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Register a new userA new method to subdivide a spherical surface into equal-area cells
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Authors
Zinovy Malkin
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A new method is proposed to divide a spherical surface into equal-area cells. The method is based on dividing a sphere into several latitudinal bands of near-constant span with further division of each band into equal-area cells. It is simple in construction and provides more uniform latitude step be-tween latitudinal bands than other methods of isolatitudinal equal-area tessellation of a spherical surface.
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A new method SREAG (spherical rectangular equal-area grid) is proposed to divide a spherical surface into equal-area cells. The method is based on dividing a sphere into latitudinal rings of near-constant width with further splitting each ring into equal-area cells. It is simple in construction and use, and provides more uniform width of the latitudinal rings than other methods of equal-area pixelization of a spherical surface. The new method provides a rectangular grid cells with the latitude- and longitude-oriented boundaries, near-square cells in the equatorial rings, and the closest to uniform width of the latitudinal rings as compared with other equal-area isolatitudinal grids. The binned data is easy to visualize and interpret in terms of the longitude-latitude rectangular coordinate system, natural for astronomy and geodesy. Grids with arbitrary number of rings and, consequently, wide and theoretically unlimited range of cell size can be built by the proposed method. Comparison with other methods used in astronomical research showed the advantages of the new approach in sense of uniformity of the ring width, a wider range of grid resolution, and simplicity of use.
A new method Spherical Rectangular Equal-Area Grid (SREAG) was proposed in Malkin (2019) for splitting spherical surface into equal-area rectangular cells. In this work, some more detailed features of SREAG are presented. The maximum number of rings that can be achieved with SREAG for coding with 32-bit integer is $N_{ring}$=41068, which corresponds to the finest resolution of $sim$16$$. Computational precision of the SREAG is tested. The worst level of precision is $7cdot10^{-12}$ for large $N_{ring}$. Simple expressions were derived to calculate the number of rings for the desired number of cells and for the required resolution.
A novel square equal-area map projection is proposed. The projection combines closed-form forward and inverse solutions with relatively low angular distortion and minimal cusps, a combination of properties not manifested by any previously published square equal-area projection. Thus, the new projection has lower angular distortion than any previously published square equal-area projection with a closed-form solution. Utilizing a quincuncial arrangement, the new projection places the north pole at the center of the square and divides the south pole between its four corners; the projection can be seamlessly tiled. The existence of closed-form solutions makes the projection suitable for real-time visualization applications, both in cartography and in other areas, such as for the display of panoramic images.
While gravitational waves have been detected from mergers of binary black holes and binary neutron stars, signals from core collapse supernovae, the most energetic explosions in the modern Universe, have not been detected yet. Here we present a new method to analyse the data of the LIGO, Virgo and KAGRA network to enhance the detection efficiency of this category of signals. The method takes advantage of a peculiarity of the gravitational wave signal emitted in the core collapse supernova and it is based on a classification procedure of the time-frequency images of the network data performed by a convolutional neural network trained to perform the task to recognize the signal. We validate the method using phenomenological waveforms injected in Gaussian noise whose spectral properties are those of the LIGO and Virgo advanced detectors and we conclude that this method can identify the signal better than the present algorithm devoted to select gravitational wave transient signal.
The vector vortex coronagraph (VVC) performance in the laboratory and in ground-based observatories has earned it a spot on the NASA mission concepts HabEx and LUVOIR. The VVC induces a phase ramp through the manipulation of the polarization state. Left- and right-circular polarizations get imprinted a phase ramp of opposite signs, which prevents model-based focal plane wavefront sensing and control strategies in natural light. We thus have to work with a polarization state than ensures circularly polarized light at the VVC mask. However, achieving this polarization state can be non trivial if there are optics that add phase retardance of any kind between the circular polarizer and the focal plane mask. Here we present the method currently used at the Caltech high contrast spectroscopy testbed (HCST) to achieve the proper circular polarization state for a VVC, which only uses the deformable mirror and appropriate rotation of the circular polarizer and analyzer optics. At HCST we achieve raw contrast levels of tentoe~for broadband light with a VVC.
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