Extremum Values

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Alexis Carlotti - One of the best experts on this subject based on the ideXlab platform.

  • apodized phase mask coronagraphs for arbitrary apertures ii comprehensive review of solutions for the vortex coronagraph
    Astronomy and Astrophysics, 2014
    Co-Authors: Alexis Carlotti, Dimitri Mawet
    Abstract:

    Context. With a clear circular aperture, the vortex coronagraph perfectly cancels an on-axis point source and offers a 0.9 or 1.75λ/D inner working angle for topological charge 2 or 4, respectively. Current and near-future large telescopes are on-axis, however, and the diffraction effects of the central obscuration, and the secondary supports are strong enough to prevent the detection of companions 10^(-3)–10^(-5) as bright as, or fainter than, their host star. Aims. Recent advances show that a ring apodizer can restore the performance of this coronagraph by compensating for the diffraction effects of a circular central obscuration in a 1D modeling of the pupil. Our aim is to extend this work and design optimal apodizers for arbitrary apertures in 2D in order to tackle the diffraction effects of the spiders and other noncircular artifacts in the pupil. Methods. We fold this analytical result into a numerical optimization scheme that yields hybrid coronagraph designs that combine the advantages of the vortex coronagraph (small in IWA) and of shaped pupils coronagraphs (robustness to central obscuration and pupil asymmetric structures). The transmission of the apodizer is maximized, while constraints are set on the Extremum Values of the electric field that is computed in chosen regions of the Lyot plane through closed form expressions derived even for topological charges. Optimal apodizers are computed for topological charges 2 and 4 vortex coronagraphs and for telescope apertures with 10–30% central obscurations and 0%, 0.5%, and 1% thick spiders. Results. We put the results of our numerical optimizations in perspective with the analytical solutions and show that our apodizations converge to the ring apodizations. We then characterize the impacts of the obscuration ratio and the thickness of the spiders on the throughput and the IWA. For the apodized charge-2 vortex coronagraph the throughputs are slightly below those of the ring apodized vortex coronagraph, and the inner working angle is mostly unaffected by the apodization. The throughputs of the apodizers for the charge-4 vortex coronagraph are higher than those of the ring apodized vortex coronagraph. This effect increases with the obscuration ratio, though the inner working angle does, too, and it ranges between 2 and 3λ/D. Conclusions. The results presented in this paper show that high contrast at small inner working angles can be obtained with a vortex coronagraph for on-axis telescopes, in spite of the presence of a secondary mirror and its secondary support structures.

  • apodized phase mask coronagraphs for arbitrary apertures ii comprehensive review of solutions for the vortex coronagraph
    arXiv: Instrumentation and Methods for Astrophysics, 2014
    Co-Authors: Alexis Carlotti, Dimitri Mawet
    Abstract:

    With a clear circular aperture, the vortex coronagraph perfectly cancels an on-axis point source and offers a 0.9 or 1.75 lambda/D inner working angle for topological charge 2 or 4, respectively. Current and near-future large telescopes are on-axis, however, and the diffraction effects of the central obscuration, and the secondary supports are strong enough to prevent the detection of companions 1e-3 - 1e-5 as bright as, or fainter than, their host star. Recent advances show that a ring apodizer can restore the performance of this coronagraph by compensating for the diffraction effects of a circular central obscuration in a 1D modeling of the pupil. We extend this work and optimize apodizers for arbitrary apertures in 2D in order to tackle the diffraction effects of the spiders and other noncircular artefacts in the pupil. We use a numerical optimization scheme to compute hybrid coronagraph designs that combine the advantages of the vortex coronagraph (small in IWA) and of shaped pupils coronagraphs (robustness to central obscuration and pupil asymmetric structures). We maximize the apodizer transmission, while constraints are set on the Extremum Values of the electric field that is computed in chosen regions of the Lyot plane through closed form expressions. Optimal apodizers are computed for topological charges 2 and 4 vortex coronagraphs and for telescope apertures with 10-30% central obscurations and 0-1% thick spiders. We characterize the impacts of the obscuration ratio and the thickness of the spiders on the throughput and the IWA for the two topological charges.

  • apodized phase mask coronagraphs for arbitrary apertures
    Astronomy and Astrophysics, 2013
    Co-Authors: Alexis Carlotti
    Abstract:

    Phase masks coronagraphs can be seen as linear systems that spatially redistribute, in the pupil plane, the energy collected by the telescope. Most of the on-axis light must ideally be rejected outside the aperture to be blocked with a Lyot stop, while almost all off-axis light must go through it. The unobstructed circular apertures of off-axis telescopes make this possible but all major telescopes are however on-axis and the performance of these coronagraphs is dramatically reduced by the central obstruction. Their performance can be restored by using an additional optimally designed apodizer that changes the amplitude in the first pupil plane so that the on-axis light is rejected outside the obstructed aperture of the telescope. The numerical optimization model is built by maximizing the apodizer's transmission while setting constraints on the Extremum Values of the electric field that the Lyot stop does not block. The coronagraphic image is compared to what a non-apodized phase mask coronagraph provides and an analysis is made of the trade-offs that exist between the apodizer transmission and the Lyot stop properties. The existence of a solution and the mask transmission depend on the aperture and the Lyot stop geometries, and on the constraints that are set on the on-axis attenuation. The system throughput is a concave function of the Lyot stop transmission. In the case of a VLT-like aperture, apodizers with a transmission of 0.16 to 0.92 associated with a four-quadrant phase mask provide contrast as low as a few 1e-10 at 1 lambda/D from the star. The system's maximum throughput is 0.64, for an apodizer with an 0.88 transmission and a Lyot stop with a 0.69 transmission. Optimizing apodizers for a vortex phase mask requires computation times much longer than in the previous case, and no result is presented for this mask.

  • apodized phase mask coronagraphs for arbitrary apertures
    Astronomy and Astrophysics, 2013
    Co-Authors: Alexis Carlotti
    Abstract:

    Context. With a clear circular aperture, the vortex coronagraph perfectly cancels an on-axis point source and offers a 0.9 or 1.75λ/D inner working angle for topological charge 2 or 4, respectively. Current and near-future large telescopes are on-axis, however, and the diffraction effects of the central obscuration, and the secondary supports are strong enough to prevent the detection of companions 10−3–10−5 as bright as, or fainter than, their host star. Aims. Recent advances show that a ring apodizer can restore the performance of this coronagraph by compensating for the diffraction effects of a circular central obscuration in a 1D modeling of the pupil. Our aim is to extend this work and design optimal apodizers for arbitrary apertures in 2D in order to tackle the diffraction effects of the spiders and other noncircular artifacts in the pupil. Methods. We fold this analytical result into a numerical optimization scheme that yields hybrid coronagraph designs that combine the advantages of the vortex coronagraph (small in IWA) and of shaped pupils coronagraphs (robustness to central obscuration and pupil asymmetric structures). The transmission of the apodizer is maximized, while constraints are set on the Extremum Values of the electric field that is computed in chosen regions of the Lyot plane through closed form expressions derived even for topological charges. Optimal apodizers are computed for topological charges 2 and 4 vortex coronagraphs and for telescope apertures with 10–30% central obscurations and 0%, 0.5%, and 1% thick spiders. Results. We put the results of our numerical optimizations in perspective with the analytical solutions and show that our apodizations converge to the ring apodizations. We then characterize the impacts of the obscuration ratio and the thickness of the spiders on the throughput and the IWA. For the apodized charge-2 vortex coronagraph the throughputs are slightly below those of the ring apodized vortex coronagraph, and the inner working angle is mostly unaffected by the apodization. The throughputs of the apodizers for the charge-4 vortex coronagraph are higher than those of the ring apodized vortex coronagraph. This effect increases with the obscuration ratio, though the inner working angle does, too, and it ranges between 2 and 3λ/D. Conclusions. The results presented in this paper show that high contrast at small inner working angles can be obtained with a vortex coronagraph for on-axis telescopes, in spite of the presence of a secondary mirror and its secondary support structures.

Gerard A Maugin - One of the best experts on this subject based on the ideXlab platform.

  • defects in gradient micropolar elasticity ii edge dislocation and wedge disclination
    Journal of The Mechanics and Physics of Solids, 2004
    Co-Authors: Markus Lazar, Gerard A Maugin
    Abstract:

    Abstract A theory of gradient micropolar elasticity based on first gradients of distortion and bend–twist tensors for an isotropic micropolar medium has been proposed in Part I of this paper. Gradient micropolar elasticity is an extension of micropolar elasticity such that in addition to double stresses double couple stresses also appear. The strain energy depends on the micropolar distortion and bend–twist terms as well as on distortion and bend–twist gradients. We use a version of this gradient theory which can be connected to Eringen's nonlocal micropolar elasticity. The theory is used to study a straight-edge dislocation and a straight-wedge disclination. As one important result, we obtained nonsingular expressions for the force and couple stresses. For the edge dislocation the components of the force stress have Extremum Values near the dislocation line and those of the couple stress have Extremum Values at the dislocation line and for the wedge disclination the components of the force stress have Extremum Values at the disclination line and those of the couple stress have Extremum Values near the disclination line.

  • defects in gradient micropolar elasticity ii edge dislocation and wedge disclination
    Journal of The Mechanics and Physics of Solids, 2004
    Co-Authors: Markus Lazar, Gerard A Maugin
    Abstract:

    Abstract A theory of gradient micropolar elasticity based on first gradients of distortion and bend–twist tensors for an isotropic micropolar medium has been proposed in Part I of this paper. Gradient micropolar elasticity is an extension of micropolar elasticity such that in addition to double stresses double couple stresses also appear. The strain energy depends on the micropolar distortion and bend–twist terms as well as on distortion and bend–twist gradients. We use a version of this gradient theory which can be connected to Eringen's nonlocal micropolar elasticity. The theory is used to study a straight-edge dislocation and a straight-wedge disclination. As one important result, we obtained nonsingular expressions for the force and couple stresses. For the edge dislocation the components of the force stress have Extremum Values near the dislocation line and those of the couple stress have Extremum Values at the dislocation line and for the wedge disclination the components of the force stress have Extremum Values at the disclination line and those of the couple stress have Extremum Values near the disclination line.

Markus Lazar - One of the best experts on this subject based on the ideXlab platform.

  • defects in gradient micropolar elasticity ii edge dislocation and wedge disclination
    Journal of The Mechanics and Physics of Solids, 2004
    Co-Authors: Markus Lazar, Gerard A Maugin
    Abstract:

    Abstract A theory of gradient micropolar elasticity based on first gradients of distortion and bend–twist tensors for an isotropic micropolar medium has been proposed in Part I of this paper. Gradient micropolar elasticity is an extension of micropolar elasticity such that in addition to double stresses double couple stresses also appear. The strain energy depends on the micropolar distortion and bend–twist terms as well as on distortion and bend–twist gradients. We use a version of this gradient theory which can be connected to Eringen's nonlocal micropolar elasticity. The theory is used to study a straight-edge dislocation and a straight-wedge disclination. As one important result, we obtained nonsingular expressions for the force and couple stresses. For the edge dislocation the components of the force stress have Extremum Values near the dislocation line and those of the couple stress have Extremum Values at the dislocation line and for the wedge disclination the components of the force stress have Extremum Values at the disclination line and those of the couple stress have Extremum Values near the disclination line.

  • defects in gradient micropolar elasticity ii edge dislocation and wedge disclination
    Journal of The Mechanics and Physics of Solids, 2004
    Co-Authors: Markus Lazar, Gerard A Maugin
    Abstract:

    Abstract A theory of gradient micropolar elasticity based on first gradients of distortion and bend–twist tensors for an isotropic micropolar medium has been proposed in Part I of this paper. Gradient micropolar elasticity is an extension of micropolar elasticity such that in addition to double stresses double couple stresses also appear. The strain energy depends on the micropolar distortion and bend–twist terms as well as on distortion and bend–twist gradients. We use a version of this gradient theory which can be connected to Eringen's nonlocal micropolar elasticity. The theory is used to study a straight-edge dislocation and a straight-wedge disclination. As one important result, we obtained nonsingular expressions for the force and couple stresses. For the edge dislocation the components of the force stress have Extremum Values near the dislocation line and those of the couple stress have Extremum Values at the dislocation line and for the wedge disclination the components of the force stress have Extremum Values at the disclination line and those of the couple stress have Extremum Values near the disclination line.

Dimitri Mawet - One of the best experts on this subject based on the ideXlab platform.

  • apodized phase mask coronagraphs for arbitrary apertures ii comprehensive review of solutions for the vortex coronagraph
    Astronomy and Astrophysics, 2014
    Co-Authors: Alexis Carlotti, Dimitri Mawet
    Abstract:

    Context. With a clear circular aperture, the vortex coronagraph perfectly cancels an on-axis point source and offers a 0.9 or 1.75λ/D inner working angle for topological charge 2 or 4, respectively. Current and near-future large telescopes are on-axis, however, and the diffraction effects of the central obscuration, and the secondary supports are strong enough to prevent the detection of companions 10^(-3)–10^(-5) as bright as, or fainter than, their host star. Aims. Recent advances show that a ring apodizer can restore the performance of this coronagraph by compensating for the diffraction effects of a circular central obscuration in a 1D modeling of the pupil. Our aim is to extend this work and design optimal apodizers for arbitrary apertures in 2D in order to tackle the diffraction effects of the spiders and other noncircular artifacts in the pupil. Methods. We fold this analytical result into a numerical optimization scheme that yields hybrid coronagraph designs that combine the advantages of the vortex coronagraph (small in IWA) and of shaped pupils coronagraphs (robustness to central obscuration and pupil asymmetric structures). The transmission of the apodizer is maximized, while constraints are set on the Extremum Values of the electric field that is computed in chosen regions of the Lyot plane through closed form expressions derived even for topological charges. Optimal apodizers are computed for topological charges 2 and 4 vortex coronagraphs and for telescope apertures with 10–30% central obscurations and 0%, 0.5%, and 1% thick spiders. Results. We put the results of our numerical optimizations in perspective with the analytical solutions and show that our apodizations converge to the ring apodizations. We then characterize the impacts of the obscuration ratio and the thickness of the spiders on the throughput and the IWA. For the apodized charge-2 vortex coronagraph the throughputs are slightly below those of the ring apodized vortex coronagraph, and the inner working angle is mostly unaffected by the apodization. The throughputs of the apodizers for the charge-4 vortex coronagraph are higher than those of the ring apodized vortex coronagraph. This effect increases with the obscuration ratio, though the inner working angle does, too, and it ranges between 2 and 3λ/D. Conclusions. The results presented in this paper show that high contrast at small inner working angles can be obtained with a vortex coronagraph for on-axis telescopes, in spite of the presence of a secondary mirror and its secondary support structures.

  • apodized phase mask coronagraphs for arbitrary apertures ii comprehensive review of solutions for the vortex coronagraph
    arXiv: Instrumentation and Methods for Astrophysics, 2014
    Co-Authors: Alexis Carlotti, Dimitri Mawet
    Abstract:

    With a clear circular aperture, the vortex coronagraph perfectly cancels an on-axis point source and offers a 0.9 or 1.75 lambda/D inner working angle for topological charge 2 or 4, respectively. Current and near-future large telescopes are on-axis, however, and the diffraction effects of the central obscuration, and the secondary supports are strong enough to prevent the detection of companions 1e-3 - 1e-5 as bright as, or fainter than, their host star. Recent advances show that a ring apodizer can restore the performance of this coronagraph by compensating for the diffraction effects of a circular central obscuration in a 1D modeling of the pupil. We extend this work and optimize apodizers for arbitrary apertures in 2D in order to tackle the diffraction effects of the spiders and other noncircular artefacts in the pupil. We use a numerical optimization scheme to compute hybrid coronagraph designs that combine the advantages of the vortex coronagraph (small in IWA) and of shaped pupils coronagraphs (robustness to central obscuration and pupil asymmetric structures). We maximize the apodizer transmission, while constraints are set on the Extremum Values of the electric field that is computed in chosen regions of the Lyot plane through closed form expressions. Optimal apodizers are computed for topological charges 2 and 4 vortex coronagraphs and for telescope apertures with 10-30% central obscurations and 0-1% thick spiders. We characterize the impacts of the obscuration ratio and the thickness of the spiders on the throughput and the IWA for the two topological charges.

Paolo Lazzeretti - One of the best experts on this subject based on the ideXlab platform.

  • electric dipole magnetic dipole polarizability and anapole magnetizability of hydrogen peroxide as functions of the hooh dihedral angle
    Journal of Physical Chemistry A, 2017
    Co-Authors: Stefano Pelloni, Patricio Federico Provasi, G. I. Pagola, Marta B. Ferraro, Paolo Lazzeretti
    Abstract:

    The trace of tensors that account for chiroptical response of the H2O2 molecule is a function of the HO–OH dihedral angle. It vanishes at 0° and 180°, due to the presence of molecular symmetry planes, but also for Values in the range 90–100° of this angle, in which the molecule is unquestionably chiral. Such an atypical effect is caused by counterbalancing contributions of diagonal tensor components with nearly maximal magnitude but opposite sign, determined by electron flow in open or closed helical paths, and associated with induced electric and magnetic dipole moments and anapole moments. For Values of dihedral angle external to the 90–100° interval, the helical paths become smaller in size, thus reducing the amount of cancellation among diagonal components. Shrinking of helical paths determines the appearance of Extremum Values of tensor traces approximately at 50° and 140° dihedral angles.