Characterizations of transparent particle holography in near-field using Debye series.

The effects of the individual scattering process on the formations of both the particle hologram and its corresponding reconstructed three-dimensional particle image are investigated using the Debye series. A particle hologram model using the Debye series decomposes the object wave into different scattering modes and thus permits evaluating the effects of the individual scattering process [diffraction, reflection, transmission, refractions with (p-1) internal reflections] on the particle holography quantitatively. In the Gabor inline holography of a transparent droplet, the transmission light causes small discrepancies between the hologram fringes of an opaque particle (diffraction) and a transparent particle near the zero point of the Bessel-like modulation function, eventually giving rise to the glory spot in the center of the reconstructed dark particle image. For off-axis holography, this paper reveals the effects of reflection, particularly total reflection by bubbles, transmission, and refractions with (p-1) internal reflections of the scattered light on the formation and the reconstructed glory spot images of typical forward and backward off-axis holography.

Recovering the size of nanoparticles by digital in-line holography.

The development of methods to measure the size of nanoparticles is a challenging topic of research. The proposed method is based on the metrology of the stable vapor bubble created by thermal coupling between a laser pulse and the nanoparticle in a droplet. The measurement is realized by digital in-line holography. The size of the nanoparticle is deduced from numerical simulations computed with a photo-thermal finite element method.

Extended wavelet transformation to digital holographic reconstruction: application to the elliptical, astigmatic Gaussian beams.

Wavelet analysis provides an efficient tool in numerous signal processing problems and has been implemented in optical processing techniques, such as in-line holography. This paper proposes an improvement of this tool for the case of an elliptical, astigmatic Gaussian (AEG) beam. We show that this mathematical operator allows reconstructing an image of a spherical particle without compression of the reconstructed image, which increases the accuracy of the 3D location of particles and of their size measurement. To validate the performance of this operator we have studied the diffraction pattern produced by a particle illuminated by an AEG beam. This study used mutual intensity propagation, and the particle is defined as a chirped Gaussian sum. The proposed technique was applied and the experimental results are presented.

Digital in-line holography with a rectangular complex coherence factor.

We propose in this paper the study of a particular spatially partially coherent source applied to digital in-line holography of dense particle flow. A source with a rectangular complex coherence factor is implemented. The effects of such a source on the intensity distribution of the diffraction pattern are described. In particular, we show that this type of source allows us to eliminate the diffraction pattern along one axis while all the information about the dimension of the particle is kept along the other perpendicular axis. So particle images can be well reconstructed along one direction and the speckle can be largely limited.

Three-dimensional velocity near-wall measurements by digital in-line holography: calibration and results.

Velocity measurements in the vicinity of an obstacle remain very complicated even when optical diagnostics based on displacement of micrometric tracers are considered. In the present paper, digital in-line holography with a divergent beam is proposed to measure the three-dimensional (3D) velocity vector fields in a turbulent boundary layer and, in particular, on the near wall region of a wind tunnel. The seeding droplets (1-5 µm) transported by a turbulent airflow are illuminated by a couple of laser pulses coming from a fiber coupled laser diode. These double exposure holograms are then recorded through a transparent glass reticle specially designed for this application with an accurate surface positioning combined with a particularly attractive in situ calibration method of the investigation volume (less than 10 mm(3)). The method used for processing holograms recorded in such a configuration is detailed. Our original calibration procedure and the assessment of its accuracy are presented. Our holographic probe has been tested in a wind tunnel for a large range of different velocities. Then 3D velocity vector fields extracted from more than 13000 holograms are analyzed. Statistical results show the capability of our approach to access in a turbulent boundary layer. In particular, it leads to relevant measurements for fluid mechanics such as velocity fluctuation and the shear stress in the very close vicinity of a wall.

Cylindrical interferometric out-of-focus imaging for the analysis of droplets in a volume.

We propose an original cylindrical interferometric out-of-focus imaging setup to realize the characterization of spherical droplets in a volume. The longitudinal position of the droplets is determined through the orientation of the fringes while the diameter of the droplets is obtained from the frequency of the fringes. The experiments agree with the simulations.

Interferometric laser imaging for droplet sizing revisited: elaboration of transfer matrix models for the description of complete systems.

We report the development of an interferometric laser imaging for droplet sizing (ILIDS) numerical simulator. It is based on the use of generalized Huygens-Fresnel integrals associated to transfer matrices that describe the whole imaging setup. This simulator allows easy simulation of any kind of ILIDS setup. Simulations are shown to be in good agreement with experimental results. This simulator offers important perspectives in the design, realization, and calibration of ILIDS instruments, as airborne instruments, or in situ measurements in flows.

Extended ABCD matrix formalism for the description of femtosecond diffraction patterns; application to femtosecond digital in-line holography with anamorphic optical systems.

We present a new model to predict diffraction patterns of femtosecond pulses through complex optical systems. The model is based on the extension of an ABCD matrix formalism combined with generalized Huygens-Fresnel transforms (already used in the CW regime) to the femtosecond regime. The model is tested to describe femtosecond digital in-line holography experiments realized in situ through a cylindrical Plexiglas pipe. The model allows us to establish analytical relations that link the holographic reconstruction process to the experimental parameters of the pipe and of the incident beam itself. Simulations and experimental results are in good concordance. Femtosecond digital in-line holography is shown to allow significant coherent noise reduction, and this model will be particularly efficient to describe a wide range of optical geometries. More generally, the model developed can be easily used in any experiment where the knowledge of the precise evolution of femtosecond transverse patterns is required.

Micropipe flow visualization using digital in-line holographic microscopy.

Digital in-line holography is used to visualize particle motion within a cylindrical micropipe. Analytical expression of the intensity distribution recorded in the CCD sensor plane is derived using the generalized Huygens-Fresnel integral associated with the ABCD matrices formalism. Holograms obtained in a 100microm in diameter micropipe are then reconstructed using fractional Fourier transformation. Astigmatism brought by the cylindrical micropipe is finally used to select a three dimensional region of interest in the microflow and thus to improve axial localization of objects located within a micropipe. Experimental results are presented and a short movie showing particle motion within a micropipe is given.

Digital phase contrast with the fractional Fourier transform.

A new method of digital phase contrast based on fractional-order Fourier reconstruction is proposed. We show that the diffraction patterns produced by pure phase objects exhibit linear chirp functions that can be advantageously processed using the fractional Fourier transform. The optimal fractional orders lead to the longitudinal location of the phase object, while the analysis of the reconstructed pattern leads to its diameter and to the value of the phase shift. Simulations and experimental results are given. The configuration tested in this paper is a very general Gaussian illumination.

Digital in-line holography in thick optical systems: application to visualization in pipes.

We apply digital in-line holography to image opaque objects through a thick plano-concave pipe. Opaque fibers and opaque particles are considered. Analytical expression of the intensity distribution in the CCD sensor plane is derived using a generalized Fresnel transform. The proposed model has the ability to deal with various pipe shapes and thicknesses and compensates for the lack of versatility of classical digital in-line holography models. Holograms obtained with a 12 mm thick plano-concave pipe are then reconstructed using a fractional Fourier transform. This method allows us to get rid of astigmatism. Numerical and experimental results are presented.

Generation of femtosecond diffraction-compensated beam through an opaque disk.

The generation of a femtosecond diffraction-compensated beam through an opaque disk is presented: 100 fs pulses are focused in the vicinity of an opaque disk. A bright beam surrounded by concentric rings is generated. The beam can be collimated by a lens. A non-diffracting femtosecond beam which conserves a 500microm large central spot over more than 1.7m is then observed, without any nonlinear mechanism. Our theoretical analysis predicts well the results.

Digital in-line holography with an elliptical, astigmatic Gaussian beam: wide-angle reconstruction.

We demonstrate that the effect of object shift in an elliptical, astigmatic Gaussian beam does not affect the optimal fractional orders used to reconstruct the holographic image of a particle or another opaque object in the field. Simulations and experimental results are presented.

Generation of nondiffracting beams through an opaque disk.

A new method of generating nondiffracting beams is presented. It consists of focusing a Gaussian beam in the vicinity of an opaque disk. A beam is generated whose central peak is surrounded by a wide number of bright rings (approximately 250). After collimation, the beam propagates without changing the rings' radii, similar to a diffraction-free beam. The central peak can conserve its dimension over more than 5 m. The diameter of the central peak is adjusted by choosing the focal length of the collimating lens. Experimental results are well predicted by our theoretical developments that simulate exactly the paraxial diffraction.

Fractional-order Fourier analysis for ultrashort pulse characterization.

We report what we believe to be the first experimental demonstration of ultrashort pulse characterization using fractional-order Fourier analysis. The analysis is applied to the interpretation of spectral interferometry resolved in time (SPIRIT) traces [which are spectral phase interferometry for direct electric field reconstruction (SPIDER)-like interferograms]. First, the fractional-order Fourier transformation is shown to naturally allow the determination of the cubic spectral phase coefficient of pulses to be analyzed. A simultaneous determination of both cubic and quadratic spectral phase coefficients of the pulses using the fractional-order Fourier series expansion is further demonstrated. This latter technique consists of localizing relative maxima in a 2D cartography representing decomposition coefficients. It is further used to reconstruct or filter SPIRIT traces.

Application of the two-dimensional fractional-order Fourier transformation to particle field digital holography.

We demonstrate that the fractional-order Fourier transformation is a suitable method to analyze the diffraction patterns of particle field holograms. This method permits reconstruction of in-line digital holograms beyond the Fraunhofer condition (d2/lambdaz approximately/= 10). We show that the diameter of spherical particles is measured with good accuracy. Simulation and experimental results are presented.

Characterization of diffraction patterns directly from in-line holograms with the fractional Fourier transform.

We show that the fractional Fourier transform is a suitable mechanism with which to analyze the diffraction patterns produced by a one-dimensional object because its intensity distribution is partially described by a linear chirp function. The three-dimensional location and the diameter of a fiber can be determined, provided that the optimal fractional order is selected. The effect of compaction of the intensity distribution in the fractional Fourier domain is discussed. A few experimental results are presented.