851,592 research outputs found

    Cross talk for angle- and wavelength-multiiplexed image plane holograms

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    The cross talk for image plane holograms is calculated and compared with previously derived results for Fourier plane holograms. Image plane storage is found to have significantly smaller cross talk

    Architectures For Focal Plane Image Processing

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    Point Charge Dynamics Near a Grounded Conducting Plane

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    The classic image problem in electromagnetism involves a grounded infinite conducting plane and a point charge. The force of attraction between the point charge and the plane is identified using an equivalent-field picture of an image charge with opposite sign equidistant behind the plane resulting in a 1/{\it r}2^{\rm 2} force of attraction between the original charge and the plane. If the point charge is released from rest it will reach the plane in a time τ\tau. This time τ\tau has not been calculated correctly up to now. Clarification of the inconsistency is presented along with a correct solution to the classic image problem. Other electromagnetism problems are mentioned with attractive 1/{\it r}n^{\it n} forces (where {\it n} ≥\ge 1). Such situations arise between a point charge and a line charge (1/{\it r}), between a line charge and a point dipole (1/{\it r}2^{2}), between a point charge and a point dipole (1/{\it r}3)^{3}), and between a point dipole and a second point dipole (1/{\it r}4^{4}).Comment: 6 pages, 4 figure

    Tropical Quadrics Through Three Points

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    We tropicalize the rational map that takes triples of points in the projective plane to the plane of quadrics passing through these points. The image of its tropicalization is contained in the tropicalization of its image. We identify these objects inside the tropical Grassmannian of planes in projective 5-space, and we explore a small tropical Hilbert scheme.Comment: 9 pages, 3 figure
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