Planck Pre-Launch Status Papers - APC - Université Paris Diderot ...

F. Villa et al.: Calibration of LFI flight model radiometersby a factor a to the sky load and reference load temperature. By ˜G refdifferencing these two signals a very stable output is obtained,which allows the measurement of very faint signals.Assuming negligible mismatches between the two radiometerlegs and within the phase switch, the differenced radiometeroutput at each detector averaged over the bandwidth β can bewritten in terms of overall gain, G tot in units of V/K, and noisetemperature, T N ,as) )]V out = G tot[(˜T sky + T N − r ·(˜T ref + T N×G tot = a · k · β · G fe L wg G be×T N ≃ T (fe)N+ T (be)N· (1)G feHere we further define the waveguide losses as L wg ,thefront-endnoise temperature a T (fe)N,andtheback-endnoisetemperatureasT (be)N,andwithk,theBoltzmannconstant.Thenoisecontributionof the waveguides due to its attenuation is negligible and notconsidered here.The ohmic losses of the feedhorn – OMT assembly, L fo ,andof the 4K Reference load system, L 4K ,modifytheactualskyand reference load through the following equations˜T sky = T (sky+ 1 − 1 )T phys (2)L fo L fo˜T ref = T (ref+ 1 − 1 )T phys , (3)L 4K L 4Kwhere T phys its the physical temperature (close to 20 K at operationalconditions).The r factor in Eq. (1) isthegainmodulationfactorcalculatedasr = ˜T sky + T N, (4)˜T ref + T Nwhich nulls the radiometer output. A more general form of theaveraged power output, which takes into account various nonidealbehaviors of the radiometer components, can be found inSeiffert et al. (2002)andMennella et al. (2003). The key parametersneeded to reconstruct the required signal (differences of T skyfrom one point of the sky to another) are therefore the photometriccalibration, G tot ,andthegainmodulationfactor,r,whichis used to suppress the effect of 1/ f noise. Deviations from thisfirst approximation are treated as systematic effects.2.2. Signal modelTo better understand the purpose of the calibration, it is usefulto write Eqs. (1) to(4) appropriatelysothattheattenuationcoefficientsare taken into account in the RCA parameters insteadof considering their effects as a target effective temperature. Forthe sky signal the output can be written as( )V skyout = ˜G skytot Tsky + ˜T skyN , (5)˜G skytot = a · k · β 1 1G fe G be , (6)L fo L wg˜T skyN = T N + [ ](L fo − 1) T phys , (7)and equivalently for the reference signal), (8)Vout ref = ˜G reftot(Tref + ˜T refNtot = a · k · β 1L 4KG fe1L wgG be , (9)˜T refN = T N + [ (L 4K − 1) T phys]. (10)Differencing Eqs. (5) and(8) weobtainthedifferenced (sky –ref) output similar to Eq. (1)[( )V out = G ∗ tot Tsky + ˜T ( )] skyN − r∗T ref + ˜T Nref , (11)G ∗ tot = G tot1L fo, (12)r ∗ = r L foL 4K· (13)Equations (5), (8), and (11) arethebasisfortheRCAcalibration,because all parameters involved were measured during theRCA test campaign by stimulating each RCA at cryo temperature(close to the operational in-flight conditions) with severalknown T sky and T ref values.2.3. Radiometer chain assembly calibration planEach RCA calibration included (i) functional tests, to verify thefunctionality of the RCA; (ii) bias tuning, to set the best amplifiergains and phase switch bias currents for maximum performance(i.e. minimum noise temperature and best radiometerbalancing); (iii) basic radiometer property measurements to estimateG ∗ , ˜T skyN, ˜TN ref;(iv)noiseperformancemeasurementstoevaluate 1/ f ,whitenoiselevelandther ∗ parameter; (v) spectralresponse measurements to derive the relative bandshape; (vi)susceptibility measurements of radiometer thermal variations toestimate the dependence of noise and gain with temperature. Thelist of tests is given in Table 1 together with a brief descriptionof the purpose of each test.Although the calibration plan was the same for all RCAs, thedifferences in the setup between 30/44 GHz and 70 GHz resultedin a different test sequence and procedures, which retained theobjective of RCA calibration unchanged.At 70 GHz the RCA tests were carried out in a dedicatedcryogenic chamber developed by DA-Design 4 (formerly YlinenElectronics), which was capable of accommodating two RCAsat one time. Thus the RCA test campaign was planned for threeRCA pairs, namely RCA18 and RCA23, RCA19 and RCA20, RCA21and RCA22.At30and44GHz,onlyoneRCAatatimewascalibrated.Due to the different length of the waveguides, the thermalinterfaces were not exactly the same for different RCAs, whichresulted in a slightly different thermal behavior of the cryogenicchamber and thus slightly different calibration conditions.3. Radiometer chain assembly calibration facilitiesIn both cases, the calibration facilities used the cryogenic chamberdescribed in Terenzi et al. (2009b), a calibration load, theskyload (Terenzi et al. 2009a), electronic ground support equipment(EGSE) and software (Malaspina et al. 2009). The heartof the EGSE was a breadboard of the LFI flight data acquisitionelectronics (DAE) with Labwindow TM5 software to controlthe power supplies to the FEMs and BEMs, read all the housekeepingparameters and digitize the scientific signal at 8 KHzwithout any average or time integration. The EGSE sent datacontinuously to a workstation operating the Rachel (RAdiometer4 http://www.da-design.fi/space5 http://www.ni.com/lwcvi/Page 3 of 14