Herschel Open Time Cycle 1 DP
workshop
ESAC, 16-18 March 2011
Sideband
Deconvolution
HIPE: Sideband Deconvolution Team
Steve Lord, Colin Borys, Joan Xie, Claudia Comito
(Bonn)
- page 1
HIFI is a Heterodyne
Down-conversion is accomplished by forming the
product:
cosX cos LO = (1/2) [ cos (X - LO) + cos (X + LO) ]
Like AM radio:
- page 2
AM Radio – Time plot
Center, colored red, is the carrier wave at 558
kHz; the two mirrored audio spectra (green) are
the lower and upper sideband.
- page 3
Herschel Open Time Cycle 1 DP
workshop
ESAC, 16-18 March 2011
LO
LSB + USB = DSB
• Lower sideband spectrum is reversed and added
• Two frequency scales result in the DSB result
• The lines may blend but they can be recovered
(deconvolved)
• The continuum levels add (double) in the DSB
• The continuum slope is flattened but may be
recovered (deconvolved)
•The noise adds in quadrature , increasing as sqrt(2)
- page 4
LO
0
[GHz]
In regions rich with lines, the user needs
a way to sort this out.
T[K]
Additionally, the upper and lower
sidebands may have different gains.
800.0
816.0
[GHz]
[GHz]
Double sideband
spectrum
- page 5
850
35
800
0
Every spectrum taken with HIFI contains
the upper and lower sideband data folded
together.
Synthetic Spectrum
T [K]
T[K]
HIFI Deconvolution tool:
deconvolves HIFI’s native dual
sideband observations; a crucial
processing need for spectral
surveys.
200
Deconvolution Tool Demo
Intro - The Problem
804.
812.
Formulation of the Problem
• Start with a guess of the answer – a model with no assumptions for the SSB
spectrum – flat
• "Observe it" – using knowledge of the instrument
• compare the observations of the model with the real observations
• compute a chi square and a delta (differential) chi-square
• each model "spectral channel" was in part responsible for some of the chi
square change
• follow the slope of the chi square downward (it's partial derivitive w.r.t. the
channel flux (and optionally the sideband gain)
• new downward steps always move at right angles to previous ones in the
Conjugate Gradient Method
• Stop, when solution converges asymptotically, as defined by the "tolerance"
- page 6
The Solution - Details
With a series of LO settings, the double sidebands are marched across
the band, providing a sufficient number of over-lapping “confused”
observed double sideband spectra to constrain the single sideband
result - I.e., the source’s true spectrum – The number of overlaps of
each sideband on itself is the "Redundancy", R
The iterative chi-square minimization method, the Conjugate Gradient
Method finds the best single sideband solution using knowledge of the
chi-square gradients. Since the problem is constrained, other methods
could be used.
CGM minimizes chi-square of the model residuals.
Successfully used on CSO surveys and HIFI.
Planned for SOFIA and ALMA
(Comito & Schilke 2002), Lord, Xie, Borys...
- page 7
Conjugant Gradient Method
- page 8
Other Problems Deconvolving
• Bad Standing Waves
• Bad Baselines
• "Spurs"
• Gain Variations - in time or between sidebands:
(this one is difficult)
Some mitigation is possible
– Data cleanup
– Maximum Entropy added in....
- page 9
10 Iterations take a few minutes
Convergence after 20 iterations is typical
Blue – input spectrum, Black – iterative models.
Simulation c/o Claudia Comito
- page 10
Real Data ... Processed without
cleaning
- page 11
Successful processing – only
three scans of one line
SSB
The gap is the
range of
frequencies
between the
sidebands never
observed
DSB
- page 12
Success - Orion
Astrochemestry!
- page 13
Several Routes:
Ongoing testing
Synthetic spectra
HIFI Simulator
Herschel
Observations!!
Level 0.5
(erased)
Level 1
Bonn Simulator
HCSS HICLASS
Level 2 (HCSS 1.2 Only)
CLASS90 DECON
HCSS DECON
HCSS
CLASS90 Scripts
CLASS
DECON
HCSS Scripts
HCSS
Deconvolution - Status and
Improvement Details
Items Complete:
•Conjugate Gradient Method available in HCSS v2,3,.. for all users
•HCSS JAVA HIFI Deconvolution Package – up and running HCSS v2,3,4
•Interfaced and End-to-End tested with HCSS HIFI Simulator and
Observations
•HCSS 1,2,3… will convert Contexts (Resampling, Upper, Lower Freq.s) to
Level 2
•Integrated w/HIPE – runs with scripts or GUI – viewing with spectrum
explorer
Additional features Added:
•Included Frequency Switching Spectral Survey Deconvolutions
•Channel-by-channel weights (from Cal) included in the JAVA Software
•Improving HIPE GUI with DSB Display Capabilities, DSP products, RMS
vs. iteration number, SSB viewing
• Importing Ghost visualization tools
- page 15
HCSS Decon & XCLASS Decon
Mostly in synch - but some development differences
HCSS/HIFI (IPAC)
Deconvolution
Comment
CLASS (Bonn)
Deconvolution
Comment
Sampling
Sampled Twice
Regretted
Sampled Once
Better, but…
Freq. Switch
Implemented
Tested
Implemented
Tested 2011
Channel
Weights
Implemented
Tests –
ongoing
Not implementable
w/o CLASS Flag
Work-around planned
Piecewise
Gain Fits
On Hold
Wait and
see if works
Prototype
soon?
RMS
Max Entropy
- page 16
Implemented
As expected
by HSPOT
As expected
by HSPOT
One
Implemented
"Offset" bug
needs fixing
Tested
HIPE Deconvolution Task
Can now turn on diagnostic
mode
Specify Scan Index (LO setting)
Specify USB/LSB frequency axis
- page 17
HIPE Deconvolution Task
Interim output: DSB Input, DSB Model(iteration) for
i-th LO setting, Gains(iteration) Chi-Square(iter).
LO’s
listed:
- page 18
HIPE Deconvolution Task
Metadata includes the
doDeconvoluion inputs
- page 19
HIPE Deconvolution Task
DSB Model (iteration) vs. DSB input
SSB vs. Iteration
(grows!)
Chi-Square
vs. Iteration
- page 20
HIPE Deconvolution Task
Errors causing aborts are now
reported with messages: e.g.:
“Exceeded Maximum Iterations”
Now run time
- page 21