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.

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 particle's size or location (i.e., whether inside or outside the detector field of view).

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.

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.

On-axis Digital Holography is becoming widely used for its time-resolved 3D imaging capabilities. A 3D volume can be reconstructed from a single hologram. Digital Holography (DH) is applied as a metrological tool in experimental mechanics, biology, 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 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 influence of the 3D location of the source, the numerical aperture and the signal-to-noise ratio are studied.