Corinne Fournier

Inverse-problem approach for particle digital holography: accurate location based on local optimization

We propose a microparticle localization scheme in digital holography. Most conventional digital holography methods are based on Fresnel transform and present several problems such as twin-image noise, border effects, and other effects. To avoid these difficulties, we propose an inverse-problem approach, which yields the optimal particle set that best models the observed hologram image. We resolve this global optimization problem by conventional particle detection followed by a local refinement for each particle. Results for both simulated and real digital holograms show strong improvement in the localization of the particles, particularly along the depth dimension. In our simulations, the position precision is > or =1 microm rms. Our results also show that the localization precision does not deteriorate for particles near the edge of the field of view.

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.

Inverse problem approach in particle digital holography: out-of-field particle detection made possible

We propose a microparticle detection scheme in digital holography. In our inverse problem approach, we estimate the optimal particles set that best models the observed hologram image. Such a method can deal with data that have missing pixels. By considering the camera as a truncated version of a wider sensor, it becomes possible to detect particles even out of the camera field of view. We tested the performance of our algorithm against simulated and experimental data for diluted particle conditions. With real data, our algorithm can detect particles far from the detector edges in a working area as large as 16 times the camera field of view. A study based on simulated data shows that, compared with classical methods, our algorithm greatly improves the precision of the estimated particle positions and radii. This precision does not depend on the particles size or location (i.e., whether inside or outside the detector field of view).

Digital in-line holography: influence of the reconstruction function on the axial profile of a reconstructed particle image

The numerical reconstruction of an in-line digital hologram is a critical point in digital holographic particle image velocimetry. In particular, the shape of the axial profile of the reconstructed particles plays an important role in depth recovery. We show that this profile presents some oscillations when reconstructing by convolution with the Fresnel function. A window can be introduced in the expression of the reconstruction function in order to control these oscillations. The effects of this windowing are discussed and a criterion for the choice of window is given. The method is then illustrated by the processing of a digital hologram of Lycopode particles.

Twin-image noise reduction by phase retrieval in in-line digital holography

In-line digital holography conciles the applicative interest of a simple optical set-up with the speed, low cost and potential of digital reconstruction. We address the twin-image problem that arises in holography due to the lack of phase information in intensity measurements. This problem is of great importance in in-line holography where spatial elimination of the twin-image cannot be carried out as in off-axis holography. Applications in digital holography of particle fields greatly depend on its suppression to reach greater particle concentrations, keeping a sufficient signal to noise ratio in reconstructed images. We describe in this paper methods to improve numerically the reconstructed images by twin-image reduction.

Direct extraction of the mean particle size from a digital hologram

Digital holography, which consists of both acquiring the hologram image in a digital camera and numerically reconstructing the information, offers new and faster ways to make the most of a hologram. We describe a new method to determine the rough size of particles in an in-line hologram. This method relies on a property that is specific to interference patterns in Fresnel holograms: Self-correlation of a hologram provides access to size information. The proposed method is both simple and fast and gives results with acceptable precision. It suppresses all the problems related to the numerical depth of focus when large depth volumes are analyzed.

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.

Numerical suppression of the twin image in in-line holography of a volume of micro-objects

We address the twin-image problem that arises in holography due to the lack of phase information in intensity measurements. This problem is of great importance in in-line holography where spatial elimination of the twin image cannot be carried out as in off-axis holography. A unifying description of existing digital suppression methods is given in the light of deconvolution techniques. Holograms of objects spread in 3D cannot be processed through available approaches. We suggest an iterative algorithm and demonstrate its efficacy on both simulated and real data. This method is suitable to enhance the reconstructed images from a digital hologram of small objects.

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.

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.