Multispectral in-line hologram reconstruction with aberration compensation applied to Gram-stained bacteria microscopy.

In multispectral digital in-line holographic microscopy (DIHM), aberrations of the optical system affect the repeatability of the reconstruction of transmittance, phase and morphology of the objects of interest. Here we address this issue first by model fitting calibration using transparent beads inserted in the sample. This step estimates the aberrations of the optical system as a function of the lateral position in the field of view and at each wavelength. Second, we use a regularized inverse problem approach (IPA) to reconstruct the transmittance and phase of objects of interest. Our method accounts for shift-variant chromatic and geometrical aberrations in the forward model. The multi-wavelength holograms are jointly reconstructed by favouring the colocalization of the object edges. The method is applied to the case of bacteria imaging in Gram-stained blood smears. It shows our methodology evaluates aberrations with good repeatability. This improves the repeatability of the reconstructions and delivers more contrasted spectral signatures in transmittance and phase, which could benefit applications of microscopy, such as the analysis and classification of stained bacteria.

Accurate unsupervised estimation of aberrations in digital holographic microscopy for improved quantitative reconstruction.

In the context of digital in-line holographic microscopy, we describe an unsupervised methodology to estimate the aberrations of an optical microscopy system from a single hologram. The method is based on the Inverse Problems Approach reconstructions of holograms of spherical objects. The forward model is based on a Lorenz-Mie model distorted by optical aberrations described by Zernike polynomials. This methodology is thus able to characterize most varying aberrations in the field of view in order to take them into account to improve the reconstruction of any sample. We show that this approach increases the repeatability and quantitativity of the reconstructions in both simulations and experimental data. We use the Cramér-Rao lower bounds to study the accuracy of the reconstructions. Finally, we demonstrate the efficiency of this aberration calibration with image reconstructions using a phase retrieval algorithm as well as a regularized inverse problems algorithm.

Automatic numerical focus plane estimation in digital holographic microscopy using calibration beads.

We present a new method to achieve autofocus in digital holographic microscopy. The method is based on inserting calibrated objects into a sample placed on a slide. Reconstructing a hologram using the inverse problems approach makes it possible to precisely locate and measure the inserted objects and thereby derive the slide plane location. Numerical focusing can then be performed in a plane at any chosen distance from the slide plane of the sample in a reproducible manner and independently of the diversity of the objects in the sample.

New Freeware for Image Analysis of Lissamine Green Conjunctival Staining.

PURPOSE: Lissamine green (LG) is often used in addition to fluorescein to assess the severity of conjunctival damage in dry eye syndrome, which is graded manually. Our purpose was to describe an algorithm designed for image analysis of LG conjunctival staining. METHODS: Twenty pictures of patients suffering from dry eye with visible LG conjunctival staining were selected. The images were taken by 2 different digital slit lamps with a white light source and a red filter transmitting over the wavelengths absorbed by LG. Conjunctival staining appeared in black on a red background. The red channel was extracted from the original image. Stained areas were then detected using a Laplacian of Gaussian filter and applying a threshold whose value was determined manually on a subset of images. The same algorithm parameters remained constant thereafter. LG-stained areas were also drawn manually by 2 experts as a reference. RESULTS: The delineation obtained by the algorithm closely matched the actual contours of the punctate dots. In 19 cases of 20 (95%), the algorithm found the same Oxford grade as the experts, even for confluent staining that was detected as a multitude of dots by the algorithm but not by the experts, resulting in a high overestimation of the total number of dots (without mismatching the Oxford grade estimated by the experts). The results were similar for the 2 slit-lamp imaging systems. CONCLUSIONS: This efficient new image-analysis algorithm yields results consistent with subjective grading and may offer advantages of automation and scalability in clinical trials.

From Fienup's phase retrieval techniques to regularized inversion for in-line holography: tutorial.

This paper includes a tutorial on how to reconstruct in-line holograms using an inverse problems approach, starting with modeling the observations, selecting regularizations and constraints, and ending with the design of a reconstruction algorithm. A special focus is placed on the connections between the numerous alternating projections strategies derived from Fienup's phase retrieval technique and the inverse problems framework. In particular, an interpretation of Fienup's algorithm as iterates of a proximal gradient descent for a particular cost function is given. Reconstructions from simulated and experimental holograms of micrometric beads illustrate the theoretical developments. The results show that the transition from alternating projections techniques to the inverse problems formulation is straightforward and advantageous.

Reconstruction of in-line holograms: combining model-based and regularized inversion.

In-line digital holography is a simple yet powerful tool to image absorbing and/or phase objects. Nevertheless, the loss of the phase of the complex wavefront on the sensor can be critical in the reconstruction process. The simplicity of the setup must thus be counterbalanced by dedicated reconstruction algorithms, such as inverse approaches, in order to retrieve the object from its hologram. In the case of simple objects for which the diffraction pattern produced in the hologram plane can be modeled using few parameters, a model fitting algorithm is very effective. However, such an approach fails to reconstruct objects with more complex shapes, and an image reconstruction technique is then needed. The improved flexibility of these methods comes at the cost of a possible loss of reconstruction accuracy. In this work, we combine the two approaches (model fitting and regularized reconstruction) to benefit from their respective advantages. The sample to be reconstructed is modeled as the sum of simple parameterized objects and a complex-valued pixelated transmittance plane. These two components jointly scatter the incident illumination, and the resulting interferences contribute to the intensity on the sensor. The proposed hologram reconstruction algorithm is based on alternating a model fitting step and a regularized inversion step. We apply this algorithm in the context of fluid mechanics, where holograms of evaporating droplets are analyzed. In these holograms, the high contrast fringes produced by each droplet tend to mask the diffraction pattern produced by the surrounding vapor wake. With our method, the droplet and the vapor wake can be jointly reconstructed.

Wavefront division digital holographic microscopy.

Digital holographic microscopy is the state of the art quantitative phase imaging of micro-objects including living cells. It is an ideal tool to image and quantify cell thickness profiles with nanometer thickness resolution. Digital holographic techniques usually are implemented using a two-beam setup that may be bulky and may not be field portable. Self-referencing techniques provide compact geometry but suffer from a reduction of the field of view. Here, we discuss the development of a wavefront division digital holographic microscope providing the full field of view with a compact system. The proposed approach uses a wavefront division module consisting of two lenses. The developed microscope is tested experimentally by measuring the physical and mechanical properties of red blood cells.

Regularized reconstruction of absorbing and phase objects from a single in-line hologram, application to fluid mechanics and micro-biology.

Reconstruction of phase objects is a central problem in digital holography, whose various applications include microscopy, biomedical imaging, and fluid mechanics. Starting from a single in-line hologram, there is no direct way to recover the phase of the diffracted wave in the hologram plane. The reconstruction of absorbing and phase objects therefore requires the inversion of the non-linear hologram formation model. We propose a regularized reconstruction method that includes several physically-grounded constraints such as bounds on transmittance values, maximum/minimum phase, spatial smoothness or the absence of any object in parts of the field of view. To solve the non-convex and non-smooth optimization problem induced by our modeling, a variable splitting strategy is applied and the closed-form solution of the sub-problem (the so-called proximal operator) is derived. The resulting algorithm is efficient and is shown to lead to quantitative phase estimation on reconstructions of accurate simulations of in-line holograms based on the Mie theory. As our approach is adaptable to several in-line digital holography configurations, we present and discuss the promising results of reconstructions from experimental in-line holograms obtained in two different applications: the tracking of an evaporating droplet (size ∼ 100µm) and the microscopic imaging of bacteria (size ∼ 1µm).

Self-calibration for lensless color microscopy.

Lensless color microscopy (also called in-line digital color holography) is a recent quantitative 3D imaging method used in several areas including biomedical imaging and microfluidics. By targeting cost-effective and compact designs, the wavelength of the low-end sources used is known only imprecisely, in particular because of their dependence on temperature and power supply voltage. This imprecision is the source of biases during the reconstruction step. An additional source of error is the crosstalk phenomenon, i.e., the mixture in color sensors of signals originating from different color channels. We propose to use a parametric inverse problem approach to achieve self-calibration of a digital color holographic setup. This process provides an estimation of the central wavelengths and crosstalk. We show that taking the crosstalk phenomenon into account in the reconstruction step improves its accuracy.

Size of the Lesions of Superficial Punctate Keratitis in Dry Eye Syndrome Observed With a Slit Lamp.

PURPOSE: To evaluate the size distribution of epithelial lesions of superficial punctate keratitis (SPK) in dry eye after staining of the ocular surface by sodium fluorescein. METHODS: Fluorescein was instilled in 10 patients with dry eye graded using the Oxford Scheme. Pictures were taken using a standard Topcon slit lamp with cobalt blue light, without barrier filter. Two magnifications (×10 and ×16) were used and calibrated using a certified standard reference grating, allowing the diameter of the observed objects to be determined with ImageJ software. The most visible and isolated SPK lesions (green dots) were selected. The size of 254 SPK lesions was measured by tracing the irradiance profile and manually measuring the full width at half maximum. RESULTS: For all patients, with the 2 magnifications combined, the median diameter was 20.9 µm (15.2-26.6 µm, 10-90 percentile). There was a significant difference between the size of SPK lesions measured with ×10 and ×16 magnifications, respectively, 24.3 µm (18.2-29.8) versus 19.0 µm (15.2-26.6) (P < 0.001). CONCLUSIONS: Lesions seem to be smaller than normal superficial epithelial cells (which are approximately 25 × 50 µm) and might correspond to the staining of dying shrunken cells, according to recent investigations. These new quantitative data will help in developing automated recognition algorithms to obtain reliable objective classification of corneal staining.

Co-design of an in-line holographic microscope with enhanced axial resolution: selective filtering digital holography.

Common-path digital in-line holography is considered as a valuable 3D diagnostic technique for a wide range of applications. This configuration is cost effective and relatively immune to variation in the experimental environment. Nevertheless, due to its common-path geometry, the signal-to-noise ratio of the acquired hologram is weak as most of the detector (i.e., CCD/CMOS sensor) dynamics are occupied by the reference field signal, whose energy is orders of magnitude higher than the field scattered by the imaged object. As it is intrinsically impossible to modify the ratio of energy of reference to the object field, we propose a co-design approach (optics/data processing) to tackle this issue. The reference to the object field ratio is adjusted by adding a 4-f device to a conventional in-line holographic setup, making it possible to reduce the weight of the reference field while keeping the object field almost constant. Theoretical analysis of the Crámer-Rao lower bounds of the corresponding imaging model illustrates the advantages of this approach. These lower bounds can be asymptotically reached using a parametric inverse problem reconstruction. This implementation results in a 60% gain in axial localization accuracy (for 100 µm diameter spherical objects) compared to a classical in-line holography setup.

3D tracking the Brownian motion of colloidal particles using digital holographic microscopy and joint reconstruction.

In-line digital holography is a valuable tool for sizing, locating, and tracking micro- or nano-objects in a volume. When a parametric imaging model is available, inverse problem approaches provide a straightforward estimate of the object parameters by fitting data with the model, thereby allowing accurate reconstruction. As recently proposed and demonstrated, combining pixel super-resolution techniques with inverse problem approaches improves the estimation of particle size and 3D position. Here, we demonstrate the accurate tracking of colloidal particles in Brownian motion. Particle size and 3D position are jointly optimized from video holograms acquired with a digital holographic microscopy setup based on a low-end microscope objective (×20, NA 0.5). Exploiting information redundancy makes it possible to characterize particles with a standard deviation of 15 nm in size and a theoretical resolution of 2×2×5 nm3 for position under additive white Gaussian noise assumption.

Digital holography super-resolution for accurate three-dimensional reconstruction of particle holograms.

In-line digital holography (DH) is used in many fields to locate and size micro or nano-objects spread in a volume. To reconstruct simple shaped objects, the optimal approach is to fit an imaging model to accurately estimate their position and their characteristic parameters. Increasing the accuracy of the reconstruction is a big issue in DH, particularly when the pixel is large or the signal-to-noise ratio is low. We suggest exploiting the information redundancy of videos to improve the reconstruction of the holograms by jointly estimating the position of the objects and the characteristic parameters. Using synthetic and experimental data, we checked experimentally that this approach can improve the accuracy of the reconstruction by a factor more than the square root of the image number.

In-line particle holography with an astigmatic beam: setup self-calibration using an "inverse problems" approach.

The use of digital in-line holography for the characterization of confined flows in cylindrical geometry confinements (e.g., cylindrical pipe or cylindrical capillaries) is discussed. Due to cylindrical geometry of the walls, the illuminating laser wave can be strongly astigmatic, which renders the use of classical reconstruction techniques impossible. Contrary to plane wave holography setup, the diffraction pattern of the particles strongly depends on the axial distance of the latter to the entry face of the confinement structure. To address this reconstruction issue, we propose to use an "inverse problems" approach. This approach amounts to finding the best match (least squares solution) between a diffraction pattern model and the captured hologram. For this purpose, a direct imaging model for astigmatic holograms, based on the use of transfer matrices, is presented and validated by comparing experimental and simulated holograms. The accuracy of the "inverse problems" reconstruction is then used to calibrate the experimental setup adjustable parameters. Finally, the approach is tested through experimental astigmatic hologram reconstruction, thus paving the way to its use in pipe flow studies.

Evaporating droplet hologram simulation for digital in-line holography setup with divergent beam.

Generalized Lorenz-Mie theory (GLMT) for a multilayered sphere is used to simulate holograms produced by evaporating spherical droplets with refractive index gradient in the surrounding air/vapor mixture. Simulated holograms provide a physical interpretation of experimental holograms produced by evaporating Diethyl Ether droplets with diameter in the order of 50 µm and recorded in a digital in-line holography configuration with a divergent beam. Refractive index gradients in the surrounding medium lead to a modification of the center part of the droplet holograms, where the first fringe is unusually bright. GLMT simulations reproduce this modification well, assuming an exponential decay of the refractive index from the droplet surface to infinity. The diverging beam effect is also considered. In both evaporating and nonevaporating cases, an equivalence is found between Gaussian beam and plane wave illuminations, simply based on a magnification ratio to be applied to the droplets' parameters.

Fast and accurate 3D object recognition directly from digital holograms.

Pattern recognition methods can be used in the context of digital holography to perform the task of object detection, classification, and position extraction directly from the hologram rather than from the reconstructed optical field. These approaches may exploit the differences between the holographic signatures of objects coming from distinct object classes and/or different depth positions. Direct matching of diffraction patterns, however, becomes computationally intractable with increasing variability of objects due to the very high dimensionality of the dictionary of all reference diffraction patterns. We show that most of the diffraction pattern variability can be captured in a lower dimensional space. Good performance for object recognition and localization is demonstrated at a reduced computational cost using a low-dimensional dictionary. The principle of the method is illustrated on a digit recognition problem and on a video of experimental holograms of particles.

Accurate 3D tracking and size measurement of evaporating droplets using in-line digital holography and "inverse problems" reconstruction approach.

Digital in-line holography was used to study a fast dynamic 3D phenomenon: the evaporation of free-falling diethyl ether droplets. We describe an unsupervised reconstruction algorithm based on an "inverse problems" approach previously developed by our team to accurately reconstruct 3D trajectories and to estimate the droplets' size in a field of view of 7 × 11 × 20 mm 3. A first experiment with non-evaporating droplets established that the radius estimates were accurate to better than 0.1 µm . With evaporating droplets, the vapor around the droplet distorts the diffraction patterns in the holograms. We showed that areas with the strongest distortions can be discarded using an exclusion mask. We achieved radius estimates better than 0.5 µm accuracy for evaporating droplets. Our estimates of the evaporation rate fell within the range predicted by theoretical models.

Three-dimensional reconstruction of particle holograms: a fast and accurate multiscale approach.

In-line digital holography is an imaging technique that is being increasingly used for studying three-dimensional flows. It has been previously shown that very accurate reconstructions of objects could be achieved with the use of an inverse problem framework. Such approaches, however, suffer from higher computational times compared to less accurate conventional reconstructions based on hologram backpropagation. To overcome this computational issue, we propose a coarse-to-fine multiscale approach to strongly reduce the algorithm complexity. We illustrate that an accuracy comparable to that of state-of-the-art methods can be reached while accelerating parameter-space scanning.

On the single point resolution of on-axis digital holography.

On-axis digital holography (DH) is becoming widely used for its time-resolved three-dimensional (3D) imaging capabilities. A 3D volume can be reconstructed from a single hologram. DH is applied as a metrological tool in experimental mechanics, biology, and fluid dynamics, and therefore the estimation and the improvement of the resolution are current challenges. However, the resolution depends on experimental parameters such as the recording distance, the sensor definition, the pixel size, and also on the location of the object in the field of view. This paper derives resolution bounds in DH by using estimation theory. The single point resolution expresses the standard deviations on the estimation of the spatial coordinates of a point source from its hologram. Cramér-Rao lower bounds give a lower limit for the resolution. The closed-form expressions of the Cramér-Rao lower bounds are obtained for a point source located on and out of the optical axis. The influences of the 3D location of the source, the numerical aperture, and the signal-to-noise ratio are studied.

Inline hologram reconstruction with sparsity constraints.

Inline digital holograms are classically reconstructed using linear operators to model diffraction. It has long been recognized that such reconstruction operators do not invert the hologram formation operator. Classical linear reconstructions yield images with artifacts such as distortions near the field-of-view boundaries or twin images. When objects located at different depths are reconstructed from a hologram, in-focus and out-of-focus images of all objects superimpose upon each other. Additional processing, such as maximum-of-focus detection, is thus unavoidable for any successful use of the reconstructed volume. In this Letter, we consider inverting the hologram formation model in a Bayesian framework. We suggest the use of a sparsity-promoting prior, verified in many inline holography applications, and present a simple iterative algorithm for 3D object reconstruction under sparsity and positivity constraints. Preliminary results with both simulated and experimental holograms are highly promising.