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Variable-Step Frequency Integration in the Decade/Century-Band Imaging

This abstract presents a novel approach to frequency integration in the context of decade/century band imaging, introduced at the SKA Japan Workshop. We propose a variable-step frequency integration method to mitigate frequency integration issues, resulting in sharper synthesized beams and images. Through simulations, our method demonstrates improved point distribution and reduced bandwidth effects, essential for detecting low-flux sources. The findings suggest that this technique could significantly enhance image quality in radio astronomy applications.

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Variable-Step Frequency Integration in the Decade/Century-Band Imaging

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  1. Variable-Step Frequency Integration in the Decade/Century-Band Imaging 2010 Nov 4-5 SKA Japan Workshop @ Mitaka Tomoharu Kurayama (Kagoshima Univ.) SKA Japan Workshop

  2. Abstract In decade/century-band imaging, we have a problem in the frequency integration. We propose the variable-step frequency integration in order to minimize this problem. From the simple simulation, synthesized beams and images become more sharp in the variable-step frequency integration. SKA Japan Workshop

  3. Synthesis Imaging • Visibilities • (Observables) • Image • Fourier Transform I(l,m) V(u,v) dec m l v u RA • (Taylor, Carilli & Perleyed. 1999) Synthesized images are Fourier transforms of visibilities on (u, v) planes. SKA Japan Workshop

  4. Integration for Weak Sources • sensitivity • Integration of images • Integration of visibilities V3(u,v) I3(l,m) V2(u,v) I2(l,m) V1(u,v) I1(l,m) dec m l v u frequency RA frequency We can detect low-flux sources by integrating frequency points. SKA Japan Workshop

  5. Current Data Analysis Making images with Fourier transform V3(u,v) V(u,v) V2(u,v) I(l,m) V1(u,v) dec m v l u v u RA Frequency-integrated visibilities Images frequency Integrating frequency points of visibilities SKA Japan Workshop

  6. What is (u, v)? • observing source • w-direction • Ly • v-direction • Lx • earth • u-direction • (u, v)s depend on frequencies! (u, v) : Projected baseline lengths in the unit of wavelengths SKA Japan Workshop

  7. Problem in Decade/Century Bands • Decade band • 22 GHz • 10 GHz • Bandwidth ~ 0.25 GHz • integrating area • 1 GHz • We can NOT ignore the effect of bandwidth in the case of decade/century band. e.g.) VERA SKA Japan Workshop

  8. Visibility Gridding • gridding • When the point distribution is more uniform, • We can get more points in the process of gridding, and • The quality of image becomes more sharp. • Requirement of FFT : • Data points are on rectangular grids • We need ‘gridding’ before Fourier transform SKA Japan Workshop

  9. (u, v) Loci and Frequency Step • The numbers of points are same for both loci. • The point distribution is more uniform when • length • area • Frequency : • : • : • Frequency : (u, v) change with the earth’s spin. The loci are ellipse if we can observe 24 hours. SKA Japan Workshop

  10. Simple Simulation • uv loci of one baseline, one frequency point • ~ 180 km • 12 stations • ~ 500 km • 12 stations • ~ 5 km • 30o S • 24 stations • north • Considering SKA… • Band : 1 – 10 GHz • 10-hour observation • Time step : 48 s • 48 stations SKA Japan Workshop

  11. (u, v) Loci of One Baseline SKA Japan Workshop

  12. (u, v) Loci of All Baselines SKA Japan Workshop

  13. Sampled Grids • 1024 grids • 462382 grids • 1024 grids • 758383 grids • Total : 1048576 grids SKA Japan Workshop

  14. Synthesized Beam • 0.371 • 0.235 • 0.109 • 0.122 • ~ 14 pixels • ~ 14 pixels • Width of main beam is smaller. • First sidelobe is slightly higher. SKA Japan Workshop

  15. Imaging Simulation : Method • model visibilities • 0 • 0 • 0 • 0 • model image • inverse Fourier transform • 0 • FT • 0 • observed image • 0 • 0 • 0 • 0 • 0 • 0 • 0 • 0 Making model visibilities with Fourier transform Picking up the grids covered by (u, v) loci Getting simulated images with inverse transform SKA Japan Workshop

  16. Imaging Simulation : Result (1) • model image • 1024 pixels • 1024 pixels • 1024 pixels SKA Japan Workshop

  17. Imaging Simulation : Result (2) • 100 pixels • model image SKA Japan Workshop

  18. Imaging Simulation : Result (3) • 25 pixels • model image SKA Japan Workshop

  19. Summary • We have proposed a new type of frequency integration for decade/century-band imaging. • Setting the frequency step as • From a simple simulation, we have found • The sampled points distribute more uniformly on (u, v) plane • Synthesized beams and images become more sharp SKA Japan Workshop

  20. Thank you! • 2010 Oct 24 Triathlon in Tokunoshima • (swim 2 km / bike 75 km / run 21 km) SKA Japan Workshop

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