Tomographic Diffractive Microscopy: Principles, Implementations, and Applications in Biology

Simon, Bertrand; Haeberlé, Olivier

doi:10.1007/978-3-030-21722-8_4

Cited by 3 publications

(2 citation statements)

References 193 publications

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“…Experimental setting. The observation model is set so as to reflect a tomographic diffractive microscopy setup [29] under the Born approximation, which linearizes the problem linking the optical index to the electric field. In this framework, several holograms are acquired under varying illumination conditions.…”

Section: Convergence and Time Complexity Analysismentioning

confidence: 99%

“…In this section, we present the results obtained on images from a real TDM setup [29]. The observation system is more intricated than the observation model (1.2): the image is formed in presence of a non-zero background, the holograms contain some aberrations, and the Born hypothesis remains approximate for thick samples (a few μm).…”

Section: Application On Real Imagesmentioning

confidence: 99%

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A fast homotopy algorithm for gridless sparse recovery

Courbot¹,

Colicchio²

2021

Inverse Problems

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In this paper, we study the solving of the gridless sparse optimization problem and its application to 3D image deconvolution. Based on the recent works of [14] introducing the Sliding Frank-Wolfe algorithm to solve the Beurling LASSO problem, we introduce an accelerated algorithm, denoted BSFW, that preserves its convergence properties, while removing most of the costly local descents. Besides, as the solving of BLASSO still relies on a regularization parameter, we introduce a homotopy algorithm to solve the constrained BLASSO that allows to use a more practical parameter based on the image residual, e.g. its standard deviation. Both algorithms benefit from a finite termination property, i.e. they are guaranteed to find the solution in a finite number of step under mild conditions. These methods are then applied on the problem of 3D tomographic diffractive microscopy images, with the purpose of explaining the image by a small number of atoms in convolved observations. Numerical results on synthetic and real images illustrates the improvement provided by the BSFW method, the homotopy method and their combination.

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Section: Convergence and Time Complexity Analysismentioning

confidence: 99%

Section: Application On Real Imagesmentioning

confidence: 99%

A fast homotopy algorithm for gridless sparse recovery

Courbot¹,

Colicchio²

2021

Inverse Problems

View full text Add to dashboard Cite

show abstract

Optimizing sample illumination scanning in transmission tomographic diffractive microscopy

et al. 2021

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Due to the sequential nature of data acquisition, it is preferable to limit the number of illuminations to be used in tomographic diffractive microscopy experiments, especially if fast imaging is foreseen. On the other hand, for high-quality, high-resolution imaging, the Fourier space has to be optimally filled. Up to now, the problem of optimal Fourier space filling has not been investigated in itself. In this paper, we perform a comparative study to analyze the effect of sample scanning patterns on Fourier space filling for a transmission setup. Optical transfer functions for several illumination patterns are studied. Simulation as well as experiments are conducted to compare associated image reconstructions. We found that 3D uniform angular sweeping best fills the Fourier space, leading to better quality images.

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Optimizing sample illumination scanning for reflection and 4Pi tomographic diffractive microscopy

et al. 2021

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Tomographic diffractive microscopy (TDM) is increasingly gaining attention, owing to its high-resolution, label-free imaging capability. Fast acquisitions necessitate limiting the number of holograms to be recorded. Reconstructions then rely on optimal Fourier space filling to retain image quality and resolution, that is, they rely on optimal scanning of the tomographic illuminations. In this work, we theoretically study reflection TDM, and then the 4Pi TDM, a combination of transmission and reflection systems. Image simulations are conducted to determine optimal angular sweeping. We found that three-dimensional uniform scanning fills Fourier space the best for both reflection and 4Pi configurations, providing a better refractive index estimation for the observed sample.

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Tomographic Diffractive Microscopy: Principles, Implementations, and Applications in Biology

Cited by 3 publications

References 193 publications

A fast homotopy algorithm for gridless sparse recovery

A fast homotopy algorithm for gridless sparse recovery

Optimizing sample illumination scanning in transmission tomographic diffractive microscopy

Optimizing sample illumination scanning for reflection and 4Pi tomographic diffractive microscopy

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