1. Sideband Deconvolution
HIPE: Sideband Deconvolution Team
Steve Lord, Colin Borys, Joan Xie, Claudia Comito (Bonn)

2. 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:

3. 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.

4. 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)

5. Deconvolution Tool Demo Intro - The Problem
HIFI Deconvolution tool: deconvolves HIFI’s native dual sideband observations; a crucial processing need for spectral surveys.
Synthetic Spectrum
T[K]
T [K] LO
Every spectrum taken with HIFI contains the upper and lower sideband data folded together.
In regions rich with lines, the user needs a way to sort this out.
Additionally, the upper and lower sidebands may have different gains.
[GHz]
T[K]
[GHz]
[GHz]
Double sideband spectrum
Decon Workshop, Bonn, April 2010

6. 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"

7. 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.
and their tuning & performance.
Simulating the instrument allows
thorough testing of modes in
years before launch.
Cologne simulator: observation chain –
specify complex spatial and source spectrum,
continuum, cal chopping, comb calibrations,
pass ban response, standing waves,
Temporal variations in these.
Successfully used on CSO surveys and HIFI. Planned for SOFIA and ALMA
(Comito & Schilke 2002), Lord, Xie, Borys...
Decon Workshop, Bonn, April 2010

8. Conjugant Gradient Method

9. 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....

10. 10 Iterations take a few minutes Convergence after 20 iterations is typical
Blue – input spectrum, Black – iterative models.
Simulation c/o Claudia Comito

11. Real Data ... Processed without cleaning

12. Successful processing – only three scans of one line
SSB
The gap is the range of frequencies between the sidebands - never observed
DSB

13. Success - Orion Astrochemestry!

14. Several Routes: CLASS HCSS CLASS90 Scripts HCSS Scripts CLASS90 DECON
Ongoing testing
Herschel
Observations!!
Synthetic spectra
HIFI Simulator
Level 0.5
(erased)
Level 1
Bonn Simulator
Level 2 (HCSS 1.2 Only)
CLASS90 DECON
HCSS HICLASS
HCSS DECON
HCSS DECON
CLASS90 Scripts
HCSS Scripts
CLASS
HCSS

15. 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
and their tuning & performance.
Simulating the instrument allows
thorough testing of modes in
years before launch.
Cologne simulator: observation chain –
specify complex spatial and source spectrum,
continuum, cal chopping, comb calibrations,
pass ban response, standing waves,
Temporal variations in these.
Decon Workshop, Bonn, April 2010

16. HCSS Decon & XCLASS Decon
Mostly in synch - but some development differences
HCSS/HIFI (IPAC)
Deconvolution
Comment
CLASS (Bonn) Deconvolution
Sampling
Sampled Twice
Regretted
Sampled Once
Better, but…
Freq. Switch
Implemented
Tested
Tested 2011
Channel
Weights
Tests – ongoing
Not implementable
w/o CLASS Flag
Work-around planned
Piecewise Gain Fits
On Hold
Wait and see if works
Prototype
soon?
RMS
As expected by HSPOT
As expected
by HSPOT
Max Entropy
One "Offset" bug needs fixing
Decon Workshop, Bonn, April 2010

17. HIPE Deconvolution Task
Can now turn on diagnostic mode
Specify Scan Index (LO setting)
Specify USB/LSB frequency axis

18. HIPE Deconvolution Task
Interim output: DSB Input, DSB Model(iteration) for i-th LO setting, Gains(iteration) Chi-Square(iter).
LO’s listed:

19. HIPE Deconvolution Task
Metadata includes the doDeconvoluion inputs

20. HIPE Deconvolution Task
DSB Model (iteration) vs. DSB input
SSB vs. Iteration (grows!)
Chi-Square vs. Iteration

21. HIPE Deconvolution Task
Errors causing aborts are now reported with messages: e.g.: “Exceeded Maximum Iterations” Now run time