Refractive index map reconstruction in optical deflectometry using total-variation regularization

Jacques, Laurent; Gonzalez, Adriana Gonzalez; Foumouo, Emmanuel; Antoine, Philippe

doi:10.1117/12.892729

Cited by 4 publications

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“…to the 2-D Fourier transform of the RIM. Mathematically, the DFST establishes the following equivalence [22] (proved in Appendix A):…”

Section: Principlesmentioning

confidence: 99%

“…We briefly explain this system for the sake of completeness in order to set the experimental background surrounding the actual deflection measurement process. More details can be found in [4,18,22,24].…”

Section: Deflection Measurementsmentioning

confidence: 99%

“…We can now explain how we use the DFST relation (4) for defining the forward model that links any discrete 2-D RIM representation to its FDM vector. In a previous work [22], the data available in the frequency polar grid P M were first interpolated to a Cartesian frequency grid in order to reconstruct the 2-D RIM using a Fast Fourier Transform (FFT). However, the polar to Cartesian frequency interpolation introduced a hardly controlled colored distortion.…”

Section: Forward Modelmentioning

confidence: 99%

“…The evolution of the primal and dual residual norms (26) and the convergence condition in (22) along the iterations is depicted in Fig. 13.…”

Section: Algorithm Convergencementioning

confidence: 99%

“…In tomographic problems, this operator requires to map spatial data in a Cartesian grid to Fourier data in a Polar grid. Previous works have used gridding techniques to interpolate data from a polar to a cartesian or pseudo polar grid before applying the Fourier Transform [22,38]. However, the error introduced when using these techniques is not bounded and introduces an uncontrolled distortion.…”

Section: Introductionmentioning

confidence: 99%

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Compressive Optical Deflectometric Tomography: A Constrained Total-Variation Minimization Approach

González¹,

Jacques²,

Vleeschouwer³

et al. 2012

Preprint

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Optical Deflectometric Tomography (ODT) provides an accurate characterization of transparent materials whose complex surfaces present a real challenge for manufacture and control. In ODT, the refractive index map (RIM) of a transparent object is reconstructed by measuring light deflection under multiple orientations. We show that this imaging modality can be made compressive, i.e., a correct RIM reconstruction is achievable with far less observations than required by traditional minimum energy (ME) or Filtered Back Projection (FBP) methods. Assuming a cartoon-shape RIM model, this reconstruction is driven by minimizing the map Total-Variation under a fidelity constraint with the available observations. Moreover, two other realistic assumptions are added to improve the stability of our approach: the map positivity and a frontier condition. Numerically, our method relies on an accurate ODT sensing model and on a primal-dual minimization scheme, including easily the sensing operator and the proposed RIM constraints. We conclude this paper by demonstrating the power of our method on synthetic and experimental data under various compressive scenarios. In particular, the potential compressiveness of the stabilized ODT problem is demonstrated by observing a typical gain of 24 dB compared to ME and of 30 dB compared to FBP at only 5% of 360 incident light angles for moderately noisy sensing.

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“…to the 2-D Fourier transform of the RIM. Mathematically, the DFST establishes the following equivalence [22] (proved in Appendix A):…”

Section: Principlesmentioning

confidence: 99%

Section: Deflection Measurementsmentioning

confidence: 99%

Section: Forward Modelmentioning

confidence: 99%

“…The evolution of the primal and dual residual norms (26) and the convergence condition in (22) along the iterations is depicted in Fig. 13.…”

Section: Algorithm Convergencementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Compressive Optical Deflectometric Tomography: A Constrained Total-Variation Minimization Approach

González¹,

Jacques²,

Vleeschouwer³

et al. 2012

Preprint

Self Cite

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A simple low cost latent fingerprint sensor based on deflectometry and WFT analysis

Dhanotia

Chatterjee

Bhatia

et al. 2018

Optics & Laser Technology

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Collimation testing using deflectometry in conjunction with windowed Fourier transform analysis

2017

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In this paper, we demonstrate a simple automated procedure for the detection of collimation of an optical beam by incorporating the windowed Fourier fringe analysis technique into a deflectometric setup. The experimental arrangement consists of a deflectometry-based system in which light from a laser is expanded and passed through a collimating lens. The transmitted light illuminates a coarse sinusoidal grating. The grating image is directly captured through a charge-coupled device. Typical image patterns corresponding to "in-focus," "at-focus," and "out-of-focus" positions of an optical beam are recorded. Depending on the position of the collimating lens, the grating line spacing and the resulting phase of the emerging wavefront varies. Direct phase measurement using the windowed Fourier transform method has been used to obtain the slope map of the wavefront. The slope of the phase map depicts the diverging, collimated, or converging nature of the optical beam. The positioning error of light beam collimation was approximately 1 μm. The experimental arrangement is simple, low cost, and compact. The technique is fully automatic and provides high resolution, high precision, and good sensitivity.

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Refractive index map reconstruction in optical deflectometry using total-variation regularization

Cited by 4 publications

References 0 publications

Compressive Optical Deflectometric Tomography: A Constrained Total-Variation Minimization Approach

Compressive Optical Deflectometric Tomography: A Constrained Total-Variation Minimization Approach

A simple low cost latent fingerprint sensor based on deflectometry and WFT analysis

Collimation testing using deflectometry in conjunction with windowed Fourier transform analysis

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