Bertrand Lefloch (IPAG, France) IRAM Summer School 20111.

Millimeter Line Calibration

Bertrand Lefloch (IPAG, France)

IRAM Summer School 2011 1


Introduction


Introduction : my first steps as a radioastronomer…

June 1988 : Commissioning of the Plateau de Bure antennas…

A pointed single dish-telescope does not image the sky !

Planets are used for pointing and calibration…

Atmosphere is not always cooperative at mm wavelengths…


Noise and Signal in Radioastronomy

Astrophysical signals are extremely weak :

flux unit : 1Jy = 10-23 erg s-1 cm-2 Hz-1 sr-1

Radioastronomical signals are largely dominated by the noise of the electronic chain amplification by many orders of magnitude required sensitive and stable detectors


Introduction : Instrumentation in Radioastronomy

mm submmfar IR mid IR

In the mm and submm windows, line observations are carried out by means of SIS heterodyne receivers, allowing a high spectral resolution : R = Δ n/ = 10 n -7

velocity resolution Δv= 0.03 km/s

c= (kT/µmH ) ½ = 0.18 km/s (10K)

Comparison : Optical/mid IR (H2 )Gratings in the optical : R = Δ n/ = n10 -4

Velocity resolution Δv= 30 km/s

PACS : R = 1500 – 2000SPIRE : R = 40 - 1000

Heterodyne receivers allow to study the gas kinematics (subsonic motions, turbulence) at a resolution out of reach to any other instruments.

(FXD’s talk)

PACS

A. Navarini’s talk


Introduction: Imaging with Single-Dish Telescopes

Single-dish telescopes are able to produce high-quality images of molecular lines at millimeter and submillimeter wavelengths.:

-More sensitive heterodyne receivers(200 50K,… on the way to the quantum limit ! )-Heterodyne arrays

Direct comparison with optical/near IR images is now possible and meaningful, allowing to bring more constraints on excitation conditions and source modelling.


- Outline of the Lecture: - 0. Introduction- 1. Calibration - 2. Heterodyne Detection- 3. Spectral Line Observations: spectral surveys and mapping- 3.1 Observing modes and Time estimates (proposals !)

Outline


Calibration


The Framework

corrected for atmospheric absorption

Telescope Beam

Source Brightness Distribution

⊗

Atmosphere


Determine the properties of the antenna : antenna calibration (efficiency)

Characterize the behaviour of the receiver and the electronic chain (instrumental calibration)

Characterize the behaviour of the atmosphere

When we talk of calibration, we want to

- How to convert Voltage (receiver output) into a Power (K) ?- How to correct for the effect of the atmosphere ? - How to retrieve TB from TA’ ?


The Nyquist Theorem relates the electric power dissipated in a device and the thermal agitation measured by temperature T

Energy available in the resistance is : E = kT (2 deg of freedom)

Exchange on a timescale , t hence the power dissipation :

P = E/ - t kT Dn

Dn (bandwidth in which energy is dissipated), the exchangeable power is : Pn = kT Dn

Proportional to its temperature : Noise Temperature

<i> = 0

<i2> ≠ 0 (e- thermal

motion)

The Nyquist Theorem

Reciprocity Theorem (based on the Maxwell equations): it is always possible to express the properties of an antenna either as a transmitter or as a receiver, without distinguishing between the two. (think of your mobile phone !)


At low frequency (radio) : Rayleigh-Jeans regime

2hn3 1 2k T n2 2kT

c2 exp(hn/kT) –1 c2 l2 In = Bn(T) =

______

_______________ =

_________ = ____

The power received is directly proportional to the brightness temperature T

At high-frequency : Wien regime

At mm and submm , l the RJ approx. is not always valid.

At 230 GHz, T=10K deviation by about 10 %

One introduces : J n (TB) = - Bn (TB) [K]

The Black Body Law and the Rayleigh-Jeans Approximation

A system in thermodynamical equilibrium with its own radiation (absorption emission of photons) is characterized by a radiation spectrum which follows the Planck law:

Definition of Source Brightness Temperature

l2

2 k


The Beam Pattern

The IRAM 30m is a Nasmyth telescope: Parabolic main reflector: widely favored to collect the astronomical signal (stigmatism, polarization)

Advantages : Focus close to vertex of primary dish easy access to receivers

Large FoV use of several receivers simultaneously

Drawbacks :

Receiver must move in elevation when the telescope tracks the source on the sky :

Cassegrain Nasmyth

Illumination losses : blockage of the quadrupod+ secondary + standing waves

Losses by diffraction (spillover) are oriented to the sky, colder than ground


The Beam Pattern The Beam (Power) Pattern P(Ω) is the response of the antenna as a

function of direction.

Normalized Beam Pattern : Pn (Ω) = P(Ω) / Pmax

The Beam Pattern P(Ω) can be expressed as the sum of 2 factors :

P(Ω) = P1 (Ω) + Pe (Ω)

P1 (Ω) : diffracted beam, formed by radiation coherently focused in the focal plane P1 (Ω) = Pml (Ω) + Psl (Ω) Main diffraction lobe Secondary diffraction lobes

Pe (Ω) : error beam, formed by spillover + scattered radiation in the focal plane (FT) grading function : response of the antenna in the aperture plane (collecting surface)

Useful References : Born M. & Wolf E.« Principles of Optics »Greve A., Kramer C., Wild W., 1998, A&A Supp. Series, 133, 271 Kutner M.L. & Ulich B.L., 1977, ApJ 250, 341

TR

Beam solid angle

-A = ∫∫Pn(-,φ)d-

S(-0,φ0) = - ∫∫B(-,φ)Pn(-0--,φ0-φ) d- = 1

-A

1

-A

- B * Pn

The Antenna Temperature is the equivalent noise temperature of a resistance radiating the same power available at the output terminals of the receiver.

W = ½ Ae B*Pn = kTA (Nyquist)Ae = l2/-A (an important relation between the effective collecting surface and the beam solid angle)

TA = - ∫∫- B(-,φ). Pn(-0--,φ0-φ) d-1 l2

-A 2k

Here, TA is the antenna temperature uncorrected for the rearward losses.

Brightness temperature TB: temperature of the equivalent blackbody that radiates the same specific intensity at n

B(TB,-) = Bn (TB). -(-)

Antenna Temperature

15IRAM Summer School 2011

Antenna TemperatureRayleigh-Jeans approximation :

Bn(TB,-) = 2 k TB(-)

l2

TA (Ω0) = - ∫∫TB(-). Pn(-0--).d-1

-A

General case :

J n (TB) = - Bn (TB) [K] or Jn (TB) =

l2

2 k

hn 1

k exp(hn/kTB) - 1

TA’ (Ω0) = - ∫∫Jn(TB) Ψ(-). Pn(-0--).d-

1

-A

TA (antenna temperature) has nothing to do with the actual temperature of the structure of the antenna.

TB is the thermodynamical temperature of the radiating material only for an optically thick and thermalized layer

Relation can be inverted if Pn(-) and TA(-) are fully known large scale maps + low rms

Only an approximate (de) convolution is performed

TA ‘ is the antenna temperature and has been corrected from atmospheric attenuation exp(- t A)

Jn(TB,-) is the source brightness distributionPn (Ω) is the normalized antenna beam pattern : Pn (0) = 1


In the case of unpolarized emission, the antenna receiver will detect only half the incoming signal and the collected power density is (source spatially incoherent : intensities are added).

W = ½ Ae ∫∫B(-,φ).Pn(-,φ) d- / ∫∫Pn(-,φ)d-

W [erg s-1 Hz-1]

Ae Effective aperture [cm-2]

B(-,φ) is the brightness distribution of the source [erg s-1 cm-2 Hz-1 sr-1]

General case : the source and the main beam do not have the same reference.

dS(φ) = B(φ). Pn(φ0-φ)dφ

S(-0,φ0) = ∫∫B(-,φ)Pn(-0--,φ0-φ) d-

∫∫Pn(-0--,φ0-φ)d-

Antenna Temperature


½ Ae

Pc = amount of power collected by an antenna illuminated by a plane wave with power density |S|.

Effective aperture Ae: equivalent surface detecting Pc

In practice, Ae ≠ physical surface of the antenna = Ag = p D2/4 (707 m2 for the IRAM 30m)

Aperture EfficiencyηA =

Ae

Ag

The effective aperture efficiency usually depends on the relative orientation of the antenna and the illuminating radiation. The effective collecting area and the antenna beam solid angle are related via :

Ae . -A = l 2

You cannot have both a large collecting area AND a large beam solid angle…

The directivity of the antenna and the effective aperture efficiency are not independent :

Aperture Efficiency

IRAM Summer School 2011

Flux of a point source : W= k TA = ½ Sn Ae = 1/2 -A Sn Ag

18


Aperture Efficiency : measurement

Ruze’s Formula e measures the roughness of the

surface (errors rms)

(Measurements by Juan Penalver in august 2007)


Gain and Efficiency

Antenna Beam Solid Angle

-A = ∫4p

Pn(-,φ) d- = ∫ ∫ Pn(-,φ) sin - d- dφ pp/2

0 -p/2

Can be represented as a solid angle with Pn= 1 inside -A

= 0 elsewhere

Main-beam solid angle

The main beam is the region where Pn(-) > 0.5

-mb = ∫ Pn(-,φ) d- Pn(-) > 0.5

Half-Power Beam Width HPBW

That characterizes the resolving power of the telescope


Main-Beam Efficiency

Beff = --mb

-A

-mb is integrated over the main beam : P(Ω) > 0.5

-A is integrated over 4 p steradian

Beff ( -mb ) does not depend on the actual value of -A (antenna beam solid angle) but on the quality of the antenna. It should be as large as possible, i.e. the power pattern be concentrated in the main beam as much as possible.

Tmb = - ∫∫- Jn(TB) Ψ(-). Pn(-0--,φ0-φ) d-1 l2

-mb 2k

One defines the Main Beam brightness temperature Tmb :

Tmb -A = or TA ‘ -mb

TA’ = Beff Tmb


Main Beam Efficiency

B (-,φ) = Jn(TB).-(-,φ) = 2k TB / l2 .-(-,φ)

Tmb = TB . (1/ -mb ) ∫∫ -(-,φ) . Pn(-0--,φ0-φ) d-

Under “reasonable conditions”, Tmb is a good approximation to TB

Source flux density : Sn= ∫s Bn (TB). d- = Jn(TB). -s

TA’ = (1/2k) Ae ∫∫ Jn(TB )-(-,φ) . Pn(-0--,φ0-φ) d- = (S n Ae /2k) . (1/ -s) ∫∫ -(-,φ) . Pn(-0--,φ0-φ) d- = K (K 1 if -s << -mb)

At the IRAM 30m, the antenna temperature is corrected for the readward losses :

TA* Fe = T’A we obtain the relation : TA * = (S n K) Ae /2kFe

Flux density /beam


Efficiencies at the IRAM 30m telescope

The aperture efficiency can be written as :

TA* Fe = T’A = Beff Tmb : TA* = Beff / Feff Tmb

-A = (2k/Ag).Fe TA*/Sn,b

The choice of the T-scale does matter !

-A depends a lot on frequency : it limits the possibility of observing at high-frequency (Ruze)


A Taper is applied at the edge of the (secondary) reflector in order to decrease the level of the sidelobes (10-15 dB otherwise)

The radio feeds which collect the signal are usually scalar horns (monomodes) whose lowest mode ( E field) is approximately gaussian in the aperture. In other words, the grading function is well approximated by a Gaussian. Feed Horns have typical tapers of 10-15 dB.

Improvement of Beff and decrease of ηA

Impact of taper on antenna parameters

Apodizing Function

Gradings and Electric Field Pattern


The Main Beam Pattern

Grading : exp( -0.1/2 (r/R)2) r≤R

Power Patter in the image plane : Pn(-) = exp( -ln2 . (2 -/-B)2)

-B is the half-power beamwidth (HPBW) = 1.2 l / D

Airy disk (uniform illumination) : 1.02 l / D

-MB = 1.133 -MB2

-o2 = -B 2 + -S2

TMB = TS

. -S2 / (-B2+ -S2)

Gaussian Beam

Taper has broadened the beam by 20% but the sidelobe levels has been decreased to less than 1%

The diffraction losses have diminished too.

The beam efficiency is higher (and the aperture efficiency lower).

Observed Source (gaussian)



The Source flux density Sn is the power radiated per unit area and per unit frequency

Source Brightness and Main Beam Brightness Temperature

Rayleigh -Jeans regime (hn << kT) :

For a planet of diameter -s

The Antenna Temperature corrected for atmospheric losses is :

Brightness Distribution of the source:

The beam of the telecope is well approximated by a Gaussian with HPFW -B :

P(-) = exp -ln2 (2-/-B)2

Brightness Distribution of Planet:

-(-) = 1 - ≤ -s/2

= 0 elsewhere

T’A = ∫ 2p J n (Tb) exp -ln2 2 sin - d-1

-A

-s/2

0

2-

-B - -

at the brigntness peak

p -B2 ln 2 -s

2

4 ln 2 -B2

1 – exp -

-MB = -p B2 / 4 ln 2

T’A = J n (TB) (1 – exp(x2))-MB

-A

x = √ln 2 .( -s/-B )

x Jn (Tb)


Source Brightness Temperature and Main Beam Temperature

Beff


Source Brightness Temperature and Main-Beam Temperature

T’A = J n (TB) (1 – exp(-x2))-MB

-A

= Beff J n (TB) ( 1 – exp(-x2))

Tmb ≠ Jn(TB) in general

For an extended source -s > 2.6 -B , one has

Tmb ≈ Jn(TB)Tmb is then a good approximation to the source Brightness

Temperature

Beff can be derived from the measured antenna temperature of a planet, of known extent and brigthness . The best case if when -s - -MB

It is possible to determine ηA and Aeff from planet flux measurements : that is the method adopted in practice !

The scale T’A is adopted at the JCMT

Beff Tmbx = √ln 2 .( -s/-B )


Planets as Calibrators

Some planets are good calibrators because their temperatures and fluxes are well known.

Secondary calibrators : compact HII regions,etc…

Mercury, Venus : large diameter variations. Fast and large phase effects for mercury not used.

Mars : VERY important ! Nearly a BB in the mm and submm : solid surface, tenuous atm

Its temperature varies with heliocentric distance :

TB = <TB> (1.524/R) ½ (Ulich, 1981)

Jupiter : diameter 32-42’’. Strong atmospheric lines which may influence observations with small bandwidth. Flux density is large and constant with time.

Saturn : changing tilt angle of the rings wrt Earth Emission variations : not negligible !

Strong ellipticity (e = 0.096)

Uranus : small (3’’), weak. Atm absorp. Lines of CH4.

Neptune : Weaker than Uranus. Small (3’’). Broad CO absorption and HCN emission lines (Marten et al. 1993).

Planetary Brightness Temperatures derived from bolometric measurements with bandwidths of several 10 GHz.

The Martian temperatures are given at the mean distance of 1.524 AU

(1) Ulich et al. (1980); (2) Ulich et al. (1981); (3) empirical fit by Griffin & Orton (1993); (4) Griffin et al. (1986); (5) Hildebrand et al. (1985).

Some frequencies are to be avoided when using planets as calibrators (planetary atm lines):

CH4 (82.0,82.9,94.1,95.2,98.3)

HCN (88.6,265.9,345.5,..)13CO (110.2,220.4,330.6), 12CO (115.3,230.5,345.8)…..


Summary of Lecture 1 : Beam Pattern

- The Beam Pattern is the response of the Antenna as a function of direction

Two contributing factors : P(Ω) = P1 (Ω) + Pe (Ω)

P1 (Ω) : diffracted beam, formed by radiation coherently focused in the focal plane P1 (Ω) = Pml (Ω) + Psl (Ω) Main diffraction lobe Secondary diffraction lobes

Pe (Ω) : error beam, formed by spillover + scattered radiation in the focal plane

Main Beam : Pn (Ω) > 0.5HPBW ( resolving power of the instrument) - 1.2 l/D (almost Airy disk)

IRAM : HPBW= 2460’’ / (n GHz)

Main Beam efficiency : Beff = Ωmb / ΩA Beff = 0.81 86 GHz 0.74 145GHz 0.53 260 GHz -A = ∫

4p Pn(-,φ) d- 0.32 330 GHz


Summary of Lecture 1 : Temperatures

The Antenna Temperature is the equivalent noise temperature of a resistance radiating the same power available at the output terminals of the receiver.

Power collected by the Antenna is the convolution of the beam pattern Pn (response) with the Sky Brightness Distribution B:

W = ½ Ae B*Pn = kTA (Nyquist)

In the general case, after correction for atm. Absorption:

How to retrieve TB (or Jn (TB)) from TA’ ?

Special case : Very extended, uniform source with -s = -A Ψ(-) = 1 for - < -A :

TA’ = Jn(TB)

Main Beam Brightness temperature (Tmb -mb = TA -A )

For sources of extent -s > 2.6 -B , Tmb ≈ Jn(TB)

For small sources -s << -B , Tmb = Jn(TB) . Ωs/Ωmb dilution factor

TA’ (Ω0) = - ∫∫Jn(TB) Ψ(-). Pn(-0--).d-

1

-A

TA’ = Beff Tmb

Beam Pattern and telescope deformations

The surface of a radiotelescope cannot be perfect !Primarily, deformations of the main reflector surface

large-scale deformations : gravity, wind, ∆T (day/night)

small-scale deformations : surface errors (Main dish)

Large-scale deformations :

Gravity homology (van Hoerner, 1967) : the antenna surface maintains its parabolic shape and its focal length under the influence of gravity. The orientation of the parabola axis changes.

Thermal Gradients in the structure Coma, Astigmatism

They can be eliminated by some active optics design

(Greve et al. 1996, Radio Science, 31,5,1053)

Active Surface Corrections at the CSO : 33% 56% at 350µm

The large-scale deformations affect the central part of the beam and maintain the whole beam structure : primary+secondary lobes, whereas small-scale deformations produce one or several extended error beams.


Effelsberg beam at 7mm


Gain – Elevation Effect The surface deformations with respect to the perfect paraboloid shape

vary with elevation for a homologous telescope.

Gain-El curve measured at IRAM 30m on quasar and planets at 3, 2 and 1.3 and 0.8mm

Beam Pattern of IRAM 30m telescopeContours : -21,-18,-15,-12,-9,-6,-3 db

90

67.5

43

22.5

0

Effect more and more pronounced with n : Main beam remains circularSide lobes level increases

Error Beam

The surface of the primary reflector consists of 210 panels, distributed in 7 rings of frames,

1 frame : 2 panels 1x2m, 15 screws: 5 rows - 0.5m spacing.

Two types of surface errors

each panel : adjustment deformation / screw : correlation length lc= 0.3-0.5m

between two panels (displacement, misalignment, etc..): correlated deformations lc= 1.5-2.0m



Error Beam

The antenna gain G =

d = 4p e/ l

P(-,φ)

∫∫P(-,φ). d-

In pratice, if d ≠0 at x0, then there’s an area around that point where the deformation is ≠0 too : Correlation length lc

G/G0 = exp(-(4pe/l)2) + plc 2 (1- e-d2) lc sin -e

l d2 8 e exp -

2

Ruze Formula (1952,1966)

e= axial displacement will induce a change

in the optical path of the incoming wavefront the diffraction pattern beam pattern and the gain

Reduction of the axial gain Increase of the error lobe level

Error beam of width -e ~ l/lc

Effect more pronounced with increasing n - (D/lc) HPBW


The IRAM 30m Beam Pattern

From Scans across the moon (Greve et al. 1998)

The Beam Pattern is the sum of all these contributions

Error Beam at the JCMT


At 450 µm, the first error beam can not be neglected in many cases: Relative amplitude : 6-8% ; Size : 30’’…


Error Beam : Should you care ?

For small sources ( - - a few HPBW) : not really…

For very extended sources : Tmb is no longer a good approximation to the true TB …(Orion)

The intensity spatial distribution is also modified by the low-level contribution of the error beam dramatic when modelling intensity profiles to retrieve density distribution n(r) in pre/protostellar cores, in molecular clouds.

Motte et al. (1998)


Error Beam : Everybody should care !

Garcia-Burillo et al. (1993)

Error beam contribution

Observed Spectrum

M51 CO 2-1 (Schuster et al. 2007)


Atmospheric Calibration


Why should we care ?

1. emits thermal radiation and eventually add noise

2. attenuates the incoming radiation

3. is turbulent : it introduces time-dependent phase shifts in the propagation of the incoming electromagnetic radiation, hence affects the intensity of the signal.



Atmosphere: the constituents

Species molec. weight Volume abundance amu N2 28 0.78084 O2 32 0.20948 Ar 40 0.00934 99.966% CO2 44 3.33 10-4

Ne 20.2 1.82 10-5 He 4 5.24 10-6

CH4 16 2.0 10-6

Kr 83.8 1.14 10-6

H2 2 5 10-7 => evaporated O3 48 4 10-7

N2O 44 2.7 10-7

H2O 18 a few 10-6 variable!


The AtmosphereHeating : photoabsorption in UV bands O, O2

Thermosphere

O2 + hv (< 175nm) O(3P) + O(1D)*

Schumann – Runge continuum

+ hv (< 242nm) O(3P) + O(3P) Herzberg continuum

Heating : photoabsorption in UV bands O2, O3

O3 + hv (<1175nm) O2 + OChapuis band

+ hv( < 310nm) O2 + O*

Hartley band

Troposphere: the lowest portion of the atmosphere, contains approximately 75% of the atmosphere's mass and almost all of its water vapor and aerosols. The average depth is about 11 km in the middle latitudes. The lowest part of the troposphere, where friction with the Earth's surface influences air flow, is the planetary boundary layer. This layer is typically a few hundred meters to 2 km deep depending on the landform and time of the day. The temperature decreases in the troposphere.

100 km

Stratosphere: has a positive thermal gradient, hence is dynamically stable. It is heated from above by conduction (from O3 layer that blocks UV radiation) and from below by convection, which balances out at the base.

Modelling in ATM at IRAM


The Atmosphere : a simple model

The atmosphere is a highly complex and nonlinear system (weather forecast)

For our purpose we describe it as being

Static / d dt = 0 and v = 0

1-dimensional f(r, ,f q) -> f(z)

Plane-parallel Dz / R << 1

In Local Thermodynamic Equilibrium (LTE) at temperature T(z)

Equation of state ideal gas


The Atmospheric Model

Equation of statep = (r/M) RT = S pi

Hydrostatic equilibrium dp / dz = -r g = - pM / (RT) g

dp / p = -gM / (RT) dz

p = p0 exp(-z/H)

with the pressure scale heightH = RT/gM (= 6 ... 8.5km for T=210 ... 290K)

Temperature structure of the Troposhere dT/dz = -b (= 6.5 K/km) for z < 11 km

T = T0 – b (z-z0)


Atmospheric Calibration: some key-players

O2: Mixing ratio (% N2 = 20/79) is constant up to an altitude of 80km, where photodissociation processes start to become important.

Magnetic Dipole transitions at 60 and 118 Ghz

H2O: concentrated mainly at low altitude (a few kms), where the vertical profiles can vary a lot as the physical conditions in the lower atmosphere allow 3 phases of water to coexist. Beyond 15-20km of altitude, the atmosphere is extremely extremely dry : H2O becomes a very rare gas.

Electric Dipole transitions at 22, 183, etc… Ghz

O3: mixing ratio vertical profile displays a maximum in the lower stratosphere (30-40 km), depending on the geographical latitude. Less abundant than O2 and H2O…a forest of lines in the submm and FIR range…

CO: photochemical and biological processes in the lower atmophere cause its abundance to increase in the first 5km, then decreases up to z= 25 km. Its abundance increases again at higher altitude.

22GHz

Atmospheric Transmission : Windows

H2O

183GHz

H2O

2 mm129-174 GHz

3 mm

81-116 GHz

1 mm

201-256/269 GHz

0.8 mm

277-371 GHz

325GHz 380GHz

368GHz

O2

118GHz60GHz

O2


exp(-t)


Question : What limits the atmospheric transmission at low frequency ?

Absorption by the ionosphere :

νp= 9 ne1/2 Hz =

1/2

in the ionosphere : ne = 1012 cm-3

νp= 9 MHz

The atmospheric opacity varies between day and night, due to recombinations in the plasma at night, so that ne decreases

tν = 0.046 (ν/100MHz) -2 day

tν = 0.0046 (ν/100MHz) -2 night

1 neqe 2

2 p me e0

Atmospheric Windows: the low frequency limit


Plasma Frequency of the ionosphere


Windows in the Far-Infrared

Currently, the highest freq. range observed from ground are at the Caltech Submm Observatory (900 GHz) and APEX.

Projects under study to observe THz windows from the ground:

CCAT : 25m telescope in Atacama

(350 – 1400 GHz)


At the IRAM 30m telescope, the atmospheric opacity is estimated at the same time as the receiver calibration using the Chopper Wheel Method, using an atmospheric model (ATM).

In addition to opacity, stability can be an obstacle to line observations :

Refractive index n= f(p,T,H) is important !enters into the determination of the pointing direction of the telescope. determined from

meteorological station at the IRAM 30m.

Dependence on humidity H : - is strong at low elevation (< 30deg)

- can be a local phenomenon

- can be very time variable

Anomalous refraction (radio seeing):

Variation of refractive index caused by fluctuation in water vapour partial pressure change Dl in electrical (optical) path of the incoming EM wave (E. exp (i nr.k )) slow timescale (% optical)


Phase variation of wavefront Image motion

Independent of l

Downes & Altenhoff (1989)

A screen of humid air moves across the aperture at a scale size > aperture

Sky opacity and Sky brightness change too at a low level


Anomalous Refraction

Pointing Scans on 1757-240 on Sept. 5th…

An outstanding example on Venus on 17-04-1998 !

10’’Amplitude of Anom. Refrac. may not be an at all l

Make fast pointing scans will help… 1.3mm

3mm

Usual values at the 30m: < 3’’


Receiver Calibration


Receiver Temperature and Y factor

The Receiver Temperature TR measures the noise performance of the receiver. It is determined by placing an absorber at a given temperature in front of the receiver.

Using the Nyquist theorem : P = k . T

Hot Load : usually ambient (receiver Cabin) temperature TH

Cold Load : typically Nitrogen (TC = 77K) or internal load in Rx (25K / EMIR)

Output Power : P = g . (TX + TR)

Y = PH / PC

TR = TH – Y. TC

Y - 1

Dark Counts <c> (constant offset delivered by backend) are sometimes not negligible : P = g. (Tx + TR) + <c>

Y = (PH – <c> ) / (PC – <c>)

TR is overestimated when <c> are neglected !


Receiver Calibration : the Chopper Wheel Method

Basic Idea

VH = G(TH + TR) Vsky = G(Tsky + TR) Von = G(Tsky + TR + TA )Voff = G(Tsky + TR)

ΔVcal = VH – Vsky = G(TH – Tsky)= G(TH – TH(1- e- t A)) = G TH e-tA

ΔVsig = Von – Voff = GTA = G TA * e-tA

TA * = TH

ΔVsig

ΔVcal

TA* is obtained directly

TR is not determined

(Penzias & Burrus, 1973, ARAA, 11, 51)(Kutner & Ulich 1981, ApJ, 250, 341)

At 0th order

Approx : Th Eq


We now consider : relative gains of image/ signal band: G s ≠Gi and Gs + Gi = 1, Gim = Gi /Gs : Gs = 1/(1+Gim )

TH ≠Tsky

T J(n,T) for radiation temperatures Rayleigh-Jeans Temperature 3K background radiation not negligible Spillover losses Forward efficiency

VH = g.( Gs J(ns,TH) + Gi J(ni, TH) +TR )

Vsky = g. (Gs [Fe.J(ns,Tsky) + (1 – Fe ).J(ns,Tcab)] + Gi [Fe.J(ni,Tsky) + (1 – Fe ).J(ni,Tcab)] + TR)

J(n,Tsky) = J(n,Tatm) (1 – exp(-t A)) + J(n,Tbg).exp(-t A)

Simplification : J(ni,T) = J(ns ,T) :

The relation between DVsig and DVcal now becomes :

TA* x DVcal / DVsig = Tcal

D Vsig = Von – Voff = g.Gs.Fe.TA * . exp(-tsA) = g.Fe.TA

* exp(-tsA)/(1 + Gim )

Receiver Calibration : the Chopper-Wheel Method

A heterodyne receiver receives signals at nLO +/- nIF


D Vsig = Von – Voff = g.Gs.Fe.J(ns,TA)exp(-tsA) = g.Fe.J(ns,TA) exp(-tsA)/(1 + Gim )

DVcal = VH – Vsky = g.J(n,TH)

- g. ((1+Gim ) -1 [Fe.J(ns ,Tsky) + (1 – Fe ).J(ns,Tcab)]

- g. Gim (1+Gim ) -1[Fe.J(ni,Tsky) + (1 – Fe ).J(ni,Tcab)]

J(n,Tsky) = J(n,Tatm) (1 – exp(-t A)) + J(n,Tbg).exp(-t A)

DVcal / DVsig x TA* = (1+ Gim ) exp( tsA). (gFe) -1 (VH – Vsky)

= (1+ Gim ) exp( tsA). Fe -1 ( J(n,TH) - J(n,Tcab) ) (A)

- ( J(ns ,Tatm) (exp( tsA) – 1) + J(n,Tbg) )

- Gim ( J(ns ,Tatm) (exp( tsA) – exp( (ts –ti )A) + J(n,Tbg) exp( (ts –ti )A) )

+ (1+ Gim ) J(n,Tcab) exp( tsA)

DVcal / DVsig x TA* = (A) + J(ns ,Tatm) - J(n,Tbg) + (1+ Gim ) (J(n,Tcab) - J(ns ,Tatm) ) exp( tsA) (B)

- Gim (– J(ns ,Tatm) exp( (ts –ti )A) + J(n,Tbg) exp( (ts –ti )A) )

= (A) + (B) + J(ns ,Tatm) - J(n,Tbg) + Gim ( J(ns ,Tsky) - J(n,Tbg) ) (exp( (ts –ti )A) - 1 + 1)

= (A) + (B) + (C) + (1 + Gim ) ( J(ns ,Tsky) - J(n,Tbg) )


g and TR cancel out !


Spectral line calibration in the signal sideband

TA* x DVcal / DVsig = Tcal with

Tcal = (1+ Gim ) exp( tsA). Fe -1 ( J(n,TH) - J(n,Tcab) ) Signal in the signal sideband

+ (1+ Gim ) (J(n,Tcab) - J(ns ,Tatm) ) exp( tsA)

+ Gim ( J(ns ,Tatm) - J(n,Tbg) ) (exp( (ts –ti )A) - 1 )

+ (1 + Gim ) ( J(ns ,Tatm) - J(n,Tbg) )

Spectral line calibration in the image sideband

Definition of Tcal is changed to : Tcal = D Vcal /gGi Fe exp(-ti A)

Continuum calibration

Tcal = D Vcal / ( gGi Fe exp(-ti A) + gGsFeexp(-tsA) )



The System Temperature Tsys measures the performance of the receiver plus the atmosphere when looking at the sky (off source):

V sky = g (Gs [Fe.J(ns,Tsky) + (1 – Fe ).J(ns,Tcab)] + Gi [Fe.J(ni,Tsky) + (1 – Fe ).J(ni,Tcab)] + TR)

= g Fe (Gs J(ns,Tsky) + Gi J(ni,Tsky) ) + g (1 – Fe ) J(ns,Tcab) + g TR

J(n,Tsky) = Gs J(ns,Tsky ) + Gi J(ni,Tsky) = Gs Tskys + Gi Tsky

i = Tskys + Gim Tsky

i /(1 + Gim)

T sys / TA* = V sky / (V on – V off ) = (V sky / D V cal ) x ( D V cal / D V sig )

= V sky / g.Gs.Fe.TA * exp(-tsA)

Tsys = (1 + Gim) Vsky [ Fe Tsky + (1-Fe) Tcab + TR] / Fe exp (-tsA)

T sys / TA* = V sky / (V on – V off ) = (V sky / D V cal ) x ( D V cal / D V sig )

T sys = T cal x V sky / D V cal

System Temperature

Tcal / TA*

( Gim = Gi / Gs )


Calibration at the IRAM 30m telescopeThe Chopper Wheel method is extended to include a measurement on the cold load

Convergence test when performed for several Rx !


Calibration : example at APEX

Cold Load Hot Load Sky

The 3 spectra are very similar…

the receiver bandpass dominates the emission


Example at APEX

OFF ON

ON-OFF/OFF

The spectrum is still to be calibrated !


Psky = G.( Fe Tsky + (1-Fe ) T cab + TR )

= G. (Fe [ Tatm( 1 –exp(-t A)) + T bg exp(-t A)] + (1-Fe ) T cab + TR )

= G. Fe Tatm (1- exp(-t A)) + G ( (1-Fe ) T cab + TR )

A skydip is performed by moving the antenna in elevation at equal airmass numbers

A= 1/sin (El)

Fe can be derived independently of the

amount of water vapor. The atmospheric

model is used to compute Tatm .

The Forward efficiencies are measured by the IRAM

staff. You normally don’t have to care about measuring

it…..

Forward Efficiency : Skydip


Supplement


The Cornell Caltech Atacama Telescope

Bertrand Lefloch (IPAG, France) IRAM Summer School 20111.

Documents

Transcript of Bertrand Lefloch (IPAG, France) IRAM Summer School 20111.