A Quick Review. Spectral Line Calibration Techniques with Single Dish Telescopes. The Rayleigh-Jeans Approximation. Antenna Temperature

Transcription

1 Spectral Line Calibration Techniques with Single Dish Telescopes A Quick Review K. O Neil NRAO - GB A Quick Review A Quick Review The Rayleigh-Jeans Approximation Antenna Temperature Planck Law for Blackbody radiation: B= 2hν 3 1 c 2 e hν/kt - 1 If ν~ghz, often hν << kt. Taylor series gives: 2kTν B= 2 2kT = Source flux in Rayleigh Jeans limit: 2k S= Ωs T(θ,φ)dΩ If brightness temperature is constant across source: S = c 2 λ 2 λ 2 2kT Ω S λ 2 B=Brightness, ν = frequency; h = x J s; k = x J K -1 ;T = temperature Antenna theorem: A e Ω A = ε r λ 2 Measured flux: S = 2kT A λ 2 Ω A 2kT = A A Temperature: e T A = (A e /λ 2 ) T src (θ,φ)p n (θ,φ)dω = (ε r /Ω A ) T src (θ,φ)p n (θ,φ)dω A = area; Ω = Solid angle of tel. pattern; ε r = fractional power transmission; λ = wavelength; S=Flux, k = x J K -1, T = temperature; P = antenna power pattern A Quick Review Antenna Temperature Temperature: T A = (A e /λ 2 ) T src (θ,φ)p n (θ,φ)dω = (ε r /Ω A ) T src (θ,φ)p n (θ,φ)dω Point Source: T A = (ε r /Ω A ) T src (θ,φ) dω = ε r (Ω S /Ω A )T avg Source > Beam, T=T const T A = (ε r T const /Ω A ) P n (θ,φ) dω = ε r (Τ const /Ω A )Ω b A Quick Review Minimal Detectable Temperature Set by the system noise T sys = T A + (1/ε)T R + T LP [1/ε -1] Sensitivity is rms noise of system: T rms = K S T sys / ( ν t n) B rms = (2k/λ 2 ) K S T sys / ( ν t n) S rms = (2k/A e ) K S T sys / ( ν t n) T min ~ 5 X T rms T R = receiver temperature; T LP = transmission line temperature; ε = efficiency transmission; K S = telescope sensitivity constant (~1); ε r = fractional power of antenna transmission; Ω A = antenna solid angle; P n(θ,φ) = antenna power pattern; Ω b = solid angle subtended by main beam and side lobes n = pre-detection bandwidth (Hz); t = integration time, one record; n= number of records 1

2 A Quick Review Antenna Temperature Telescope observes a point source (flux density S) Telescope feed replaced with matched load (resistor) Determining the Source Temperature Load temperature adjusted until power received equals power of the source This is equal to the Antenna Temperature Measured Intensities Measured Intensities T meas (α,δ,az,za) = T src (α,δ,az,za) + T RX + T gr (za,az) + T cel (α,δ,t) + T CMB + T atm (za) T meas = T source + T everything else Arbitrary Units ON T source + T everything else Arbitrary Units OFF T everything else channel channel Relative Intensities Relative Intensities ON - OFF (T source + T everything else ) - (T everything else ) (ON OFF)/OFF [(T source + T everything else ) - (T everything else )]/ T everything else Arbitrary Units % T sy s channel channel 2

3 Baseline Fitting with Best Fit Line T source = (ON OFF) OFF?????? Image on right courtesy of C. Conselice Baseline Fitting with Best Fit Line Frequency Switching Simplest & most efficient method Not feasible if: Line of interest is large compared with bandpass Standing waves in data Cannot readily fit bandpass Errors are primarily from quality of fit Raw spectra Frequency Switching Frequency Switching Allows for rapid switch between ON & OFF observations Does not require motion of telescope Can be very efficient Disadvantages: Frequency of line of interest must be known System must be stable Will not work with time or frequency varying baselines Calibrated spectra 3

4 Position Switching Position Switching ON Source OFF Source Little a priori information needed Typically gives very good results Disadvantages: System must be stable in time Requires re-pointing the telescope Results in time off source Sky position must be carefully chosen Source must not be too extended Best results if the same sky (AZ, EL) position used Beam Switching Beam Switching 2 Beams Same idea as position switching Removes need to move telescope Disadvantages/Caveats: Requires hardware to exist Sky position must be carefully chosen Source must not be extended beyond throw Same idea as position switching Removes need to move telescope Always on source! Disadvantages/Caveats: Requires additional hardware Sky position must be carefully chosen Source must not be extended beyond beam separation Baseline Fitting with an Average Fit Position Switching on Strong Continuum ON Source 1 OFF Source 1 Alternative if frequency switching is not an option May lose detailed information for individual fits System must be very stable ON Source 2 OFF Source 2 4

5 Position Switching on Strong Continuum Position Switching on Strong Continuum Possibly only alternative if T src > few x T sys Designed to remove residual standing waves [(On Off)] 1 [(On Off)] 2 Result: R= [On(ν) Off(ν)] source1 [On(ν) Off(ν)] source2 [(On Off)/Off] 1 [(On Off)/Off] 2 Standard (On Off)/Off From ATOM by Ghosh & Salter From ATOM bu Ghosh & Salter Position Switching on Strong Continuum (ON OFF)/OFF [(T source + T everything else ) - (T everything else )]/ T everything else Standard (On Off)/Off Result = T source T system [(On Off)/Off] 1 [(On Off)/Off] 2 Units are: % System Temperature [(On Off)] 1 [(On Off)] 2 Need to determine system temperature to calibrate data From ATOM by Ghosh & Salter Determining System Temperature T meas (α,δ,az,za) = T src (α,δ,az,za) + T RX + T gr (za,az) + T cel (α,δ,t) + T CMB + T atm (za) T meas = T source + T system 5

6 Theory 1 - Noise Diodes Measure various components of T sys: Decreasing T RX Can be readily measured/monitored Confidence T CMB Well known (2.7 K) T cel (α,δ,t) Can be determined from other (tel.) measurements T atm (za) Can be determined from other (tel.) measurements T gr (za,az) Can be calculated 1 - Noise Diodes 1 - Noise Diode Measurement Considerations Frequency dependence T src /T sys = (ON OFF)/OFF... T diode / T sys = (On Off) / Off T sys = T diode * Off/(On Off) Lab measurements of the GBT L-Band calibration diode, taken from work of M. Stennes & T. Dunbrack - February 14, Noise Diode Measurement Considerations 1 - Noise Diode Measurement Considerations Time stability Accuracy of measurements: Typically measured against another diode or other calibrator Errors inherent in instruments used to measure both diodes Measurements often done in lab. Have numerous losses through path from diode injection to back ends σ 2 measured value = σ2 standard cal + σ2 instrumental error + σ2 loss uncertainties 6

7 1 - Noise Diode Measurement Considerations The Y-Factor (Two Diodes) Frequency dependence Time stability Accuracy of measurements T 1 + T off T 1 - YT 2 Y = T T off = 2 + T off Y - 1 σ 2 measured value = σ2 standard cal + σ2 instrumental error + σ2 loss uncertainties σ 2 total = σ2 freq. dependence + σ2 stability + σ2 measured value + σ2 conversion error Can be more accurate than just one diode Ignores effects of the antenna Same idea as two diodes Takes antenna into account True temperature measurement (no conversion) Cooling System T cold Absorber (T hot/cold ) Hot Load T hot T off = T 1 - YT 2 Y - 1 7

8 Same idea as two diodes Takes antenna into account True temperature measurement (no conversions) Requires a reliable load able to encompass the receiver, Requires a reliable load able to encompass the receiver, with response fast enough for on-the-fly measurements with response fast enough for on-the-fly measurements 3 - Astronomical Measurements Use sources with well determined fluxes for calibration Easy to obtain high spectral frequency resolution Uses same hardware as observations Requires extremely reliable measurements of source flux Error will always be dominated by source error Determining T sys Theory: Needs detailed understanding of telescope & structure Atmosphere & ground scatter must be stable and understood Noise Diodes: Can be fired rapidly to monitor temperature Requires no lost time Depends on accurate measurements of diodes Hot/Cold Loads: Can be very accurate Observations not possible when load on Must be in mm range for on-the-fly measurements Astronomical Measurements: Can be very accurate Uses the same hardware as astronomical measurements Must know source fluxes extremely well (ON OFF) T source = T OFF system Determining Telescope Response Blank Sky or other From diodes, Hot/Cold loads, etc. Telescope response has not been accounted for! 8

9 1 - Ideal Telescope Main Beam Brightness: T MB = η beam T measured Flux Density: S = 2k T(θ,φ) Pn (θ,φ)dω λ 2 Units: W m -2 Hz -1 or Jy (1 Jy = W m -2 Hz -1 ) Accurate gain, telescope response can be modeled Can be used to determine the flux density of standard continuum sources Not practical in cases where telescope is non-ideal (blocked aperture, cabling/electronics losses, ground reflection, etc) Ω = Solid angle of tel. pattern; η beam = telescope efficiency; λ = wavelength; S=Flux, k = constants, T = temperature; P = antenna power pattern 1 - Ideal Telescope 2 - Bootstrapping Observe source with pre-determined fluxes Determine telescope gain T source = (ON OFF) T system 1 OFF GAIN OFF T GAIN = system (ON OFF) T source 2 - Bootstrapping 3 - Pre-determined Gain Values Useful when gain is not readily modeled Offers ready means for determining telescope gain Requires flux of calibrator sources be known in advance Not practical if gain changes rapidly with position Pre-determined Gain curves: Allows for accurate representation of gain at all positions Saves observing time Can be only practical solution 9

10 3 - Pre-determined Gain Values 3 - Pre-determined Gain Values Average Gain [(pola+polb)/2]: gainavg(az,za,f=1415mhz) = *za *(za-14) *(za-14) x10-08*cos(az) x10-07*sin(az) x10-08*cos(2*az) *sin(2*az) *cos(3*az) *sin(3*az) gainavg(az,za,f=1175mhz) = *za *(za-14) *(za-14) x10-06*cos(az) x10-07*sin(az) x10-07*cos(2*az) x10-07*sin(2*az) *cos(3*az) *sin(3*az) gainavg(az,za,f=1300mhz) = *za *(za-14) *(za-14) x10-07*cos(az) x10-07*sin(az) x10-07*cos(2*az) x10-07*sin(2*az) *cos(3*az) *sin(3*az) gainavg(az,za,f=1375mhz) = *za *(za-14) *(za-14) x10-07*cos(az) x10-06*sin(az) x10-08*cos(2*az) x10-07*sin(2*az) *cos(3*az) *sin(3*az) gainavg(az,za,f=1550mhz) = *za *(za-14) (za-14) x10-07*cos(az) x10-07*sin(az) x10-08*cos(2*az) x10-07*sin(2*az) *cos(3*az) *sin(3*az) 3 - Pre-determined Gain Values Pre-determined Gain values: Allows for accurate representation of gain at all positions Saves observing time Can be only practical solution Caveat: Observers should always check the predicted gain during observations against a number of calibrators! T source = (ON OFF) 1 T OFF system GAIN Blank Sky or other From diodes, Hot/Cold loads, etc. Great, you re done? done! Theoretical, or Observational A Few Other Issues Other Issues Pointing Results in reduction of telescope gain Typically can be corrected in telescope pointing model or offset 10

11 Other Issues Focus Other Issues Side Lobes* Allows in extraneous or unexpected radiation Can result in false detections, over-estimates of flux, incorrect gain determination Results in reduction of telescope gain Can be corrected mechanically if rcvr/subreflector can be adjusted Solution is to fully understand shape and variance in side lobes Beam Other Issues Comatic Error Sub-reflector shifted perpendicular from main beam Results in an offset between the beam and sky pointing Other Issues Deformities in the reflectors Astigmatism Image from ATOM 99-02, Heiles Image from ATOM 99-02, Heiles Can result in false detections, over-estimates of flux, incorrect gain determination Solution is to fully understand beam shape The End List of useful references pp in book 11