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Data Reduction and Analysis Techniques

Data Reduction and Analysis Techniques. Ronald J. Maddalena. Existing Analysis Systems. Continuum - Point Sources On-Off Observing. Continuum - Point Sources On-Off Observing. Known: Equivalent temperature of noise diode or calibrator (T cal ) = 3 K Bandwidth (BW) = 10 MHz Gain = 2 K / Jy.

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Data Reduction and Analysis Techniques

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  1. Data Reduction and Analysis Techniques Ronald J. Maddalena

  2. Existing Analysis Systems

  3. Continuum - Point SourcesOn-Off Observing

  4. Continuum - Point SourcesOn-Off Observing

  5. Known: Equivalent temperature of noise diode or calibrator (Tcal) = 3 K Bandwidth (BW) = 10 MHz Gain = 2 K / Jy Desired: Antenna temperature of the source (Tsrc) Flux density (S) of the source. System Temperature(Tsys) Accuracy of antenna temperature (σsrc) Continuum - Point SourcesOn-Off Observing

  6. Continuum - Point SourcesOn-OffObserving

  7. Continuum - Point SourcesAssumptions: • Narrow bandwidths, • Linear power detector, • Source intensity << Tsys, • Noise diode temperature << Tsys, • treference = tsignal • tcal_on = tcal_off • Blanking time << tsignal

  8. Phases of a ObservationTotal Power

  9. Phases of a ObservationTotal Power

  10. Continuum - Point SourcesTotal Power

  11. Phases of a ObservationSwitched Power

  12. Phases of a ObservationSwitched Power

  13. Continuum - Point SourcesBeam-Switched Observation

  14. Continuum - Point SourcesOn-The-Fly Observation

  15. Continuum - Point SourcesOn-The-Fly Observation If total power: If beam-switching (switched power):

  16. Baseline Fitting Polynomials • Set order of polynomial • Define areas devoid of emission. • --------------------------- • Creates false features • Introduces a random error to an observation,

  17. Continuum - Point Sources Gaussian Fitting • Restrict data to between the half power points, • Define initial guesses • Set flags to fit or hold constant each parameter • Set number of iterations • Set convergence criteria • ---------------------------- • Fitted parameters • Chi-square of the fit • Parameter standard deviations.

  18. Template Fitting • Create a template: • Sufficient knowledge of the telescope beam, or • Average of a large number of observations. • --------------- • Convolve the template with the data => x-offset. • Shift by the x-offset. • Perform a linear least-squares fit of the template to the data:

  19. Template Fitting

  20. Averaging Data • Tsys changes due to atmosphere emission. • Tant changes due to atmosphere opacity. • -------------------- • Use weighted average • Weights: 1/σ2.

  21. Continuum - Extended SourcesOn-The-Fly Mapping • Telescope slews • A few samples /sec. • Highly oversampled. • Could be beam switching • ---------------------- • Convert Power into Tant. • Fit baseline to each row? • Grid into a matrix

  22. Continuum - Extended SourcesOn-The-Fly Mapping - Common Problems • Striping (Emerson 1995; Klein and Mack 1995). • If beam-switched, Emerson, Klein, and Haslam (1979) to reconstruct the image. • Make multiple maps with the slew in diferent direction.

  23. Spectral-Line - Point SourcesPosition-Switched Observing

  24. SIGNAL REFERENCE Avrg Tsys Spectral-Line - Point SourcesPosition-Switched Observing

  25. Spectral-Line - Point SourcesFrequency-Switched Observing - In band Tsys(REF)*[(SIG-REF)/REF - (SIG’-REF’)/REF’

  26. Spectral-Line - Point SourcesFrequency-Switched Observing - In Band Tsys(REF)*(SIG-REF)/REF + Tsys(SIG)*(REF’-SIG’)/SIG’

  27. Spectral-LineBaseline Fitting • Polynomial: same as before • Sinusoid

  28. Spectral-LineRipples

  29. Spectral-LineOther Algorithms • Averaging: Weighted by 1/σ2 • Velocity Calibration • Velocity/Frequency Shifting • Doppler tracking limitations • Gaussian fitting • Multi-component fits should be done simultaneosuly • Smoothing • Decimating vs. non-decimating routines • Moments for Integrated Intensities; Velocity centroids, ….

  30. Spectral-LineRFI Excision

  31. Spectral-Line MappingGrid and On-the-Fly Velocity DEC RA

  32. Spectral-Line MappingGrid and On-the-Fly (If V1=V2 => Channel Map) Velocity For {v=vmin} {v <=vmax} {v++} { if T(α,δ,v) > Tmin then W(α,δ)=W(α,δ)+ T(α,δ,v) endif endfor DEC RA

  33. Spectral-Line MappingGrid and On-the-Fly Velocity (Position-velocity map) DEC RA

  34. Spectral-Line MappingRudimentary Analysis

  35. ConclusionThe Future of Single-Dish Data Analysis • Increase in the use of RDBMS. • Support the analysis of archived data. • Sophisticated visualization tools. • Sophisticated, robust algorithms (mapping). • Data pipelining for the general user. • Automatic data calibration using sophisticated models of the telescope. • Algorithms that deal with data sets. • Analysis systems supported by cross-observatory groups

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