of Mk and f, respectively

G1, G2:

Linear Gratings in transmission

K :

Image length

I, J :

Matrices’ indexes

L1, L2:

Lenses to expand the laser beam

L3, L5:

Lenses carries out the FT

L4, L6:

Lenses carries out the IFT

\( {\hat{M}}_{AS,k} \) and \( {\hat{M}}_k \) :

FT of MAS, k and Mk, respectively

\( {M}_{AS,k}\left(\overrightarrow{x}\right) \) :

Analytic signal defined in the spectral domain

maxV :

Maximum possible pixel value

N :

Image width

p1, p2 :

Pitches of the gratings G1 and G2, respectively

r:

Order of diffraction

R :

Correlation coefficient

x :

Spatial domain

ω :

Pulsation

θ:

Angle between the gratings G1 and G2

λ:

Wavelength of light used

ν :

Frequency

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Acknowledgements

This work was carried out at the level of the Applied Optics Laboratory with the collaboration of the Applied Precision Mechanic Laboratory, Institute of Optics and Precision Mechanics, Ferhat Abbas University Setif 1, Algeria.

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Authors and Affiliations

  1. Applied Optics Laboratory, Institute of Optics and Precision Mechanics, Ferhat Abbas University Setif 1, 19000, Setif, Algeria

    M. Messagier & S. Meguellati

  2. Applied Precision Mechanic Laboratory, Institute of Optics and Precision Mechanics, Ferhat Abbas University Setif 1, 19000, Setif, Algeria

    H. Mahgoun

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  1. M. Messagier
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  2. S. Meguellati
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Correspondence to M. Messagier.

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Messagier, M., Meguellati, S. & Mahgoun, H. Fringe Pattern Denoising Using Two-Dimensional Variational Mode Decomposition (2D-VMD) Method for Inspection of Flatness of Reduced Surfaces. Exp Tech 46, 27–41 (2022). https://doi.org/10.1007/s40799-021-00459-z

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