Single-dish antenna at (sub)mm wavelengths

Transcription

1 Single-dish antenna at (sub)mm wavelengths P. Hily-Blant Institut de Planétologie et d Astrophysique de Grenoble Université Joseph Fourier October 15, 2012

2 Introduction

3 A single-dish antenna

4 Spectral surveys Caux et al 2011 (IRAM spectral survey of I16293)

5 Spectro-imaging

6 Few fw (1e-15 W) Receiver cabin Gain ~ 120 db Few mw Backends Frontends

7 Questions Wishes Measure some power emitted in a (narrow) frequency range from a particular location Possibly want to make some (spectral/continuum) maps Eventually determine some chemical and/or physical properties Questions Measurement fidelity? Calibration (amplitude, frequency) Spatial resolution?

8 General properties

9 Primary vs Secondary focus Primary focus Sky Ts=tau Tatm=30 100K F D Ground Tg=300K D Secondary focus

10 (dis)advantages f /D f e /D = m f /D IRAM-30m, m = 27.8 f /D = 0.35, f e /D 10 or 300 m Rx alignement easier: 1 on the sky f e / mm in focal plane increase effective area (or on-axis gain) decrease spillover but increase mechanical load obstruction by subreflector ( = 2 m at 30-m) wider main-beam

11 World map of radiotelescopes

12 Main single-dish antenna at λmm Large aperture: f/d 1 Obs. D ν λ HPBW Latitude (m) (GHz) (mm) ( ) (deg) IRAM APEX JCMT CSO Herschel space

13 Terminology (1): receivers Central frequency ν 0 = GHz Instantaneous bandwidth: ν = 1 32 GHz bolometers ν 50 GHz one polarization (linear, circular) taper (apodization at the rim)

14 Terminology (2): backends Spectrometers: digital: autocorrelators (AC), Fast Fourier Transform Spectrometer (FTS) (analogical: filter banks (FB), acousto-optic (AOS)) Spectral resolution Large resolution power δν khz R = ν 0 /δν

15 Collected power from a source Consider an unpolarized point source Monochromatic (and monomode) power collected by an area A e : p ν = 1 2 A e S ν [W Hz 1 ] Flux density S ν measured in Jy: Power in the bandwidth ν: 1Jy = J s 1 m 2 Hz 1 p = 1 2 A e S ν ν [W] Note: A 1 Jy source observed with a 10 3 m 2 radiotelescope during 40 yrs (e.g. Orion) with 50 MHz bandwidth 40 GeV

16 Collected power from a source Consider an unpolarized extended source Monochromatic (and monomode) power collected by an area A e from solid angle δω: δp ν = 1 2 A e I ν δω [W Hz 1 ] Brightness I ν measured in Jy sr 1 : 1 Jy sr 1 = J s 1 m 2 Hz 1 sr 1

17 Collected power from a source Effective area of the antenna: A e = ηa geom η < 1 Question: η =?

18 Perfect antenna

19 Emitted power by an antenna Diffraction theory (Huygens-Fresnel, Fraunhoffer approx.): E f f (l, m) F[E ant (x, y )] E ant (x, y ) (grading): bounded on a finite domain r E f f (l, m) concentrated on a finite domain Ω ( r Ω 1) sharp cut of the antenna domain oscillations (side-lobes) apodization or taper: decrease the level of the sidelobes, to the cost of increasing Ω

20 Antenna power pattern Reciprocity: antenna in emission Distribution of electric field on the dish: E ant (x, y ) Far-field radiated by the dish: E f f (l, m) F[E ant (x, y )] Power emitted is a function of direction: E f f (l, m) 2 Power pattern: P(l, m) E f f (l, m) 2 Beam solid angle: Ω A = 4π P(Ω) dω 4π Effective area: A(l, m) = A e P(l, m) A e Fundamental relation: A e Ω A = λ 2

21 Power pattern P(l, m)

22 Power collected by an antenna (2) Given a source of brightness I ν (l, m) = I ν (Ω) Source flux density: S ν = Ω s I ν (Ω) dω Observed flux density: I(l1,m1) S1 SOURCE S0 I(l3,m3) I(0,0) S3 S obs = P(Ω) I ν (Ω) dω < S ν Ω S A(l1,m1) A(0,0) A(l3,m3) Power received from dω i : dp ν = 1 2 A(Ω i ) I ν (Ω i ) dω i Incoherent emission: add intensities Pointing towards a fixed position of the source at a fixed position p ν (l = 0, m = 0) = A e 2 Ω S P(Ω) I ν (Ω) dω = 1 2 A es obs

23 SOURCE S1 S0 S3 I(l1,m1) I(0,0) I(l3,m3) Antenna tilted towards Ω 0 = (l 0, m 0 ) A( l0 l1, m0 m1) A( l0, m0) A(0,0) Power received from the direction Ω i dp ν (Ω i ) = 1 2 A(Ω 0 Ω i ) I ν (Ω i ) dω i Incoherent emission: add intensities Scanning a source leads to a convolution S obs (Ω 0 ) = P(Ω Ω 0 )I ν (Ω) dω Ω S p ν (Ω 0 ) = A e 2 Ω S P(Ω 0 Ω) I ν (Ω) dω = 1 2 A es obs (Ω 0 )

24 Convolution: consequences θ obs = θ 2 mb + θ2 sou Note: When quoting sizes from observations, must quote the deconvolved size (when needed).

25 Real antenna

26 Systematic deformations (1) Defocus

27 Systematic deformations (2) Coma: misaligned subref.

28 Systematic deformations (3) Astigmatism Beam deformation (no pointing error)

29 Beam pattern Main lobe Secondary lobes (finite surface antenna) Error lobes (surface irregularities) main-beam collects less power if correlation length l Gaussian error-beam Θ EB λ/l real beam = main-beam + error-beam(s) Questions: Power collected in each e-beam? FWHMs of the e-beams? Greve et al 1998

30 Error-Beams at IRAM-30m

31 Temperature scales

32

33 Antenna temperature: T A Johnson noise in terms of an equivalent temperature: the average power transferred from a conductor (in thermal equilibrium) to a line within δν: δp = k T δν Antenna temperature defined by p ν = kt A [W Hz 1 ] = [J] = [J K 1 ][K] On the other hand: p ν = Ae 2 (P I ν) = λ2 2Ω A (P I ν ) Antenna temperature: T A (Ω 0 ) = A e I ν (Ω)P(Ω Ω 0 ) dω 2k Ω S Using A e Ω A = λ 2, we may write: T A (Ω 0 ) = 1 λ 2 Ω A Ω S 2k I ν(ω)p(ω Ω 0 ) dω

34 Speaking in terms of temperatures Black-body radiation at temperature T : B ν (T ) = 2hν3 c 2 1 e hν/kt 1 Dimensions of brightness: J s 1 m 2 Hz 1 sr 1 Rayleigh-Jeans approximation: hν kt λ 2 2k B ν(t ) T Flux density of a black-body: S ν = B ν (T, Ω) dω = 4πB ν (T ) Ω S

35 Definitions: T B, T R Brightness temperature T B of source brightness I ν : I ν (Ω) = B ν (T B ) Radiation temperature, T R, in the Rayleigh-Jeans regime approximation I ν (Ω) = 2k ν2 c 2 T R(Ω) = 2k λ 2 T R [ J s 1 m 2 Hz 1 sr 1 ] Relationship between T B and T R : T R = J ν (T B ) = hν k In the following: I ν (Ω) T R (Ω) 1 exp(hν/kt B ) 1 = T 0 exp(t 0 /T B ) 1

36 R-J approximation in the (sub)mm 2k λ 2 J ν(t B ) = B ν (T B )

37 Consequences Monochromatic power received by the antenna: p ν (Ω 0 ) = k Ω A Ω S P(Ω) T R (Ω 0 Ω) dω Observed flux density (p ν = 1/2A e S ν ) S obs (Ω 0 ) = 2k λ 2 P(Ω) T R (Ω 0 Ω) dω Ω S

38 Antenna temperature: T A Antenna temperature: T A (Ω 0 ) = A e λ 2 Using A e Ω A = λ 2, we may write: Ω S P(Ω)T R (Ω Ω 0 ) dω T A (Ω 0 ) = 1 Ω A Ω S P(Ω)T R (Ω Ω 0 ) dω Note that: T A (Ω 0 ) = Ω S P(Ω)T R (Ω Ω 0 ) dω P(Ω) dω 4π

39 From T A to T A Tr ATMOSPHERE Tatm ~ 300 K opacity tau Tatm.(1 exp( tau)) At frequency ν: T A = { } η s TR e τν + (1 e τν )T atm + (1 η s )T gr Correct for atmospheric attenuation: Tr.exp( tau) T A = T Ae τν Tgr=300K Note: for space-based telescopes (e.g. HIFI/Herschel): T A = T A

40 From T A to T A Correct for rear-sidelobes: measure the monochromatic power recieved from the forward 2π sr. Hence, Ω A = P 4π P 2π = 2π P(Ω) dω: TA(Ω 0 ) = T A = 1 P(Ω) T R (Ω 0 Ω) dω F eff P 2π Ω S T A = e τν F eff T A Forward efficiency: F eff = P 2π /P 4π

41 From T A to T mb Take into account main-beam and error-lobes Same as TA but in Ω mb instead of 2π. Hence, Ω A P mb = mb P(Ω) dω: T mb (Ω 0 ) = T A B eff = Ω S P(Ω) T R (Ω 0 Ω) dω P mb, Beam efficiency: B eff = P mb /P 4π Useful relation for a Gaussian beam: Ω mb = P(Ω) dω = θmb 2 mb

42 Temperature scales Definitions Consequences Forward efficiency: F eff = P 2π P 4π Beam efficiency: B eff = P mb P 4π T mb = F eff B eff T A = P 2π P mb T A What you measure is T A or T mb (usually T R )

43 Limiting cases Small sources: Ω S Ω mb T mb P(0)Ω S T R Ω P mb = T S R P mb Gaussian sources & beam: Ω S P(Ω)T R (Ω 0 Ω) dω = 1.133(θsou 2 + θmb 2 ) and P mb = 1.133θ 2 mb hence T R = T mb Large sources: Ω S P mb T A T R R P(Ω) dω 2π P 2π T R θ 2 mb θ 2 sou +θ2 mb : beam dilution Special case: Ω S = P R mb P(Ω) dω Ω T mb = T S R P mb = T R Main-beam temperature gives the source brightness General (worse) case: Ω S P mb TA = TR P 2π Ω S P(Ω) dω Main-beam temperature usually quoted If source of uniform brightness and beam pattern known, feasible, but in real life... Which scale to use:ta, T mb?

44 Which temperature scale? Source size Temperature scales Ω S = 2π T R = TA Ω S = Ω mb T R = T mb 2π < Ω S T R < TA Ω mb < Ω S < 2π TA < T R < T mb Ω mb > Ω S T mb < T R

45 Calibration

46 Goals of the calibration Overview Atmospheric calibration: atmospheric emission/abs at frequency ν: radiative transfer turbulence affects the intensity through phase shifts Full detection chain calibration (antenna, receiver, ) Antenna-sky coupling: F eff Receiver: gain, noise, stability Cables, backends (e.g. dark currents) Goals Input is an e-m field and output at backends are counts Question 1: how to convert from counts to power in physical units? Question 2: how to correct for the atmospheric contribution?

47 Notations Telescope pointing at a source receives C sou = χ { T rec + F eff e τν T sou + T sky } where T sky = F eff (1 e τν )T atm + (1 F eff )T gr T rec : noise contribution from the receiver F eff e τν T sou : signal from the scientific target after propagation through the atmosphere T sky : signal emitted by the atmosphere (T atm ) and the ground (T gr ) Orders of magnitude (IRAM-30m): T atm T gr 290 K T rec K at GHz at the IRAM-30m ν GHz = : F eff (ν) 90 80%, B eff (ν) 80 35%, T sky K at GHz Note: if τ ν 1 (good weather), T sky F eff τ ν T atm

48 The Chopper Wheel method Perform 3 measurements: hot, empty sky, source C sou = χ { T rec + T sky + F eff e τν T sou } C atm = χ { T rec + T sky } C hot = χ {T rec + T hot } Making differences: C sig = C sou C atm = χf eff e τν T sou C cal = C hot C atm = χ(t hot T sky ) T sou = T cal C sig C cal Definition of T cal (correcting for atm contrib. and spillover) T cal = (T hot T sky ) eτν F eff

49 Calibration outputs (1): T cal Rewrite T sky and C cal : T sky = T gr + F eff (T atm T gr ) F eff e τν T atm T cal = T gr + e τν [T gr T atm ] + e τν /F eff [T hot T gr ] C cal = χ{ (T hot T gr ) + F eff (T gr T atm ) + F eff e τν T atm } Assume T hot = T atm = T gr. Then T cal = T hot T sou = T hot C sig C cal, T cal = T atm = T gr = T hot No need to know e τν and F eff (Penzias & Burrus ARAA 1973): But T rec not known

50 The refined Chopper Wheel method General case: different T atm, T hot and T gr must solve for e τν and F eff. e τν : model of the atmosphere trying to reproduce T sky varying the amount of dominant species in the model (hence providing us with pwv). F eff : skydips (measure atm. at several elevations) Perform measurements: hot, cold, empty sky, source C sou = χ { T rec + T sky + F eff e τν T sou } C atm = χ { T rec + T sky } C hot = χ {T rec + T hot } C col = χ {T rec + T col }

51 Calibration outputs (2): T rec Using hot & cold loads measurements lead to T rec : T rec = T hot YT col Y 1 Y = C hot C col = T rec + T hot T rec + T col

52 Calibration outputs (3): T sys System temperature: describes the noise including all sources from the sky down to the backends T sys = T cal C off / C cal used to determine the total statistical noise. For heterodyne receivers, noise is given by the radiometer formula : σ T = κ T sys δν t δ ν : spectral resolution t: total integration time κ depends on the observing mode: example: position switching, ON-OFF 2, t ON = t OFF t = 2t ON 2, κ = 2

53 From T mb to S ν, from Kelvin to Jansky flux density: S ν = Ω S I ν (Ω) dω = 2k λ 2 Ω S T R dω power received by the antenna: kt A = k T A F eff = 1 2 S νa e S ν TA = 2k A F eff η A Jy K 1 1 Jy = J s 1 m 2 Hz 1 values of S ν /TA are tabulated e.g. on IRAM-30m web page ( 100 GHz, 340 GHz) How to convert the temperatures into J s 1 m 2 Hz 1 sr 1? I ν (Ω) = 2k λ 2 T R(Ω)

54 Summary

55 Image formation: total power telescope antenna scans the source image: convolution of I 0 by beam pattern I ν = P I 0,ν measure directly the brightness distribution I 0

56 Interferometer field of view F = D (P I) + N F = dirty map = FT of observed visibilities D = dirty beam ( deconvolution) P = power pattern of single-dish (primary beam B in the following) I = sky brightness distribution N = noise distribution An interferometer measures the product P I P has a finite support limits the size of the field of view

57 Physical parameters Chose an adapted temperature scale (T A, T mb) Correct for error-beam pick-up when needed Amplitude calibration: often enough 10% accuracy

58

59 Summary full-aperture antenna: P I interferometry sensitive to P I amplitude calibration: converts counts into temperatures corrects for atmospheric absorption corrects for spillover lobe = main-lobe + error-lobes (e.g. as much as 50% in error-lobes at 230GHz for the 30m) Pay attention to the temperature scale to use (T A, T mb,...)

60

61 Image formation: correlation telescope antennas fixed w.r.t. the source correlation temperature: T (0, 0) Fourier transform of I 0 P measure the Fourier transform of the brightness distribution I 0 image built afterwards

62 Interferometer field of view Measurement equation of an interferometric observation: F = D (B I) + N F = dirty map = FT of observed visibilities D = dirty beam ( deconvolution) B = primary beam I = sky brightness distribution N = noise distribution An interferometer measures the product B I B has a finite support limits the size of the field of view B is a Gaussian primary beam correction possible (proper estimate of the fluxes) but strong increase of the noise

63 Primary beam width Aperture function Voltage pattern 2 Transfert function T (u, v ) Power pattern B(l, m) = Primary beam Gaussian illumination = to a good approximation, B is a Gaussian of 1.2 λ/d FWHM Plateau de Bure D = 15 m Frequency Wavelength Field of View 85 GHz 3.5 mm GHz 3.0 mm GHz 2.6 mm GHz 1.4 mm GHz 1.3 mm GHz 1.2 mm 20