Data Reduction and Analysis Techniques

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Data Reduction and Analysis Techniques

• Ronald J. Maddalena

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Existing Analysis Systems
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Continuum - Point SourcesOn-Off Observing
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Continuum - Point SourcesOn-Off Observing
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Continuum - Point SourcesOn-Off Observing

• 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 (ssrc)

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Continuum - Point SourcesOn-Off Observing
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Continuum - Point SourcesAssumptions

• Narrow bandwidths,
• Linear power detector,
• Source intensity ltlt Tsys,
• Noise diode temperature ltlt Tsys,
• treference tsignal
• tcal_on tcal_off
• Blanking time ltlt tsignal

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Phases of a ObservationTotal Power
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Phases of a ObservationTotal Power
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Continuum - Point SourcesTotal Power
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Phases of a ObservationSwitched Power
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Phases of a ObservationSwitched Power
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Continuum - Point SourcesBeam-Switched
Observation
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Continuum - Point SourcesOn-The-Fly Observation
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Continuum - Point SourcesOn-The-Fly Observation
If total power
If beam-switching (switched power)
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Baseline Fitting Polynomials

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

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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.

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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 gt x-offset.
• Shift by the x-offset.
• Perform a linear least-squares fit of the
  template to the data

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Template Fitting
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Averaging Data

• Tsys changes due to atmosphere emission.
• Tant changes due to atmosphere opacity.
• --------------------
• Use weighted average
• Weights 1/s2.

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Continuum - Extended Sources On-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

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Continuum - Extended Sources On-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.

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Spectral-Line - Point SourcesPosition-Switched
Observing
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Spectral-Line - Point SourcesPosition-Switched
Observing
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Spectral-Line - Point SourcesFrequency-Switched
Observing - In band
Tsys(REF)(SIG-REF)/REF - (SIG-REF)/REF
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Spectral-Line - Point SourcesFrequency-Switched
Observing - In Band
Tsys(REF)(SIG-REF)/REF Tsys(SIG)(REF-SIG)/SI
G
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Spectral-LineBaseline Fitting

• Polynomial same as before
• Sinusoid

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Spectral-LineRipples
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Spectral-LineOther Algorithms

• Averaging Weighted by 1/s2
• 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, .

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Spectral-LineRFI Excision
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Spectral-Line MappingGrid and On-the-Fly
Velocity
DEC
RA
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Spectral-Line MappingGrid and On-the-Fly
(If V1V2 gt Channel Map)
Velocity
For vvmin v ltvmax v if T(a,d,v) gt
Tmin then W(a,d)W(a,d) T(a,d,v)
endif endfor
DEC
RA
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Spectral-Line MappingGrid and On-the-Fly
Velocity
(Position-velocity map)
DEC
RA
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Spectral-Line MappingRudimentary Analysis
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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