ミリ波サブミリ波で探る遠方宇宙 - 電波望遠鏡の信号処理開発 - / FMLO 2017-08-24

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1. ϛϦ೾αϒϛϦ೾Ͱ୳ΔԕํӉ஦ - ి೾๬ԕڸͷ৴߸ॲཧ։ൃ - ୩ޱڿ੕ / ೓೔ग़จ༸ ౦ژେֶେֶӃɾఱจֶڭҭݚڀηϯλʔ 2017.08.24 - 25 / ిࢠ৘ใ௨৴ֶձ ৴߸ॲཧݚڀձ @ ౦ژిػେֶ ౦ژઍॅΩϟϯύε
2. Akio Taniguchi / ۜՏܗ੒γϛϡϨʔγϣϯ (Boylan-Kolchin et al. 2009) ϛϦ೾αϒϛϦ೾Ͱ୳ΔԕํӉ஦ - ి೾๬ԕڸͷ৴߸ॲཧ։ൃ 2 19 2017.08.24 Introduction - ి೾๬ԕڸͷࢹ໺ͷൺֱ - ׯবܭํࣜ ୯Ұڸํࣜ ALMA (NAOJ/ESO/NRAO) ASTE (NAOJ) • ෳ਺ͷΞϯςφΛ૊Έ߹ΘͤɺҰͭͷ Ծ૝తͳେޱܘΛ࣮ݱ͢Δํࣜ • ୯Ұڸʹରͯ͠ߴ͍ۭؒ෼ղೳ
 (~ࢹྗ)Λୡ੒Մೳ • ୯ҰͷΞϯςφʹΑΔ؍ଌํࣜ • ׯবܭʹରͯ͠ɺଟૉࢠΧϝϥʹΑΔ
 ޿͍ࢹ໺ͷ؍ଌ͕Մೳ
3. Akio Taniguchi / ۜՏܗ੒γϛϡϨʔγϣϯ (Boylan-Kolchin et al. 2009) ϛϦ೾αϒϛϦ೾Ͱ୳ΔԕํӉ஦ - ి೾๬ԕڸͷ৴߸ॲཧ։ൃ 2 19 2017.08.24 Introduction - ి೾๬ԕڸͷࢹ໺ͷൺֱ - ׯবܭํࣜ ୯Ұڸํࣜ 7.5 arcmin ※Χϝϥ؍ଌͷ৔߹ 0.4 arcmin ALMA (NAOJ/ESO/NRAO) ASTE (NAOJ) • ෳ਺ͷΞϯςφΛ૊Έ߹ΘͤɺҰͭͷ Ծ૝తͳେޱܘΛ࣮ݱ͢Δํࣜ • ୯Ұڸʹରͯ͠ߴ͍ۭؒ෼ղೳ
 (~ࢹྗ)Λୡ੒Մೳ • ୯ҰͷΞϯςφʹΑΔ؍ଌํࣜ • ׯবܭʹରͯ͠ɺଟૉࢠΧϝϥʹΑΔ
 ޿͍ࢹ໺ͷ؍ଌ͕Մೳ
4. Akio Taniguchi / Ӊ஦େن໛ߏ଄ͷ؍ଌతݚڀ΍ɺະ஌ͷఱମͷ୳ ࡧʹ͸ɺ୯ҰڸʹΑΔ޿ࢹ໺Πϝʔδϯά͕ඞਢ ۜՏܗ੒γϛϡϨʔγϣϯ (Boylan-Kolchin et al. 2009) ϛϦ೾αϒϛϦ೾Ͱ୳ΔԕํӉ஦ - ి೾๬ԕڸͷ৴߸ॲཧ։ൃ 2 19 2017.08.24 Introduction - ి೾๬ԕڸͷࢹ໺ͷൺֱ - 7.5 ar ※Χϝϥ؍ 0.4 arcmin ALMA (NAOJ/ESO/NRAO) ASTE (NAOJ)
5. Akio Taniguchi / ϛϦ೾αϒϛϦ೾Ͱ୳ΔԕํӉ஦ - ి೾๬ԕڸͷ৴߸ॲཧ։ൃ 3 19 2017.08.24 Introduction - ి೾๬ԕڸʢ୯Ұڸʣͷ؍ଌํࣜ - ࿈ଓ೾ࡱ૾؍ଌ ෼ޫ؍ଌ • ۭؒํ޲ʹฒ΂ͨෳ਺ࡱ૾ૉࢠ • ૉࢠ਺ ~ 100 - 10000 • ޿͍प೾਺ଳҬ (਺ेGHz)ͷి࣓೾ ͷ࿈ଓޫΛޫࢠͱͯ͠ݕग़͢Δ • प೾਺ํ޲ʹฒ΂ͨ෼ޫνϟϯωϧ • νϟϯωϧ਺ ~ 1000 - 10000 • ۭؒํ޲ͷ৘ใ͸ಘΒΕͳ͍୅ΘΓʹɺ
 ి࣓೾ΛεϖΫτϧͱͯ͠ಘΔ Hatsukade et al. 2011 Kaifu et al. 2004
6. Akio Taniguchi / ϛϦ೾αϒϛϦ೾Ͱ୳ΔԕํӉ஦ - ి೾๬ԕڸͷ৴߸ॲཧ։ൃ 4 19 2017.08.24 Introduction - ϛϦ೾αϒϛϦ೾ʹ͓͚Δ୯Ұڸ؍ଌͱͦͷ՝୊ - • ՝୊̍ɿۭؒ෼ղೳͷ޲্ • (ۭؒ෼ղೳ) = (೾௕) / (ޱܘ) [radian] • ۭؒ෼ղೳͷ޲্ʹ͸ɺ૷ஔΛେܕԽ͢Δ΄͔ͳ͍ˠ஍্؍ଌ • ՝୊̎ɿେؾΛىݯͱ͢ΔࡶԻͷআڈ • େؾ์ࣹ͕ײ౓Λ੍ݶ (“background-limited” ͳ؍ଌ)ɻ • ରྲྀݍதʹඇҰ༷ʹ෼෍͢Δ H2O ෼ࢠ͕ɺ෩ʹ৐ͬͯӡಈɻ • ఱମ৴߸ͷ 103-104 ഒ΋ͷύϫʔΛ࣋ͭ೤ࡶԻΛ์ࣹ
 ๬ԕڸ։ޱΛԣ੾Δ࣌ؒεέʔϧ (~1 s) Ͱมಈɻ ϛϦ೾αϒϛϦ೾ʹ͓͚Δ޿ࢹ໺؍ଌͷ՝୊ ɾେؾ์ࣹ(౳ͷࡶԻ)Λޮ཰Α͘আڈͰ͖Δ͜ͱ ɾඍऑͳఱମ৴߸Λݕग़ɾ࠶ݱͰ͖Δ͜ͱ ాଜཅҰ "ϛϦ೾αϒϛϦ೾ΧϝϥʹΑΔ޿ࢹ໺Πϝʔδϯά"ΑΓ
7. Akio Taniguchi / ϛϦ೾αϒϛϦ೾Ͱ୳ΔԕํӉ஦ - ి೾๬ԕڸͷ৴߸ॲཧ։ൃ 5 19 2017.08.24 Introduction - େؾ౳Λىݯͱ͢ΔࡶԻ੒෼ͷআڈ - ~1 km ਫৠؾϨΠϠʔ angular diameter of ASTE FoV (7.5’) 1.3 m near-field beam 10 m ASTE๬ԕڸ • ૬ؔࡶԻ (correlated noise) • શͯͷ(·ͨ͸ෳ਺ͷ)ΧϝϥϐΫηϧ·ͨ ͸෼ޫܭνϟϯωϧʹڞ௨ʹ߱Γ஫͙ࡶԻ • ૬ؔࡶԻݯ (1) େؾ์ࣹ • ͓΋ʹେؾ (H2O ճసભҠ) ์ࣹ͕ىݯ • ਫৠؾϨΠϠʔͷߴ͞(ްΈ) ~ 1 km • ๬ԕڸʹͱͬͯ͸ɺFresnel ྖҬʢۙ๣քʣ • ֤ݕग़ث͸ಉ͡େؾΛݟ͍ͯΔ • ૬ؔࡶԻݯ (2) ૷ஔىݯͷࡶԻ • ճ࿏΍έʔϒϧΛڞ༗͢Δݕग़ثͷαϒηο τʹ৐ΔɺϚΠΫϩϑΥχοΫࡶԻɺརಘ มಈ ࿈ଓ೾Χϝϥ ాଜཅҰ "ϛϦ೾αϒϛϦ೾ΧϝϥʹΑΔ޿ࢹ໺Πϝʔδϯά"
8. Akio Taniguchi / ϛϦ೾αϒϛϦ೾Ͱ୳ΔԕํӉ஦ - ి೾๬ԕڸͷ৴߸ॲཧ։ൃ 6 19 2017.08.24 Introduction - େؾ౳Λىݯͱ͢ΔࡶԻ੒෼ͷআڈ - 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) (ࣗݾ)෼ࢄʹର͢Δڞ෼ࢄͷ૬ରతͳେ͖͞. ʢࣗݾ෼ࢄ = residual white noise ʹن֨Խ͍ͯ͠Δʣ ڞ෼ࢄߦྻ ը૾ ੜσʔλ େؾআڈࡁΈ େؾʴ૷ஔআڈࡁΈ over-filter ͯ͠൓૬ؔΛ ͍ࣔͯ͠Δ͕ɺઈର஋͸ খ͍͞ͷͰ OK Ϙϩϝʔλग़ྗ఻ૹ༻έʔ ϒϧͷ૊͝ͱʹ૬ؔϊΠ ζ͕ൃੜ͍ͯ͠Δ 30% 4% x10^4 Kovacs 2008 ੺Ң (J2000) ੺ܦ (J2000) 10 Jy 0.05 Jy 0.05 Jy ఱମ ఱମ ఱମ
9. Akio Taniguchi / Observing time (sec) Intensity (K) Time frequency (Hz) PSD (K/Hz) ૬ؔࡶԻ ఱମ৴߸ ϛϦ೾αϒϛϦ೾Ͱ୳ΔԕํӉ஦ - ి೾๬ԕڸͷ৴߸ॲཧ։ൃ 7 19 2017.08.24 Signal Processing of Camera - ૬ؔࡶԻͷ෼཭ʹΑΔߴޮ཰ɾߴײ౓؍ଌͷ࣮ݱ - • ࿈ଓ೾ଟૉࢠΧϝϥͰ͸͢Ͱʹߴޮ཰ (ηobs=90-100%)ͳ؍ଌʂ • എܠࡶԻ੒෼͸ૉࢠʹڞ௨ʹ߱Γ஫͙ (૬ؔࡶԻ)ͱ͍͏ੑ࣭Λར༻ • ๬ԕڸͷࢹ໺ΛৼΓճ͠, ఱମ৴߸͕ೖࣹ͢ΔૉࢠΛ࣍ʑʹม͑ͳ͕ Β, ΧϝϥͷεφοϓγϣοτΛߴස౓ (~10Hz)ʹऔಘ͢Δ؍ଌख๏ • ఱମ৴߸͸ۭ࣌ؒؒͰߴप೾ଆ΁มௐ (~10 Hz) • ૬ؔࡶԻ͸ҰํͰ௿प೾ଆ (<1 Hz)ͷ੒෼͕୎ӽ (1/f, 1/f2 like) • ओ੒෼෼ੳʹΑͬͯ૬ؔࡶԻ(=෼ࢄ͕େ͖͍)ΛϑΟϧλΞ΢τ(HPF) AzTEC/ASTE (Wilson et al. 2008) Χϝϥ1ૉࢠͷ࣌ܥྻσʔλͱύϫʔεϖΫτϧີ౓(PSD) FFT
10. Akio Taniguchi / ϛϦ೾αϒϛϦ೾Ͱ୳ΔԕํӉ஦ - ి೾๬ԕڸͷ৴߸ॲཧ։ൃ 7 19 2017.08.24 Signal Processing of Camera - ૬ؔࡶԻͷ෼཭ʹΑΔߴޮ཰ɾߴײ౓؍ଌͷ࣮ݱ - • ࿈ଓ೾ଟૉࢠΧϝϥͰ͸͢Ͱʹߴޮ཰ (ηobs=90-100%)ͳ؍ଌʂ • എܠࡶԻ੒෼͸ૉࢠʹڞ௨ʹ߱Γ஫͙ (૬ؔࡶԻ)ͱ͍͏ੑ࣭Λར༻ • ๬ԕڸͷࢹ໺ΛৼΓճ͠, ఱମ৴߸͕ೖࣹ͢ΔૉࢠΛ࣍ʑʹม͑ͳ͕ Β, ΧϝϥͷεφοϓγϣοτΛߴස౓ (~10Hz)ʹऔಘ͢Δ؍ଌख๏ • ఱମ৴߸͸ۭ࣌ؒؒͰߴप೾ଆ΁มௐ (~10 Hz) • ૬ؔࡶԻ͸ҰํͰ௿प೾ଆ (<1 Hz)ͷ੒෼͕୎ӽ (1/f, 1/f2 like) • ओ੒෼෼ੳʹΑͬͯ૬ؔࡶԻ(=෼ࢄ͕େ͖͍)ΛϑΟϧλΞ΢τ(HPF) AzTEC/ASTE (Wilson et al. 2008) Χϝϥ1ૉࢠͷ࣌ܥྻσʔλͱύϫʔεϖΫτϧີ౓(PSD) Time frequency (Hz) PSD (K/Hz) Observing time (sec) Intensity (K) ओ੒෼෼ੳ(HPF) FFT
11. Akio Taniguchi / ϛϦ೾αϒϛϦ೾Ͱ୳ΔԕํӉ஦ - ి೾๬ԕڸͷ৴߸ॲཧ։ൃ 8 19 2017.08.24 Signal Processing of Camera - ओ੒෼෼ੳ (PCA)ʹΑΔ૬ؔࡶԻͷਪఆɾআڈ - ૬ؔࡶԻ ఱମ৴߸ ؍ଌσʔλ D (=ΧϝϥϐΫηϧ਺)࣍ݩ্ۭؒͰ෼ࢄ͕େ͖͍੒෼ (ओ੒෼) → ૬ؔࡶԻ Ϛοϓ ෮ௐ, ੵ෼ D࣍ݩۭؒ ࣌ܥྻσʔλ ΛD࣍ݩۭؒ ্ʹϓϩοτ ্͔Βkݸͷओ ੒෼͔Β࣌ܥྻ σʔλΛ࠶ߏ੒ →૬ؔࡶԻ ϐΫηϧDݸ ࣌ࠁ t Ͱͷ εφοϓ γϣοτ
12. Akio Taniguchi / ϛϦ೾αϒϛϦ೾Ͱ୳ΔԕํӉ஦ - ి೾๬ԕڸͷ৴߸ॲཧ։ൃ 8 19 2017.08.24 Signal Processing of Camera - ओ੒෼෼ੳ (PCA)ʹΑΔ૬ؔࡶԻͷਪఆɾআڈ - ૬ؔࡶԻ ఱମ৴߸ ؍ଌσʔλ Ϛοϓ ෮ௐ, ੵ෼ ओ੒෼1 ओ੒෼2 D࣍ݩۭؒ ࣌ܥྻσʔλ ΛD࣍ݩۭؒ ্ʹϓϩοτ ্͔Βkݸͷओ ੒෼͔Β࣌ܥྻ σʔλΛ࠶ߏ੒ →૬ؔࡶԻ ϐΫηϧDݸ ࣌ࠁ t Ͱͷ εφοϓ γϣοτ ఱମ৴߸ ؍ଌσʔλ ऩଋ൑ఆ(NO) ૬ؔࡶԻΛ൓෮తʹਪఆ
13. Akio Taniguchi / ϛϦ೾αϒϛϦ೾Ͱ୳ΔԕํӉ஦ - ి೾๬ԕڸͷ৴߸ॲཧ։ൃ 9 19 2017.08.24 Signal Processing of Camera - ओ੒෼෼ੳ (PCA)ʹΑΔ૬ؔࡶԻͷਪఆɾআڈ - 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 • ੕ܗ੒ྖҬM17ͷϚοϐϯά؍ଌͷྫ • ໌Δ͍ఱମ৴߸ࣗମ͕૬ؔࡶԻͱͯ͠Ϟσϧ͞Εͯ͠·͏ˠαΠυϩʔϒ • ൓෮తʹਪఆ͢Δ͜ͱͰαΠυϩʔϒ௿ݮɾ޿͕ͬͨ੒෼͕ճ෮ Chapin et al. 2013 ໌Δ͍ఱମ৴߸ʹΑ ΔαΠυϩʔϒͷൃੜ αΠυϩʔϒͷ௿ݮ ޿͕ͬͨ੒෼ͷճ෮
14. Akio Taniguchi / ϛϦ೾αϒϛϦ೾Ͱ୳ΔԕํӉ஦ - ి೾๬ԕڸͷ৴߸ॲཧ։ൃ 10 19 2017.08.24 Signal Processing of Spectrometer - ैདྷͷ"εΠονϯά"෼ޫ؍ଌͱͦͷ໰୊఺ - • OFF఺؍ଌʹΑΔ؍ଌޮ཰ͷ௿Լ • ૯؍ଌ࣌ؒͷ50%Ҏ্͸ఱମΛݟΒΕͳ͍ • ON-OFFʹΑΔϕʔεϥΠϯ͏ͶΓͷൃੜ • ઢ෯͕޿͘ڧ౓ͷऑ͍ԕํӉ஦ͷًઢ؍ଌ͸ෆར • ON-OFFʹΑΔϊΠζͷ෇Ճ • ON఺ͱಉ͡OFF఺ͷ؍ଌ࣌ؒͰ΋√2ഒѱԽ ASTE ON OFF → εΠονϯά؍ଌʹΑΔେؾ์ࣹ౳ͷ෼཭ ৴߸ڧ౓ प೾਺ ఱମ+େؾ (ON఺) ৴߸ڧ౓ େؾ (OFF఺) प೾਺ ఱମεϖΫτϧ ৴߸ڧ౓ प೾਺
15. Akio Taniguchi / ϛϦ೾αϒϛϦ೾Ͱ୳ΔԕํӉ஦ - ి೾๬ԕڸͷ৴߸ॲཧ։ൃ 10 19 2017.08.24 Signal Processing of Spectrometer - ैདྷͷ"εΠονϯά"෼ޫ؍ଌͱͦͷ໰୊఺ - • OFF఺؍ଌʹΑΔ؍ଌޮ཰ͷ௿Լ • ૯؍ଌ࣌ؒͷ50%Ҏ্͸ఱମΛݟΒΕͳ͍ • ON-OFFʹΑΔϕʔεϥΠϯ͏ͶΓͷൃੜ • ઢ෯͕޿͘ڧ౓ͷऑ͍ԕํӉ஦ͷًઢ؍ଌ͸ෆར • ON-OFFʹΑΔϊΠζͷ෇Ճ • ON఺ͱಉ͡OFF఺ͷ؍ଌ࣌ؒͰ΋√2ഒѱԽ Φϑ఺
 ๬ԕڸҠಈ
 ͦͷଞ 62% Φϯ఺
 ʢflaggedʣ 25% Φϯ఺
 ʢusedʣ 13% ݕग़ૉࢠ มௐํ๏ ֓೦ਤ ࿈ଓ೾ଟૉࢠ Χϝϥ Χϝϥͷૉࢠ (Nch=100-10000) ๬ԕڸࢹ໺ΛৼΔ (ۭؒํ޲2࣍ݩ) ෼ޫ؍ଌʁ ෼ޫܭνϟϯωϧ (Nch=4096) ؍ଌप೾਺ΛৼΔ (प೾਺ํ޲1࣍ݩ) ૬ؔࡶԻͷ෼཭ʹΑΔେؾ์ࣹ౳ͷ෼཭
16. Akio Taniguchi / ϛϦ೾αϒϛϦ೾Ͱ୳ΔԕํӉ஦ - ి೾๬ԕڸͷ৴߸ॲཧ։ൃ 11 19 2017.08.24 ෮ௐɾੵ෼ ہ෦ൃৼث(LO)ͷप೾਺Λมௐ(FM)ͤ͞ఱମ৴߸͕ೖࣹ͢Δ෼ޫܭ νϟϯωϧΛ࣍ʑͱมԽͤ͞ͳ͕Β, ෼ޫܭग़ྗΛߴස౓(10Hz)ʹऔಘ ͢Δ͜ͱͰ, νϟϯωϧʹڞ௨ʹ߱Γ஫͙૬ؔࡶԻΛ෼཭͢Δ؍ଌख๏ “ ” Frequency Modulation Local Oscillator (Y. Tamura, A. Taniguchi et al.) Signal Processing of Spectrometer - प೾਺มௐ๏: ૬ؔࡶԻͷ෼཭ʹΑΔߴޮ཰ͷ෼ޫ؍ଌ -
17. Akio Taniguchi / ϛϦ೾αϒϛϦ೾Ͱ୳ΔԕํӉ஦ - ి೾๬ԕڸͷ৴߸ॲཧ։ൃ 12 19 2017.08.24 Signal Processing of Spectrometer - ओ੒෼෼ੳ (PCA)ʹΑΔ૬ؔࡶԻͷਪఆɾআڈ - ૬ؔࡶԻ ఱମ৴߸ ؍ଌσʔλ εϖΫτϧ ෮ௐ, ੵ෼ ओ੒෼1 ओ੒෼2 D࣍ݩۭؒ ࣌ܥྻσʔλ ΛD࣍ݩۭؒ ্ʹϓϩοτ ্͔Βkݸͷओ ੒෼͔Β࣌ܥྻ σʔλΛ࠶ߏ੒ →૬ؔࡶԻ ෼ޫνϟϯωϧDݸ ࣌ࠁ t Ͱͷ εϖΫτϧ ఱମ৴߸ ؍ଌσʔλ ऩଋ൑ఆ(NO) ૬ؔࡶԻΛ൓෮తʹਪఆ
18. Akio Taniguchi / ϛϦ೾αϒϛϦ೾Ͱ୳ΔԕํӉ஦ - ి೾๬ԕڸͷ৴߸ॲཧ։ൃ 13 19 2017.08.24 Signal Processing of Spectrometer - प೾਺มௐ๏ʹΑΔ෼ޫ؍ଌͱैདྷख๏ͱͷൺֱ - 13CO(1-0) CH3CN O3(஍ٿେؾ) O3(஍ٿେؾ) εΠονϯά؍ଌͱͷ࢒ࠩ प೾਺มௐ๏ʹΑΔ ΦϦΦϯ࠲M42ͷ 110 GHzଳ෼ޫ؍ଌ ৴߸ڧ౓ (K) ؍ଌप೾਺ (GHz)
19. Akio Taniguchi / ϛϦ೾αϒϛϦ೾Ͱ୳ΔԕํӉ஦ - ి೾๬ԕڸͷ৴߸ॲཧ։ൃ 13 19 2017.08.24 Signal Processing of Spectrometer - प೾਺มௐ๏ʹΑΔ෼ޫ؍ଌͱैདྷख๏ͱͷൺֱ - 13CO(1-0) CH3CN O3(஍ٿେؾ) O3(஍ٿେؾ) εΠονϯά؍ଌͱͷ࢒ࠩ प೾਺มௐ๏ʹΑΔ ΦϦΦϯ࠲M42ͷ 110 GHzଳ෼ޫ؍ଌ ৴߸ڧ౓ (K) ؍ଌप೾਺ (GHz)
20. Akio Taniguchi / ϛϦ೾αϒϛϦ೾Ͱ୳ΔԕํӉ஦ - ి೾๬ԕڸͷ৴߸ॲཧ։ൃ 14 19 2017.08.24 DD-MM-YYYY Improving PCA Cleaning - ओ੒෼෼ੳ (PCA)ʹΑΔ૬ؔࡶԻਪఆͷ՝୊1 - PCAʹ࢖ͬͨओ੒෼ͷ਺ k ଟ͗͢ গͳ͗͢ 8% 8% 40% 40% 10% 10% ɾɾɾ ෼ޫܭνϟϯωϧ (ch) ෼ޫܭνϟϯωϧ (ch) ڞ෼ࢄߦྻ ͏ͶΓͷऔΕ۩߹ ًઢͷ࠶ݱੑ εϖΫτϧ •૬ؔࡶԻΛਪఆ͢ΔͨΊͷ"࠷దͳ"ओ੒෼਺ͷܾఆ͸ዞҙత • σʔλ͔Βܾఆ͢Δ৔߹ɺڞ෼ࢄߦྻͷ૯౰ͨΓܭࢉͰܾఆ • ܭࢉίετ͕ߴ͘O(ND2)ɺ൓෮ਪఆͷղੳʹ૊ΈࠐΊͳ͍
21. Akio Taniguchi / ϛϦ೾αϒϛϦ೾Ͱ୳ΔԕํӉ஦ - ి೾๬ԕڸͷ৴߸ॲཧ։ൃ 15 19 2017.08.24 Improving PCA Cleaning - ֬཰తओ੒෼෼ੳ (PPCA)ʹΑΔओ੒෼਺ͷਪఆ (Minka 2001) - • ૬ؔࡶԻͷਪఆʹ֬཰తͳղऍΛ༩͑, ٬؍తʹධՁ͢Δ͜ͱ͕Ͱ͖Δ • ૯౰ͨΓܭࢉʹൺ΂, ܭࢉྔ͕1έλҎ্গͳͯ͘ࡁΉͨΊ, ൓෮Ϟσϧ ΁૊ΈࠐΜͰ΋ݱ࣮తͳ࣌ؒͰղੳ͕Մೳ: O(ND2) → O(min(N,D)k) ૬ؔࡶԻͷਪఆʹ༻͍ͨओ੒෼਺ k ࣗݾ෼ࢄʹର͢Δڞ෼ࢄͷׂ߹ ૯౰ͨΓܭࢉ ֬཰Ϟσϧ 1.5% TA* (K) ओ੒෼਺ k͕࠷దͳ৔߹ ૬ؔࡶԻ෼཭ޙͷσʔλͷڞ෼ࢄ੒෼ͷׂ߹ (=૬ؔࡶԻͷ࢒Γ۩߹)ΛධՁ
22. Akio Taniguchi / ϛϦ೾αϒϛϦ೾Ͱ୳ΔԕํӉ஦ - ి೾๬ԕڸͷ৴߸ॲཧ։ൃ 16 19 2017.08.24 DD-MM-YYYY Improving PCA Cleaning - ओ੒෼෼ੳ (PCA)ʹΑΔ૬ؔࡶԻਪఆͷ՝୊2 - 13CO(1-0) CH3CN O3(஍ٿେؾ) O3(஍ٿେؾ) प೾਺มௐ๏ʹΑΔ ΦϦΦϯ࠲M42ͷ 110 GHzଳ෼ޫ؍ଌ ຊདྷͷO3 •஍ٿେؾًઢ (O3ͳͲ)͸ඇৗʹ޿͍प೾਺෯Λ࣋ͭ • େ෦෼͕૬ؔࡶԻͱͯ͠Ϟσϧ͞ΕΔͨΊɺ୯७ͳPCAͰ͸࠶ݱ͕ࠔ೉ • େؾًઢ͕ඃΔप೾਺ʹଘࡏ͢Δఱମ৴߸ͷڧ౓͕ਖ਼͘͠ਪఆ͞Εͳ͍
23. Akio Taniguchi / ϛϦ೾αϒϛϦ೾Ͱ୳ΔԕํӉ஦ - ి೾๬ԕڸͷ৴߸ॲཧ։ൃ 17 19 2017.08.24 Improving PCA Cleaning - ॏΈ෇͖ओ੒෼෼ੳ (Bailey 2012)ʹΑΔ஍ٿେؾًઢͷ෼཭ - figure from Bishop's talk (2004) ૬ؔࡶԻ ఱମ৴߸ ؍ଌσʔλ model weight D࣍ݩۭؒ E-M steps ஍ٿେؾϞσϧ ॏΈ • EMΞϧΰϦζϜΛ༻͍ͯɺओ੒෼ͷਪఆͷࡍʹॏΈΛ͚ͭΔ • ஍ٿେؾεϖΫτϧΛॏΈͱ͠ɺӨڹΛ࠷খݶʹ૬ؔࡶԻΛਪఆ model by am (Paine 2017)
24. Akio Taniguchi / ϛϦ೾αϒϛϦ೾Ͱ୳ΔԕํӉ஦ - ి೾๬ԕڸͷ৴߸ॲཧ։ൃ 17 19 2017.08.24 Improving PCA Cleaning - ॏΈ෇͖ओ੒෼෼ੳ (Bailey 2012)ʹΑΔ஍ٿେؾًઢͷ෼཭ - figure from Bishop's talk (2004) ૬ؔࡶԻ ఱମ৴߸ ؍ଌσʔλ model weight D࣍ݩۭؒ E-M steps ஍ٿେؾϞσϧ ॏΈ • EMΞϧΰϦζϜΛ༻͍ͯɺओ੒෼ͷਪఆͷࡍʹॏΈΛ͚ͭΔ • ஍ٿେؾεϖΫτϧΛॏΈͱ͠ɺӨڹΛ࠷খݶʹ૬ؔࡶԻΛਪఆ model by am (Paine 2017)
25. Akio Taniguchi / ϛϦ೾αϒϛϦ೾Ͱ୳ΔԕํӉ஦ - ి೾๬ԕڸͷ৴߸ॲཧ։ൃ 17 19 2017.08.24 Improving PCA Cleaning - ॏΈ෇͖ओ੒෼෼ੳ (Bailey 2012)ʹΑΔ஍ٿେؾًઢͷ෼཭ - figure from Bishop's talk (2004) ૬ؔࡶԻ ఱମ৴߸ ؍ଌσʔλ model weight D࣍ݩۭؒ E-M steps ஍ٿେؾϞσϧ ॏΈ • EMΞϧΰϦζϜΛ༻͍ͯɺओ੒෼ͷਪఆͷࡍʹॏΈΛ͚ͭΔ • ஍ٿେؾεϖΫτϧΛॏΈͱ͠ɺӨڹΛ࠷খݶʹ૬ؔࡶԻΛਪఆ model by am (Paine 2017)
26. Akio Taniguchi / ϛϦ೾αϒϛϦ೾Ͱ୳ΔԕํӉ஦ - ి೾๬ԕڸͷ৴߸ॲཧ։ൃ 17 19 2017.08.24 Improving PCA Cleaning - ॏΈ෇͖ओ੒෼෼ੳ (Bailey 2012)ʹΑΔ஍ٿେؾًઢͷ෼཭ - figure from Bishop's talk (2004) ૬ؔࡶԻ ఱମ৴߸ ؍ଌσʔλ model weight D࣍ݩۭؒ E-M steps ஍ٿେؾϞσϧ ॏΈ • EMΞϧΰϦζϜΛ༻͍ͯɺओ੒෼ͷਪఆͷࡍʹॏΈΛ͚ͭΔ • ஍ٿେؾεϖΫτϧΛॏΈͱ͠ɺӨڹΛ࠷খݶʹ૬ؔࡶԻΛਪఆ model by am (Paine 2017)
27. Akio Taniguchi / ϛϦ೾αϒϛϦ೾Ͱ୳ΔԕํӉ஦ - ి೾๬ԕڸͷ৴߸ॲཧ։ൃ 17 19 2017.08.24 Improving PCA Cleaning - ॏΈ෇͖ओ੒෼෼ੳ (Bailey 2012)ʹΑΔ஍ٿେؾًઢͷ෼཭ - figure from Bishop's talk (2004) ૬ؔࡶԻ ఱମ৴߸ ؍ଌσʔλ model weight D࣍ݩۭؒ E-M steps ஍ٿେؾϞσϧ ॏΈ • EMΞϧΰϦζϜΛ༻͍ͯɺओ੒෼ͷਪఆͷࡍʹॏΈΛ͚ͭΔ • ஍ٿେؾεϖΫτϧΛॏΈͱ͠ɺӨڹΛ࠷খݶʹ૬ؔࡶԻΛਪఆ model by am (Paine 2017)
28. Akio Taniguchi / ϛϦ೾αϒϛϦ೾Ͱ୳ΔԕํӉ஦ - ి೾๬ԕڸͷ৴߸ॲཧ։ൃ 18 19 2017.08.24 Signal Processing of Spectrometer - ॏΈ෇͖ओ੒෼෼ੳʹΑΔ஍ٿେؾًઢͷ෼཭ - 13CO(1-0) CH3CN O3(஍ٿେؾ) O3(஍ٿେؾ) ୯७ͳPCA • ୯७ͳPCAͰ͸ճ෮Ͱ͖ͳ͔ͬͨ஍ٿେؾًઢͷճ෮ʹ੒ޭ • ͜ΕΛআڈ͢Δ͜ͱͰఱମ৴߸ͷΈͷεϖΫτϧΛಘΒΕΔ ؍ଌप೾਺ (GHz) 110.0 110.5 111.0 109.5 6 0 2 8 4 10 ৴߸ڧ౓ (K) PCA + Weight
29. Akio Taniguchi / ϛϦ೾αϒϛϦ೾Ͱ୳ΔԕํӉ஦ - ి೾๬ԕڸͷ৴߸ॲཧ։ൃ 18 19 2017.08.24 Signal Processing of Spectrometer - ॏΈ෇͖ओ੒෼෼ੳʹΑΔ஍ٿେؾًઢͷ෼཭ - 13CO(1-0) CH3CN O3(஍ٿେؾ) O3(஍ٿେؾ) ୯७ͳPCA • ୯७ͳPCAͰ͸ճ෮Ͱ͖ͳ͔ͬͨ஍ٿେؾًઢͷճ෮ʹ੒ޭ • ͜ΕΛআڈ͢Δ͜ͱͰఱମ৴߸ͷΈͷεϖΫτϧΛಘΒΕΔ ؍ଌप೾਺ (GHz) 110.0 110.5 111.0 109.5 6 0 2 8 4 10 ৴߸ڧ౓ (K) PCA + Weight
30. ϛϦ೾αϒϛϦ೾Ͱ୳ΔԕํӉ஦ - ి೾๬ԕڸͷ৴߸ॲཧ։ൃ Akio Taniguchi / 19 2017.08.24 19 • PPCAͷಋೖʹΑΔओ੒෼਺ͷϕΠζਪఆ • ॏΈ෇͖PCAʹΑΔ஍ٿେؾًઢͷআڈ Improving PCA Cleaning Signal Processing of Camera/Spectrometer Introduction • ୯Ұڸ؍ଌͰ͸େؾ౳ͷࡶԻ੒෼ͷআڈ͕伴 • ͜ΕΒͷ੒෼͸૬ؔࡶԻˠPCA౳ʹΑΔআڈ Summary • Χϝϥͷࢹ໺Λมௐ͢Δ͜ͱͰఱମ/ࡶԻΛ෼཭ • ෼ޫܭप೾਺Λมௐ͢Δ͜ͱͰఱମ/ࡶԻΛ෼཭ x2