1. PACS SVR 22/23 June 2006 Instrument Performance Prediction1 PACS Instrument Model and Performance Prediction A. Poglitsch

2. PACS SVR 22/23 June 2006 Instrument Performance Prediction2 PACS Instrument Model Purpose of instrument model: provide best guess of in-orbit performance based on existing knowledge of the instrument and its subunits and the satellite –Incomplete knowledge about FM subunit / instrument / system performance –Some knowledge of QM instrument performance, but with degraded subunit and OGSE performance Instrument model is a “living document” that has been maintained since the early design phases of PACS and updated whenever new test results became available Parameters lacking experimental values have been assigned calculated or estimated values PACS instrument model is not a deliverable document (but has been used regularly as a reference for preparation and evaluation of tests and their results)

3. PACS SVR 22/23 June 2006 Instrument Performance Prediction3 Spectrometer Model Model strategy Determine the background power reaching an individual detector (pixel) and determine the NEP of an individual detector under this background (photon noise + detector/readout noise) Determine the coupling of an astronomical (point) source to the detector array –Telescope PSF –Vignetting / diffraction in instrument –Transmission of optical elements (mirrors, filters, grating) –Detector (quantum) efficiency –Effective number of pixels (spatial/spectral) needed for optimum source/line extraction and resulting total noise and fraction of detected source flux Combine above results to calculate “raw” noise referred to sky Add overheads created by need for background subtraction (AOT-dependent)

4. PACS SVR 22/23 June 2006 Instrument Performance Prediction4 Detector Performance Relative spectral response within modules Relative photometric response within modules Absolute photometric peak responsivity (module average)

5. PACS SVR 22/23 June 2006 Instrument Performance Prediction5 HS Detector Performance Model Observed noise consistent with photon noise + CRE noise (input- equivalent current noise density) Peak QE=0.26; QE( ) follows directly from rel. spectral responsivity Average CRE noise 3.7x10 -16 A/√Hz, average peak responsivity 45 A/W bias [mV] signal 4.7x10 -15 W 2.9x10 -15 W Circles: measured noise Dashed line: CRE noise Squares: CRE noise subtr. Solid lines: combined model Dotted lines: background noise noise bias [mV]

6. PACS SVR 22/23 June 2006 Instrument Performance Prediction6 LS Detector Model No reliable measurement of peak QE available; assumed to be the same as for HS detectors (by design) –Quite limited consequence for system performance – CRE noise and responsivity dominate (see below) CRE noise same as for HS detector Average peak responsivity 10…12 A/W

7. PACS SVR 22/23 June 2006 Instrument Performance Prediction7 Spectrometer Model: Background Basics  : etendue of optical train (conserved by optics, except for detector light cones) : optical frequency  : detected optical bandwidth (around given frequency) T: temperature of emitter em: emissivity of emitter t: transmission of all optics between respective emitter and detector  : detector quantum efficiency (Calculated for groups/ elements along optical train from telescope to detector)

8. PACS SVR 22/23 June 2006 Instrument Performance Prediction8 Spectrometer Model: Background Etendue throughout optical train, for all contributions from outside of the 5K environment [deviations are lumped into effective emissivities]  cold := 4  correcting for the effective cone acceptance angle seeing the 5K optics

9. PACS SVR 22/23 June 2006 Instrument Performance Prediction9 Spectrometer Model: Background/Straylight Temperatures and Emissivities TelescopeBaffleShieldCold optics T80 K60 K23 K5.5 K  4%1% 15% PACS-external contributions dominant

10. PACS SVR 22/23 June 2006 Instrument Performance Prediction10 Spectrometer Model: Background/Straylight Transmission to Detector and Bandwidth Wavelength [µm] Background optical bandwidth/pixel [Hz] Telescope background transmission Bandwidth same for all background contributions except 5K post- grating (which is negligible) Effective transmission for background contributions varies slightly (pupil aperture sizes etc.)

11. PACS SVR 22/23 June 2006 Instrument Performance Prediction11 Spectrometer Model: Transmission Breakdown Wavelength [µm] Filter transmission Filter transmission based on RT FTS measurements of FM filters Dichroic will be replaced before ILT Calculated grating efficiency

12. PACS SVR 22/23 June 2006 Instrument Performance Prediction12 Spectrometer Model: Transmission Breakdown Wavelength [µm] Calculated slicer efficiency Slicer efficiency: vignetting of diffraction side lobes by optics Additional transmission factors –Lyot stop efficiency: 0.9 (diffraction by field stop plus telescope/instrument alignment tolerances) –Mirror train: 0.85 (dissipation, scattering)

13. PACS SVR 22/23 June 2006 Instrument Performance Prediction13 Spectrometer Model: Additional Optical Efficiencies Relevant for Source Coupling Wavelength [µm] Telescope efficiency: fraction of power received from point source measured in central peak of PSF Pixel efficiency: inverse number of pixels (spatial/spectral) needed to retrieve power of unresolved spectral line in central peak of PSF Estimated telescope main beam efficiency (diffraction + WFE) Calculated pixel efficiency

14. PACS SVR 22/23 June 2006 Instrument Performance Prediction14 Background Power and BLIP Noise per Pixel HS detector QE based on measurement (peak QE + relative spectral responsivity) LS detector QE based on assumed, same peak QE + relative spectral responsivity measurement Background power [W] BLIP NEP [W/√Hz] QE Wavelength [µm]

15. PACS SVR 22/23 June 2006 Instrument Performance Prediction15 BLIP Noise vs. Readout Noise NEI [A/√Hz] = NEP [W/√Hz] x responsivity [A/W] NEI [A/√Hz] Wavelength [µm] BLIPNEP converted to electrical noise (solid lines) Readout noise (dashed line) BLIPNEP (and, therefore, QE) significant/dominant noise source in “red” band (1st order, HS) BLIPNEP (and, therefore, QE) not dominant noise source – readout noise and responsivity relevant

16. PACS SVR 22/23 June 2006 Instrument Performance Prediction16 Total Noise at Detector and Coupling to Sky Wavelength [µm] Total NEP at detector: BLIP NEP and electrical readout-noise equivalent power Coupling correction: inverse of all optical efficiencies; factor 2 for background subtraction; chopper duty-cycle of ≥0.8 Wavelength [µm] Total NEP [W/√Hz] Coupling correction

17. PACS SVR 22/23 June 2006 Instrument Performance Prediction17 Predicted Sensitivity Calculated for (off-array) chopping Wavelength switching could have advantage (spectral line always within instantaneous coverage) or disadvantage (off-line switching and likely need for off-position observation) Wavelength [µm] Point source continuum sensitivity per spectral resolution element [Jy] (5 , 1h) Wavelength [µm] Point source line sensitivity [W/m 2 ] (5 , 1h)

18. PACS SVR 22/23 June 2006 Instrument Performance Prediction18 Operation/Performance under p+ Irradiation Simulated chopped observation with one ramp/chopper plateau. For each bias value, 5 ramp lengths tested: 1s, 1/2 s, 1/4 s, 1/8s, 1/16 s. The detector was in its high responsivity plateau, ~2 hours after the last curing. Instrument model value, based on lab measurements without irradiation NEP as a function of detector/readout setting With optimum bias setting (lower than in lab!) and ramp length / chopping parameters, NEP close to lab values possible in space Curing may be necessary only after solar flare, or once per day (self- curing under telescope IR background sufficient)

19. PACS SVR 22/23 June 2006 Instrument Performance Prediction19 Spectral Resolving Power Simple calculation, requiring some fine tuning –Pixel sampling –Exact grating illumination (physical optics) Wavelength [µm] Resolving power

20. PACS SVR 22/23 June 2006 Instrument Performance Prediction20 Main Limitations of Spectrometer Model No “systematics”/ higher-order effects and their implications for AOTs considered –no real instrument simulator No end-to-end test of instrument in representative high-energy radiation environment Limited feed-back from QM ILT –Serious uncertainty about detector responsivity makes evaluation of instrument optical efficiency difficult –Defocus, low transmission and high/inhomogeneous window emissivity have hampered PSF determination –Lack of laser source (or adequate gas cell) – no unresolved, strong lines available

21. PACS SVR 22/23 June 2006 Instrument Performance Prediction21 Photometer Model Model strategy Determine the background power reaching an individual detector (pixel) and determine the NEP of an individual detector under this background (photon noise + detector/readout noise) Determine the coupling of an astronomical (point) source to the detector array –Telescope PSF –Vignetting / diffraction in instrument –Transmission of optical elements (mirrors, filters) –Detector (quantum) efficiency –Effective number of pixels needed for optimum source extraction and resulting total noise and fraction of detected source flux Combine above results to calculate “raw” noise referred to sky Add overheads created by need for background subtraction (AOT-dependent)

22. PACS SVR 22/23 June 2006 Instrument Performance Prediction22 Bolometer Performance Pixel yield ~98% NEP “blue” ~1.7...2 x nominal –Small variation with BG power –But 1/f noise –Best NEP only for fast modulation (chopping/ scanning) NEP “red” slightly higher “blue” BFP NEP vs. background power

23. PACS SVR 22/23 June 2006 Instrument Performance Prediction23 Photometer Model: Background Basics  : etendue of optical train (conserved by optics, except for detector light cones) : optical frequency  : detected optical bandwidth (around given frequency) T: temperature of emitter em: emissivity of emitter t: transmission of all optics between respective emitter and detector  : detector quantum efficiency (Calculated for groups/ elements along optical train from telescope to detector) Crude approximation for large bandwidth of photometer! (But it doesn’t matter.)

24. PACS SVR 22/23 June 2006 Instrument Performance Prediction24 Photometer Model: Background Etendue throughout optical train, for all contributions from outside of the 5K environment [deviations are lumped into effective emissivities]  cold := 10  correcting for the effective detector/baffle acceptance cone seeing the 5K optics “Red” Photometer: 6.4”□ pixels “Blue” Photometer: 3.2”□ pixels

25. PACS SVR 22/23 June 2006 Instrument Performance Prediction25 Photometer Model: Background/Straylight Temperatures and Emissivities TelescopeBaffleShieldCold optics T80 K60 K23 K5.5 K  4%1% 15% PACS-external contributions dominant

26. PACS SVR 22/23 June 2006 Instrument Performance Prediction26 Photometer Model: Background/Straylight Transmission to Detector and Bandwidth Bandwidth same for all background contributions except 5K post- grating (which is negligible) Filter transmission based on RT FTS measurements of FM filters Dichroic will be replaced before ILT Lyot Stop Mirror Train Filter Chain Total  “Red” 130-210µm 0.90.850.50.3832.2 “Green” 85-130µm 0.90.850.450.3442.4 “Blue” 60-85µm 0.90.850.350.2682.9

27. PACS SVR 22/23 June 2006 Instrument Performance Prediction27 Photometer Background Power and Noise per Pixel QE assumed to be 0.8 (from bolometer absorber structure reflectivity measurement) for BLIPNEP Realisation of “measured NEP” requires modulation near 3 Hz (1/f noise) BG [pW] BLIPNEP [W/√Hz] Measured NEP [W/√Hz] “Red” 130-210µm 5.21.24 x 10 -16 3 x 10 -16 tbc “Green” 85-130µm 2.91.15 x 10 -16 2.5 x 10 -16 “Blue” 60-85µm 3.41.54 x 10 -16 2.5 x 10 -16

28. PACS SVR 22/23 June 2006 Instrument Performance Prediction28 Photometer Model: Additional Optical Efficiencies Relevant for Source Coupling Telescope efficiency: fraction of power received from point source measured in central peak of PSF Pixel efficiency: inverse number of pixels needed to retrieve power in central peak of PSF eff_teleff_pix “Red” 130-210µm 0.770.181 “Green” 85-130µm 0.730.113 “Blue” 60-85µm 0.640.162

29. PACS SVR 22/23 June 2006 Instrument Performance Prediction29 Total Coupling to Sky Coupling correction –inverse of all optical efficiencies –factor 2 for background subtraction –chopper duty-cycle of ≥0.8 Coup_corr “Red” 130-210µm 17.7 “Green” 85-130µm 26.3 “Blue” 60-85µm 32.2

30. PACS SVR 22/23 June 2006 Instrument Performance Prediction30 Predicted Sensitivity Point source sensitivity equivalent to mapping speed of ~10’ x 10’ in 1 day on-array chopping/ line scanning off-position chopping wavelength [µm] [mJy] (point source; 5  /1h) 50100150200 5 4 3 2 1 0 Photometric Bands wavelength [µm] filter transmission

31. PACS SVR 22/23 June 2006 Instrument Performance Prediction31 Main Limitations of Photometer Model No “systematics”/ higher-order effects and their implications for AOTs considered –no real instrument simulator Origin of 1/f noise not clear –Is it driven thermally? –Will operation in PACS cryostat be representative for in-orbit Herschel cryostat thermal (in)stability? Limited feed-back from QM ILT –Serious uncertainty about detector responsivity makes evaluation of instrument optical efficiency difficult –Defocus, low transmission and high/inhomogeneous window emissivity have hampered PSF determination