First- and second-order Poisson spots

Kelly, William R.; Shirley, Eric L.; Migdall, Alan L.; Polyakov, Sergey V.; Hendrix, Kurt

doi:10.1119/1.3119181

Cited by 10 publications

(2 citation statements)

References 6 publications

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“…Therefore, the field distribution is the complement of that generated by a circular aperture and can be calculated using the Babinet principle [95][96][97][98]. In 1922, Coulson and Becknell 7 have investigated experimentally a variant of the Poisson-Arago spot [101,102] by measuring the intensity patterns generated by a disk rotated around its diagonal and illuminated by a point light source.…”

Section: C1: Cusps and Multiple Diffractionmentioning

confidence: 99%

Single-slit focusing and its representations

et al. 2017

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theory of light. Three years later he participated with his Mémoire sur la Diffraction de la Lumière in the Grand Prix of the French Academy of Sciences [2]. It was on this occasion that Siméon Poisson predicted that an opaque disc illuminated by parallel light would create a bright spot in the center of a shadow. This phenomenon was experimentally confirmed by Francois Arago and led to the victory of the wave over the particle theory. In the present article we discuss an effect related to the Poisson spot which is the onedimensional analogue of the camera obscura [3,4].Indeed, we have recently found [5] that a rectangular matter wave packet which undergoes free time evolution according to the Schrödinger equation focuses before it spreads. This phenomenon has been confirmed for light [6], water and surface plasmon waves [7]. In the present article we illustrate this effect in Wigner phase space and verify it using classical light in real space.Our article is organized as follows: in Sect. 2 we first give a brief history of the diffraction of waves, and then review several focusing effects especially those associated with the phenomenon of diffraction in time introduced in Moshinsky [8].We dedicate Sect. 3 to the discussion of the focusing of a rectangular wave packet from the point of view of the timedependent wave function. In particular, we show this effect Abstract We illustrate the phenomenon of the focusing of a freely propagating rectangular wave packet using three different tools: (1) the time-dependent wave function in position space, (2) the Wigner phase-space approach, and (3) an experiment using laser light.

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Section: C1: Cusps and Multiple Diffractionmentioning

confidence: 99%

Single-slit focusing and its representations

et al. 2017

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“…3 Our approach embodies an analog, employing x-rays, of the optical phenomenon that produces an intensity maximum, known as Poisson's spot, 4 at the center of the geometric shadow of circular opaque objects. In common with short wavelength Poisson spot techniques employing x-ray zone plates 5 or molecular beams 6 we measure the relative intensity of diffraction maxima at the center of a circular geometric shadow.…”

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High intensity x-ray diffraction in transmission mode employing an analog of Poisson’s spot

Evans

Rogers

Chan

et al. 2010

Applied Physics Letters

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Poisson's spot is a diffraction phenomenon producing an intensity maximum at the center of the geometric shadow of circular opaque objects. In an analog of the Poisson spot experiment, we show that a tubular cone of x-rays incident upon a crystalline sample produces diffraction spots or foci, corresponding to Bragg maxima within a transmission shadow. We discuss the beam geometry and the intensity gain recorded at the foci in transmission mode. We describe the geometric growth and decay of the foci over a linear axis with the aid of a movie sequence synchronized with the plotting of a diffractogram. The mean signal of a small central area in each successive camera image provides the intensity data for the diffractogram. © 2010 American Institute of Physics. ͓doi:10.1063/1.3514235͔The characterization and measurement of crystallographic structure are of fundamental importance in many branches of science. Angular dispersive x-ray diffraction 1 employed routinely for such analysis dominates this field. However, the coherently scattered or diffracted x-ray signatures are weaker, by orders of magnitude, in comparison with the interrogating x-ray beam. State of the art commercially available powder diffractometers may employ highly sensitive large-area detectors with high quantum efficiency and low noise operating over relatively long integration periods. 2This conventional approach is not ideal for the development of scanning techniques and direct imaging applications, which would benefit from higher intensity signals, reduced integration periods, and converging diffracted beams. In this paper we report examples of diffraction image sequences, which demonstrate the growth and collapse of x-ray foci along the symmetry axis of a tubular interrogating x-ray beam.3 Our approach embodies an analog, employing x-rays, of the optical phenomenon that produces an intensity maximum, known as Poisson's spot, 4 at the center of the geometric shadow of circular opaque objects. In common with short wavelength Poisson spot techniques employing x-ray zone plates 5 or molecular beams 6 we measure the relative intensity of diffraction maxima at the center of a circular geometric shadow. Unlike these techniques, we employ an annular zone, defined at the intersection of a tubular cone of x-rays and a crystalline sample, enabling constructive on-axis interference to form intense spots or foci. The relative intensity and distribution of the foci correspond to the Bragg maxima determined by the crystalline structure of the sample.Consideration of diffraction patterns composed of individual Debye ring contributions hypothesizes the formation of a Poisson spot analog in Fig. 1. A tubular cone of x-rays with its symmetry axis incident normally upon a planar polycrystalline sample and image plane ͑positioned on the transmission side of the sample͒ will produce a continuum of relatively inclined Debye cones resulting in planar patterns composed of elliptical rings. The resultant circular termini and spot intensity fluctuations are due to rotatio...

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