A new off-point-less method for sub/mm spectroscopy with FMLO / FMLO 2017-08-30

"OFXPGGQPJOUMFTTNFUIPE GPSTVCNNTQFDUSPTDPQZXJUI'.-0 Akio Taniguchi (IoA, UTokyo) D3 Workshop @ Nobeyama
Radio Observatory

Akio Taniguchi / A new off-point-less method for sub/mm spectroscopy
with FMLO 2 20 2017.08.30 Introduction - Very quick look at the sub/millimeter astronomy - 100 GHz 1 THz 10 THz 10 GHz ν 1 mm 1 cm 100 μm 10 μm 10 cm λ cm mm FIR/submm Near-/Mid-IR ൩ظܕ੕ͷ࣭ྔ์ग़ ௒৽੕࢒֚ ੕ܗ੒ྖҬ ݪ࢝࿭੕ܥԁ൫ ڊେϒϥοΫϗʔϧ ͷߴΤωϧΪʔݱ৅

with FMLO 2 20 2017.08.30 Introduction - Very quick look at the sub/millimeter astronomy - 100 GHz 1 THz 10 THz 10 GHz ν 1 mm 1 cm 100 μm 10 μm 10 cm λ cm mm FIR/submm Near-/Mid-IR ॳظӉ஦Ͱ஀ੜɾ੒௕ ͢Δരൃత੕ܗ੒ۜՏ

Akio Taniguchi / ۜՏܗ੒γϛϡϨʔγϣϯ (Boylan-Kolchin et al. 2009) A new
off-point-less method for sub/mm spectroscopy with FMLO 3 20 2017.08.30 Introduction - Two types of sub/millimeter telescopes - Interferometer Single dish ALMA (NAOJ/ESO/NRAO) ASTE (NAOJ) • observing with multiple antennas to achieve larger virtual diameter and aperture • higher spatial resolution (~ 0.01") • lower field of view • observing with single antenna • wider field of view (FoV) • lower spatial resolution (~ 10")

Akio Taniguchi / ۜՏܗ੒γϛϡϨʔγϣϯ (Boylan-Kolchin et al. 2009) A new
off-point-less method for sub/mm spectroscopy with FMLO 3 20 2017.08.30 Introduction - Two types of sub/millimeter telescopes - Interferometer Single dish 7.5 arcmin ※in the case of camera observation 0.4 arcmin ALMA (NAOJ/ESO/NRAO) ASTE (NAOJ) • observing with multiple antennas to achieve larger virtual diameter and aperture • higher spatial resolution (~ 0.01") • lower field of view • observing with single antenna • wider field of view (FoV) • lower spatial resolution (~ 10")

Akio Taniguchi / Wide field imaging and spectroscopy are necessary
to "survey" distant galaxies ۜՏܗ੒γϛϡϨʔγϣϯ (Boylan-Kolchin et al. 2009) A new off-point-less method for sub/mm spectroscopy with FMLO 3 20 2017.08.30 Introduction - Two types of sub/millimeter telescopes - 7.5 ar ※in the case of ca 0.4 arcmin ALMA (NAOJ/ESO/NRAO) ASTE (NAOJ)

with FMLO 4 20 2017.08.30 Introduction - Observing methods of single dish radio telescopes - Continuum camera Spectroscopy • spatially aligned photon detector pixels (dP → dT) • Npixel ~ 102 - 104 • Nfreq ~ 1 (no spectral info)  (dν ~ several ten GHz)  • Spectroscopic channels  along frequency (filter-bank) • Nfreq ~ 103 - 104 (R ~104-105) • Npixel ~ a few (no spatial info) Hatsukade et al. 2011 Kaifu et al. 2004 Map Spectrum

with FMLO 5 20 2017.08.30 Introduction - Issues of sub/millimeter single dish observations - • Issue 1ɿImproving spatial resolution • (resolution) = (wavelength) / (diameter) [radian] • higher resolution requires larger diameter  → ground-base (such as 45m, LMT, LST 50m) • Issue 2ɿRemoving background noise from atmosphere • mainly attributed to H2O molecules not uniformly distributed in the troposphere, which move on wind flow • it restricts sensitivity (“background-limited” observations) • it yields thermal noise 103-104 times larger than astronomical signal and its power fluctuates ~ 1s ɾRemoving background noise efficiently ɾReproducing (much smaller) astronomical signal

with FMLO 6 20 2017.08.30 Introduction - Removing background noise as "correlated" noise - ~1 km H2O layer angular diameter of ASTE FoV (7.5’) 1.3 m near-field beam 10 m ASTE 10m • Correlated noise • thermal noises which commonly enter all (or partial) pixels of camera with same power (common mode) • Source 1: atmospheric emission • mainly attributed to H2O rotational emission • thickness of H2O layer ~ 1 km (near-ﬁeld)  → detectors of camera see the same sky • Source 2: instruments (detector, etc) • microphonic noise, gain ﬂuctuation • commonly added to the readout cable or circuit of sub-group of detectors Camera ాଜཅҰ "ϛϦ೾αϒϛϦ೾ΧϝϥʹΑΔ޿ࢹ໺Πϝʔδϯά"

with FMLO 7 20 2017.08.30 Introduction - Removing background noise from atmosphere and instruments - 25OOO Jy/beam 0 mJy/beam 255OO' mJy/beam 25OOO 255OO Figure 2. Dealing with degeneracies. The awkward choice between keeping more extended emission or paying the price of higher map noise: an example of a simulated 100 mJy point source implanted in a single 8-minute blank-field LABOCA scan and reduced three different ways. Shown are a direct map (top left), produced with signal centering only, a map with correlated sky removal (top center), and with additional band-cable decorrelation (top right) taking place before the mapping step. The corresponding effective map rms values are 4.4, 0.012, and 0.011 Jy/beam respectively. Below the maps are the normalized (see Sec. 5.9) residual pixel-to-pixel covariances after the reduction, for the 234 working channels in the array, here with the diagonal 1 values zeroed. The left map preserves source structures on all scales, but these would only be seen if are well in excess of the whopping ∼4 Jy/beam apparent noise level. As the covariance matrix below it demonstrates the data has strong correlated signals across the full array (consistent with atmospheric noise), at levels thousands of times above the detector white noise level. Note, that the larger scales are more severely affected in the map. After removal of the atmospheric noise, the image (top center) no longer contains scales >FoV (∼11’), but pixel ID (1→234) pixel ID (1→234) Relative power of covariance for (self) variance ʢnormalized to self variance = residual white noiseʣ Covariance Matrix Continuum Map Raw data Removing Atmosphere Removing Atm. + instrument 30% 4% x10^4 Kovacs 2008 Dec. (J2000) R.A. (J2000) 10 Jy 0.05 Jy 0.05 Jy source source source

with FMLO 8 20 2017.08.30 Signal Processing of Camera - High efficiency observation by removing correlated noise - • High efficiency is already done with multi pixel camera • removal of correlated noises which commonly fall on the array detecters • High-rate-sampling mapping of multi-pixel camera (~10 Hz)  with modulation of field of view (FoV) • astronomical signals are modulated at high frequency domain (~10 Hz) • correlated noises dominated at low frequency domain (1/f, 1/f2 like) • finally correlated noises are removed by high-pass filter such as PCA Power spectrum density (PSD) of timeseries data of one pixel Observing time (sec) Intensity (K) Time frequency (Hz) PSD (K/Hz) noises signal AzTEC/ASTE (Wilson et al. 2008) FFT

with FMLO 8 20 2017.08.30 Signal Processing of Camera - High efficiency observation by removing correlated noise - • High efficiency is already done with multi pixel camera • removal of correlated noises which commonly fall on the array detecters • High-rate-sampling mapping of multi-pixel camera (~10 Hz)  with modulation of field of view (FoV) • astronomical signals are modulated at high frequency domain (~10 Hz) • correlated noises dominated at low frequency domain (1/f, 1/f2 like) • finally correlated noises are removed by high-pass filter such as PCA Power spectrum density (PSD) of timeseries data of one pixel AzTEC/ASTE (Wilson et al. 2008) Time frequency (Hz) PSD (K/Hz) Observing time (sec) Intensity (K) PCA (HPF) FFT

with FMLO 9 20 2017.08.30 Signal Processing of Camera - Estimating and removing correlated noise by Principal Component Analysis - Correlated noise Signal Raw data map integration PC1 PC2 D-dim space ϐΫηϧDݸ snapshot at t=ti plot time-series data in D-dimensional space reconstruct time-series data using large k PCs → correlated noises

with FMLO 9 20 2017.08.30 Signal Processing of Camera - Estimating and removing correlated noise by Principal Component Analysis - Correlated noise Signal Raw data map integration PC1 PC2 D-dim space ϐΫηϧDݸ snapshot at t=ti plot time-series data in D-dimensional space reconstruct time-series data using large k PCs → correlated noises Signal Raw data if not converged estimate correlated noise iteratively

with FMLO 10 20 2017.08.30 Signal Processing of Camera - Estimating and removing correlated noise by Principal Component Analysis - Figure 17. An 850 µm rotating PONG map of M17. Intensity is logarithmically scaled between −0.0003 (white) and +0.01 pW (black). Iteration numbers are given in the corner of each panel. Panels (a) and (b) show the results for a reduction using the baseline parameters (the solution halted after reaching the map-based convergence criterion in 17 iterations). Panel (a) also depicts the array footprint (position angle indicative of the start of the observation), and a 300 arcsec line shows the spatial scale corresponding to the FLT high-pass filter. Similar to Fig. 11(c), the high-pass filtering introduces ringing around bright sources. Panels (c) and (d) show the ‘bright extended’ reduction, in which a zero mask is created iteratively from all of the pixels that lie below a S/N of 5. While this region (outside the red contour) only avoids the brightest peaks early in the solution, in the final iteration, it skirts most of the bright, extended emission, and significantly helps with negative ringing. mode subtraction and high-pass filtering. The first panel also depicts the array footprint, and the angular scale (300 arcsec) corresponding to the high-pass filter edge (0.6 Hz). Much like the reduction of a point source without any prior constraints field clearly contains extended structure. Furthermore, the goal of such maps may be to detect previously unknown cool, dense regions of the interstellar medium that may not have appeared at other wavelengths (e.g. the first optically-thick cloud-collapse stages of • Mapping observation of bright star forming region M17 • brighter emission is modeled as "correlated noise" → negative side lobe • iterative estimate can successfully reproduce brighter emission Chapin et al. 2013 negative side lobe pattern due to bright emission reduced side lobe pattern and proper reproduction of broad emission

with FMLO 11 20 2017.08.30 Signal Processing of Spectrometer - Conventional "switching" spectroscopy and its issues - • lower observing efﬁciency (tON / tobs) • we must see OFF point >50 % of total observing time • baseline "wiggles" onto the ﬁnal spectrum • disadvantage of high-z line (broad line width) • additional noise from OFF point • sensitivity gets sqrt(2) times worse ASTE ON OFF → Removing atmospheric emission by switching observation Intensity frequency atmosphere + signal (ON) Intensity only atmosphere (OFF) frequency astronomical signal Intensity frequency

with FMLO 11 20 2017.08.30 Signal Processing of Spectrometer - Conventional "switching" spectroscopy and its issues - • lower observing efficiency (tON / tobs) • we must see OFF point >50 % of total observing time • baseline "wiggles" onto the final spectrum • disadvantage of high-z line (broad line width) • additional noise from OFF point • sensitivity gets sqrt(2) times worse OFF  slue time  others 62% ON  ʢflaggedʣ 25% ON  ʢusedʣ 13% → Removing atmospheric emission by switching observation Intensity frequency atmosphere + signal (ON) Intensity only atmosphere (OFF) frequency astronomical signal Intensity frequency

with FMLO 11 20 2017.08.30 Signal Processing of Spectrometer - Conventional "switching" spectroscopy and its issues - • lower observing efficiency (tON / tobs) • we must see OFF point >50 % of total observing time • baseline "wiggles" onto the final spectrum • disadvantage of high-z line (broad line width) • additional noise from OFF point • sensitivity gets sqrt(2) times worse OFF  slue time  others 62% ON  ʢflaggedʣ 25% ON  ʢusedʣ 13% Detector Modulation Diagram Continuum Camera Camera's pixels (Nch=100-10000) FoV of the telescope (spacial = 2D) Spectroscopy Spectrometer's channels (Nch=4096) observed frequency (frequency = 1D) Removing asmospheric emission by estimating correlated noise

with FMLO 12 20 2017.08.30 integration Frequency Modulation Local Oscillator (Taniguchi, Tamura et al.) Signal Processing of Spectrometer - High efﬁciency spectroscopy by removing correlated noise - High-rate-sampling spectroscopy with modulation of LO frequency (FM of LO) can distinguish astronomical signal from correlated noise in Fourier domain “ ”

with FMLO 13 20 2017.08.30 Signal Processing of Spectrometer - Estimating and removing correlated noise by Principal Component Analysis - Correlated noise Spectrum integration PC1 PC2 D-dim space plot time-series data in D-dimensional space reconstruct time-series data using large k PCs → correlated noises ෼ޫνϟϯωϧDݸ Signal Raw data if not converged estimate correlated noise iteratively spectrum at t=ti

with FMLO 14 20 2017.08.30 Signal Processing of Spectrometer - Comparison between conventional and FMLO observations - 13CO(1-0) CH3CN O3(atmosphere) O3(atmosphere) Residual from switching observation Intensity (K) Observed frequency (GHz) FMLO observation towards Orion-KL at 110 GHz (3mm) 45m

with FMLO 14 20 2017.08.30 Signal Processing of Spectrometer - Comparison between conventional and FMLO observations - 13CO(1-0) CH3CN O3(atmosphere) O3(atmosphere) Residual from switching observation Intensity (K) Observed frequency (GHz) FMLO observation towards Orion-KL at 110 GHz (3mm) • FMLO observing efﬁciency is 4.6x higher than PSW one • FMLO spectrum is 1.9x deeper than PSW one for ﬁxed observing time • no additional noise from off-point and baseline wiggle 45m

with FMLO 15 20 2017.08.30 Improving PCA Cleaning - Estimating correlated noise by PCA: Issue 1 - # of principal components too much too little 8% 8% 40% 40% 10% 10% ɾɾɾ spectrometer ch's spectrometer ch's Covariance matrix baseline ﬂatness line reproducibility Spectrum •How to determine optimal # of principal components? • brute force calculation of covariance matrices is necessary to estimate it • very high calculation cost O(ND2), unable to use it in iterative algorithm

with FMLO 16 20 2017.08.30 Improving PCA Cleaning - Optimizing PCA by Probabilistic-PCA (Minka 2001) - • probabilistic interpretation on the correlated noise estimates • total calculation amount is less than conventional method  by more than one order of magnitude: O(ND2) → O(min(N,D)k) # of principal components k Relative covariance brute force PPCA 1.5% Intensity (K) Frequency in the case of optimal # of PC Optimal # of principal components is derived by Bayes estimate

with FMLO 17 20 2017.08.30 Improving PCA Cleaning - Estimating correlated noise by PCA: Issue 2 - 13CO(1-0) CH3CN O3(atmosphere) O3(Atmosphere) FMLO observation towards Orion-KL at 110 GHz (3mm) True O3 spectrum •Difﬁculty of modeling atmospheric lines such as O3 • Simple PCA is difﬁcult to reproduce very wide spectra of them • Causing wrong intensity estimates of astronomical signal onto them Intensity (K) 45m

with FMLO 18 20 2017.08.30 Improving PCA Cleaning - Weighted PCA (Bailey 2012) for modeling atmospheric lines - ﬁgure from Bishop's talk (2004) Correlated noise Signal Raw data model weight D-dim space E-M steps Atm model Weight • Compute principal components with "weights" using EM algorithm • Minimizing the effect of atmosphere when estimating correlated noises model by am (Paine 2017)

with FMLO 19 20 2017.08.30 Signal Processing of Spectrometer - Modeling and removing atmospheric lines by weighted PCA - 13CO(1-0) CH3CN O3(Atmosphere) O3(Atmosphere) Simple PCA • Atmospheric lines are successfully reproduced with weighted PCA • Atmospheric model and weight are iteratively updated using data Observed frequency (GHz) 110.0 110.5 111.0 109.5 6 0 2 8 4 10 Intensity (K) PCA + Weight 45m

ϛϦ೾αϒϛϦ೾Ͱ୳ΔԕํӉ஦ - ి೾๬ԕڸͷ৴߸ॲཧ։ൃ Akio Taniguchi / 20 2017.08.30 20 •
Bayes estimate of optimal # of PC by PPCA • Removing atmospheric lines by weighted PCA Improving PCA Cleaning Signal Processing of Camera/Spectrometer Introduction • Removing atmospheric emission is key to single dish observations, and they can be modeled then removed by PCA because since they are "correlated" noise. Summary • Camera: separating noise/signal by modulating FoV • FMLO: separating noise/signal by modulating frequency x2

A new off-point-less method for sub/mm spectros...

A new off-point-less method for sub/mm spectroscopy with FMLO / FMLO 2017-08-30

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