Total variation regularization cost function for demodulating phase discontinuities

Legarda-Sáenz, Ricardo; Brito‐Loeza, Carlos; Espinosa-Romero, A.

doi:10.1364/ao.53.002297

Cited by 14 publications

(29 citation statements)

References 13 publications

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“…For our application, it hence allows us to recover rapid changes in the refractive index profile that are not possible using the previous approaches. A total variation regularization technique for the recovery of phase functions has recently been reported [17]. However, this is applicable to the case where the phase function itself is expected to have discontinuities or rapid changes in them.…”

Section: Introductionmentioning

confidence: 99%

Measurement of planar refractive index profiles with rapid variations in glass using interferometry and total variation regularized differentiation

Oven

2015

Journal of Modern Optics

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Planar refractive index profiles with rapid variations, formed in glass, are measured with interferometry. This involves forming a bevel in the glass and orientating the fringe pattern to be normal to the bevel edge. The index profile is determined by differentiation of the phase function of the fringe pattern. The differentiation has been performed using the total variation regularization method in order to preserve rapid changes in the derivative. This new approach avoids the necessity of filtering, in order to reduce noise, in the direction perpendicular to the bevel, which would otherwise smooth out the rapid index changes. The method is assessed using a model refractive index profile that contains an index gradient of 0.24 μm −1 and is then applied practically to measure the refractive index profile of electrically poled BK7 glass. The new approach allows the sharp transition in the index between poled and unpoled glass to be observed as well as the accumulation of potassium ions beyond the poled glass region.

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Section: Introductionmentioning

confidence: 99%

Measurement of planar refractive index profiles with rapid variations in glass using interferometry and total variation regularized differentiation

Oven

2015

Journal of Modern Optics

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“…As remarked in , this model allows the recovering of sharp phase transitions, something that other methods such as those based on L 2 regularization, fail to deliver. The model also allows to recover, at the same time, the background illumination a and the amplitude modulation b .…”

Section: Total Variation Based Modelmentioning

confidence: 98%

“…In this work, we are interested in the model presented in , where a variational method with total variation (TV) regularization to all three unknowns ϕ , a and b as shown below was presented.

\begin{array}{l} \underset{a, b, ϕ}{normalarg normalmin} italicTV ((), a, b, ϕ, g) \equiv ({|, \int_{Ω} {(I - g)}^{2} d Ω + \frac{1}{λ_{a}} \int_{Ω}, \nabla a, d Ω) \\ (}|, + \frac{1}{λ_{b}} \int_{Ω}, \nabla b, d Ω + \frac{1}{λ_{ϕ}} \int_{Ω} (||, \nabla ϕ) d Ω), \end{array}

where Ω ⊆ ℝ 2 is the domain of integration, g is a given fringe pattern, obeying the model described in (1), and λ a , λ b , λ ϕ are positive regularization parameters.…”

Section: Total Variation Based Modelmentioning

confidence: 99%

“…Very recently however, Legarda‐Saenz et al , proposed a variational model for estimating discontinuous phase maps from a single fringe pattern. Their model was also able to estimate the background illumination and the amplitude modulation.…”

Section: Introductionmentioning

confidence: 99%

“…In the literature, most methods for estimating the phase map consider it as a continuous and smooth function; see for instance the works in [4,5] and the references therein. Very recently however, Legarda-Saenz et al [6], proposed a variational model for estimating discontinuous phase maps from a single fringe pattern. Their model was also able to estimate the background illumination and the amplitude modulation.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A fast algorithm for a total variation based phase demodulation model

Brito‐Loeza

Legarda-Sáenz

Martín-González

2019

Numerical Methods Partial

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In this paper we introduce fast numerical algorithms for the solution of the model. For each variable, background illumination, amplitude modulation and phase map, we develop a fixed point method. Then, we write all three algorithms in the same framework and analyze their convergence rates, local smoothing factors by means of local Fourier analysis and present experimental evidence of their performance on synthetic and real world problems.

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Parallel algorithm for fringe pattern demodulation

Hernandez-Lopez

Legarda-Sáenz

Brito‐Loeza

2021

J Real-Time Image Proc

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Total variation regularization cost function for demodulating phase discontinuities

Abstract: We introduce a method based on the minimization of a total variation regularization cost function for computing discontinuous phase maps from fringe patterns. The performance of the method is demonstrated by numerical experiments with both synthetic and real data.

Cited by 14 publications

References 13 publications

Measurement of planar refractive index profiles with rapid variations in glass using interferometry and total variation regularized differentiation

Measurement of planar refractive index profiles with rapid variations in glass using interferometry and total variation regularized differentiation

A fast algorithm for a total variation based phase demodulation model

Parallel algorithm for fringe pattern demodulation

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