Search

Esse artigo busca trazer comentários e a errata da dissertação apresentada à Faculdade de Engenharia Elétrica e de Computação da Universidade Estadual de Campinas como parte dos requisitos exigidos para a obtenção do título de Mestre em Engenharia Elétrica, na Área de Telecomunicações e Telemática, por Juliano Carvalho Bento, sob o título “Método Analítico para Descrição de Importantes Feixes Ópticos Obstruídos e oSpotde Poisson-Arago”, defendida em 17/07/2016. É possívelacessá-la no site doRepositório da Produção Científica e Intelectual daUnicamp(). Qualquer outro comentário ou errata não hesite em enviar para.

International audience; We present a numerical and experimental demonstration of the emergence of a bright temporal spot in the initial shadow of a fully-coherent temporal signal. Impacts of nonlinearity and dispersion regimes are also investigated.

The purpose of this note is to prove dispersive estimates for the wave and the Schrodinger equations outside strictly convex obstacles in R d . If d = 3 , we show that, for both equations, the linear flow satisfies the (corresponding) dispersive estimates as in R 3 . In higher dimensions d ≥ 4 and if the domain is the exterior of a ball in R d , we show that losses in dispersion do appear and this happens at the Poisson spot.

The history of conceptions of light is among the most exciting scientific adventures. It was Fresnel's theoretical work that made it possible to establish the most solid theoretical basis of wave optics. Two centuries ago, his approach was validated by the observation of a counter-intuitive bright spot appearing at the center of the geometric shadow of an illuminated opaque circular object. This phenomenon has remained known as the Arago spot. We propose here to further extend the spatial/temporal analogy that exists between diffraction and dispersion by revisiting the Arago spot formation in the time domain through the temporal dispersive evolution of light after being briefly stopped by an obstacle. The analytical treatment that is possible for linear propagation as well as the experiments based on telecom optical fibers and fast optoelectronics confirm that we observe the emergence of light where it was initially absent. As the power increases and Kerr nonlinearity affects the propagation, the Arago spot intensity is affected by the sign of the dispersion.

Generation of subwavelength beam sizes is a fascinating challenge with several implications. The observation of a 120 nm laser spot in the visible part of the spectrum is reported here. It has a size variation of less than 10% in a distance of 50 µ m along the axis of propagation. This so-called Arago spot results from the diffraction of the light from a laser diode by the edges of an absorbing disk. Applications are discussed and hollow beams carrying orbital angular momentum with a 400 nm diameter dark spot in the center are evidenced. This paves the way toward atom lithography via atom guiding or new spectroscopy on forbidden transitions.

The phase of de Broglie matter waves is a sensitive probe for small forces. In particular, the attractive van der Waals force experienced by polarizable atoms in the close vicinity of neutral surfaces is of importance in nanoscale systems. It results in a phase shift that can be observed in matter-wave diffraction experiments. Here, we observe Poisson spot diffraction of indium atoms at submillimeter distances behind spherical submicron silicon dioxide particles to probe the dispersion forces between atoms and the particle surfaces. We compare the measured relative intensity of Poisson's spot to theoretical results derived from first principles in an earlier communication and find a clear signature of the atom-surface interaction.

We show that structured light can amplify the intensity of an Arago–Poisson bright spot, the cornerstone proof of the wave nature of light, by several orders of magnitude. Specifically, we use a thin annular beam produced by either an axicon–lens combination or two axicons to illuminate an opaque circular obstacle. Experimental results confirm the numerical calculations. By judiciously choosing our scheme’s parameters, the bright spot intensity can be higher than that of the original beam, meaning that structured light facilitates “focusing” of light behind an obstacle. This amplification, in addition to didactic elucidation of this classical effect, can find use in optical alignment/metrology, lithography, aberration measurements, as well as in basic science studies of the Arago–Poisson spot in matter waves.

When a part of an optical wave-front experiences a sharp change in its phase, Fresnel diffraction becomes appreciable. Sharp change in phase occurs as a wave-front strikes with a phase step. The intensity distributions of diffraction patterns of the phase step is formulated by applying Fresnel–Kirchhoff integral. For while the incident light on the step is coherent, the Fresnel–Kirchhoff integral can be solved by using familiar Fresnel integrals. But, when the incident light is partially coherent, one can not express the diffraction integral as the Fresnel integrals and the problem is summarized in solving some unusual integrals. In this report, we propose Fourier transform method for solving the Fresnel–Kirchhoff integral. In this regard we use discrete Fourier transform method and calculate Fresnel diffraction from the 1D phase step by FFT-based algorithms. This method does not have any restriction on the coherence and profile shape of the incident light. We show that the method have appropriate solutions for coherent and partially coherent lights. For the case of the coherent light illumination of the step, the obtained results are in good agreement with the calculated results by using the Fresnel integrals in reported literatures.

In this study, an optical scheme based on the measurement of light intensity and a proper orientation of the Fresnel Rhomb is successfully developed for simultaneous determination of the phase retardation and fast axis of a wave plate. The theoretical analysis of the principle of measuring the reflection-induced retardance of the Fresnel Rhomb and the phase retardation of a wave plate is given taking Stokes–Mueller Formalism as a mathematical tool. In this method, the fast axis position of the wave plate need not be determined in advance. In addition, the measured result is free of the intensity fluctuation of light source. An application example is also demonstrated. The measured result of the example is verified with an experiment. Some of the merits of the method, such as, a simple optical set-up, high stability and high accuracy, low cost and easier operation, are presented, and the validity of the method is demonstrated.

The possibility of X-ray phase contrast imaging using already suggested three-block interferometer consisting of bi-level Fresnel zone plates is considered. The interferometer operates in the amplitude-division mode and does not impose strong requirements to spatial and temporal coherences of an initial radiation. The use of the Fresnel zone plates as the interferometer blocks allows one to obtain an optically magnified image of an object and to condense the radiation incident on the tested object.

Aims. We seek to study the Fresnel diffraction of external occulters that differ from a single mask in a plane. Such occulters have been used in previous space missions and are planned for the future ESA Proba 3 ASPIICS coronagraph. Methods. We studied the shading efficiency of double on-axis disks and generalized results to a 3D occulter. We used standard Fourier optics in an analytical approach. We show that the Fresnel diffraction of two and three disks on axis can be expressed using a Babinet-like approach. Results are obtained in the form of convolution integrals that can be written as Bessel-Hankel integrals; these are difficult to compute numerically for large Fresnel numbers found in solar coronagraphy. Results. We show that the shading efficiency of two disks is well characterized by the intensity of the residual Arago spot, a quantity that is easier to compute and therefore allows an interesting parametric study. Very simple conditions are derived for optimal sizes and positions of two disks to produce the darkest structure around the Arago spot. These conditions are inspired from empirical experiments performed in the sixties. A differential equation is established to give the optimal envelope for a multiple-disk occulter. The solution takes the form of a simple law, the approximation of which is a conical occulter, a shape already used in the SOHO Mission. Conclusions. In addition to quantifying expected results, the present study highlights unfortunate configurations of disks and spurious diffractions that may increase the stray light. Particular attention is paid to the possible issues of the future occulter spacecraft of ASPIICS.

In this chapter I discuss the dependence of image formation on the nature of light itself. Geometrical optics is no longer sufficient to predict the relationship between the object and the image when the object's size approaches the wavelength of light because the object diffracts the incident light. Since diffraction is significant when the details in an object are similar in size to the wavelength of light, we need to understand the interaction of light with matter to predict the relationship between the object and the image formed by diffracted light. This is the realm of physical optics, which is based on the wave theory of light. I discuss the development of the wave theory of light by Huygens, Young, Fresnel, and Maxwell. I also discuss how Ernst Abbe developed a theory of image formation where the diffraction of light limits the resolving power of the light microscope.

The X-ray interferometric Fresnel holography was proposed and theoretically investigated. It was shown that under definite conditions the recorded interference pattern formed at the output surface ofthe analyzer crystal (the third block of interferometer) is the X-ray interferometric hologram (generally the Fresnel one) of the object under investigation. Further reconstruction of an image is performed with the help of visible light or a numerical method. As an example the recording of a Fresnel hologram of the simplest case of one-dimensional object, a narrow slit, and the reconstruction of an image by means of visible light were considered. This method may be used in X-ray microscopy and realized using synchrotron sources ofX-ray radiation, as well as X-ray free electron lasers.

The iterative Fresnel integrals method (IFIM) has been applied for the simulation and generation of the complete near-field Fresnel diffraction images created by N -apertures for the first time. The simulation can be performed in any PC using a MATLAB program developed by the authors. Necessary formalism was derived for the general N -slit problem, and a simulation algorithm was devised for this application. An interesting combination of interference effects with Fresnel diffraction was observed in the simulated images. Transition to the expected Fraunhofer diffraction pattern from Fresnel diffraction for N -apertures is also observed in the simulations under the appropriate conditions. Principal maxima of the expected Fraunhofer diffraction were observed at their expected positions, as well as the expected minima and the secondary maxima. The program can serve as a useful tool to study the complex phenomenon of Fresnel diffraction from N -apertures, and in addition, to study the near-field Fresnel diffraction from amplitude diffraction gratings.

Focusing characteristics of cross like Fresnel zone plate is well analyzed. This element is composed of two perpendicular linear Fresnel zone plates. Focusing properties of the element is compared to a classic and square Fresnel zone plate. Analysis clarify that focusing of the elements is well corrected in comparison to square Fresnel zone plate. Resolution is noticeably increased, DC noise and diffraction efficiency are substantially reduced and also secondary maxima have been evidently suppressed. Theoretical results have been completely verified by experiment.

We present the study of the wave motion in the Talbot interferometer with an additional element such as a lens for all related audiences. Our solutions are in the analytic form. A general principle of the Talbot effect, which is the optical near-field effect, is the Fresnel diffraction. The Fresnel integral is rather complicated. We therefore introduce an alternative method which is based on the wave propagation through the transmission functions of the grating and the lens. Our method has been proved by a simple experimental setup.

The X-ray interferometer consisting of three Fresnel zone plates with the same optical axis is considered. The interferometer operates in the amplitude-division mode and does not impose the strong requirements on the coherence of initial radiation. The interferometer is the modification of earlier one, with the main difference that the labor-intensive to manufacture multilevel Fresnel zone plates are replaced by the ordinary bi-level ones. The longitudinally and transversely defocused modifications of interferometer were considered by the numerical simulation method.

Phase shifted linear Fresnel zone plates are presented for the first time. These diffractive elements are linear Fresnel zone plates in which their phase are laterally shifted. The impact of the phase shifting on their diffractive and focusing properties are studied. It is demonstrated that by shifting the phase, two parallel linear beams can be generated at the focal plane. Furthermore, as they are propagating, a non-diffractive line-shaped beam is generated at a given distance from the focus. Transverse intensity profile of the beam at different distances as well as its cross section of propagation along the optical axis clearly shows that the intensity profile of the beam is really kept unchanged as it is propagated. All results are completely verified by experiments.

For the observer at infinity, a Schwarzschild black hole serves as an attractive opaque disk with a radius of 3$\sqrt{3} M$ that will produce the diffraction pattern of gravitational waves (GWs). In this study, we demonstrate that a bright spot, which is a diffraction effect analogous to the Poisson-Arago spot in optics, will appear when an ingoing (quasi-) plane GW is diffracted by a Schwarzschild black hole. Here, we propose the diffraction effect of the GWs described by the exact diffraction solution of the GWs using the Heun function. For the first time, the Fresnel half-wave zone method is proposed to calculate the angular part of the GW scattering stripes for the observer at infinity. The prospect of observing the diffraction bright spot is discussed with an eikonal approximation. For normal incidence (quasi)-plane waves with 100 Hz (0.1 Hz) frequency diffracted by the central black hole of the Milky Way, the time delay between the Earth bathed in a bright spot and the minimum of the first dark stripe is 3.86 (3860) days. We will witness the second bright fringe (40% amplitude of the central bright spot) after 6.2 (6200) days. This new diffraction pattern involving the early phase of inspirals and pulsars as continuous gravitational wave sources is a potential scientific target for future space-and ground-based gravitational wave detectors, respectively.

The “Association de Satellites Pour l'Imagerie et l'Interferometrie de la Couronne Solaire”, ASPIICS, selected by ESA for the PROBA-3 mission, heralds the next generation of coronagraph for solar research, exploiting formation flying to gain access to the inner corona under eclipse-like conditions for long periods of time. A detailed description of the ASPIICS instrument and of its scientific objectives can be found in [1]. ASPIICS is distributed on the two PROBA 3 spacecrafts (S/C) separated by 150 m. The coronagraph optical assembly is hosted by the “coronagraph S/C” protected from direct solar disk light by the occulting disk on the “occulter S/C”. The most critical issue in the design of a solar coronagraph is the reduction of the stray light due to the diffraction and scattering of the solar disk light by the occulter, the aperture and the optics. In the present article, we deal with two of these issues: - The analysis of the stray light inside the telescope. - The optimization of the external occulter edge, in order to eliminate the Poisson spot behind the occulter and to lower the stray light level going through the entrance pupil of the telescope. This work was performed in the framework of the ESA STARTIGER program which took place at the Laboratoire d’Astrophysique de Marseille (LAM) during a 6-month period from September 2009 to March 2010. In general, it is a very complicated task to combine the above two stray light issues together in the simulation and design phase as it requires to consider the propagation inside the telescope of the light diffracted by the external occulter. Actually, the present literature only reports diffraction calculations performed for simple occulting systems (i.e., two disks and serrated disk). A more pragmatic approach, also driven by the tight schedule of the STARTIGER program, is to separate the two contributions, and perform two different stray light analyses. This paper is dedicated to the description of both analyses: in particular, the first part is dedicated to the evaluation of the stray light inside the telescope, assuming a simple disk as occulter, and a preliminary baffle design is presented; the second part describes the investigation on the geometry of the external occulter, with a detailed description of the laboratory setup that has been designed and implemented to compare together several types of occulting systems.

The vector diffraction of linearly polarized plane wave passing through a thin circular plate with a sub-wavelength radius is investigated by the finite element method. The transverse distribution and propagating evolution of the diffracted field with different intensity expressions are analyzed and compared. It shows that there are not only the component of the incident polarization, but also those of other two vertical directions in the near-field diffracted region. Regardless of the relationship between the wavelength and the radius of the circular plate, the diffracted field could evolve into a steady annular diffracted pattern, in which there is a central bright spot (so-called Poisson spot). There is an obvious difference of the diffracted properties between two intensity expressions from the square of electric field and the average magnitude of the Poynting vector as the propagation distance is very small, while they can be considered same with a large propagation distance (e.g. more than a wavelength).

One of the important current problems is imaging and detection of objects hidden by obscuring obstacles. There have been extensive works reported on “Through-Wall Imaging” in recent years. This paper extends the previous works to the case where the wall is non-penetrating and the diffraction around the edge becomes important. This hard-wall imaging is related to the historical problem of “Poisson Spot” and “Anti-Podal point.” This paper makes use of the modified time-reversal technique and GTD, and shows the formulations of the multistatic data matrix, eigenvectors and steering vectors to form the imaging function. Signal processing includes the multiplicative modified time reversal technique to eliminate the unwanted extraneous images. Numerical examples include comparisons between the modified and the conventional time-reversal imaging to show the effectiveness of the hard-wall imaging method.

Fresnel theory, with certain level of assumptions, explains satisfactorily observed diffraction patterns. It is a scalar theory and basically it deals special way of superposition of fields originated from several points of Huygens wave front. In the present paper a total new approach is proposed according to which the interacting electric fields are not originated from the secondary emitters of the same wave front, instead, they are originated from the successive Huygens wave fronts. The proposed approach is explained with the help of the circular aperture. This new view supports Fresnels theory without a set of assumptions.

The geometrical optics in Fresnel quantum holography for quantum entangled two-photon source and classical thermal light source based on the second-order correlation measurement has been discussed. We theoretically prove that the Fresnel quantum hologram of the detected object can be obtained through second-order correlation measurement and the optical reconstruction process can be accomplished by making use of a point light source.

It is shown that when a coherent beam of light illuminates a Fresnel's double mirror, Fresnel diffraction becomes appreciable. The subject fundamentally differs from interference. We calculate the diffracted field by applying Fresnel–Kirchhoff integral. We modified the common Fresnel's double mirror by imposing an initial height between the mirrors, as the height is chosen small enough so that the application of Fresnel's double mirror is maintained. We show by simulation and experiment that a phase singularity causes from the initial height and modifies the diffracted field from the Fresnel's double mirror. One can adjust the location of the line singularity by changing the angle between the mirrors. Also, the anomalous behavior of a polychromatic beam diffracted from the modified Fresnel's double mirror at the neighborhood of the line singularity, is investigated by simulation.

There are many 3D data structures for computing diffraction field, the description based on 3D point-cloud is the elemental method of other descriptions, the diffraction field of 3D scene can be thought as the superposition of the diffraction field of each sampled light point and other descriptions can be thought as grouping with point-cloud by different way. The paper focuses on devising a computation method of 3D Fresnel field which is based on Fresnel diffraction field propagation reversibility. The proposed method combines the reversibility of Fresnel propagation and the requirement of sampling spacing by Nyquist criterion, i.e. to find the best space positions to optimize the number of sampling points and the reconstruction for the 3D Fresnel field. The method can be applied to reduce the computational complexity and improve computational efficiency.

In this work, we propose and analyze a novel kind of binary Fresnel zone plate with single focus. It consists of a Fresnel zone plate whose zones have rough edges. We give analytical results for the intensity along the optical axis and demonstrate that lateral roughness of the zones produces the disappearance of secondary foci as a blurring of the edges. Besides, we corroborate its behavior by numerical simulations and experiments. This kind of Fresnel zone plate can be useful in a wide range of photonic applications, even for focusing with soft and hard X-rays or extreme ultraviolet radiation.

The experimental study about the diffraction of high-density grating in deep Fresnel region is performed in this paper. A microscope-magnification method is advanced, and the diffraction intensity distributions of high-density grating in deep Fresnel region are measured. The quasi-Talbot image of grating is also obtained in experiment. The corresponding theoretic results are also provided for convenient comparison with the experimental ones. The coincidence of experimental and theoretical results verifies the reliability of microscope-magnification method. This method can be used in the measurement of the diffraction of sub-wavelength structure in near field and deep Fresnel region.

Recently there have been experimental results on Poisson spot matter wave interferometry followed by theoretical models describing the relative importance of the wave and particle behaviors for the phenomenon. We propose an analytical theoretical model for the Poisson's spot with matter waves based on Babinet principle in which we use the results for a free propagation and single slit diffraction. We take into account effects of loss of coherence and finite detection area using the propagator for a quantum particle interacting with an environment. We observe that the matter wave Gouy phase plays a role in the existence of the central peak and thus corroborates the predominantly wavelike character of the Poisson's spot. Our model shows remarkable agreement with the experimental data for deuterium ($D_{2}$) molecules., 8 pages, 5 figures

The intensity distribution in the vicinity of the focus of circular Fresnel zone plate formed by Bessel-Gauss beam is studied. Dark hollow beams are obtained near focus under the illumination of high order Bessel-Gauss beam, the width and the length of central hollow depends on the order of the beam and the number of plate zones. These beams with special intensity distribution in the field of laser processing and trapping particles have potential application value.

Diffraction of matter-waves is an important demonstration of the fact that objects in nature possess a mixture of particle-like and wave-like properties. Unlike in the case of light diffraction, matter-waves are subject to a vacuum-mediated interaction with diffraction obstacles. Here we present a detailed account of this effect through the calculation of the attractive Casimir-Polder potential between a dielectric sphere and an atomic beam. Furthermore, we use our calculated potential to make predictions about the diffraction patterns to be observed in an ongoing experiment where a beam of indium atoms is diffracted around a silicon dioxide sphere. The result is an amplification of the on-axis bright feature which is the matter-wave analogue of the well-known `Poisson spot' from optics. Our treatment confirms that the diffraction patterns resulting from our complete account of the sphere Casimir-Polder potential are indistinguishable from those found via a large-sphere non-retarded approximation in the discussed experiments, establishing the latter as an adequate model., 13 pages, 10 figures

The presence of a bright (Poisson) spot in the geometrical shadow of circular/spherical shapes has been known for the past two centuries. A broad class of telescopes that involve simultaneous transmit and receive require suppression of the reflected light from the secondary mirror on the detector. For instance, the on-axis design of optical telescope for the evolved Laser Interferometric Space Antenna (eLISA), a re-scoped version of the baseline LISA mission concept, requires suppression of reflected laser light from the secondary mirror on the detector. In the past few years, the hypergaussian functions with petal-shaped realization have been shown to significantly suppress intensity along the optical axis. This work reports on fabrication of a series of petal-shaped masks using a variety of techniques such as 3D printing, photolithography, and wire Electro Discharge Machining. These masks are designed and fabricated to operate in the range of Fresnel numbers between 4 and 120. This paper discusses the challenges, successes, and failures of each fabrication technique and the optical performance of typical masks with suggestions for potential follow up work.

A technique and investigation results are presented on the effect of the number of Fresnel zones on the diffraction efficiency and quality of the wave front formed by a diffractive optical element. Equations are presented for the microstructure reliefs of diffractive optical elements making (regardless of the number of Fresnel zones) the wavefront shape coinciding with the calculated one and ensuring 100% diffraction efficiency at a single wavelength and, in the case of two-layer structures, almost 100% diffraction efficiency in a wide spectral range.

We applied the iterative Fresnel integrals method for the numerical computation of Fresnel diffraction patterns from rectangular apertures tilted at an arbitrary angle to the optical axis. Detailed theoretical formalism is developed and discussed, and then is applied for the numerical computation and simulation of the actual diffraction patterns for an arbitrary optical configuration. The generated intensity distributions (images) show distortion and stretching in the direction of the tilt, but not in the other orthogonal direction. Significant decrease of the intensity is also predicted and observed, the decrease being proportionate with the tilt angle. The simulated images qualitatively resemble those published in the literature. In addition to single-axis tilts, simultaneous rotations (tilts) of the aperture in two orthogonal coordinate axes were also briefly considered and simulated.

In high frequency, due to the locality of the scattering, the importance of currents is localized near the scattering centers, which correspond the stationary phase points and the edge diffraction points, as is defined by the GTD. This localization would provide the reduction of unknowns in the method of moments (MoM), though the area of importance moves with the location of the source and the observer. If this concept is extended for the observer on the surface of scatterer, the reaction matrix is transformed into the sparse band matrix. Authors have proposed the use of Fresnel zone number as the threshold for the truncation of the scatterers or the reaction matrix. This talk reviews the concept and the advancement of the high frequency technique based upon the locality of scattering in terms of Fresnel zone number.

A physical interpretation of the focal shift is given based on geometrical optics. The results of an analytical study of the focal shift depending on the Fresnel numbers are presented. The effect of the aperture diameter and the width of the central zone of the phase Fresnel lens on the distribution of the light intensity along the axis upon illumination by a convergent light beam is analyzed.

During late 1970s and early 1980s, Fresnel lenses have received more attention in the field of solar energy application. This paper briefly examines the Fresnel lens development since 1970s and investigates the losses inherent in the linear Fresnel lenses. The research develops the formulation that helps to quantify the linear lens’ transmittance loss and prism-tip scattering loss and then derive a realistic model to simulate the measured data. In addition, the research has identified an elliptical-based lens that comes closest to the condition of minimum deviation. Such lens closely duplicates the curvature needed for maximum transmission. The researcher applies different design wavelengths to study the contribution of each wavelength interval on the receiving plane.

A significant challenge for the successful implosion of direct-drive inertial fusion energy targets is the repeated alignment of multiple laser beams on moving targets with accuracy on the order of 20 ?m. Adding to the difficulty, targets will be traveling up to 100 m/s through a chamber environment that may disturb their trajectories. In the High Average Power Laser program, we have developed a target tracking and engagement system that is capable of meeting the goals for an inertial fusion power plant. The system consists of separate axial and transverse target detection techniques and a final correction technique using a short-pulse laser to interrogate the target's position 1-2 ms before a chamber center. Steering mirrors are then directed to engage the target at the chamber center. Over the past few years, we have constructed and improved upon an integrated tabletop demonstration operating at reduced speeds and path lengths. In August 2007, initial engagement of moving targets in air using a simulated driver beam was 150- ?m rms. Since then, we have taken an encompassing look at all error sources that contribute to the overall engagement error. By focusing on those individual component errors that have the most influence and improving their accuracy, we have substantially reduced the overall engagement error. In August 2008, we had achieved an engagement of 42-?m rms in air by using this approach, and in March 2009, 34-?m rms in vacuum. The final elements, which we believe are necessary to meet our goal, necessitate engaging lightweight targets in a prototypic vacuum environment with an understanding of the scalability of demonstration-scale errors to full-scale errors. In this paper, we present the latest improvements from the identification and reduction of errors and the resulting engagement data demonstrating near completion of the viability demonstration of direct-drive target engagement to 20 ?m.

We review three different methods of generating digital Fresnel holograms of 3-D real-existing objects illuminated by incoherent light. In the first method, a scanning hologram is generated by a unique scanning system in which Fresnel zone plates (FZP) are created by a homodyne rather than the common heterodyne interferometer. During the scanning, the FZP projected on the observed object is frozen rather than varied as previously. In each scanning period, the system produces an on-axis Fresnel hologram. The twin image problem is solved by a linear combination of at least three holograms taken with three FZPs with different phase values. The second hologram reviewed here is the digital incoherent modified Fresnel hologram. To calculate this hologram, multiple-viewpoint projections of the 3-D scene are acquired, and a Fresnel hologram of the 3-D scene is directly computed from these projections. This method enables to obtain digital holograms by using a simple digital camera, which operates under regular light conditions. The last digital hologram reviewed here is the Fresnel incoherent correlation hologram. In this motionless holographic technique, light is reflected from the 3-D scene, propagates through a diffractive optical element (DOE), and is recorded by a digital camera. Three holograms are recorded sequentially, each for a different phase factor of the DOE. The three holograms are superposed in the computer, such that the result is a complex-valued Fresnel hologram that does not contain a twin image.

Although Thomas Young is generally given credit for being the first to provide evidence against Newton’s corpuscular theory of light, it was Augustin Fresnel who first stated the modern theory of diffraction. We review the history surrounding Fresnel’s 1818 paper and the role of the Poisson spot in the associated controversy. We next discuss the boundary-diffraction-wave approach to calculating diffraction effects and show how it can reduce the complexity of calculating diffraction patterns. We briefly discuss a generalization of this approach that reduces the dimensionality of integrals needed to calculate the complete diffraction pattern of any order diffraction effect. We repeat earlier demonstrations of the conventional Poisson spot and discuss an experimental setup for demonstrating an analogous phenomenon that we call a “second-order Poisson spot.” Several features of the diffraction pattern can be explained simply by considering the path lengths of singly and doubly bent paths and distinguishing between first- and second-order diffraction effects related to such paths, respectively.

An indirect algorithm for Fresnel diffraction calculation at any distance is presented in this paper. Using this indirect algorithm, the Fresnel diffraction on a near plane can be realized in two steps, the first is to acquire the diffractive field on a far field and the second is to obtain the diffractive field on a near plane using an inverse Fresnel integral. Compared with conventional algorithms, this algorithm is valid at any range of distance. The sampling theorem, as the basis of this indirect algorithm, is discussed in detail. Theoretical calculations show good agreements with experimental results.