Analysis of the principal component algorithm in phase-shifting interferometry

Vargas, Javier; Quiroga, Juan Antonio; Belenguer, T.

doi:10.1364/ol.36.002215

Cited by 97 publications

(53 citation statements)

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“…Thus, we will present first the procedure to demodulate the isoclinic fringe pattern using the proposed PCA algorithm and, afterwards, we will make use the information obtained from the isoclinics fringe pattern to demodulate the isochromatics one. However, we will first summarize the PCA method for phase demodulation [10].…”

Section: Theoretical Foundationmentioning

confidence: 99%

“…From construction, X C is symmetric and it is always possible to find a linear transformation A, (a KK  matrix) that diagonalizes it, so that the transformed covariance matrix ·· T YX  C A C A is diagonal. In the literature, the linear transformations A is also known as Karhunen-Loève or Hotelling transforms [10].…”

Section: Pca Analysis Of Phase Shifted Interferogramsmentioning

confidence: 99%

“…For example, if they increase monotonically, we could still recover the correct sign of the global phase [12]. For additional details about the PCA algorithm the reader can refer to [9][10] and [14].…”

Section: Pca Analysis Of Phase Shifted Interferogramsmentioning

confidence: 99%

“…PCA is a self-calibrating PSA method [9][10] that can demodulate the phase from a set of interferograms with unknown phase steps. In the photoelastic case, the self-calibrating character means that we do not need to set the polariscope elements at precise angular positions.…”

Section: Introductionmentioning

confidence: 99%

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Application of principal component analysis in phase-shifting photoelasticity

Quiroga¹,

Gómez‐Pedrero

2016

Opt. Express

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Principal Component Analysis Phase Shifting (PCA) is a useful tool for fringe pattern demodulation in phase shifting interferometry. The PCA has no restrictions on background intensity, fringe modulation and it is a self-calibrating Phase Sampling Algorithm (PSA). Moreover, the technique is well suited for analyzing arbitrary sets of phase-shifted interferograms due to its low computational cost. In this work, we have adapted the standard phase shifting algorithm based on the PCA to the particular case of photoelastic fringe patterns. Compared with conventional PSAs used in photoelasticity, the PCA method does not need calibrated phase steps and, given that it can deal with an arbitrary number of images, it presents good noise rejection properties, even for complicated cases such as low order isochromatic photoelastic patterns.

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Section: Theoretical Foundationmentioning

confidence: 99%

Section: Pca Analysis Of Phase Shifted Interferogramsmentioning

confidence: 99%

Section: Pca Analysis Of Phase Shifted Interferogramsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Application of principal component analysis in phase-shifting photoelasticity

Quiroga¹,

Gómez‐Pedrero

2016

Opt. Express

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“…The method requires filtering out the DC term, but it does not require normalizing the fringe patterns. In [4][5] we have shown that a sequence of phase-shifted fringe patterns free from harmonics can be expressed as a linear combination of two orthonormal signals. Therefore, any phase-shifted interferogram sequence can be described using a twodimensional vector subspace.…”

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confidence: 99%

Two-step demodulation based on the Gram–Schmidt orthonormalization method

et al. 2012

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This Letter presents an efficient, fast, and straightforward two-step demodulating method based on a Gram-Schmidt (GS) orthonormalization approach. The phase-shift value has not to be known and can take any value inside the range 0; 2π, excluding the singular case, where it corresponds to π. The proposed method is based on determining an orthonormalized interferogram basis from the two supplied interferograms using the GS method. We have applied the proposed method to simulated and experimental interferograms, obtaining satisfactory results. A complete MATLAB software package is provided at http://goo.gl/IZKF3. © 2012 Optical Society of America OCIS codes: 100.5070, 100.2650.In the past there have been reported works about phase reconstruction with only two frames [1][2][3]. In [1] is presented the standard and most used technique for obtaining the modulating phase map from two phase-shifted interferograms. The method is based on the application of the Fourier transform demodulating approach to both interferograms. Then, the phase-step map is calculated using a direct algebraic expression. As the phase step has to be equal for all pixels, it is possible to solve the local sign ambiguity and, therefore, retrieve the phase map. This method requires filtering out the DC term, but it does not need the normalization of the fringe patterns. The main drawback of this approach is that it is very sensitive to noise. In [2] is presented a self-tuning (SF) method that first retrieves the phase step between interferograms, looking for the minimum of a merit function. Then a quadrature filter is constructed from the obtained phase step and the modulating phase is determined. This method presents good results when the phase step is close to π∕2 rad, but the accuracy decreases when the phase step moves away from this value. Additionally, the method requires the interferograms to be previously normalized. In [3] is presented a recent demodulating two-step method based on a regularized optical-flow (OF) method. The method is robust against additive noise and different values of the phase step. Additionally, this approach does not require normalizing the fringe patterns but it requires subtracting the DC term.The main drawback of [3] resides on the computational requirements necessary to perform the OF analysis, which make this demodulating method costly from a processing and computational point of view. In this work, we present a novel two-step demodulation method based on the Gram-Schmidt (GS) orthonormalization approach. The method is very fast, easy to implement, does not require any minimization process, and is not computationally demanding. The method requires filtering out the DC term, but it does not require normalizing the fringe patterns. In [4][5] we have shown that a sequence of phase-shifted fringe patterns free from harmonics can be expressed as a linear combination of two orthonormal signals. Therefore, any phase-shifted interferogram sequence can be described using a twodimensional vector subspace. The orthonormal...

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2014

Fringe Pattern Analysis for Optical Metrology

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Analysis of the principal component algorithm in phase-shifting interferometry

Cited by 97 publications

References 3 publications

Application of principal component analysis in phase-shifting photoelasticity

Application of principal component analysis in phase-shifting photoelasticity

Two-step demodulation based on the Gram–Schmidt orthonormalization method

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