Motivation Basics Radio-Interferometry Simulator Summary Radio-Interferometry Simulation and Optimization D. Bento Department of Physics University of Lisbon - Science Faculty Astronomy and Astrophysics’s Project, 2013 Daniel Bento University of Lisbon - Science Faculty Radio-Interferometry 

Motivation Basics Radio-Interferometry Simulator Summary Outline Motivation Radioastronomy Simulation Development Basics Light and Radiation Interference Fenomena Radio-Interferometry Simulator Concept Mathematics Fourier Transforms UV Projection Development and Use Results Daniel Bento University of Lisbon - Science Faculty Radio-Interferometry 

Motivation Basics Radio-Interferometry Simulator Summary Radioastronomy Outline Motivation Radioastronomy Simulation Development Basics Light and Radiation Interference Fenomena Radio-Interferometry Simulator Concept Mathematics Fourier Transforms UV Projection Development and Use Results Daniel Bento University of Lisbon - Science Faculty Radio-Interferometry 

Motivation Basics Radio-Interferometry Simulator Summary Radioastronomy Understand the basics of radioastronomy Understand the radio-interferometry technique Daniel Bento University of Lisbon - Science Faculty Radio-Interferometry 

Motivation Basics Radio-Interferometry Simulator Summary Simulation Development Outline Motivation Radioastronomy Simulation Development Basics Light and Radiation Interference Fenomena Radio-Interferometry Simulator Concept Mathematics Fourier Transforms UV Projection Development and Use Results Daniel Bento University of Lisbon - Science Faculty Radio-Interferometry 

Motivation Basics Radio-Interferometry Simulator Summary Simulation Development Build a virtual radio-interferometry simulator Study the optimization aspects for a radio-interferometry system Daniel Bento University of Lisbon - Science Faculty Radio-Interferometry 

Motivation Basics Radio-Interferometry Simulator Summary Light and Radiation Outline Motivation Radioastronomy Simulation Development Basics Light and Radiation Interference Fenomena Radio-Interferometry Simulator Concept Mathematics Fourier Transforms UV Projection Development and Use Results Daniel Bento University of Lisbon - Science Faculty Radio-Interferometry 

Motivation Basics Radio-Interferometry Simulator Summary Light and Radiation Light Spectrum visible light is only a small part of all electromagnetic spectrum Figure : electromagnetic spectrum Daniel Bento University of Lisbon - Science Faculty Radio-Interferometry 

Motivation Basics Radio-Interferometry Simulator Summary Light and Radiation Black Body Radiation which we can approach radiation emission of all bodies Figure : black body radiation (Plank distribution) Daniel Bento University of Lisbon - Science Faculty Radio-Interferometry 

Motivation Basics Radio-Interferometry Simulator Summary Interference Fenomena Outline Motivation Radioastronomy Simulation Development Basics Light and Radiation Interference Fenomena Radio-Interferometry Simulator Concept Mathematics Fourier Transforms UV Projection Development and Use Results Daniel Bento University of Lisbon - Science Faculty Radio-Interferometry 

Motivation Basics Radio-Interferometry Simulator Summary Interference Fenomena Young’s Double Slit Experiment Figure : double slit experiment Daniel Bento University of Lisbon - Science Faculty Radio-Interferometry 

Motivation Basics Radio-Interferometry Simulator Summary Interference Fenomena Some measures Figure : schematic view of 3 Daniel Bento University of Lisbon - Science Faculty Radio-Interferometry 

Motivation Basics Radio-Interferometry Simulator Summary Interference Fenomena We have... maxima: sin(θ) = mλ, m ∈ Z (1) minima: sin(θ) = (m + 1/2)λ, m ∈ Z (2) λ is the wave length if d L we can approach r1 − r2 = dsin(θ) Daniel Bento University of Lisbon - Science Faculty Radio-Interferometry 

Motivation Basics Radio-Interferometry Simulator Summary Interference Fenomena ... and Observation Figure : use of interferogram Daniel Bento University of Lisbon - Science Faculty Radio-Interferometry 

Motivation Basics Radio-Interferometry Simulator Summary Concept Outline Motivation Radioastronomy Simulation Development Basics Light and Radiation Interference Fenomena Radio-Interferometry Simulator Concept Mathematics Fourier Transforms UV Projection Development and Use Results Daniel Bento University of Lisbon - Science Faculty Radio-Interferometry 

Motivation Basics Radio-Interferometry Simulator Summary Concept Basic Radio Interferometer Figure : Schema - b is the distance between antennas, with V1 and V2 signal and θ is the angle between the source and zenite Daniel Bento University of Lisbon - Science Faculty Radio-Interferometry 

Motivation Basics Radio-Interferometry Simulator Summary Concept Another view Figure : basic radio-interferometer with the base line projection u − v The distance between antennas define the maximum angular resolution of the system θ = λ/B Daniel Bento University of Lisbon - Science Faculty Radio-Interferometry 

Motivation Basics Radio-Interferometry Simulator Summary Mathematics Outline Motivation Radioastronomy Simulation Development Basics Light and Radiation Interference Fenomena Radio-Interferometry Simulator Concept Mathematics Fourier Transforms UV Projection Development and Use Results Daniel Bento University of Lisbon - Science Faculty Radio-Interferometry 

Motivation Basics Radio-Interferometry Simulator Summary Mathematics Fourier and Periodic Functions F(u, v) = ∞ −∞ ∞ −∞ f(x, y)e−i2π(xu+yv)dxdy (3) f(x, y) = ∞ −∞ ∞ −∞ F(u, v)e−i2π(xu+yv)dudv (4) Daniel Bento University of Lisbon - Science Faculty Radio-Interferometry 

Motivation Basics Radio-Interferometry Simulator Summary Mathematics Spacial Domain and Frequency Domain Figure : 2 dimensional fourier transform Daniel Bento University of Lisbon - Science Faculty Radio-Interferometry 

Motivation Basics Radio-Interferometry Simulator Summary Mathematics Base line projection This is a representation of the u − v plan (time and frequency space) Figure : uv plan Daniel Bento University of Lisbon - Science Faculty Radio-Interferometry 

Motivation Basics Radio-Interferometry Simulator Summary Mathematics Fourier Correlation gives a function of geometrical time delay τ in time and frequency space Daniel Bento University of Lisbon - Science Faculty Radio-Interferometry 

Motivation Basics Radio-Interferometry Simulator Summary Development and Use Outline Motivation Radioastronomy Simulation Development Basics Light and Radiation Interference Fenomena Radio-Interferometry Simulator Concept Mathematics Fourier Transforms UV Projection Development and Use Results Daniel Bento University of Lisbon - Science Faculty Radio-Interferometry 

Motivation Basics Radio-Interferometry Simulator Summary Development and Use About the Application Development with Python Lots of Libraries to use Big open source community Derived from C Language Daniel Bento University of Lisbon - Science Faculty Radio-Interferometry 

Motivation Basics Radio-Interferometry Simulator Summary Development and Use Using it... Let’s demonstrate it... Daniel Bento University of Lisbon - Science Faculty Radio-Interferometry 

Motivation Basics Radio-Interferometry Simulator Summary Results Outline Motivation Radioastronomy Simulation Development Basics Light and Radiation Interference Fenomena Radio-Interferometry Simulator Concept Mathematics Fourier Transforms UV Projection Development and Use Results Daniel Bento University of Lisbon - Science Faculty Radio-Interferometry 

Motivation Basics Radio-Interferometry Simulator Summary Results Source Point Figure : Simple Source Point Daniel Bento University of Lisbon - Science Faculty Radio-Interferometry 

Motivation Basics Radio-Interferometry Simulator Summary Results Source Point Figure : Radio Galaxy Daniel Bento University of Lisbon - Science Faculty Radio-Interferometry 

Motivation Basics Radio-Interferometry Simulator Summary Results MERLIN Figure : observing source at dec 90o Daniel Bento University of Lisbon - Science Faculty Radio-Interferometry 

Motivation Basics Radio-Interferometry Simulator Summary Results MERLIN Figure : uv plan for source at dec 90o with 3 hours of rotation Daniel Bento University of Lisbon - Science Faculty Radio-Interferometry 

Motivation Basics Radio-Interferometry Simulator Summary Results MERLIN Figure : single point source output Daniel Bento University of Lisbon - Science Faculty Radio-Interferometry 

Motivation Basics Radio-Interferometry Simulator Summary Results MERLIN Figure : single point source CLEAN Daniel Bento University of Lisbon - Science Faculty Radio-Interferometry 

Motivation Basics Radio-Interferometry Simulator Summary Results VLA-A Figure : uv plan for source at 90o with no rotation Daniel Bento University of Lisbon - Science Faculty Radio-Interferometry 

Motivation Basics Radio-Interferometry Simulator Summary Results VLA-A Figure : uv plan for source at 90o with rotation Daniel Bento University of Lisbon - Science Faculty Radio-Interferometry 

Motivation Basics Radio-Interferometry Simulator Summary Results VLA-A Figure : single point source output Daniel Bento University of Lisbon - Science Faculty Radio-Interferometry 

Motivation Basics Radio-Interferometry Simulator Summary Results VLA-A Figure : single point source CLEAN Daniel Bento University of Lisbon - Science Faculty Radio-Interferometry 

Motivation Basics Radio-Interferometry Simulator Summary Results VLA-A Figure : radio galaxy source output Daniel Bento University of Lisbon - Science Faculty Radio-Interferometry 

Motivation Basics Radio-Interferometry Simulator Summary Results VLA-D Figure : uv plan for source at 90o with rotation Daniel Bento University of Lisbon - Science Faculty Radio-Interferometry 

Motivation Basics Radio-Interferometry Simulator Summary Results VLA-D Figure : single point source output Daniel Bento University of Lisbon - Science Faculty Radio-Interferometry 

Motivation Basics Radio-Interferometry Simulator Summary Results VLA-D Figure : single point source CLEAN Daniel Bento University of Lisbon - Science Faculty Radio-Interferometry 

Motivation Basics Radio-Interferometry Simulator Summary Results VLA-D Figure : radio galaxy source output Daniel Bento University of Lisbon - Science Faculty Radio-Interferometry 

Motivation Basics Radio-Interferometry Simulator Summary Results VLA-(A+D) Figure : uv plan for source at 90o with rotation Daniel Bento University of Lisbon - Science Faculty Radio-Interferometry 

Motivation Basics Radio-Interferometry Simulator Summary Results VLA-(A+D) Figure : radio galaxy source output Daniel Bento University of Lisbon - Science Faculty Radio-Interferometry 

Motivation Basics Radio-Interferometry Simulator Summary Results VLA-(A+D) Figure : radio galaxy source CLEAN Daniel Bento University of Lisbon - Science Faculty Radio-Interferometry 

Motivation Basics Radio-Interferometry Simulator Summary Summary The coverage of u − v plan defines the quality of the final result The length of the base line defines the maximum angular resolution Primary Beam for each antenna should be included in simulation New projects are comming with a lot of new science to do Daniel Bento University of Lisbon - Science Faculty Radio-Interferometry 

Appendix For Further Reading For Further Reading I Diane Fisher Miller Basics of Radio Astronomy for the Goldstone-Apple Valley Radio Telescope JPL - Advanced Mission Operations Section Dale E. Gary Introduction to Radio Astronomy NJIT Samer Atiani Constructing a Radio Interferometer Faculty of Guilford College Sándor Frey Radio Interferometry - Brief history, theory & practice Institute of Geodesy, Cartography and Remote Sensing Daniel Bento University of Lisbon - Science Faculty Radio-Interferometry 

Appendix For Further Reading For Further Reading II Jamie Stevens Interferometry I - Parkes Radio School 2011 CSIRO J. Condon and S. Ransom ITN 215212: Black Hole Universe NRAO Mike Garrett Radio Astronomy - Basics of radio interferometer & Aperture Synthesis MSc. course Devaky Kunneriath Introduction to Radio Interferometry ALMA Hagit Shatkay The Fourier Transform - A Primer Department of Computer Science Brown University Daniel Bento University of Lisbon - Science Faculty Radio-Interferometry 

Appendix For Further Reading For Further Reading III Forrest M. Hoffman An Introduction to Fourier Theroy Daniel Bento University of Lisbon - Science Faculty Radio-Interferometry