Post on 21-Jul-2018
Practical Fourier Transform
Tartu, 27.Mar.2017
Boris Deshev
Fourier transform
Interference of Light
from http://www.thefouriertransform.com
Interference of Light
from http://www.thefouriertransform.com
Interference of Light
W = 3*lambdaD = 10*lambda
from http://www.thefouriertransform.com
Interference of Light
Telescope resolution
from R.Perley
-Angular resolution Θ ~ λ/D
Telescope resolutionAngular resolution Θ ~ λ/DOptical telescopes = 5*10λ -7 m
D = 10 m = 5*10Θ -8 rad; or 0.01 arcsec
Radio telescopes = 0.2 mλ
D = 500 m = 4*10Θ -4 rad; or 82 arcsec
Interference of Light
• from the van Cittert-Zernike theorem
● for small fields of view:the complex visibility,V(u,v)is the 2D Fourier transform ofthe brightness on the sky,T(x,y)
– u,v (wavelengths) are spatial frequencies inE-W and N-S directions, i.e. the baseline lengthsx,y (rad) are angles in tangent plane relative toa reference position in the E-W and N-S directions
T(x,y)x
y
from David J. Wilner
Visibility and Sky Brightness
Radio InterferometersVLA
ATCA
WSRT
ALMA
SKA
Aperture Synthesis Imaging
from Richard Porcas
Point Spread Function
Point Spread Function
~2hours measurement with WSRT
Point Spread Function
~2hours measurement with WSRT
THE END