In this work we propose an inverse problems based iterative reconstruction method for tomographic diffractive microscopy, involving measurements in off-axis configuration. More precisely, we propose a strategy that aims to eliminate reconstruction errors that can be caused by perturbations in the illumination wave of the reference arm. Our original contribution is to build the inverse problem considering as unknowns both the targeted 3D sample map and the perturbation map, that are jointly reconstructed and unmixed during the iterative process. This self-calibration process is rendered possible by the multiplicity of sample observations from multiple views, where the reference perturbed background remains invariant. We validate the feasibility of our approach on reconstructions from simulated data under different experimental conditions.
In the context of multi-wavelength in-line holographic microscopy of micrometer-sized samples, we propose a 2-step methodology to estimate geometric and chromatic aberrations of the optical system and then use this calibration step to better reconstruct the complex transmittance at focus. The first step uses an aberration-wise Lorenz-Mie model to jointly estimate the parameters of calibration beads spread in the sample and 14 Zernike coefficients at each wavelength. Then, the reconstruction step is performed using a regularized inverse problems approach reconstruction of the whole multi-wavelength data set with a colocalization hypothesis. This general methodology is applied to the case of Gram-stained bacteria on blood smears. On these samples, in addition to providing a new information (phase), we show interesting improvements on the image quality, which promises better discrimination between bacteria types and enhanced repeatability.
In-line Digital holographic microscopy is easy to implement because it only requires a coherent illumination source. An out-of-focus image (hologram) of the sample is recorded and numerically reconstructed to retrieve phase shift information due to the sample. Effects of the optical setup, such as aberrations, can distort the hologram signal, and ignoring these effects results in biased reconstructions. In this context, we study the effects of misalignment and wrong cover-slip thickness by statistically analysing the reconstructions of beads distributed in the whole field of view. Our aberration-wise reconstruction approach produces debiased estimations and allows precise and realistic estimation of optical aberrations from a single hologram.
We present a new method to achieve digital autofocus in holography. This method relies on the insertion of calibrated beads into the studied sample. Reconstructing the position and the radius of the beads using Inverse Problems Approach, based on Mie Model, makes it possible to accurately locate the slide on which the sampled is placed. Numerical focusing can then be performed using the standard backpropagation method or regularized reconstruction. Because the reconstruction plane can be chosen objectively with respect to the position of the slide, this numerical autofocus is reproducible whatever is the type of the observed biological sample.
The in-line configuration of digital holographic microscopy is the simplest to set up, but it requires numerical reconstructions, in order to retrieve the phase of the wave diffracted by the sample. These reconstructions are based on an image formation model, but the effect of the microscopy system is often neglected. Yet, some parameters, like a wrong magnification, the partial coherence of the illumination, or optical aberrations may lead to bias in the reconstruction. In the framework of inverse problems approaches, we analysed and studied the effects of some of these parameters using simulations and experiments on calibrated spherical objects and a rigorous model (Lorenz-Mie), in order to evaluate the relevance and requirements of model refinements.
Unstained biological samples (e.g. cells or bacteria) are mostly transparent objects, optically described by their optical thickness and refractive index changes. The knowledge of this information could help to better identify or at least classify cells according to their types or state. Holographic microscopy techniques are effective methods to obtain quantitative phase profiles of biological samples. These techniques, however, may require high temporal stability to measure cell thickness fluctuations. A simple and low-cost way to ensure temporal stability consists in using a “common path” configuration. In this configuration the reference and signal beams follow the same optical path, leading to high temporal stability. The beam paths are split by a glass plate whose thickness introduces a lateral shift between the beams, reflected by the front and back surfaces. This configuration is an off-axis holographic microscopy setup since the glass plate introduces an angle between the two reflected spherical wavefronts. The inverse problem approach proposes to reconstruct the objects directly from the holograms without any filtering of the signal and with prior information on the objects. In this framework, a good knowledge of the image formation model is important. We propose a reconstruction algorithm based on a parametric inverse problem approach to reconstruct phase objects holograms acquired by the lateral shearing digital holographic system. Assuming the noise in the data to be white and Gaussian, it mainly consists in fitting a model to the data. The algorithm is applied to silica micro-beads on out-of-focus off-axis holograms recorded with the lateral shearing configuration.
Digital holographic microscopy can image both absorbing and translucent objects. Due to the presence of twin-images and out-of-focus objects, the task of segmenting the objects from a back-propagated hologram is challenging. This paper investigates the use of deep neural networks to combine the real and imaginary parts of the back-propagated wave and produce a segmentation. The network, trained with pairs of back-propagated simulated holograms and ground truth segmentations, is shown to perform well even in the case of a mismatch between the defocus distance of the holograms used during the training step and the actual defocus distance of the holograms at test time.
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