Mr. Matias Fernández Lakatos Profile

Matias Fernández Lakatos

at Univ de la Republica Uruguay

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Proceedings Article | 12 March 2024 Poster + Paper

Integration with one partial derivative applied to quantitative phase imaging

M. Fernández Lakatos, Gastón Ayubi, Erna Frins

Proceedings Volume 12852, 128520F (2024) https://doi.org/10.1117/12.3000403

KEYWORDS: Phase imaging, Image restoration, Phase reconstruction, Phase shifts, Reconstruction algorithms, Algorithm development, X-ray microscopy

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In many quantitative phase imaging techniques, phase reconstruction is achieved by integrating information from two-dimensional gradient field. Although using both derivatives gives high-quality results, the acquisition time must be evenly distributed between each derivative. To minimize this time, we use a method that integrates from a single derivative. The challenge when integrating with only one derivative is the lack of information about the derivative in the orthogonal direction. To address this, a regularization parameter was introduced. By dealing with biological samples, we can have prior knowledge that ensures the absence of singularities in the perpendicular direction, justifying the introduction of this parameter. Our objective is to find a solution that minimizes the integration along the direction of the obtained derivative while simultaneously minimizing the norm of the derivative in the orthogonal direction using the introduced parameter. This allows us to perform integration without knowing one of the derivatives. Our method reduces processing time by utilizing Fourier properties, which are computationally efficient. We conclude that both the acquisition and processing time are reduced by not acquiring the derivative in one direction and utilizing Fourier properties for integration. We present experimental results showing the viability and potential of our proposal.

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