Fourier Transforms in Radio Astronomy

Size: px
Start display at page:

Download "Fourier Transforms in Radio Astronomy"

Transcription

1 Fourier Transforms in Radio Astronomy Kavilan Moodley, UKZN Slides taken from N Gupta s lectures: SKA School 2013

2 van-cittert Zernike theorem Extended, quasi-monochromatic, incoherent source X (l,m) Y Field at P 1 and P 2 due to an element at (l,m): to (l,m) P 1 P 2 y x (Thompson, Moran & Swenson)

3 van-cittert Zernike theorem The complex correlation at P 1 and P 2 for zero time offset: * I(l,m) small wrt receiver BW -1 u=(x 2 -x 1 )!/c v=(y 2 -y 1 )!/c (R 2 -R 1 )=(ul+vm)c/! R 2 R 1 = R V(u,v) I(l,m) (Thompson, Moran & Swenson)

4 I(l,m) is real; V(u,v) is Hermitian. Hermitian function Re f(x) Im f(x) f(x) = f*(-x)! f(x) = E(x) + i O(x) Real part is even;! Imag part is odd. Since V(u,v) is hermitian we measure only half of the (u,v)- plane and fill the other half with the complex conjugates. V(u,v) = V*(-u,-v)

5 V(u,v) FT I(l,m) I(l,m) is real; V(u,v) is Hermitian.

6 (u,v) -plane (u,v) tracks as ellipses (Thompson, Moran & Swenson)

7 (u,v) -plane (u,v) tracks as ellipses Holes correspond to missing information. (Thompson, Moran & Swenson)

8 Image reconstruction: phase vs amplitude

9 Digital images: Quantization Lim (1990)

10 Digital images: Pixelization Lim (1990)

11 Phase/amplitude-only synthesis? Lim (1990)

12 Phase/amplitude-only synthesis Lim (1990)

13 Phase/amplitude-only synthesis (Taylor, C. A. & Lipson, H., Optical Transforms, Bell, London 1964)

14 Phase/amplitude-only synthesis Duck (Amplitude) + Cat (Phase) Cat (Amplitude) + Duck (Phase) (Taylor, C. A. & Lipson, H., Optical Transforms, Bell, London 1964)

15 Amplitude: magnitude of the spatial frequency.! Phase: it s location.

16 Image analysis Lim (1990)

17 Image reconstruction: a few components required 12% 5% Lim (1990)

18 Sampling V(u,v)

19 Nyquist rate Any continuous band-limited signal can be reconstructed if sampled at the Nyquist rate. Sampling rate = 1/2f Higher frequency components will be aliased to the lower frequencies in the sampled band.

20 Sampling V(u,v) V(u) III(u/!u)= (u-i!u) o!u u o o o o o o 1/!u l If adequately sampled convolution with sinc provides exact interpolation of the original function from the samples. (Thompson, Moran & Swenson)

21 Under-Sampling: Aliasing V(u) III(u/!u)= (u-i!u) u l If aliasing is avoided convolution with sinc provides exact interpolation of the original function from the samples. (Thompson, Moran & Swenson)

22 Fast Fourier Transform: V(u, v) - I(l,m) Faster.! Requires data on uniform grid.! Gridding to resample V(u,v).

23 Fast Fourier Transform: Image domain Holes correspond to missing information.! Longest baseline: limit on resolution! Inner hole: no information on large scales (Thompson, Moran & Swenson) Pixel size: 1/(2u max ), 1/(2v max ) i.e. satisfy sampling theorem.

24 Fast Fourier Transform: Image domain Image size: whole primary beam; sources in the side lobe will be aliased back. Solution: make larger image! (Thompson, Moran & Swenson)

25 Errors in V(u,v)

26 Effect of Amplitude error (Thomson, Moran & Swenson)

27 Taylor et al. lecture (NRAO Synthesis Imaging School 2012)

28 Taylor et al. lecture (NRAO Synthesis Imaging School 2012)

29 V (obs) = G ij V(true) -Observing set-up! -bad data.! poor calibration/! baseline-based errors

30 Diffuse extended emission 1) Weighting: surface brightness sensitivity! 2) Masking: deconvolution & flux density! (Flux calculated correctly for cleaned map.).! (Briggs et al. 1999)

31 Emission at various scales.! (Konar et al. 2006)

32 Emission at various scales.! 80x63 mas Heavier Gaussian taper 36x33 mas Momjian et al. 2003

33 Summary V(u,v) I(l,m)! Radio interferometer samples V(u, v): fourier transform to get image.! Fourier transforms also useful in identifying problems.! Use Flagging, Gridding and Weighting of the visibility to get appropriate image. References and further reading Bracewell: The Fourier Transform and its applications.! Thompson, Moran & Swenson: Interferometry and.! Synthesis in Radio Astronomy.! Synthesis Imaging in Radio Astronomy II: the NRAO lecture series.

34 END - PART I1

Introduction to Imaging in CASA

Introduction to Imaging in CASA Introduction to Imaging in CASA Mark Rawlings, Juergen Ott (NRAO) Atacama Large Millimeter/submillimeter Array Expanded Very Large Array Robert C. Byrd Green Bank Telescope Very Long Baseline Array Overview

More information

The Basics of Radio Interferometry. Frédéric Boone LERMA, Observatoire de Paris

The Basics of Radio Interferometry. Frédéric Boone LERMA, Observatoire de Paris The Basics of Radio Interferometry LERMA, Observatoire de Paris The Basics of Radio Interferometry The role of interferometry in astronomy = role of venetian blinds in Film Noir 2 The Basics of Radio Interferometry

More information

INTERFEROMETRY: II Nissim Kanekar (NCRA TIFR)

INTERFEROMETRY: II Nissim Kanekar (NCRA TIFR) INTERFEROMETRY: II Nissim Kanekar (NCRA TIFR) WSRT GMRT VLA ATCA ALMA SKA MID PLAN Introduction. The van Cittert Zernike theorem. A 2 element interferometer. The fringe pattern. 2 D and 3 D interferometers.

More information

Introduction to Interferometry. Michelson Interferometer. Fourier Transforms. Optics: holes in a mask. Two ways of understanding interferometry

Introduction to Interferometry. Michelson Interferometer. Fourier Transforms. Optics: holes in a mask. Two ways of understanding interferometry Introduction to Interferometry P.J.Diamond MERLIN/VLBI National Facility Jodrell Bank Observatory University of Manchester ERIS: 5 Sept 005 Aim to lay the groundwork for following talks Discuss: General

More information

Basic Mapping Simon Garrington JBO/Manchester

Basic Mapping Simon Garrington JBO/Manchester Basic Mapping Simon Garrington JBO/Manchester Introduction Output from radio arrays (VLA, VLBI, MERLIN etc) is just a table of the correlation (amp. & phase) measured on each baseline every few seconds.

More information

Interferometry I Parkes Radio School Jamie Stevens ATCA Senior Systems Scientist

Interferometry I Parkes Radio School Jamie Stevens ATCA Senior Systems Scientist Interferometry I Parkes Radio School 2011 Jamie Stevens ATCA Senior Systems Scientist 2011-09-28 References This talk will reuse material from many previous Radio School talks, and from the excellent textbook

More information

Introduction to Radio Interferometry Sabrina Stierwalt Alison Peck, Jim Braatz, Ashley Bemis

Introduction to Radio Interferometry Sabrina Stierwalt Alison Peck, Jim Braatz, Ashley Bemis Introduction to Radio Interferometry Sabrina Stierwalt Alison Peck, Jim Braatz, Ashley Bemis Atacama Large Millimeter/submillimeter Array Expanded Very Large Array Robert C. Byrd Green Bank Telescope Very

More information

Fundamentals of Radio Interferometry

Fundamentals of Radio Interferometry Fundamentals of Radio Interferometry Rick Perley, NRAO/Socorro Fourteenth NRAO Synthesis Imaging Summer School Socorro, NM Topics Why Interferometry? The Single Dish as an interferometer The Basic Interferometer

More information

2D Discrete Fourier Transform

2D Discrete Fourier Transform 2D Discrete Fourier Transform In these lecture notes the figures have been removed for copyright reasons. References to figures are given instead, please check the figures yourself as given in the course

More information

Fundamentals of Radio Interferometry

Fundamentals of Radio Interferometry Fundamentals of Radio Interferometry Rick Perley, NRAO/Socorro ATNF Radio Astronomy School Narrabri, NSW 29 Sept. 03 Oct. 2014 Topics Introduction: Sensors, Antennas, Brightness, Power Quasi-Monochromatic

More information

Deconvolution. Amy Mioduszewski National Radio Astronomy Observatory. Synthesis Imaging g in Radio Astronomy

Deconvolution. Amy Mioduszewski National Radio Astronomy Observatory. Synthesis Imaging g in Radio Astronomy Deconvolution Amy Mioduszewski National Radio Astronomy Observatory Synthesis Imaging g in Radio Astronomy (based on a talk given by David Wilner (CfA) at the NRAO s 2010 Synthesis Imaging Workshop) 1

More information

Introduction to Radio Interferometry Anand Crossley Alison Peck, Jim Braatz, Ashley Bemis (NRAO)

Introduction to Radio Interferometry Anand Crossley Alison Peck, Jim Braatz, Ashley Bemis (NRAO) Introduction to Radio Interferometry Anand Crossley Alison Peck, Jim Braatz, Ashley Bemis (NRAO) Atacama Large Millimeter/submillimeter Array Expanded Very Large Array Robert C. Byrd Green Bank Telescope

More information

Large-field imaging. Frédéric Gueth, IRAM Grenoble. 7th IRAM Millimeter Interferometry School 4 8 October 2010

Large-field imaging. Frédéric Gueth, IRAM Grenoble. 7th IRAM Millimeter Interferometry School 4 8 October 2010 Large-field imaging Frédéric Gueth, IRAM Grenoble 7th IRAM Millimeter Interferometry School 4 8 October 2010 Large-field imaging The problems The field of view is limited by the antenna primary beam width

More information

Fundamentals of Interferometry

Fundamentals of Interferometry Fundamentals of Interferometry ERIS, Rimini, Sept 5-9 2011 Outline What is an interferometer? Basic theory Interlude: Fourier transforms for birdwatchers Review of assumptions and complications Interferometers

More information

Fundamentals of Interferometry

Fundamentals of Interferometry Fundamentals of Interferometry ERIS, Dwingeloo, Sept 8-13 2013 Outline What is an interferometer? Basic theory Interlude: Fourier transforms for birdwatchers Review of assumptions and complications Interferometers

More information

Image-Domain Gridding on Accelerators

Image-Domain Gridding on Accelerators Netherlands Institute for Radio Astronomy Image-Domain Gridding on Accelerators Bram Veenboer Monday 26th March, 2018, GPU Technology Conference 2018, San Jose, USA ASTRON is part of the Netherlands Organisation

More information

Phased Array Feeds & Primary Beams

Phased Array Feeds & Primary Beams Phased Array Feeds & Primary Beams Aidan Hotan ASKAP Deputy Project Scientist 3 rd October 2014 CSIRO ASTRONOMY AND SPACE SCIENCE Outline Review of parabolic (dish) antennas. Focal plane response to a

More information

Phased Array Feeds A new technology for multi-beam radio astronomy

Phased Array Feeds A new technology for multi-beam radio astronomy Phased Array Feeds A new technology for multi-beam radio astronomy Aidan Hotan ASKAP Deputy Project Scientist 2 nd October 2015 CSIRO ASTRONOMY AND SPACE SCIENCE Outline Review of radio astronomy concepts.

More information

Introduction to interferometry with bolometers: Bob Watson and Lucio Piccirillo

Introduction to interferometry with bolometers: Bob Watson and Lucio Piccirillo Introduction to interferometry with bolometers: Bob Watson and Lucio Piccirillo Paris, 19 June 2008 Interferometry (heterodyne) In general we have i=1,...,n single dishes (with a single or dual receiver)

More information

Radio Astronomy: SKA-Era Interferometry and Other Challenges. Dr Jasper Horrell, SKA SA (and Dr Oleg Smirnov, Rhodes and SKA SA)

Radio Astronomy: SKA-Era Interferometry and Other Challenges. Dr Jasper Horrell, SKA SA (and Dr Oleg Smirnov, Rhodes and SKA SA) Radio Astronomy: SKA-Era Interferometry and Other Challenges Dr Jasper Horrell, SKA SA (and Dr Oleg Smirnov, Rhodes and SKA SA) ASSA Symposium, Cape Town, Oct 2012 Scope SKA antenna types Single dishes

More information

Aliasing and Antialiasing. What is Aliasing? What is Aliasing? What is Aliasing?

Aliasing and Antialiasing. What is Aliasing? What is Aliasing? What is Aliasing? What is Aliasing? Errors and Artifacts arising during rendering, due to the conversion from a continuously defined illumination field to a discrete raster grid of pixels 1 2 What is Aliasing? What is Aliasing?

More information

Imaging Simulations with CARMA-23

Imaging Simulations with CARMA-23 BIMA memo 101 - July 2004 Imaging Simulations with CARMA-23 M. C. H. Wright Radio Astronomy laboratory, University of California, Berkeley, CA, 94720 ABSTRACT We simulated imaging for the 23-antenna CARMA

More information

Principles of Radio Interferometry. Ast735: Submillimeter Astronomy IfA, University of Hawaii

Principles of Radio Interferometry. Ast735: Submillimeter Astronomy IfA, University of Hawaii Principles of Radio Interferometry Ast735: Submillimeter Astronomy IfA, University of Hawaii 1 Resources IRAM millimeter interferometry school hdp://www.iram- inshtute.org/en/content- page- 248-7- 67-248-

More information

Practicalities of Radio Interferometry

Practicalities of Radio Interferometry Practicalities of Radio Interferometry Rick Perley, NRAO/Socorro 13 th Synthesis Imaging Summer School 29 May 5 June, 2012 Socorro, NM Topics Practical Extensions to the Theory: Finite bandwidth Rotating

More information

ECE 484 Digital Image Processing Lec 10 - Image Restoration I

ECE 484 Digital Image Processing Lec 10 - Image Restoration I ECE 484 Digital Image Processing Lec 10 - Image Restoration I Zhu Li Dept of CSEE, UMKC Office: FH560E, Email: lizhu@umkc.edu, Ph: x 2346. http://l.web.umkc.edu/lizhu slides created with WPS Office Linux

More information

Cross Correlators. Jayce Dowell/Greg Taylor. University of New Mexico Spring Astronomy 423 at UNM Radio Astronomy

Cross Correlators. Jayce Dowell/Greg Taylor. University of New Mexico Spring Astronomy 423 at UNM Radio Astronomy Cross Correlators Jayce Dowell/Greg Taylor University of New Mexico Spring 2017 Astronomy 423 at UNM Radio Astronomy Outline 2 Re-cap of interferometry What is a correlator? The correlation function Simple

More information

Next Generation Very Large Array Memo No. 47 Resolution and Sensitivity of ngvla-revb. C.L. Carilli (NRAO)

Next Generation Very Large Array Memo No. 47 Resolution and Sensitivity of ngvla-revb. C.L. Carilli (NRAO) Next Generation Very Large Array Memo No. 47 Resolution and Sensitivity of ngvla-revb C.L. Carilli (NRAO) Abstract I investigate the noise performance vs. resolution for the new ngvlarevb configuration.

More information

Next Generation Very Large Array Memo No. 16 More on Synthesized Beams and Sensitivity. C.L. Carilli, NRAO, PO Box O, Socorro, NM

Next Generation Very Large Array Memo No. 16 More on Synthesized Beams and Sensitivity. C.L. Carilli, NRAO, PO Box O, Socorro, NM Next Generation Very Large Array Memo No. 16 More on Synthesized Beams and Sensitivity C.L. Carilli, NRAO, PO Box O, Socorro, NM Abstract I present further calculations on synthesized beams and sensitivities

More information

Spectral Line II: Calibration and Analysis. Spectral Bandpass: Bandpass Calibration (cont d) Bandpass Calibration. Bandpass Calibration

Spectral Line II: Calibration and Analysis. Spectral Bandpass: Bandpass Calibration (cont d) Bandpass Calibration. Bandpass Calibration Spectral Line II: Calibration and Analysis Bandpass Calibration Flagging Continuum Subtraction Imaging Visualization Analysis Spectral Bandpass: Spectral frequency response of antenna to a spectrally flat

More information

Radio Interferometry -- II

Radio Interferometry -- II Radio Interferometry -- II Rick Perley, NRAO/Socorro ATNF School on Radio Astronomy Narrabri, NSW 29 Sept 3 Oct, 2014 Topics Practical Extensions to the Theory: Finite bandwidth Rotating reference frames

More information

Phased Array Feeds A new technology for wide-field radio astronomy

Phased Array Feeds A new technology for wide-field radio astronomy Phased Array Feeds A new technology for wide-field radio astronomy Aidan Hotan ASKAP Project Scientist 29 th September 2017 CSIRO ASTRONOMY AND SPACE SCIENCE Outline Review of radio astronomy concepts

More information

Image Scaling. This image is too big to fit on the screen. How can we reduce it? How to generate a halfsized

Image Scaling. This image is too big to fit on the screen. How can we reduce it? How to generate a halfsized Resampling Image Scaling This image is too big to fit on the screen. How can we reduce it? How to generate a halfsized version? Image sub-sampling 1/8 1/4 Throw away every other row and column to create

More information

Filters. Materials from Prof. Klaus Mueller

Filters. Materials from Prof. Klaus Mueller Filters Materials from Prof. Klaus Mueller Think More about Pixels What exactly a pixel is in an image or on the screen? Solid square? This cannot be implemented A dot? Yes, but size matters Pixel Dots

More information

Mosaicking. Brian Mason (NRAO) Sixteenth Synthesis Imaging Workshop May 2018

Mosaicking. Brian Mason (NRAO) Sixteenth Synthesis Imaging Workshop May 2018 Mosaicking Brian Mason (NRAO) Sixteenth Synthesis Imaging Workshop 16-23 May 2018 The simplest observing scenario for an interferometer: Source at known location Size

More information

Announcements. Image Processing. What s an image? Images as functions. Image processing. What s a digital image?

Announcements. Image Processing. What s an image? Images as functions. Image processing. What s a digital image? Image Processing Images by Pawan Sinha Today s readings Forsyth & Ponce, chapters 8.-8. http://www.cs.washington.edu/education/courses/49cv/wi/readings/book-7-revised-a-indx.pdf For Monday Watt,.3-.4 (handout)

More information

Wide-band Wide-field Imaging

Wide-band Wide-field Imaging Wide-band Wide-field Imaging Colloquium, Socorro, Feb. 11th 2011 S. Bhatnagar K. Golap, U. Rau, J. Robnett NRAO Algorithms R&D Group activities R&D for new post-processing algorithms required for wideband

More information

Examples of image processing

Examples of image processing Examples of image processing Example 1: We would like to automatically detect and count rings in the image 3 Detection by correlation Correlation = degree of similarity Correlation between f(x, y) and

More information

Fundamentals of Radio Interferometry. Robert Laing (ESO)

Fundamentals of Radio Interferometry. Robert Laing (ESO) Fundamentals of Radio Interferometry Robert Laing (ESO) 1 ERIS 2015 Objectives A more formal approach to radio interferometry using coherence functions A complementary way of looking at the technique Simplifying

More information

Image Processing. Image Processing. What is an Image? Image Resolution. Overview. Sources of Error. Filtering Blur Detect edges

Image Processing. Image Processing. What is an Image? Image Resolution. Overview. Sources of Error. Filtering Blur Detect edges Thomas Funkhouser Princeton University COS 46, Spring 004 Quantization Random dither Ordered dither Floyd-Steinberg dither Pixel operations Add random noise Add luminance Add contrast Add saturation ing

More information

Fundamentals of Radio Interferometry

Fundamentals of Radio Interferometry Fundamentals of Radio Interferometry Rick Perley, NRAO/Socorro 15 th Synthesis Imaging School Socorro, NM 01 09 June, 2016 Topics The Need for Interferometry Some Basics: Antennas as E-field Converters

More information

Calibration. (in Radio Astronomy) Ishwara Chandra CH NCRA-TIFR. Acknowledgments:

Calibration. (in Radio Astronomy) Ishwara Chandra CH NCRA-TIFR. Acknowledgments: Calibration (in Radio Astronomy) Ishwara Chandra CH NCRA-TIFR Acknowledgments: Synthesis Imaging in Radio Astronomy II: Chapter 5 Low Frequency Radio Astronomy (blue book): Chapter 5 Calibration and Advanced

More information

קורס גרפיקה ממוחשבת 2008 סמסטר ב' Image Processing 1 חלק מהשקפים מעובדים משקפים של פרדו דוראנד, טומס פנקהאוסר ודניאל כהן-אור

קורס גרפיקה ממוחשבת 2008 סמסטר ב' Image Processing 1 חלק מהשקפים מעובדים משקפים של פרדו דוראנד, טומס פנקהאוסר ודניאל כהן-אור קורס גרפיקה ממוחשבת 2008 סמסטר ב' Image Processing 1 חלק מהשקפים מעובדים משקפים של פרדו דוראנד, טומס פנקהאוסר ודניאל כהן-אור What is an image? An image is a discrete array of samples representing a continuous

More information

Radio Interferometer Array Point Spread Functions I. Theory and Statistics

Radio Interferometer Array Point Spread Functions I. Theory and Statistics ALMA MEMO 389 Radio Interferometer Array Point Spread Functions I. Theory and Statistics David Woody Abstract This paper relates the optical definition of the PSF to radio interferometer arrays. The statistical

More information

THEORY OF MEASUREMENTS

THEORY OF MEASUREMENTS THEORY OF MEASUREMENTS Brian Mason Fifth NAIC-NRAO School on Single-Dish Radio Astronomy Arecibo, PR July 2009 OUTLINE Antenna-Sky Coupling Noise the Radiometer Equation Minimum Tsys Performance measures

More information

REDUCTION OF ALMA DATA USING CASA SOFTWARE

REDUCTION OF ALMA DATA USING CASA SOFTWARE REDUCTION OF ALMA DATA USING CASA SOFTWARE Student: Nguyen Tran Hoang Supervisor: Pham Tuan Anh Hanoi, September - 2016 1 CONTENS Introduction Interferometry Scientific Target M100 Calibration Imaging

More information

Transforms and Frequency Filtering

Transforms and Frequency Filtering Transforms and Frequency Filtering Khalid Niazi Centre for Image Analysis Swedish University of Agricultural Sciences Uppsala University 2 Reading Instructions Chapter 4: Image Enhancement in the Frequency

More information

Radio Interferometry. Xuening Bai. AST 542 Observational Seminar May 4, 2011

Radio Interferometry. Xuening Bai. AST 542 Observational Seminar May 4, 2011 Radio Interferometry Xuening Bai AST 542 Observational Seminar May 4, 2011 Outline Single-dish radio telescope Two-element interferometer Interferometer arrays and aperture synthesis Very-long base line

More information

IMAGE PROCESSING (RRY025) THE CONTINUOUS 2D FOURIER TRANSFORM

IMAGE PROCESSING (RRY025) THE CONTINUOUS 2D FOURIER TRANSFORM IMAGE PROCESSING (RRY5) THE CONTINUOUS D FOURIER TRANSFORM INTRODUCTION A vital tool in image processing. Also a prototype of other image transforms, cosine, Wavelet etc. Applications Image Filtering -

More information

Volume 82 VERY LONG BASELINE INTERFEROMETRY AND THE VLBA. J. A. Zensus, P. J. Diamond, and P. J. Napier

Volume 82 VERY LONG BASELINE INTERFEROMETRY AND THE VLBA. J. A. Zensus, P. J. Diamond, and P. J. Napier ASTRONOMICAL SOCIETY OF THE PACIFIC CONFERENCE SERIES Volume 82 VERY LONG BASELINE INTERFEROMETRY AND THE VLBA Proceedings of a Summer School held in Socorro, New Mexico 23-30 June 1993 NRAO Workshop No.

More information

Image Sampling. Moire patterns. - Source: F. Durand

Image Sampling. Moire patterns. -  Source: F. Durand Image Sampling Moire patterns Source: F. Durand - http://www.sandlotscience.com/moire/circular_3_moire.htm Any questions on project 1? For extra credits, attach before/after images how your extra feature

More information

Wide-field, wide-band and multi-scale imaging - II

Wide-field, wide-band and multi-scale imaging - II Wide-field, wide-band and multi-scale imaging - II Radio Astronomy School 2017 National Centre for Radio Astrophysics / TIFR Pune, India 28 Aug 8 Sept, 2017 Urvashi Rau National Radio Astronomy Observatory,

More information

Chapter 4: Fourier Optics

Chapter 4: Fourier Optics Chapter 4: Fourier Optics P4-1. Calculate the Fourier transform of the function rect(2x)rect(/3) The rectangular function rect(x) is given b 1 x 1/2 rect( x) when 0 x 1/2 P4-2. Assume that ( gx (, )) G

More information

Computer Graphics (Fall 2011) Outline. CS 184 Guest Lecture: Sampling and Reconstruction Ravi Ramamoorthi

Computer Graphics (Fall 2011) Outline. CS 184 Guest Lecture: Sampling and Reconstruction Ravi Ramamoorthi Computer Graphics (Fall 2011) CS 184 Guest Lecture: Sampling and Reconstruction Ravi Ramamoorthi Some slides courtesy Thomas Funkhouser and Pat Hanrahan Adapted version of CS 283 lecture http://inst.eecs.berkeley.edu/~cs283/fa10

More information

Sideband Smear: Sideband Separation with the ALMA 2SB and DSB Total Power Receivers

Sideband Smear: Sideband Separation with the ALMA 2SB and DSB Total Power Receivers and DSB Total Power Receivers SCI-00.00.00.00-001-A-PLA Version: A 2007-06-11 Prepared By: Organization Date Anthony J. Remijan NRAO A. Wootten T. Hunter J.M. Payne D.T. Emerson P.R. Jewell R.N. Martin

More information

Wide Bandwidth Imaging

Wide Bandwidth Imaging Wide Bandwidth Imaging 14th NRAO Synthesis Imaging Workshop 13 20 May, 2014, Socorro, NM Urvashi Rau National Radio Astronomy Observatory 1 Why do we need wide bandwidths? Broad-band receivers => Increased

More information

Image Processing. What is an image? קורס גרפיקה ממוחשבת 2008 סמסטר ב' Converting to digital form. Sampling and Reconstruction.

Image Processing. What is an image? קורס גרפיקה ממוחשבת 2008 סמסטר ב' Converting to digital form. Sampling and Reconstruction. Amplitude 5/1/008 What is an image? An image is a discrete array of samples representing a continuous D function קורס גרפיקה ממוחשבת 008 סמסטר ב' Continuous function Discrete samples 1 חלק מהשקפים מעובדים

More information

Wide-Band Imaging. Outline : CASS Radio Astronomy School Sept 2012 Narrabri, NSW, Australia. - What is wideband imaging?

Wide-Band Imaging. Outline : CASS Radio Astronomy School Sept 2012 Narrabri, NSW, Australia. - What is wideband imaging? Wide-Band Imaging 24-28 Sept 2012 Narrabri, NSW, Australia Outline : - What is wideband imaging? - Two Algorithms Urvashi Rau - Many Examples National Radio Astronomy Observatory Socorro, NM, USA 1/32

More information

Last Lecture. photomatix.com

Last Lecture. photomatix.com Last Lecture photomatix.com Today Image Processing: from basic concepts to latest techniques Filtering Edge detection Re-sampling and aliasing Image Pyramids (Gaussian and Laplacian) Removing handshake

More information

Recent imaging results with wide-band EVLA data, and lessons learnt so far

Recent imaging results with wide-band EVLA data, and lessons learnt so far Recent imaging results with wide-band EVLA data, and lessons learnt so far Urvashi Rau National Radio Astronomy Observatory (USA) 26 Jul 2011 (1) Introduction : Imaging wideband data (2) Wideband Imaging

More information

Radio Interferometry -- II

Radio Interferometry -- II Radio Interferometry -- II Rick Perley, NRAO/Socorro 15 th Synthesis Imaging Summer School June 1 9, 2016 Socorro, NM Topics Practical Extensions to the Theory: Real Sensors Finite bandwidth Rotating reference

More information

Applying full polarization A-Projection to very-wide fields of view instruments: An imager for LOFAR Cyril Tasse

Applying full polarization A-Projection to very-wide fields of view instruments: An imager for LOFAR Cyril Tasse Applying full polarization A-Projection to very-wide fields of view instruments: An imager for LOFAR Cyril Tasse ASTRON/Leiden: Joris van Zwieten, Bas van der Tol, Ger van Diepen NRAO: Sanjay Bhatnagar

More information

LOFAR: From raw visibilities to calibrated data

LOFAR: From raw visibilities to calibrated data Netherlands Institute for Radio Astronomy LOFAR: From raw visibilities to calibrated data John McKean (ASTRON) [subbing in for Manu] ASTRON is part of the Netherlands Organisation for Scientific Research

More information

Atacama Large Millimeter/submillimeter Array Expanded Very Large Array Robert C. Byrd Green Bank Telescope Very Long Baseline Array

Atacama Large Millimeter/submillimeter Array Expanded Very Large Array Robert C. Byrd Green Bank Telescope Very Long Baseline Array Atacama Large Millimeter/submillimeter Array Expanded Very Large Array Robert C. Byrd Green Bank Telescope Very Long Baseline Array Basics of Interferometry Data Reduction Scott Schnee (NRAO) ALMA Data

More information

Adaptive selective sidelobe canceller beamformer with applications in radio astronomy

Adaptive selective sidelobe canceller beamformer with applications in radio astronomy Adaptive selective sidelobe canceller beamformer with applications in radio astronomy Ronny Levanda and Amir Leshem 1 Abstract arxiv:1008.5066v1 [astro-ph.im] 30 Aug 2010 We propose a new algorithm, for

More information

Pupil Planes versus Image Planes Comparison of beam combining concepts

Pupil Planes versus Image Planes Comparison of beam combining concepts Pupil Planes versus Image Planes Comparison of beam combining concepts John Young University of Cambridge 27 July 2006 Pupil planes versus Image planes 1 Aims of this presentation Beam combiner functions

More information

Spectral Line Imaging

Spectral Line Imaging ATNF Synthesis School 2003 Spectral Line Imaging Juergen Ott (ATNF) Juergen.Ott@csiro.au Topics Introduction to Spectral Lines Velocity Reference Frames Bandpass Calibration Continuum Subtraction Gibbs

More information

When, why and how to self-cal Nathan Brunetti, Crystal Brogan, Amanda Kepley

When, why and how to self-cal Nathan Brunetti, Crystal Brogan, Amanda Kepley When, why and how to self-cal Nathan Brunetti, Crystal Brogan, Amanda Kepley Atacama Large Millimeter/submillimeter Array Expanded Very Large Array Robert C. Byrd Green Bank Telescope Very Long Baseline

More information

Sampling and Pyramids

Sampling and Pyramids Sampling and Pyramids 15-463: Rendering and Image Processing Alexei Efros with lots of slides from Steve Seitz Today Sampling Nyquist Rate Antialiasing Gaussian and Laplacian Pyramids 1 Fourier transform

More information

EVLA and LWA Imaging Challenges

EVLA and LWA Imaging Challenges EVLA and LWA Imaging Challenges Steven T. Myers IGPP, Los Alamos National Laboratory and National Radio Astronomy Observatory, Socorro, NM 1 EVLA key issues 2 Key algorithmic issues ambitious goals / hard

More information

Cvision 2. António J. R. Neves João Paulo Silva Cunha. Bernardo Cunha. IEETA / Universidade de Aveiro

Cvision 2. António J. R. Neves João Paulo Silva Cunha. Bernardo Cunha. IEETA / Universidade de Aveiro Cvision 2 Digital Imaging António J. R. Neves (an@ua.pt) & João Paulo Silva Cunha & Bernardo Cunha IEETA / Universidade de Aveiro Outline Image sensors Camera calibration Sampling and quantization Data

More information

ECE 484 Digital Image Processing Lec 09 - Image Resampling

ECE 484 Digital Image Processing Lec 09 - Image Resampling ECE 484 Digital Image Processing Lec 09 - Image Resampling Zhu Li Dept of CSEE, UMKC Office: FH560E, Email: lizhu@umkc.edu, Ph: x 2346. http://l.web.umkc.edu/lizhu slides created with WPS Office Linux

More information

Error Recognition Emil Lenc (and Arin)

Error Recognition Emil Lenc (and Arin) Error Recognition Emil Lenc (and Arin) University of Sydney / CAASTRO www.caastro.org CASS Radio Astronomy School 2017 Based on lectures given previously by Ron Ekers and Steven Tingay CSIRO; Swinburne

More information

Last Lecture. photomatix.com

Last Lecture. photomatix.com Last Lecture photomatix.com HDR Video Assorted pixel (Single Exposure HDR) Assorted pixel Assorted pixel Pixel with Adaptive Exposure Control light attenuator element detector element T t+1 I t controller

More information

Practicalities of Radio Interferometry

Practicalities of Radio Interferometry Practicalities of Radio Interferometry Rick Perley, NRAO/Socorro Fourth INPE Course in Astrophysics: Radio Astronomy in the 21 st Century Topics Practical Extensions to the Theory: Finite bandwidth Rotating

More information

Interference [Hecht Ch. 9]

Interference [Hecht Ch. 9] Interference [Hecht Ch. 9] Note: Read Ch. 3 & 7 E&M Waves and Superposition of Waves and Meet with TAs and/or Dr. Lai if necessary. General Consideration 1 2 Amplitude Splitting Interferometers If a lightwave

More information

Richard Dodson 1/28/2014 NARIT-KASI Winter School

Richard Dodson 1/28/2014 NARIT-KASI Winter School Goals: Technical introduction very short So what to cover? Things which are essential: How radio power is received - I How an interferometer works -II Antenna Fundamentals Black Body Radiation Brightness

More information

Atacama Large Millimeter/submillimeter Array Expanded Very Large Array Robert C. Byrd Green Bank Telescope Very Long Baseline Array

Atacama Large Millimeter/submillimeter Array Expanded Very Large Array Robert C. Byrd Green Bank Telescope Very Long Baseline Array Atacama Large Millimeter/submillimeter Array Expanded Very Large Array Robert C. Byrd Green Bank Telescope Very Long Baseline Array Self-Calibration Ed Fomalont (NRAO) ALMA Data workshop Dec. 2, 2011 Atacama

More information

VLBI Post-Correlation Analysis and Fringe-Fitting

VLBI Post-Correlation Analysis and Fringe-Fitting VLBI Post-Correlation Analysis and Fringe-Fitting Michael Bietenholz With (many) Slides from George Moellenbroek and Craig Walker NRAO Calibration is important! What Is Delivered by a Synthesis Array?

More information

Physics 3340 Spring Fourier Optics

Physics 3340 Spring Fourier Optics Physics 3340 Spring 011 Purpose Fourier Optics In this experiment we will show how the Fraunhofer diffraction pattern or spatial Fourier transform of an object can be observed within an optical system.

More information

Sampling and Reconstruction

Sampling and Reconstruction Sampling and reconstruction COMP 575/COMP 770 Fall 2010 Stephen J. Guy 1 Review What is Computer Graphics? Computer graphics: The study of creating, manipulating, and using visual images in the computer.

More information

Error Recognition and Data Analysis

Error Recognition and Data Analysis Error Recognition and Data Analysis Greg Taylor (UNM) With help from: Urvashi Rao, Sanjay Bhatnagar, Gustaaf van Moorsel, Justin Linford, Ed Fomalont Fifteenth Synthesis Imaging Workshop 1-8 June 2016

More information

Image acquisition. Midterm Review. Digitization, line of image. Digitization, whole image. Geometric transformations. Interpolation 10/26/2016

Image acquisition. Midterm Review. Digitization, line of image. Digitization, whole image. Geometric transformations. Interpolation 10/26/2016 Image acquisition Midterm Review Image Processing CSE 166 Lecture 10 2 Digitization, line of image Digitization, whole image 3 4 Geometric transformations Interpolation CSE 166 Transpose these matrices

More information

Prof. Feng Liu. Fall /04/2018

Prof. Feng Liu. Fall /04/2018 Prof. Feng Liu Fall 2018 http://www.cs.pdx.edu/~fliu/courses/cs447/ 10/04/2018 1 Last Time Image file formats Color quantization 2 Today Dithering Signal Processing Homework 1 due today in class Homework

More information

GPU based imager for radio astronomy

GPU based imager for radio astronomy GPU based imager for radio astronomy GTC2014, San Jose, March 27th 2014 S. Bhatnagar, P. K. Gupta, M. Clark, National Radio Astronomy Observatory, NM, USA NVIDIA-India, Pune NVIDIA-US, CA Introduction

More information

06: Thinking in Frequencies. CS 5840: Computer Vision Instructor: Jonathan Ventura

06: Thinking in Frequencies. CS 5840: Computer Vision Instructor: Jonathan Ventura 06: Thinking in Frequencies CS 5840: Computer Vision Instructor: Jonathan Ventura Decomposition of Functions Taylor series: Sum of polynomials f(x) =f(a)+f 0 (a)(x a)+ f 00 (a) 2! (x a) 2 + f 000 (a) (x

More information

Why Single Dish? Why Single Dish? Darrel Emerson NRAO Tucson

Why Single Dish? Why Single Dish? Darrel Emerson NRAO Tucson Why Single Dish? Darrel Emerson NRAO Tucson Why Single Dish? What's the Alternative? Comparisons between Single-Dish, Phased Array & Interferometers Advantages and Disadvantages of Correlation Interferometer

More information

Very Long Baseline Interferometry

Very Long Baseline Interferometry Very Long Baseline Interferometry Cormac Reynolds, JIVE European Radio Interferometry School, Bonn 12 Sept. 2007 VLBI Arrays EVN (Europe, China, South Africa, Arecibo) VLBA (USA) EVN + VLBA coordinate

More information

Why Single Dish? Darrel Emerson NRAO Tucson. NAIC-NRAO School on Single-Dish Radio Astronomy. Green Bank, August 2003.

Why Single Dish? Darrel Emerson NRAO Tucson. NAIC-NRAO School on Single-Dish Radio Astronomy. Green Bank, August 2003. Why Single Dish? Darrel Emerson NRAO Tucson NAIC-NRAO School on Single-Dish Radio Astronomy. Green Bank, August 2003. Why Single Dish? What's the Alternative? Comparisons between Single-Dish, Phased Array

More information

Digital Signal Processing

Digital Signal Processing COMP ENG 4TL4: Digital Signal Processing Notes for Lecture #29 Wednesday, November 19, 2003 Correlation-based methods of spectral estimation: In the periodogram methods of spectral estimation, a direct

More information

Measurement Techniques

Measurement Techniques Measurement Techniques Anders Sjöström Juan Negreira Montero Department of Construction Sciences. Division of Engineering Acoustics. Lund University Disposition Introduction Errors in Measurements Signals

More information

Reading Instructions Chapters for this lecture. Computer Assisted Image Analysis Lecture 2 Point Processing. Image Processing

Reading Instructions Chapters for this lecture. Computer Assisted Image Analysis Lecture 2 Point Processing. Image Processing 1/34 Reading Instructions Chapters for this lecture 2/34 Computer Assisted Image Analysis Lecture 2 Point Processing Anders Brun (anders@cb.uu.se) Centre for Image Analysis Swedish University of Agricultural

More information

Why? When? How What to do What to worry about

Why? When? How What to do What to worry about Tom Muxlow Data Combination Why? When? How What to do What to worry about Combination imaging or separate imaging??..using (e-)merlin (e-)merlin covers a unique range of telescope separations, intermediate

More information

High Fidelity Imaging of Extended Sources. Rick Perley NRAO Socorro, NM

High Fidelity Imaging of Extended Sources. Rick Perley NRAO Socorro, NM High Fidelity Imaging of Extended Sources Rick Perley NRAO Socorro, NM A Brief History of Calibration (VLA) An Amazing Fact: The VLA was proposed, and funded, without any real concept of how to calibrate

More information

Sampling and reconstruction. CS 4620 Lecture 13

Sampling and reconstruction. CS 4620 Lecture 13 Sampling and reconstruction CS 4620 Lecture 13 Lecture 13 1 Outline Review signal processing Sampling Reconstruction Filtering Convolution Closely related to computer graphics topics such as Image processing

More information

Optical Coherence: Recreation of the Experiment of Thompson and Wolf

Optical Coherence: Recreation of the Experiment of Thompson and Wolf Optical Coherence: Recreation of the Experiment of Thompson and Wolf David Collins Senior project Department of Physics, California Polytechnic State University San Luis Obispo June 2010 Abstract The purpose

More information

Image and Video Processing

Image and Video Processing Image and Video Processing () Image Representation Dr. Miles Hansard miles.hansard@qmul.ac.uk Segmentation 2 Today s agenda Digital image representation Sampling Quantization Sub-sampling Pixel interpolation

More information

Fringe Parameter Estimation and Fringe Tracking. Mark Colavita 7/8/2003

Fringe Parameter Estimation and Fringe Tracking. Mark Colavita 7/8/2003 Fringe Parameter Estimation and Fringe Tracking Mark Colavita 7/8/2003 Outline Visibility Fringe parameter estimation via fringe scanning Phase estimation & SNR Visibility estimation & SNR Incoherent and

More information

Fundamentals of Radio Interferometry

Fundamentals of Radio Interferometry Fundamentals of Radio Interferometry Rick Perley, NRAO/Socorro Green Bank Interferometry School NRAO/GB 12 14 July, 2015 Topics The Need for Interferometry Some Basics: Antennas as E-field Converters Conceptual

More information

Sampling and pixels. CS 178, Spring Marc Levoy Computer Science Department Stanford University. Begun 4/23, finished 4/25.

Sampling and pixels. CS 178, Spring Marc Levoy Computer Science Department Stanford University. Begun 4/23, finished 4/25. Sampling and pixels CS 178, Spring 2013 Begun 4/23, finished 4/25. Marc Levoy Computer Science Department Stanford University Why study sampling theory? Why do I sometimes get moiré artifacts in my images?

More information