Reconstructing the Optical Parameters of a Layered Medium with Optical Coherence Elastography

Elbau, Peter; Mindrinos, Leonidas; Veselka, Leopold

doi:10.1007/978-3-030-48634-1_8

Cited by 3 publications

(5 citation statements)

References 9 publications

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“…Because of the linearity of the equation it is sufficient to solve the problem for every plane wave. The result for these backscattered fields for such a sample is well known in this plane wave case, see [ 25 , 26 ]. For the simplest case

we consider an (arbitrary) plane wave as incident illumination from the top,

with amplitude function

and propagation vector

which we consider implicitly as a function of

and

We obtain the reflected electric field

where

denotes an arbitrary point of the top boundary (that is

) of the object,

the wave vector and

the sum of the reflection coefficients

of the differently polarized parts

…”

Section: Mathematical Modelmentioning

confidence: 80%

See 1 more Smart Citation

A Quantitative Model for Optical Coherence Tomography

Veselka

Krainz

Mindrinos

et al. 2021

Sensors

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Optical coherence tomography (OCT) is a widely used imaging technique in the micrometer regime, which gained accelerating interest in medical imaging in the last twenty years. In up-to-date OCT literature, certain simplifying assumptions are made for the reconstructions, but for many applications, a more realistic description of the OCT imaging process is of interest. In mathematical models, for example, the incident angle of light onto the sample is usually neglected or a plane wave description for the light–sample interaction in OCT is used, which ignores almost completely the occurring effects within an OCT measurement process. In this article, we make a first step to a quantitative model by considering the measured intensity as a combination of back-scattered Gaussian beams affected by the system. In contrast to the standard plane wave simplification, the presented model includes system relevant parameters, such as the position of the focus and the spot size of the incident laser beam, which allow a precise prediction of the OCT data. The accuracy of the proposed model—after calibration of all necessary system parameters—is illustrated by simulations and validated by a comparison with experimental data obtained from a 1300 nm nswept-source OCT system.

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we consider an (arbitrary) plane wave as incident illumination from the top,

with amplitude function

and propagation vector

which we consider implicitly as a function of

and

We obtain the reflected electric field

where

denotes an arbitrary point of the top boundary (that is

) of the object,

the wave vector and

the sum of the reflection coefficients

of the differently polarized parts

…”

Section: Mathematical Modelmentioning

confidence: 80%

“…For such a multi-layer structure, at least locally in the illuminated spot, the depth-dependent refractive index can be simplified to a piecewise constant function. The corresponding inverse problem has been examined in [3,8,26] and in [9] where additional inclusions have been discussed.…”

Section: Introductionmentioning

confidence: 99%

A Quantitative Model for Optical Coherence Tomography

Veselka

Krainz

Mindrinos

et al. 2021

Sensors

Self Cite

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Section: The Sample Fieldmentioning

confidence: 97%

A Quantitative Model for Optical Coherence Tomography

Veselka¹,

Krainz²,

Mindrinos³

et al. 2021

Preprint

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Optical coherence tomography (OCT) is a widely used imaging technique in the micrometer regime, which gained accelerating interest in medical imaging in the last twenty years. In up-to-date OCT literature [5,6] certain simplifying assumptions are made for the reconstructions, but for many applications a more realistic description of the OCT imaging process is of interest. In mathematical models, for example, the incident angle of light onto the sample is usually neglected or a plane wave description for the light-sample interaction in OCT is used, which ignores almost completely the occurring effects within an OCT measurement process. In this article, we make a first step to a quantitative model by considering the measured intensity as a combination of back-scattered Gaussian beams affected by the system. In contrast to the standard plane wave simplification, the presented model includes system relevant parameters such as the position of the focus and the spot size of the incident laser beam, which allow a precise prediction of the OCT data and therefore ultimately serves as a forward model. The accuracy of the proposed model-after calibration of all necessary system parameters-is illustrated by simulations and validated by a comparison with experimental data obtained from a 1300 nm swept-source OCT system.

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“…We additionally assign to every layer Ω j its width, which is given by the positive real number d j = a j − a j+1 . The light E : R × R 3 → C 3 in the presence of the sample, equation (7), is then modeled as a solution of the vectorial Helmholtz equation for all x ∈ R 3 :…”

Section: Light Scatteringmentioning

confidence: 99%

“…For such a multi-layer structure, at least locally in the illuminated spot, the depth-dependent refractive index can be simplified to a piecewise constant function. The corresponding inverse problem has been examined in [1,6,20] and in [7] where additional inclusions have been discussed.…”

Section: Introductionmentioning

confidence: 99%

Quantitative parameter reconstruction from optical coherence tomographic data

Veselka,

Elbau,

Mindrinos

et al. 2023

Inverse Problems

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Quantitative tissue information, like the light scattering properties, is considered as a key player in the detection of cancerous cells in medical diagnosis. A promising method to obtain these data is optical coherence tomography (OCT). In this article, we will therefore discuss the refractive index reconstruction from OCT data, employing a Gaussian beam based forward model. We consider in particular samples with a layered structure, meaning that the refractive index as a function of depth is well approximated by a piecewise constant function. For the reconstruction, we present a layer-by-layer method where in every step the refractive index is obtained via a discretized least squares minimization. For an approximated form of the minimization problem, we present an existence and uniqueness result. The applicability of the proposed method is then verified by reconstructing refractive indices of layered media from both simulated and experimental OCT data.

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Reconstructing the Optical Parameters of a Layered Medium with Optical Coherence Elastography

Cited by 3 publications

References 9 publications

A Quantitative Model for Optical Coherence Tomography

A Quantitative Model for Optical Coherence Tomography

A Quantitative Model for Optical Coherence Tomography

Quantitative parameter reconstruction from optical coherence tomographic data

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