Numerical evaluation of the limit of concentration of colloidal samples for their study with digital lensless holographic microscopy.

The number of colloidal particles per unit of volume that can be imaged correctly with digital lensless holographic microscopy (DLHM) is determined numerically. Typical in-line DLHM holograms with controlled concentration are modeled and reconstructed numerically. By quantifying the ratio of the retrieved particles from the reconstructed hologram to the number of the seeding particles in the modeled intensity, the limit of concentration of the colloidal suspensions up to which DLHM can operate successfully is found numerically. A new shadow density parameter for spherical illumination is defined. The limit of performance of DLHM is determined from a graph of the shadow density versus the efficiency of the microscope.

Automatic three-dimensional tracking of particles with high-numerical-aperture digital lensless holographic microscopy.

We present an automatic procedure for 3D tracking of micrometer-sized particles with high-NA digital lensless holographic microscopy. The method uses a two-feature approach to search for the best focal planes and to distinguish particles from artifacts or other elements on the reconstructed stream of the holograms. A set of reconstructed images is axially projected onto a single image. From the projected image, the centers of mass of all the reconstructed elements are identified. Starting from the centers of mass, the morphology of the profile of the maximum intensity along the reconstruction direction allows for the distinguishing of particles from others elements. The method is tested with modeled holograms and applied to automatically track micrometer-sized bubbles in a sample of 4 mm3 of soda.

Diffraction-based modeling of high-numerical-aperture in-line lensless holograms.

Conventionally, for modeling in-line lensless holograms of systems with high numerical apertures and diverging spherical illumination, the samples are considered as an ensemble of secondary point sources. On following Huygens's principle, the in-line hologram is the result of the amplitude superposition of the secondary spherical wavefronts with the wavefront originated in the point source. Albeit simple, this approach limits the shapes of the objects that can be modeled and the computation time rises with the complexity of the sample. In this work, we present a diffraction-based approach to model in-line lensless holograms. Samples with any shape or size can be modeled for in-line holographic systems with numerical apertures up to 0.57. The method is successfully applied to model objects of intricate submicrometer structures and/or multiple samples lying within a unique sample volume.

Magnified reconstruction of digitally recorded holograms by Fresnel-Bluestein transform.

A method for numerical reconstruction of digitally recorded holograms with variable magnification is presented. The proposed strategy allows for smaller, equal, or larger magnification than that achieved with Fresnel transform by introducing the Bluestein substitution into the Fresnel kernel. The magnification is obtained independent of distance, wavelength, and number of pixels, which enables the method to be applied in color digital holography and metrological applications. The approach is supported by experimental and simulation results in digital holography of objects of comparable dimensions with the recording device and in the reconstruction of holograms from digital in-line holographic microscopy.

Interference in phase space.

The phase-space representation of interference based on the marginal power spectrum gives new insight on interference, enlarging its potential applications by means of the principle of spatial coherence modulation. Carrier and (0,pi)-rays produced by three different types of supports are introduced for describing interference as the result of adding the radiant energy propagated by the carriers and the modulating energy (which can be positive or negative) propagated by the (0,pi)-rays. Numerical examples are presented.