1. Adwin Boogert, NHSC/IPAC, Pasadena, CA, USA
HIFI Standing Waves
Adwin Boogert, NHSC/IPAC, Pasadena, CA, USA

2. HIFI Standing Waves Standing wave characteristics depend on HIFI band:
Bands 1-5: up to 10 optical (pre-mixing) standing waves detected.
Different shapes between bands with beam-splitter (1,2,5) and diplexer (3,4).
Bands 6 and 7 have electronic (post-mixing) standing waves, whose shape and amplitude depend on HEB current.

3. HIFI Standing Waves
Band 2 (beamsplitter)
(courtesy Ronan Higgins)

4. HIFI Standing Waves
Band 4 (diplexer)
(courtesy Ronan Higgins)

5. HIFI Standing Waves
Diplexer vs. beamsplitter
(courtesy Ronan Higgins)

6. HIFI Standing Waves (courtesy Ronan Higgins) Bands 6 and 7
Standing wave shows
'dispersed' sine wave
(courtesy Ronan Higgins)

7. HIFI Standing Waves (courtesy Ronan Higgins) Bands 6 and 7
empirical solution:
match standing wave
with stability
observation at equal
HEB current.
(courtesy Ronan Higgins)

8. HIFI Standing Waves
To remove standing waves one needs to know if they are additive or multiplicative to stellar signal.
Standing wave amplitude in principle multiplicative with incoming wave intensity
Ground based telescopes thermal background MUCH larger than stellar signal. Standing wave amplitudes large w.r.t. stellar signal, but ideally they are subtracted in chop/nod process. Residual standing waves may come from system instabilities and are additive w.r.t. weak stellar signal.
How about HIFI at Herschel? Will system instabilities give dominating additive residual standing wave term or only (small) multiplicative term?

9. HIFI Standing Waves Removing additive (residual) waves:
If waves additive: determine properties in DSB spectrum away from stellar lines and subtract wave from entire spectrum.
Multiple-sine wave fitting tool available in IDL. Being implemented in HCSS.

10. HIFI Standing Waves Band 1A: ILT (worst case!) Band 1A
Frequency [GHz]
Normalized Intensity
Band 1A:
Band 1A
Standing wave removal needed for all HIFI AOTs, either as a residual (e.g. chopped/nodded spectra) or if OFF sky not taken with FSwitch or LoadChop modes.
Robust sine wave fitting routine for ISO/SWS and Spitzer/IRS defringing available in IDL. Fits multiple sine waves, using Bayesian statistics. Little user interaction. Contains line blanking routine.
Tool being developed in HIPE. May be used for PACS and SPIRE spectra as well.
ILT (worst case!)
IF frequency [MHz]

11. HIFI Standing Waves
'Fringes'-diagnostic plot --- 2 vs frequency, with clear minimum (red)
Standing waves successfully removed in gas cell spectra. (residual) standing wave patterns likely different in space. However, algorithm very flexible! Initial guesses easily adjusted.

12. HIFI Standing Waves (courtesy Patrick Hennebelle)
Sine wave fitting method obviously fails for multiplicative waves:
(courtesy Patrick Hennebelle)

13. HIFI Standing Waves
Before, during or after deconvolution spectral scans? Depends on pre-mixing wave stability and whether it is additive or multiplicative:
If pre-mixing waves depend on LO frequency: remove before deconvolution
If waves additive and pre-mixing wave independent of LO frequency, they will be deconvolved like additive stellar signals and can be removed afterwards.
If waves multiplicative: need to remove wave before or during deconvolution (together with gain solution). Need to know pre-mixing wave characteristics.
Needs much more testing!