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Noise Diodes, Calibration, Baselines & Nonlinearities

Noise Diodes, Calibration, Baselines & Nonlinearities. Ron Maddalena NRAO, Green Bank, WV Shelly Hynes Louisiana School for Math, Science and the Arts, Natchitoches, LA Charles Figura Wartburg College, Waverly, IA July 27, 2006. Calibration Data. June 18, 2006

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Noise Diodes, Calibration, Baselines & Nonlinearities

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  1. Noise Diodes, Calibration, Baselines & Nonlinearities Ron Maddalena NRAO, Green Bank, WV Shelly Hynes Louisiana School for Math, Science and the Arts, Natchitoches, LA Charles Figura Wartburg College, Waverly, IA July 27, 2006

  2. Calibration Data • June 18, 2006 • C-Band – Off-On Observations • Multiple calibration sources, same hardware, same attenuator/filter settings • Tcal calibration data – Various combinations of polarization, high/low noise diodes • Data consists of: • Sigon = On source, noise diode on • Sigoff = On source, noise diode off • Refon = Off source, noise diode on • Refoff = Off source, noise diode off

  3. Sig and Ref Definitions

  4. Sig and Ref Definitions

  5. Current Calibration Method So Tsys loses all frequency information…

  6. Astronomical Tcal If h is unknown… Source: Johnson et.al., 2002

  7. Linear Vector Tcal Expressions

  8. Now Tsys retains the frequency structure

  9. Power Characterization

  10. ‘Resids’ for Spectral Processor

  11. Resids vs. Power InC-Band

  12. Nonlinear Theory • Include a second-order correction for gain – • So the temperature equations become

  13. Non-Linear SolutionsFor Calibration

  14. Nonlinear Application • Evaluate C, B, Tcal, using a known calibration source. • Because nonlinearity is encapsulated within P’out, we can use the previous expressions from the linear case:

  15. Calibration Data • June 18, 2006 • C-Band – Off-On Observations • Multiple calibration sources, same hardware, same attenuator/filter settings • Tcal calibration data – Various combinations of polarization, high/low noise diodes • July 15, 2006 • 3C147 • C-Band, low-diode, linear polarization • Various attenuator settings at various places • S-band Scal calibration data – Various combinations of polarization, high/low noise diodes

  16. Tsys Comparison Nonlin Lin

  17. Tcal Comparison Nonlin Lin

  18. Baseline Improvement NonLin Linear Cat Traditional

  19. Source of ‘Baselines’ – TraditionalAssuming Linear

  20. Source of ‘Baselines’ – Traditional Non-Linear

  21. Time Dependence NonLin Linear Cat S13C11x July 15, 2006, t = 0 hours

  22. Time Dependence NonLin Linear Cat S34C11x July 15, 2006, t = 2 hours

  23. TA Comparisons t = 2 hours Red – Early Blue - Late

  24. Time Dependence NonLin Linear Cat S69C11x July 15, 2006, t = 4 hours

  25. TA Comparisons t = 4 hours Red – Early Black - Late

  26. Time Dependence NonLin S34C11x NonLin S377C11x

  27. Noise Estimates – Vector Tcal Assuming Tcal << Tsys Assume Tsys = 10*Tcal, NChan = 1, tref = tsig Tsrc = 0 --- σ2=2*Tsys/(ChanWidth * tsig) Tsrc = Tcal ---σ2=4.2*Tsys/(ChanWidth * tsig) Tsrc = 2Tcal --- σ2=10.4*Tsys/(ChanWidth * tsig) Tsrc = Tsys --- σ2=205*Tsys/(ChanWidth * tsig)

  28. System Determination -3dB (IF) -6dB (IFR) -6dB (CR) -6dB (IF) -10dB (IF)

  29. System Determination +3dB (IF) +6dB (CR) +6dB (IF) +10dB (IFR) +10dB (IF)

  30. System Determination-3dB IFRack NonLin Linear Cat

  31. System Determination-6dB IFRack NonLin Linear Cat

  32. System Restoration NonLin Linear Cat

  33. Summary • Using a vector form of Tcal for baselines is better than traditional, regardless of linear or non-linear assumptions. • Baselines are slightly improved by the quadratic approximation, • Cannot achieve good noise, good baselines, and good calibration simultaneously – Compromise!! • System rebalancing restores original nonlinearity. • Data taken with major ‘distortions’ to power levels can be recovered. • ‘C’ remains fairly constant with time.

  34. Conclusions • Extended sources should not be used to determine linearities, Scals, etc. • Polarized sources must be corrected for. • Very bright sources cannot be handled by the 2nd order nonlinear approximation.

  35. Recommendations • At a minimum, use the vector form of Tcal. • Use compact sources for calibrations. • For many observations, the linear approximation is sufficient. • Balancing often isn’t necessary and actually may be detrimental since C will change. • Don’t skimp on channels – more channels, less compromises between noise and baseline

  36. Catalog Calibration

  37. Non-Linear Derivation Prefoff = A + BPout + CPout2 (Eq1) Prefon = A + B (Pout+Pcal) + C (Pout+Pcal)2 (Eq2) Psourceoff = A + B (Pout+Psource) + C (Pout+Psource)2 (Eq3) Psourceon = A + B (Pout+Pcal+Psource) + C (Pout+Pcal+Psource)2 (Eq4)

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